Volume 6: Scientific Metaphysics.

Book 1: Ontology and Cosmology

A. Tychism

Chapter 1: The Architecture of Theories †1

§1. Philosophic Architectonic E

7. Of the fifty or hundred systems of philosophy that have been advanced at different times of the world's history, perhaps the larger number have been, not so much results of historical evolution, as happy thoughts which have accidentally occurred to their authors. An idea which has been found interesting and fruitful has been adopted, developed, and forced to yield explanations of all sorts of phenomena. The English have been particularly given to this way of philosophizing; witness, Hobbes, Hartley, Berkeley, James Mill. Nor has it been by any means useless labor; it shows us what the true nature and value of the ideas developed are, and in that way affords serviceable materials for philosophy. Just as if a man, being seized with the conviction that paper was a good material to make things of, were to go to work to build a papier mâché house, with roof of roofing paper, foundations of pasteboard, windows of paraffined paper, chimneys, bath tubs, locks, etc., all of different forms of paper, his experiment would probably afford valuable lessons to builders, while it would certainly make a detestable house, so those one-idea'd philosophies are exceedingly interesting and instructive, and yet are quite unsound.

8. The remaining systems of philosophy have been of the nature of reforms, sometimes amounting to radical revolutions, suggested by certain difficulties which have been found to beset systems previously in vogue; and such ought certainly to be in large part the motive of any new theory. This is like partially rebuilding a house. The faults that have been committed are, first, that the repairs of the dilapidations have generally not been sufficiently thorough-going, and, second, that not sufficient pains have been taken to bring the additions into deep harmony with the really sound parts of the old structure.

When a man is about to build a house, what a power of thinking he has to do before he can safely break ground! With what pains he has to excogitate the precise wants that are to be supplied! What a study to ascertain the most available and suitable materials, to determine the mode of construction to which those materials are best adapted, and to answer a hundred such questions! Now without riding the metaphor too far, I think we may safely say that the studies preliminary to the construction of a great theory should be at least as deliberate and thorough as those that are preliminary to the building of a dwelling house.

9. That systems ought to be constructed architectonically has been preached since Kant, but I do not think the full import of the maxim has by any means been apprehended. What I would recommend is that every person who wishes to form an opinion concerning fundamental problems should first of all make a complete survey of human knowledge, should take note of all the valuable ideas in each branch of science, should observe in just what respect each has been successful and where it has failed, in order that, in the light of the thorough acquaintance so attained of the available materials for a philosophical theory and of the nature and strength of each, he may proceed to the study of what the problem of philosophy consists in, and of the proper way of solving it. I must not be understood as endeavoring to state fully all that these preparatory studies should embrace; on the contrary, I purposely slur over many points, in order to give emphasis to one special recommendation, namely, to make a systematic study of the conceptions out of which a philosophical theory may be built, in order to ascertain what place each conception may fitly occupy in such a theory, and to what uses it is adapted.

The adequate treatment of this single point would fill a volume, but I shall endeavor to illustrate my meaning by glancing at several sciences and indicating conceptions in them serviceable for philosophy. As to the results to which long studies thus commenced have led me, I shall just give a hint at their nature.

10. We may begin with dynamics — field in our day of perhaps the grandest conquest human science has ever made — I mean the law of the conservation of energy. But let us revert to the first step taken by modern scientific thought — and a great stride it was — the inauguration of dynamics by Galileo. A modern physicist on examining Galileo's works is surprised to find how little experiment had to do with the establishment of the foundations of mechanics. His principal appeal is to common sense and il lume naturale. He always assumes that the true theory will be found to be a simple and natural one. And we can see why it should indeed be so in dynamics. For instance, a body left to its own inertia moves in a straight line, and a straight line appears to us the simplest of curves. In itself, no curve is simpler than another. A system of straight lines has intersections precisely corresponding to those of a system of like parabolas similarly placed, or to those of any one of an infinity of systems of curves. But the straight line appears to us simple, because, as Euclid says, it lies evenly between its extremities; that is, because viewed endwise it appears as a point. That is, again, because light moves in straight lines. Now, light moves in straight lines because of the part which the straight line plays in the laws of dynamics. Thus it is that, our minds having been formed under the influence of phenomena governed by the laws of mechanics, certain conceptions entering into those laws become implanted in our minds, so that we readily guess at what the laws are. †1 Without such a natural prompting, having to search blindfold for a law which would suit the phenomena, our chance of finding it would be as one to infinity. The further physical studies depart from phenomena which have directly influenced the growth of the mind, the less we can expect to find the laws which govern them "simple," that is, composed of a few conceptions natural to our minds.

11. The researches of Galileo, followed up by Huygens and others, led to those modern conceptions of Force and Law, which have revolutionized the intellectual world. The great attention given to mechanics in the seventeenth century soon so emphasized these conceptions as to give rise to the Mechanical Philosophy, or doctrine that all the phenomena of the physical universe are to be explained upon mechanical principles. Newton's great discovery imparted a new impetus to this tendency. The old notion that heat consists in an agitation of corpuscles was now applied to the explanation of the chief properties of gases. The first suggestion in this direction was that the pressure of gases is explained by the battering of the particles against the walls of the containing vessel, which explained Boyle's law of the compressibility of air. Later, the expansion of gases, Avogadro's chemical law, the diffusion and viscosity of gases, and the action of Crookes's radiometer were shown to be consequences of the same kinetical theory; but other phenomena, such as the ratio of the specific heat at constant volume to that at constant pressure, require additional hypotheses, which we have little reason to suppose are simple, so that we find ourselves quite afloat. In like manner with regard to light. That it consists of vibrations was almost proved by the phenomena of diffraction, while those of polarization showed the excursions of the particles to be perpendicular to the line of propagation; but the phenomena of dispersion, etc., require additional hypotheses which may be very complicated. Thus, the further progress of molecular speculation appears quite uncertain. If hypotheses are to be tried haphazard, or simply because they will suit certain phenomena, it will occupy the mathematical physicists of the world say half a century on the average to bring each theory to the test, and since the number of possible theories may go up into the trillions, only one of which can be true, we have little prospect of making further solid additions to the subject in our time. When we come to atoms, the presumption in favor of a simple law seems very slender. There is room for serious doubt whether the fundamental laws of mechanics hold good for single atoms, and it seems quite likely that they are capable of motion in more than three dimensions. †1

12. To find out much more about molecules and atoms we must search out a natural history of laws of nature which may fulfill that function which the presumption in favor of simple laws fulfilled in the early days of dynamics, by showing us what kind of laws we have to expect and by answering such questions as this: Can we, with reasonable prospect of not wasting time, try the supposition that atoms attract one another inversely as the seventh power of their distances, or can we not? To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for. That a pitched coin should sometimes turn up heads and sometimes tails calls for no particular explanation; but if it shows heads every time, we wish to know how this result has been brought about. Law is par excellence the thing that wants a reason.

§2. Three Theories of Evolution †1 E

13. Now the only possible way of accounting for the laws of nature and for uniformity in general is to suppose them results of evolution. This supposes them not to be absolute, not to be obeyed precisely. It makes an element of indeterminacy, spontaneity, or absolute chance in nature. †2 Just as, when we attempt to verify any physical law, we find our observations cannot be precisely satisfied by it, and rightly attribute the discrepancy to errors of observation, so we must suppose far more minute discrepancies to exist owing to the imperfect cogency of the law itself, to a certain swerving of the facts from any definite formula.

14. Mr. Herbert Spencer †3 wishes to explain evolution upon mechanical principles. This is illogical, for four reasons. First, because the principle of evolution requires no extraneous cause, since the tendency to growth can be supposed itself to have grown from an infinitesimal germ accidentally started. Second, because law ought more than anything else to be supposed a result of evolution. Third, because exact law obviously never can produce heterogeneity out of homogeneity; and arbitrary heterogeneity is the feature of the universe the most manifest and characteristic. Fourth, because the law of the conservation of energy is equivalent to the proposition that all operations governed by mechanical laws are reversible; so that an immediate corollary from it is that growth is not explicable by those laws, even if they be not violated in the process of growth. In short, Spencer is not a philosophical evolutionist, but only a half-evolutionist — or, if you will, only a semi-Spencerian. Now philosophy requires thorough-going evolutionism or none.

15. The theory of Darwin was that evolution had been brought about by the action of two factors: first, heredity, as a principle making offspring nearly resemble their parents, while yet giving room for "sporting" or accidental variations — for very slight variations often, for wider ones rarely; and, second, the destruction of breeds or races that are unable to keep the birth rate up to the death rate. This Darwinian principle is plainly capable of great generalization. Wherever there are large numbers of objects having a tendency to retain certain characters unaltered, this tendency, however, not being absolute but giving room for chance variations, then, if the amount of variation is absolutely limited in certain directions by the destruction of everything which reaches those limits, there will be a gradual tendency to change in directions of departure from them. Thus, if a million players sit down to bet at an even game, since one after another will get ruined, the average wealth of those who remain will perpetually increase. Here is indubitably a genuine formula of possible evolution, whether its operation accounts for much or little in the development of animal and vegetable species.

16. The Lamarckian theory †1 also supposes that the development of species has taken place by a long series of insensible changes, but it supposes that those changes have taken place during the lives of the individuals, in consequence of effort and exercise, and that reproduction plays no part in the process except in preserving these modifications. Thus, the Lamarckian theory only explains the development of characters for which individuals strive, while the Darwinian theory only explains the production of characters really beneficial to the race, though these may be fatal to individuals. †P1 But more broadly and philosophically conceived, Darwinian evolution is evolution by the operation of chance, and the destruction of bad results, while Lamarckian evolution is evolution by the effect of habit and effort.

17. A third theory of evolution is that of Mr. Clarence King. †1 The testimony of monuments and of rocks is that species are unmodified or scarcely modified, under ordinary circumstances, but are rapidly altered after cataclysms or rapid geological changes. Under novel circumstances, we often see animals and plants sporting excessively in reproduction, and sometimes even undergoing transformations during individual life, phenomena no doubt due partly to the enfeeblement of vitality from the breaking up of habitual modes of life, partly to changed food, partly to direct specific influence of the element in which the organism is immersed. If evolution has been brought about in this way, not only have its single steps not been insensible, as both Darwinians and Lamarckians suppose, but they are furthermore neither haphazard on the one hand, nor yet determined by an inward striving on the other, but on the contrary are effects of the changed environment, and have a positive general tendency to adapt the organism to that environment, since variation will particularly affect organs at once enfeebled and stimulated. This mode of evolution, by external forces and the breaking up of habits, seems to be called for by some of the broadest and most important facts of biology and paleontology; while it certainly has been the chief factor in the historical evolution of institutions as in that of ideas; and cannot possibly be refused a very prominent place in the process of evolution of the universe in general.

§3. The Law of Habit E

18. Passing to psychology, we find the elementary phenomena of mind fall into three categories. †2 First, we have Feelings, comprising all that is immediately present, such as pain, blue, cheerfulness, the feeling that arises when we contemplate a consistent theory, etc. A feeling is a state of mind having its own living quality, independent of any other state of mind. Or, a feeling is an element of consciousness which might conceivably override every other state until it monopolized the mind, although such a rudimentary state cannot actually be realized, and would not properly be consciousness. Still it is conceivable, or supposable, that the quality of blue should usurp the whole mind, to the exclusion of the ideas of shape, extension, contrast, commencement and cessation, and all other ideas whatsoever. A feeling is necessarily perfectly simple, in itself, for if it had parts these would also be in the mind, whenever the whole was present, and thus the whole could not monopolize the mind. †P1

19. Besides Feelings, we have Sensations of reaction; as when a person blindfold suddenly runs against a post, when we make a muscular effort, or when any feeling gives way to a new feeling. Suppose I had nothing in my mind but a feeling of blue, which were suddenly to give place to a feeling of red; then, at the instant of transition, there would be a shock, a sense of reaction, my blue life being transmuted into red life. If I were further endowed with a memory, that sense would continue for some time, and there would also be a peculiar feeling or sentiment connected with it. This last feeling might endure (conceivably I mean) after the memory of the occurrence and the feelings of blue and red had passed away. But the sensation of reaction cannot exist except in the actual presence of the two feelings blue and red to which it relates. Wherever we have two feelings and pay attention to a relation between them of whatever kind, there is the sensation of which I am speaking. But the sense of action and reaction has two types: it may either be a perception of relation between two ideas, or it may be a sense of action and reaction between feeling and something out of feeling. And this sense of external reaction again has two forms; for it is either a sense of something happening to us, by no act of ours, we being passive in the matter, or it is a sense of resistance, that is, of our expending feeling upon something without. The sense of reaction is thus a sense of connection or comparison between feelings, either, A, between one feeling and another, or B between feeling and its absence or lower degree; and under B we have, first, the sense of the access of feeling, and second, the sense of remission of feeling.

20. Very different both from feelings and from reaction-sensations or disturbances of feeling are general conceptions. When we think, we are conscious that a connection between feelings is determined by a general rule, we are aware of being governed by a habit. Intellectual power is nothing but facility in taking habits and in following them in cases essentially analogous to, but in non-essentials widely remote from, the normal cases of connections of feelings under which those habits were formed.

21. The one primary and fundamental law of mental action consists in a tendency to generalization. Feeling tends to spread; connections between feelings awaken feelings; neighboring feelings become assimilated; ideas are apt to reproduce themselves. These are so many formulations of the one law of the growth of mind. When a disturbance of feeling takes place, we have a consciousness of gain, the gain of experience; and a new disturbance will be apt to assimilate itself to the one that preceded it. Feelings, by being excited, become more easily excited, especially in the ways in which they have previously been excited. The consciousness of such a habit constitutes a general conception.

22. The cloudiness of psychological notions may be corrected by connecting them with physiological conceptions. †1 Feeling may be supposed to exist wherever a nerve-cell is in an excited condition. The disturbance of feeling, or sense of reaction, accompanies the transmission of disturbance between nerve-cells, or from a nerve-cell to a muscle-cell, or the external stimulation of a nerve-cell. General conceptions arise upon the formation of habits in the nerve-matter, which are molecular changes consequent upon its activity and probably connected with its nutrition.

23. The law of habit exhibits a striking contrast to all physical laws in the character of its commands. A physical law is absolute. What it requires is an exact relation. Thus, a physical force introduces into a motion a component motion to be combined with the rest by the parallelogram of forces; but the component motion must actually take place exactly as required by the law of force. On the other hand, no exact conformity is required by the mental law. Nay, exact conformity would be in downright conflict with the law; since it would instantly crystallize thought and prevent all further formation of habit. The law of mind only makes a given feeling more likely to arise. It thus resembles the "non-conservative" forces of physics, such as viscosity and the like, which are due to statistical uniformities in the chance encounters of trillions of molecules.

§4. Objective Idealism †1 E

24. The old dualistic notion of mind and matter, so prominent in Cartesianism, as two radically different kinds of substance, will hardly find defenders today. Rejecting this, we are driven to some form of hylopathy, otherwise called monism. Then the question arises whether physical laws on the one hand and the psychical law on the other are to be taken —

(a) as independent, a doctrine often called monism, but which I would name neutralism; or,

(b) the psychical law as derived and special, the physical law alone as primordial, which is materialism; or,

(c) the physical law as derived and special, the psychical law alone as primordial, which is idealism.

The materialistic doctrine seems to me quite as repugnant to scientific logic as to common sense; since it requires us to suppose that a certain kind of mechanism will feel, which would be a hypothesis absolutely irreducible to reason — an ultimate, inexplicable regularity; while the only possible justification of any theory is that it should make things clear and reasonable.

Neutralism is sufficiently condemned by the logical maxim known as Ockham's razor, i.e., that not more independent elements are to be supposed than necessary. By placing the inward and outward aspects of substance on a par, it seems to render both primordial.

25. The one intelligible theory of the universe is that of objective idealism, that matter is effete mind, inveterate habits becoming physical laws. But before this can be accepted it must show itself capable of explaining the tri-dimensionality of space, the laws of motion, and the general characteristics of the universe, with mathematical clearness and precision; for no less should be demanded of every philosophy.

§5. The Nature of Space †1E

26. Modern mathematics is replete with ideas which may be applied to philosophy. I can only notice one or two. The manner in which mathematicians generalize is very instructive. Thus, painters are accustomed to think of a picture as consisting geometrically of the intersections of its plane by rays of light from the natural objects to the eye. But geometers use a generalized perspective. For instance, in the figure

inline image

let O be the eye, let A B C D E be the edgewise view of any plane, and let a f e D c be the edgewise view of another plane. The geometers draw rays through O cutting both these planes, and treat the points of intersection of each ray with one plane as representing the point of intersection of the same ray with the other plane. Thus, e represents E, in the painter's way. D represents itself. C is represented by c, which is farther from the eye; and A is represented by a which is on the other side of the eye. Such generalization is not bound down to sensuous images. Further, according to this mode of representation every point on one plane represents a point on the other, and every point on the latter is represented by a point on the former. But how about the point f which is in a direction from O parallel to the represented plane, and how about the point B which is in a direction parallel to the representing plane? Some will say that these are exceptions; but modern mathematics does not allow exceptions which can be annulled by generalization. As a point moves from C to D and thence to E and off toward infinity, the corresponding point on the other plane moves from c to D and thence to e and toward f. But this second point can pass through f to a; and when it is there the first point has arrived at A. We therefore say that the first point has passed through infinity, and that every line joins in to itself somewhat like an oval. Geometers talk of the parts of lines at an infinite distance as points. This is a kind of generalization very efficient in mathematics.

27. Modern views of measurement have a philosophical aspect. †1 There is an indefinite number of systems of measuring along a line; thus, a perspective representation of a scale on one line may be taken to measure another, although, of course, such measurements will not agree with what we call the distances of points on the latter line. To establish a system of measurement on a line we must assign a distinct number to each point of it, and for this purpose we shall plainly have to suppose the numbers carried out into an infinite number of places of decimals. These numbers must be ranged along the line in unbroken sequence. Further, in order that such a scale of numbers should be of any use, it must be capable of being shifted into new positions, each number continuing to be attached to a single distinct point. Now it is found that if this is true for "imaginary" as well as for real points (an expression which I cannot stop to elucidate), †2 any such shifting will necessarily leave two numbers attached to the same points as before. So that when the scale is moved over the line by any continuous series of shiftings of one kind, there are two points which no numbers on the scale can ever reach, except the numbers fixed there. This pair of points, thus unattainable in measurement, is called the Absolute. These two points may be distinct and real, or they may coincide, or they may be both imaginary. As an example of a linear quantity with a double absolute we may take probability, which ranges from an unattainable absolute certainty against a proposition to an equally unattainable absolute certainty for it. A line, according to ordinary notions, we have seen is a linear quantity where the two points at infinity coincide. A velocity is another example. A train going with infinite velocity from Chicago to New York would be at all the points on the line at the very same instant, and if the time of transit were reduced to less than nothing it would be moving in the other direction. An angle is a familiar example of a mode of magnitude with no real immeasurable values. One of the questions philosophy has to consider is whether the development of the universe is like the increase of an angle, so that it proceeds forever without tending toward anything unattained, which I take to be the Epicurean view, or whether the universe sprang from a chaos in the infinitely distant past to tend toward something different in the infinitely distant future, or whether the universe sprang from nothing in the past to go on indefinitely toward a point in the infinitely distant future, which, were it attained, would be the mere nothing from which it set out. †1

28. †2 The doctrine of the absolute applied to space comes to this, that either —

First, space is, as Euclid teaches, both unlimited and immeasurable, so that the infinitely distant parts of any plane seen in perspective appear as a straight line, in which case the sum of the three angles of a triangle amounts to 180°; or,

Second, space is immeasurable but limited, so that the infinitely distant parts of any plane seen in perspective appear as a circle, beyond which all is blackness, and in this case the sum of the three angles of a triangle is less than 180° by an amount proportional to the area of the triangle; or,

Third, space is unlimited but finite (like the surface of a sphere), so that it has no infinitely distant parts; but a finite journey along any straight line would bring one back to his original position, and looking off with an unobstructed view one would see the back of his own head enormously magnified, in which case the sum of the three angles of a triangle exceeds 180° by an amount proportional to the area.

29. Which of these three hypotheses is true we know not. †1 The largest triangles we can measure are such as have the earth's orbit for base, and the distance of a fixed star for altitude. The angular magnitude resulting from subtracting the sum of the two angles at the base of such a triangle from 180° is called the star's parallax. The parallaxes of only about forty stars have been measured as yet. Two of them come out negative, that of Arided ({a} Cygni), a star of magnitude 1 1/2, which is -0.''082, according to C. H. F. Peters, and that of a star of magnitude 7 3/4, known as Piazzi III 422, †2 which is -0.''045, according to R. S. Ball. But these negative parallaxes are undoubtedly to be attributed to errors of observation; †3 for the probable error of such a determination is about ±0.''075, and it would be strange indeed if we were to be able to see, as it were, more than half way round space, without being able to see stars with larger negative parallaxes. Indeed, the very fact that of all the parallaxes measured only two come out negative would be a strong argument that the smallest parallaxes really amount to +0.''1, were it not for the reflection that the publication of other negative parallaxes may have been suppressed. I think we may feel confident that the parallax of the farthest star lies somewhere between -0.''05 and +0.''15, and within another century our grandchildren will surely know whether the three angles of a triangle are greater or less than 180° — that they are exactly that amount is what nobody ever can be justified in concluding. It is true that according to the axioms of geometry the sum of the three sides of a triangle are precisely 180°; but these axioms are now exploded, and geometers confess that they, as geometers, know not the slightest reason for supposing them to be precisely true. †4 They are expressions of our inborn conception of space, and as such are entitled to credit, so far as their truth could have influenced the formation of the mind. But that affords not the slightest reason for supposing them exact.

30. Now, metaphysics has always been the ape of mathematics. Geometry suggested the idea of a demonstrative system of absolutely certain philosophical principles; and the ideas of the metaphysicians have at all times been in large part drawn from mathematics. The metaphysical axioms are imitations of the geometrical axioms; and now that the latter have been thrown overboard, without doubt the former will be sent after them. It is evident, for instance, that we can have no reason to think that every phenomenon in all its minutest details is precisely determined by law. That there is an arbitrary element in the universe we see — namely, its variety. This variety must be attributed to spontaneity in some form.

31. Had I more space, I now ought to show how important for philosophy is the mathematical conception of continuity. Most of what is true in Hegel is a darkling glimmer of a conception which the mathematicians had long before made pretty clear, and which recent researches have still further illustrated.

§6. First, Second, and Third †1 E

32. Among the many principles of Logic which find their application in Philosophy, I can here only mention one. Three conceptions are perpetually turning up at every point in every theory of logic, and in the most rounded systems they occur in connection with one another. They are conceptions so very broad and consequently indefinite that they are hard to seize and may be easily overlooked. I call them the conceptions of First, Second, Third. First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction with, something else. Third is the conception of mediation, whereby a first and second are brought into relation. To illustrate these ideas, I will show how they enter into those we have been considering. The origin of things, considered not as leading to anything, but in itself, contains the idea of First, the end of things that of Second, the process mediating between them that of Third. †1 A philosophy which emphasizes the idea of the One is generally a dualistic philosophy in which the conception of Second receives exaggerated attention; for this One (though of course involving the idea of First) is always the other of a manifold which is not one. The idea of the Many, because variety is arbitrariness and arbitrariness is repudiation of any Secondness, has for its principal component the conception of First. In psychology Feeling is First, Sense of reaction Second, General conception Third, or mediation. †2 In biology, the idea of arbitrary sporting is First, heredity is Second, the process whereby the accidental characters become fixed is Third. †3 Chance is First, Law is Second, the tendency to take habits is Third. †4 Mind is First, Matter is Second, Evolution is Third.

33. Such are the materials out of which chiefly a philosophical theory ought to be built, in order to represent the state of knowledge to which the nineteenth century has brought us. Without going into other important questions of philosophical architectonic, we can readily foresee what sort of a metaphysics would appropriately be constructed from those conceptions. Like some of the most ancient and some of the most recent speculations it would be a Cosmogonic Philosophy. It would suppose that in the beginning — infinitely remote — there was a chaos of unpersonalized feeling, which being without connection or regularity would properly be without existence. This feeling, sporting here and there in pure arbitrariness, would have started the germ of a generalizing tendency. Its other sportings would be evanescent, but this would have a growing virtue. Thus, the tendency to habit would be started; and from this, with the other principles of evolution, all the regularities of the universe would be evolved. At any time, however, an element of pure chance survives and will remain until the world becomes an absolutely perfect, rational, and symmetrical system, in which mind is at last crystallized in the infinitely distant future.

34. That idea has been worked out by me with elaboration. †1 It accounts for the main features of the universe as we know it — the characters of time, space, matter, force, gravitation, electricity, etc. It predicts many more things which new observations can alone bring to the test. May some future student go over this ground again, and have the leisure to give his results to the world.

Chapter 2: The Doctrine of Necessity Examined †1

§1. The Mechanical Philosophy E

35. In The Monist for January, 1891, †2 I endeavored to show what elementary ideas ought to enter into our view of the universe. I may mention that on those considerations I had already grounded a cosmical theory, and from it had deduced a considerable number of consequences capable of being compared with experience. This comparison is now in progress, but under existing circumstances must occupy many years.

36. I propose here to examine the common belief that every single fact in the universe is precisely determined by law. It must not be supposed that this is a doctrine accepted everywhere and at all times by all rational men. Its first advocate appears to have been Democritus, the atomist, who was led to it, as we are informed, by reflecting upon the "impenetrability, translation, and impact of matter ({antitypia kai phora kai plégé tés hylés})." †3 That is to say, having restricted his attention to a field where no influence other than mechanical constraint could possibly come before his notice, he straightway jumped to the conclusion that throughout the universe that was the sole principle of action — a style of reasoning so usual in our day with men not unreflecting as to be more than excusable in the infancy of thought. But Epicurus, in revising the atomic doctrine and repairing its defenses, found himself obliged to suppose that atoms swerve from their courses by spontaneous chance; and thereby he conferred upon the theory life and entelechy. †4 For we now see clearly that the peculiar function of the molecular hypothesis in physics is to open an entry for the calculus of probabilities. Already, the prince of philosophers had repeatedly and emphatically condemned the dictum of Democritus (especially in the Physics, Book II, chapters 4, 5, 6), holding that events come to pass in three ways, namely, (1) by external compulsion, or the action of efficient causes, (2) by virtue of an inward nature, or the influence of final causes, and (3) irregularly without definite cause, but just by absolute chance; and this doctrine is of the inmost essence of Aristotelianism. It affords, at any rate, a valuable enumeration of the possible ways in which anything can be supposed to have come about. The freedom of the will, too, was admitted both by Aristotle †1 and by Epicurus. †2 But the Stoa, †3 which in every department seized upon the most tangible, hard, and lifeless element, and blindly denied the existence of every other, which, for example, impugned the validity of the inductive method and wished to fill its place with the reductio ad absurdum, very naturally became the one school of ancient philosophy to stand by a strict necessitarianism, thus returning to a single principle of Democritus that Epicurus had been unable to swallow. Necessitarianism and materialism with the Stoics went hand in hand, as by affinity they should. At the revival of learning, Stoicism met with considerable favor, partly because it departed just enough from Aristotle to give it the spice of novelty, and partly because its superficialities well adapted it for acceptance by students of literature and art who wanted their philosophy drawn mild. Afterwards, the great discoveries in mechanics inspired the hope that mechanical principles might suffice to explain the universe; and, though without logical justification, this hope has since been continually stimulated by subsequent advances in physics. Nevertheless, the doctrine was in too evident conflict with the freedom of the will and with miracles to be generally acceptable, at first. But meantime there arose that most widely spread of philosophical blunders, the notion that associationalism belongs intrinsically to the materialistic family of doctrines; and thus was evolved the theory of motives; and libertarianism became weakened. At present, historical criticism has almost exploded the miracles, great and small; so that the doctrine of necessity has never been in so great vogue as now.

37. The proposition in question is that the state of things existing at any time, together with certain immutable laws, completely determine the state of things at every other time (for a limitation to future time is indefensible). Thus, given the state of the universe in the original nebula, and given the laws of mechanics, a sufficiently powerful mind could deduce from these data the precise form of every curlicue of every letter I am now writing.

38. Whoever holds that every act of the will as well as every idea of the mind is under the rigid governance of a necessity †1 coördinated with that of the physical world will logically be carried to the proposition that minds are part of the physical world in such a sense that the laws of mechanics determine anything that happens according to immutable attractions and repulsions. In that case, that instantaneous state of things, from which every other state of things is calculable, consists in the positions and velocities of all the particles at any instant. This, the usual and most logical form of necessitarianism, is called the mechanical philosophy.

§2. Necessity Considered as a Postulate E

39. When I have asked thinking men what reason they had to believe that every fact in the universe is precisely determined by law, the first answer has usually been that the proposition is a "presupposition" or postulate of scientific reasoning. Well, if that is the best that can be said for it, the belief is doomed. Suppose it be "postulated": that does not make it true, nor so much as afford the slightest rational motive for yielding it any credence. It is as if a man should come to borrow money and, when asked for his security, should reply he "postulated" the loan. To "postulate" a proposition is no more than to hope it is true. There are, indeed, practical emergencies in which we act upon assumptions of certain propositions as true, because if they are not so, it can make no difference how we act. But all such propositions I take to be hypotheses of individual facts. For it is manifest that no universal principle can in its universality be comprised †1 in a special case or can be requisite for the validity of any ordinary inference. To say, for instance, that the demonstration by Archimedes of the property of the lever would fall to the ground if men were endowed with free will is extravagant; yet this is implied by those who make a proposition incompatible with the freedom of the will the postulate of all inference. Considering, too, that the conclusions of science make no pretense to being more than probable, and considering that a probable inference can at most only suppose something to be most frequently, or otherwise approximately, true, but never that anything is precisely true without exception throughout the universe, we see how far this proposition in truth is from being so postulated.

40. But the whole notion of a postulate being involved in reasoning appertains to a by-gone and false conception of logic. Non-deductive or ampliative inference is of three kinds: induction, hypothesis, and analogy. †2 If there be any other modes, they must be extremely unusual and highly complicated, and may be assumed with little doubt to be of the same nature as those enumerated. For induction, hypothesis, and analogy, as far as their ampliative character goes, that is, so far as they conclude something not implied in the premisses, depend upon one principle and involve the same procedure. All are essentially inferences from sampling. Suppose a ship arrives at Liverpool laden with wheat in bulk. Suppose that by some machinery the whole cargo be stirred up with great thoroughness. Suppose that twenty-seven thimblefuls be taken equally from the forward, midships, and aft parts, from the starboard, center, and larboard parts, and from the top, half depth, and lower parts of her hold, and that these being mixed and the grains counted, four-fifths of the latter are found to be of quality A. Then we infer, experientially and provisionally, that approximately four-fifths of all the grain in the cargo is of the same quality. I say we infer this experientially and provisionally. By saying that we infer it experientially, I mean that our conclusion makes no pretension to knowledge of wheat-in-itself, our {alétheia}, as the derivation of that word implies, has nothing to do with latent wheat. We are dealing only with the matter of possible experience — experience in the full acceptation of the term as something not merely affecting the senses but also as the subject of thought. If there be any wheat hidden on the ship, so that it can neither turn up in the sample nor be heard of subsequently from purchasers — or if it be half-hidden, so that it may, indeed, turn up, but is less likely to do so than the rest — or if it can affect our senses and our pockets, but from some strange cause or causelessness cannot be reasoned about — all such wheat is to be excluded (or have only its proportional weight) in calculating that true proportion of quality A, to which our inference seeks to approximate. By saying that we draw the inference provisionally, I mean that we do not hold that we have reached any assigned degree of approximation as yet, but only hold that if our experience be indefinitely extended, and if every fact of whatever nature, as fast as it presents itself, be duly applied, according to the inductive method, in correcting the inferred ratio, then our approximation will become indefinitely close in the long run; that is to say, close to the experience to come (not merely close by the exhaustion of a finite collection) so that if experience in general is to fluctuate irregularly to and fro, in a manner to deprive the ratio sought of all definite value, we shall be able to find out approximately within what limits it fluctuates, and if, after having one definite value, it changes and assumes another, we shall be able to find that out, and in short, whatever may be the variations of this ratio in experience, experience indefinitely extended will enable us to detect them, so as to predict rightly, at last, what its ultimate value may be, if it have any ultimate value, or what the ultimate law of succession of values may be, if there be any such ultimate law, or that it ultimately fluctuates irregularly within certain limits, if it do so ultimately fluctuate. Now our inference, claiming to be no more than thus experiential and provisional, manifestly involves no postulate whatever.

41. For what is a postulate? It is the formulation of a material fact which we are not entitled to assume as a premiss, but the truth of which is requisite to the validity of an inference. Any fact, then, which might be supposed postulated, must either be such that it would ultimately present itself in experience, or not. If it will present itself, we need not postulate it now in our provisional inference, since we shall ultimately be entitled to use it as a premiss. But if it never would present itself in experience, our conclusion is valid but for the possibility of this fact being otherwise than assumed, that is, it is valid as far as possible experience goes, and that is all that we claim. Thus, every postulate is cut off, either by the provisionality or by the experientiality of our inference. For instance, it has been said that induction postulates that, if an indefinite succession of samples be drawn, examined, and thrown back each before the next is drawn, then in the long run every grain will be drawn as often as any other, that is to say, postulates that the ratio of the numbers of times in which any two are drawn will indefinitely approximate to unity. But no such postulate is made; for if, on the one hand, we are to have no other experience of the wheat than from such drawings, it is the ratio that presents itself in those drawings and not the ratio which belongs to the wheat in its latent existence that we are endeavoring to determine; while if, on the other hand, there is some other mode by which the wheat is to come under our knowledge, equivalent to another kind of sampling, so that after all our care in stirring up the wheat some experiential grains will present themselves in the first sampling operation more often than others in the long run, this very singular fact will be sure to get discovered by the inductive method, which must avail itself of every sort of experience; and our inference, which was only provisional, corrects itself at last. Again, it has been said, that induction postulates that under like circumstances like events will happen, and that this postulate is at bottom the same as the principle of universal causation. †1 But this is a blunder, or bévue, due to thinking exclusively of inductions where the concluded ratio is either 1 or 0. If any such proposition were postulated, it would be that under like circumstances (the circumstances of drawing the different samples) different events occur in the same proportions in all the different sets — a proposition which is false and even absurd. †1 But in truth no such thing is postulated, the experiential character of the inference reducing the condition of validity to this, that if a certain result does not occur, the opposite result will be manifested, a condition assured by the provisionality of the inference. But it may be asked whether it is not conceivable that every instance of a certain class destined to be ever employed as a datum of induction should have one character, while every instance destined not to be so employed should have the opposite character. The answer is that, in that case, the instances excluded from being subjects of reasoning would not be experienced in the full sense of the word, but would be among these latent individuals of which our conclusion does not pretend to speak.

42. To this account of the rationale of induction I know of but one objection worth mention: it is that I thus fail to deduce the full degree of force which this mode of inference in fact possesses; that according to my view, no matter how thorough and elaborate the stirring and mixing process had been, the examination of a single handful of grain would not give me any assurance, sufficient to risk money upon, that the next handful would not greatly modify the concluded value of the ratio under inquiry, while, in fact, the assurance would be very high that this ratio was not greatly in error. If the true ratio of grains of quality A were 0.80 and the handful contained a thousand grains, nine such handfuls out of every ten would contain from 780 to 820 grains of quality A. The answer to this is that the calculation given is correct when we know that the units of this handful and the quality inquired into have the normal independence of one another, if for instance the stirring has been complete and the character sampled for has been settled upon in advance of the examination of the sample. †2 But in so far as these conditions are not known to be complied with, the above figures cease to be applicable. Random sampling and predesignation of the character sampled for should always be striven after in inductive reasoning, but when they cannot be attained, so long as it is conducted honestly, the inference retains some value. When we cannot ascertain how the sampling has been done or the sample-character selected, induction still has the essential validity which my present account of it shows it to have.

§3. The Observational Evidence for Necessitarianism E

43. I do not think a man who combines a willingness to be convinced with a power of appreciating an argument upon a difficult subject can resist the reasons which have been given to show that the principle of universal necessity cannot be defended as being a postulate of reasoning. But then the question immediately arises whether it is not proved to be true, or at least rendered highly probable, by observation of nature.

44. Still, this question ought not long to arrest a person accustomed to reflect upon the force of scientific reasoning. For the essence of the necessitarian position is that certain continuous quantities have certain exact values. Now, how can observation determine the value of such a quantity with a probable error absolutely nil? To one who is behind the scenes, and knows that the most refined comparisons of masses, lengths, and angles, far surpassing in precision all other measurements, yet fall behind the accuracy of bank accounts, and that the ordinary determinations of physical constants, such as appear from month to month in the journals, are about on a par with an upholsterer's measurements of carpets and curtains, the idea of mathematical exactitude being demonstrated in the laboratory will appear simply ridiculous. There is a recognized method of estimating the probable magnitudes of errors in physics — the method of least squares. It is universally admitted that this method makes the errors smaller than they really are; yet even according to that theory an error indefinitely small is indefinitely improbable; so that any statement to the effect that a certain continuous quantity has a certain exact value, if well founded at all, must be founded on something other than observation.

45. Still, I am obliged to admit that this rule is subject to a certain qualification. Namely, it only applies to continuous †P1 quantity. Now, certain kinds of continuous quantity are discontinuous at one or at two limits, and for such limits the rule must be modified. Thus, the length of a line cannot be less than zero. Suppose, then, the question arises how long a line a certain person had drawn from a marked point on a piece of paper. If no line at all can be seen, the observed length is zero; and the only conclusion this observation warrants is that the length of the line is less than the smallest length visible with the optical power employed. But indirect observations — for example, that the person supposed to have drawn the line was never within fifty feet of the paper — may make it probable that no line at all was made, so that the concluded length will be strictly zero. In like manner, experience no doubt would warrant the conclusion that there is absolutely no indigo in a given ear of wheat, and absolutely no attar in a given lichen. But such inferences can only be rendered valid by positive experiential evidence, direct or remote, and cannot rest upon a mere inability to detect the quantity in question. We have reason to think there is no indigo in the wheat, because we have remarked that wherever indigo is produced it is produced in considerable quantities, to mention only one argument. We have reason to think there is no attar in the lichen, because essential oils seem to be in general peculiar to single species. If the question had been whether there was iron in the wheat or the lichen, though chemical analysis should fail to detect its presence, we should think some of it probably was there, since iron is almost everywhere. Without any such information, one way or the other, we could only abstain from any opinion as to the presence of the substance in question. It cannot, I conceive, be maintained that we are in any better position than this in regard to the presence of the element of chance or spontaneous departures from law in nature.

46. Those observations which are generally adduced in favor of mechanical causation simply prove that there is an element of regularity in nature, and have no bearing whatever upon the question of whether such regularity is exact and universal or not. Nay, in regard to this exactitude, all observation is directly opposed to it; and the most that can be said is that a good deal of this observation can be explained away. Try to verify any law of nature, and you will find that the more precise your observations, the more certain they will be to show irregular departures from the law. We are accustomed to ascribe these, and I do not say wrongly, to errors of observation; yet we cannot usually account for such errors in any antecedently probable way. Trace their causes back far enough and you will be forced to admit they are always due to arbitrary determination, or chance.

§4. Absolute Chance E

47. But it may be asked whether if there were an element of real chance in the universe it must not occasionally be productive of signal effects such as could not pass unobserved. In answer to this question, without stopping to point out that there is an abundance of great events which one might be tempted to suppose were of that nature, it will be simplest to remark that physicists hold that the particles of gases are moving about irregularly, substantially as if by real chance, and that by the principles of probabilities there must occasionally happen to be concentrations of heat in the gases contrary to the second law of thermodynamics, and these concentrations, occurring in explosive mixtures, must sometimes have tremendous effects. Here, then, is in substance the very situation supposed; yet no phenomena ever have resulted which we are forced to attribute to such chance concentration of heat, or which anybody, wise or foolish, has ever dreamed of accounting for in that manner.

48. In view of all these considerations, I do not believe that anybody, not in a state of case-hardened ignorance respecting the logic of science, can maintain that the precise and universal conformity of facts to law is clearly proved, or even rendered particularly probable, by any observations hitherto made. In this way, the determined advocate of exact regularity will soon find himself driven to a priori reasons to support his thesis. These received such a socdolager from Stuart Mill †1 in his examination of Hamilton, that holding to them now seems to me to denote a high degree of imperviousness to reason, so that I shall pass them by with little notice.

49. To say that we cannot help believing a given proposition is no argument, but it is a conclusive fact if it be true; and with the substitution of "I" for "we," it is true in the mouths of several classes of minds: the blindly passionate, the unreflecting and ignorant, and the person who has overwhelming evidence before his eyes. But that which has been inconceivable today has often turned out indisputable on the morrow. Inability to conceive is only a stage through which every man must pass in regard to a number of beliefs — unless endowed with extraordinary obstinacy and obtuseness. His understanding is enslaved to some blind compulsion which a vigorous mind is pretty sure soon to cast off.

50. †1 Some seek to back up the a priori position with empirical arguments. They say that the exact regularity of the world is a natural belief, and that natural beliefs have generally been confirmed by experience. There is some reason in this. Natural beliefs, however, if they generally have a foundation of truth, also require correction and purification from natural illusions. The principles of mechanics are undoubtedly natural beliefs; but, for all that, the early formulations of them were exceedingly erroneous. The general approximation to truth in natural beliefs is, in fact, a case of the general adaptation of genetic products to recognizable utilities or ends. Now, the adaptations of nature, beautiful and often marvelous as they verily are, are never found to be quite perfect; so that the argument is quite against the absolute exactitude of any natural belief, including that of the principle of causation.

51. Another argument, or convenient commonplace, is that absolute chance is inconceivable. This word has eight current significations. The Century Dictionary †2 enumerates six. Those who talk like this will hardly be persuaded to say in what sense they mean that chance is inconceivable. Should they do so, it would easily be shown either that they have no sufficient reason for the statement or that the inconceivability is of a kind which does not prove that chance is non-existent.

52. †3 Another a priori argument is that chance is unintelligible; that is to say, while it may perhaps be conceivable, it does not disclose to the eye of reason the how or why of things; and since a hypothesis can only be justified so far as it renders some phenomenon intelligible, we never can have any right to suppose absolute chance to enter into the production of anything in nature. This argument may be considered in connection with two others. Namely, instead of going so far as to say that the supposition of chance can never properly be used to explain any observed fact, it may be alleged merely that no facts are known which such a supposition could in any way help in explaining. Or again, the allegation being still further weakened, it may be said that since departures from law are not unmistakably observed, chance is not a vera causa, †1 and ought not unnecessarily to be introduced into a hypothesis.

53. These are no mean arguments, and require us to examine the matter a little more closely. Come, my superior opponent, let me learn from your wisdom. It seems to me that every throw of sixes with a pair of dice is a manifest instance of chance.

"While you would hold a throw of deuce-ace to be brought about by necessity?" (The opponent's supposed remarks are placed in quotation marks.)

Clearly one throw is as much chance as another.

"Do you think throws of dice are of a different nature from other events?"

I see that I must say that all the diversity and specificalness of events is attributable to chance.

54. "Would you, then, deny that there is any regularity in the world?"

That is clearly undeniable. I must acknowledge there is an approximate regularity, and that every event is influenced by it. But the diversification, specificalness, and irregularity of things I suppose is chance. A throw of sixes appears to me a case in which this element is particularly obtrusive.

"If you reflect more deeply, you will come to see that chance is only a name for a cause that is unknown to us."

Do you mean that we have no idea whatever what kind of causes could bring about a throw of sixes?

"On the contrary, each die moves under the influence of precise mechanical laws."

55. But it appears to me that it is not these laws which made the die turn up sixes; for these laws act just the same when other throws come up. The chance lies in the diversity of throws; and this diversity cannot be due to laws which are immutable.

"The diversity is due to the diverse circumstances under which the laws act. The dice lie differently in the box, and the motion given to the box is different. These are the unknown causes which produce the throws, and to which we give the name of chance; not the mechanical law which regulates the operation of these causes. You see you are already beginning to think more clearly about this subject."

56. Does the operation of mechanical law not increase the diversity?

"Properly not. You must know that the instantaneous state of a system of particles is defined by six times as many numbers as there are particles, three for the coördinates of each particle's position, and three more for the components of its velocity. This number of numbers, which expresses the amount of diversity in the system, remains the same at all times. There may be, to be sure, some kind of relation between the coordinates and component velocities of the different particles, by means of which the state of the system might be expressed by a smaller number of numbers. But, if this is the case, a precisely corresponding relationship must exist between the coordinates and component velocities at any other time, though it may doubtless be a relation less obvious to us. Thus, the intrinsic complexity of the system is the same at all times."

57. Very well, my obliging opponent, we have now reached an issue. You think all the arbitrary specifications of the universe were introduced in one dose, in the beginning, if there was a beginning, and that the variety and complication of nature has always been just as much as it is now. But I, for my part, think that the diversification, the specification, has been continually taking place. Should you condescend to ask me why I so think, I should give my reasons as follows:

58. (1) Question any science which deals with the course of time. Consider the life of an individual animal or plant, or of a mind. Glance at the history of states, of institutions, of language, of ideas. Examine the successions of forms shown by paleontology, the history of the globe as set forth in geology, of what the astronomer is able to make out concerning the changes of stellar systems. Everywhere the main fact is growth and increasing complexity. Death and corruption are mere accidents or secondary phenomena. Among some of the lower organisms, it is a moot point with biologists whether there be anything which ought to be called death. Races, at any rate, do not die out except under unfavorable circumstances. From these broad and ubiquitous facts we may fairly infer, by the most unexceptionable logic, that there is probably in nature some agency by which the complexity and diversity of things can be increased; and that consequently the rule of mechanical necessity meets in some way with interference.

59. (2) By thus admitting pure spontaneity or life as a character of the universe, acting always and everywhere though restrained within narrow bounds by law, producing infinitesimal departures from law continually, and great ones with infinite infrequency, I account for all the variety and diversity of the universe, in the only sense in which the really sui generis and new can be said to be accounted for. The ordinary view has to admit the inexhaustible multitudinous variety of the world, has to admit that its mechanical law cannot account for this in the least, that variety can spring only from spontaneity, and yet denies without any evidence or reason the existence of this spontaneity, or else shoves it back to the beginning of time and supposes it dead ever since. The superior logic of my view appears to me not easily controverted.

60. (3) When I ask the necessitarian how he would explain the diversity and irregularity of the universe, he replies to me out of the treasury of his wisdom that irregularity is something which from the nature of things we must not seek to explain. Abashed at this, I seek to cover my confusion by asking how he would explain the uniformity and regularity of the universe, whereupon he tells me that the laws of nature are immutable and ultimate facts, and no account is to be given of them. But my hypothesis of spontaneity does explain irregularity, in a certain sense; that is, it explains the general fact of irregularity, though not, of course, what each lawless event is to be. At the same time, by thus loosening the bond of necessity, it gives room for the influence of another kind of causation, such as seems to be operative in the mind in the formation of associations, and enables us to understand how the uniformity of nature could have been brought about. That single events should be hard and unintelligible, logic will permit without difficulty: we do not expect to make the shock of a personally experienced earthquake appear natural and reasonable by any amount of cogitation. But logic does expect things general to be understandable. To say that there is a universal law, and that it is a hard, ultimate, unintelligible fact, the why and wherefore of which can never be inquired into, at this a sound logic will revolt, and will pass over at once to a method of philosophizing which does not thus barricade the road of discovery.

61. (4) Necessitarianism cannot logically stop short of making the whole action of the mind a part of the physical universe. Our notion that we decide what we are going to do, if, as the necessitarian says, it has been calculable since the earliest times, is reduced to illusion. Indeed, consciousness in general thus becomes a mere illusory aspect of a material system. What we call red, green, and violet are in reality only different rates of vibration. The sole reality is the distribution of qualities of matter in space and time. Brain-matter is protoplasm in a certain degree and kind of complication — a certain arrangement of mechanical particles. Its feeling is but an inward aspect, a phantom. For, from the positions and velocities of the particles at any one instant, and the knowledge of the immutable forces, the positions at all other times are calculable; so that the universe of space, time, and matter is a rounded system uninterfered with from elsewhere. But, from the state of feeling at any instant, there is no reason to suppose the states of feeling at all other instants are thus exactly calculable; so that feeling is, as I said, a mere fragmentary and illusive aspect of the universe. This is the way, then, that necessitarianism has to make up its accounts. It enters consciousness under the head of sundries, as a forgotten trifle; its scheme of the universe would be more satisfactory if this little fact could be dropped out of sight. On the other hand, by supposing the rigid exactitude of causation to yield, I care not how little — be it but by a strictly infinitesimal amount — we gain room to insert mind into our scheme, and to put it into the place where it is needed, into the position which, as the sole self-intelligible thing, it is entitled to occupy, that of the fountain of existence; and in so doing we resolve the problem of the connection of soul and body. †1

62. (5) But I must leave undeveloped the chief of my reasons, and can only adumbrate it. The hypothesis of chance-spontaneity is one whose inevitable consequences are capable of being traced out with mathematical precision into considerable detail. Much of this I have done and find the consequences to agree with observed facts to an extent which seems to me remarkable. †2 But the matter and methods of reasoning are novel, and I have no right to promise that other mathematicians shall find my deductions as satisfactory as I myself do, so that the strongest reason for my belief must for the present remain a private reason of my own, and cannot influence others. I mention it to explain my own position; and partly to indicate to future mathematical speculators a veritable gold mine, should time and circumstances and the abridger of all joys prevent my opening it to the world.

63. If now I, in my turn, inquire of the necessitarian why he prefers to suppose that all specification goes back to the beginning of things, he will answer me with one of those last three arguments which I left unanswered.

First, he may say that chance is a thing absolutely unintelligible, and therefore that we never can be entitled to make such a supposition. But does not this objection smack of naive impudence? It is not mine, it is his own conception of the universe which leads abruptly up to hard, ultimate, inexplicable, immutable law, on the one hand, and to inexplicable specification and diversification of circumstances on the other. My view, on the contrary, hypothetizes nothing at all, unless it be hypothesis to say that all specification came about in some sense, and is not to be accepted as unaccountable. To undertake to account for anything by saying baldly †3 that it is due to chance would, indeed, be futile. But this I do not do. I make use of chance chiefly to make room for a principle of generalization, or tendency to form habits, which I hold has produced all regularities. The mechanical philosopher leaves the whole specification of the world utterly unaccounted for, which is pretty nearly as bad as to baldly attribute it to chance. I attribute it altogether to chance, it is true, but to chance in the form of a spontaneity which is to some degree regular. It seems to me clear at any rate that one of these two positions must be taken, or else specification must be supposed due to a spontaneity which develops itself in a certain and not in a chance way, by an objective logic like that of Hegel. This last way I leave as an open possibility, for the present; †1 for it is as much opposed to the necessitarian scheme of existence as my own theory is.

64. Secondly, the necessitarian may say there are, at any rate, no observed phenomena which the hypothesis of chance could aid in explaining. In reply, I point first to the phenomenon of growth and developing complexity, which appears to be universal, and which, though it may possibly be an affair of mechanism perhaps, certainly presents all the appearance of increasing diversification. Then, there is variety itself, beyond comparison the most obtrusive character of the universe: no mechanism can account for this. Then, there is the very fact the necessitarian most insists upon, the regularity of the universe which for him serves only to block the road of inquiry. Then, there are the regular relationships between the laws of nature — similarities and comparative characters, which appeal to our intelligence as its cousins, and call upon us for a reason. Finally, there is consciousness, feeling, a patent fact enough, but a very inconvenient one to the mechanical philosopher.

65. Thirdly, the necessitarian may say that chance is not a vera causa, that we cannot know positively there is any such element in the universe. But the doctrine of the vera causa has nothing to do with elementary conceptions. Pushed to that extreme, it at once cuts off belief in the existence of a material universe; and without that necessitarianism could hardly maintain its ground. Besides, variety is a fact which must be admitted; and the theory of chance merely consists in supposing this diversification does not antedate all time. Moreover, the avoidance of hypotheses involving causes nowhere positively known to act is only a recommendation of logic, not a positive command. It cannot be formulated in any precise terms without at once betraying its untenable character — I mean as rigid rule, for as a recommendation it is wholesome enough.

I believe I have thus subjected to fair examination all the important reasons for adhering to the theory of universal necessity, and have shown their nullity. I earnestly beg that whoever may detect any flaw in my reasoning will point it out to me, either privately or publicly; for, if I am wrong, it much concerns me to be set right speedily. If my argument remains unrefuted, it will be time, I think, to doubt the absolute truth of the principle of universal law; and when once such a doubt has obtained a living root in any man's mind, my cause with him, I am persuaded, is gained. †1

Chapter 3: Causation and Force †1 P

§1. Physical Causation

66. Those who make causality one of the original uralt elements in the universe or one of the fundamental categories of thought — of whom you will find that I am not one — have one very awkward fact to explain away. It is that men's conceptions of a Cause are in different stages of scientific culture entirely different and inconsistent. The great principle of causation which, we are told, it is absolutely impossible not to believe, has been one proposition at one period of history and an entirely disparate one [at] another and is still a third one for the modern physicist. The only thing about it which has stood, to use my friend Carus's word, a {ktéma ex aei}, semper eadem, is the name of it. As Aristotle †2 remarks, what the Ionian philosophers were trying to find out as the principles of things was what they were made of. Aristotle himself, as I need not remind you, recognizes four distinct kinds of cause, †3 which go to determining a fact: the matter to which it owes its existence, the form to which it owes its nature, the efficient cause which acts upon it from past time, and the final cause which acts upon it from future time. Oh, but it is commonly said, these are merely verbal distinctions. This to my apprehension is one of those superficial explanations, which pass current till men examine them, and serve, like the elegant bankers' memorandum, pour donner le change to the unwary. They seem to me to mark different types of retroductively †4 inferred facts — facts, which it was supposed, furnished the universal process of Nature the occasions from which different features of the fact were brought about. The conception is that Nature syllogizes from one grand major premiss, and the causes are the different minor premisses of nature's syllogistic development. It is generally held that the word "cause" has simply been narrowed to that one of the four Aristotelian causes which was named from the circumstance that it alone produces an effect. But this notion that our conception of cause is that of the Aristotelian efficient cause will hardly bear examination. The efficient cause was, in the first place, generally a thing, not an event; then, something which need not do anything; its mere existence might be sufficient. Neither did the effect always necessarily follow. True when it did follow it was said to be compelled. But it was not necessary in our modern sense. That is, it was not invariable. Even in ancient literature we occasionally meet with the idea that a cause is an event of such a kind as to be necessarily followed by another event which is the effect. This is the current idea, now. But it is only in the last two centuries that it has become the dominant conception. It is not so with the most accurate thinkers of the time of Descartes.

67. Those whose admiration for John Stuart Mill knows no bounds consider it one of his most admirable aperçues that he regards the cause as the aggregate of all the circumstances under which an event occurs. †1 Whether it be admirable or not, it was certainly a commonplace remark before John Mill ever set pen to paper. But the truth is that the remark is founded upon a misconception. So far as the conception of cause has any validity — that is to say, as I shall show you — in a limited domain, the cause and its effect are two facts. Now, Mill seems to have thoughtlessly or nominalistically assumed that a fact is the very objective history of the universe for a short time, in its objective state of existence in itself. But that is not what a fact is. †2 A fact is an abstracted element of that. A fact is so much of the reality as is represented in a single proposition. If a proposition is true, that which it represents is a fact. If, according to a true law of nature as major premiss, it syllogistically follows from the truth of one proposition that another is true, then that abstracted part of the reality which the former proposition represents is the cause of the corresponding element of reality represented by the latter proposition. Thus, the fact that a body is moving over a rough surface is the cause of its coming to rest. It is absurd to say that its color is any part of the cause or of the effect. The color is a part of the reality; but it does not belong to those parts of the reality which constitute the two facts in question.

68. But the grand principle of causation which is generally held to be the most certain of all truths and literally beyond the possibility of doubt (so much so that if a scientific man seeks to limit its truth it is thought pertinent to attack his sincerity and moral character generally) involves three propositions to which I beg your particular attention. The first is, that the state of things at any one instant is completely and exactly determined by the state of things at one other instant. The second is that the cause, or determining state of things, precedes the effect or determined state of things in time. The third is that no fact determines a fact preceding it in time in the same sense in which it determines a fact following it in time. These propositions are generally held to be self-evident truths; but it is further urged that whether they be so or not, they are indubitably proved by modern science. In truth, however, all three of them are in flat contradiction to the principles of mechanics. According to the dominant mechanical philosophy, nothing is real in the physical universe except particles of matter with their masses, their relative positions in space at different instants of time, and the immutable laws of the relations of those three elements of space, time, and matter. Accordingly, at any one instant all that is real is the masses and their positions, together with the laws of their motion. But according to Newton's second law of motion the positions of the masses at any one instant are not determined by their positions at any other single instant, even with the aid of the laws. On the contrary, that which is determined is an acceleration. Now an acceleration is the relation of the position at one instant not to the position at another instant, but to the positions at a second and a third instant. Let a, b, c be the positions of a particle at three instants very near to one another, and at equal intervals of time, say, for convenience, one second.

Then we may make a table thus:

inline image

Or if the intervals are not equal:

inline image †1

69. It will be perceived that there is an essential thirdness, which the principle of causality fails to recognize, so that its first proposition is false. The second proposition, that the cause precedes the effect in time, is equally false. The effect is the acceleration. The cause which produces this effect under the law of force is, according to the doctrine of the conservation of energy, the relative positions of the particles. Now the acceleration which the position requires does not come later than the assumption of that position. It is, on the contrary, absolutely simultaneous with it. Thus, the second proposition of the principle of causation is false. The third is equally so. This proposition is that no event determines a previous event in the same sense in which it determines a subsequent one. But, according to the law of the conservation of energy, the position of the particle relative to the center of force, expressed by b, determines what the acceleration shall be at the moment the particle is in that position. That is to say, taking the number b, whose value expresses the position of the particle, we can calculate from this number alone, by the application of a rule supplied by the law of the force, a number which I may denote by Fb, which is the numerical value of the acceleration (c-2b+a)/((1 1/2s-0 1/2s)2) So that we have the equation (c-2b+a)/((1 1/2s-0 1/2s)2) = Fb. Now, if we know the positions, a and b, of the particle at the two earlier dates, this equation does enable us to calculate the position, c, of the particle at the last date. But since a and c enter into this equation in the same way, and since the difference of dates in the denominator is squared, so that if they are interchanged it makes no difference (because the square of the negative of a number is the [square of the] number itself), it follows that the very same rule, by which we could calculate the value of c, that is, the position at the latest of the three dates, from a and b, those at the two earlier dates, may usually be applied, and in precisely the same form, to calculating the position, a, of the particle at the earliest date, from c and b, its positions at the two later dates. Thus, we see that, according to the law of energy, the positions at the two later instants determine the position at the earliest instant, in precisely the same way, and no other, in which the positions at the two earlier instants determine the position at the latest instant. In short, so far as phenomena governed by the law of the conservation of energy are concerned, the future determines the past in precisely the same way in which the past determines the future; and for those cases, at least, it is a mere human and subjective fashion of looking at things which makes us prefer one of those modes of statement to the other. Thus, all three of the propositions involved in the principle of causation are in flat contradiction to the science of mechanics.

§2. Psychical Causation

70. But when from the world of physical force we turn to the psychical world all is entirely different. Here we find no evident trace of any state of mind depending in opposite ways upon two previous states of mind. Every state of mind, acting under an overruling association, produces another state of mind. Or if different states of mind contribute to producing another, they simply act concurrently, and not in opposite ways, as the two earlier positions of a particle of matter do, in determining a third position. I come down in the morning; and the sight of the newspaper makes me think of the Maine, the breakfast is brought in, and the sight of something I like puts me into a state of cheerful appetite; and so it goes all day long. Moreover, the effect is not simultaneous with the cause. I do not think of the explosion of the Maine simultaneously with seeing the newspaper, but after seeing it, though the interval be but a thirtieth of a second. Furthermore, the relations of the present to the past and to the future, instead of being the same, as in the domain of the Law of Energy, are utterly unlike. I remember the past, but I have absolutely no slightest approach to such knowledge of the future. On the other hand I have considerable power over the future, but nobody except the Parisian mob imagines that he can change the past by much or by little. Thus all three propositions of the law of causation are here fully borne out.

§3. Non-Conservative Forces

71. Even supposing the physical and the psychical laws not to be precisely as they seem to be, yet, though the gulph between the two worlds would not be of so absolute a nature, still in regard to the general features we cannot be mistaken.

But further than that, we can assert that not only is the psychical world within us governed by the law of causation, but even phenomena of psychical interest without us, even those of inanimate matter so far as they attract everyday notice, either are, or have the semblance of being, under the same governance. In order to bring this highly significant fact into evidence, it will be necessary for me to explain two characteristics of phenomena that are determined by forces obeying the law of the conservation of energy. I am sorry that I shall once more be obliged to employ some very simple algebra. The first of the two characteristics I speak of is this, that if any force obeying the law of the conservation of energy or, as we usually say, any conservative force (that is, any force whose value depends exclusively on the situation of the body acted on relatively to the bodies that act on it), if any such force, I say, can produce any given motion, then the very same force can equally produce the reverse motion. That is to say, if at any one instant all the particles were to strike fixed plastic plane surfaces, and were to strike them square, so as to rebound in the directions from which they came and with unchanged velocities, each would move backward through precisely the same path that it had moved forward, and with the same velocities, no matter for how long a time the motion might have been going on. This really follows from what I have shown, that conservative force determines the past in the same way that it determines the future. An extremely elementary demonstration would be easy; but I omit it to save time. The other characteristic of conservative force is, as its name implies, that the Energy is conserved, that is, that the living force or square of the velocity of a particle is simply a function of the position relative to the interacting particles, the exact function depending on the nature of the force plus a quantity constant throughout the motion, which has a value depending on the accidents of the particular case. You are so familiar with this that I will not waste time in proving it. But I will mention that it readily follows from the fact, that a second difference multiplied by the sum of the two adjacent first differences is equal to the difference of the squares of those differences, which is obvious.

For since Δ2 = Δ2 - Δ1 obviously (Δ1+Δ2)Δ22 = (Δ2)2 - (Δ1)2.

72. Now employing these two characteristics, and especially the former, as criteria, we at once recognize that almost all the phenomena of bodies here on earth which attract our familiar notice are non-conservative, that is, are inexplicable by means of the Law of the Conservation of Energy. For they are actions which cannot be reversed. In the language of physics they are irreversible. Such, for instance, is birth, growth, life. Such is all motion resisted by friction or by the viscosity of fluids, as all terrestrial motion is. Such is the conduction of heat, combustion, capillarity, diffusion of fluids. Such is the thunder bolt, the production of high colors by a prism, the flow of rivers, the formations of bars at their mouths, the wearing of their channels; in short, substantially everything that ordinary experience reveals, except the motions of the stars. And even those we do not see to be reversed, though we may well believe them reversible. About the only familiar actions which appear to sense reversible are the motion of a projectile, the bending of a bow or other spring, a freely swinging pendulum, a telephone, a microphone, a galvanic battery, and a dynamo. And all but two of these are unfamiliar to man in his early development. No wonder the doctrine of the conservation of energy was a late discovery.

73. It is certainly a desideratum in philosophy to unify the phenomena of mind and matter. The logic of retroduction directs us to adopt Monism as a provisional hypothesis of philosophy, whether we think it likely or not; and not to abandon it till the position is stormed and we are forced out of it. In view of this, it becomes exceedingly interesting to inquire how the physicist explains those actions which seem to violate the law of energy. Now such of them as physicists have deeply studied are all explained by the action of chance.

For example, if one horizontal layer of air moves northerly, passing over another layer at rest, the reason why the northerly current will be retarded is that the molecules are flying about in all directions and hence chance will carry a good many of them from one layer to the other. And these chance molecules, so carried from either layer to the other, will be so numerous that it is practically certain that, on the average, they will have as much northerly motion as the average of all the molecules in the layer from which they have emerged. Thus, after a while, the average northerly motion of the molecules in each layer approximates toward that of the other layer. And to say that the average northerly motion of the molecules of the upper layer becomes less is the same as to say that the northerly motion of that layer as a whole becomes less. For the motion of the layer as a whole is nothing but the average motion of its molecules.

§4. Fortuitous Distributions

74. Now in order that we may make any application of this method, of explaining non-conservative quasi-forces, to psychical phenomena it is necessary to make an exact analysis and description of its essential elements, omitting all circumstances that do not contribute to the effect. To this end, the first requisite is a definition of Chance, not as to the causes that produce it, but as to the phenomenon itself. Surely, I need not waste breath in refuting that feeblest of attempts at analysis which makes chance to consist in our ignorance. For that has already been sufficiently done in the Logic of Chance of John Venn, a logician, some of whose opinions may be untenable, but whose thought is apt to penetrate beneath the form to the matter he discusses — and after examining a hundred or two logical treatises one begins to think that a high distinction. It is the operation of chance which produces the retardation of the upper layer of air we were just considering; but surely it is no ignorance of ours that has that effect. Chance, then, as an objective phenomenon, is a property of a distribution. That is to say, there is a large collection consisting, say, of colored things and of white things. Chance is a particular manner of distribution of color among all the things. But in order that this phrase should have any meaning, it must refer to some definite arrangement of all the things.

75. Let us begin by supposing that the multitude of colored things is denumeral, †1 and that of the white things is likewise denumeral. The denumeral multitude as I explained in a former lecture is that of all the whole numbers. Every denumeral collection may be numbered. That is, the number 1 may be affixed to one of its objects, 2 to another, and so on in such a way that every object of the collection receives a number. When that is done I call the relation of an object, receiving any number but 1, to the object receiving the next lower number, a generating relation of the collection. It is by no means indispensable to introduce any mention of the numbers in defining a generating relation. I only do so for the sake of using ideas with which you are familiar and thus save time and trouble. Now I must define the important conception of independence, which incessantly recurs in the doctrine of chances. †2 A character, say blueness, is said to be independent of a character, say smoothness, in a given collection if and only if the ratio of the multitude of those objects (PQ) of the collection that are both blue and smooth to the multitude of those objects (PQ̅) of the collection that are blue but not smooth equals the ratio of the multitude of objects (P̅Q) that are not blue but are smooth to the multitude of objects (P̅Q̅) that are not blue and not smooth. Mr. Jevons †1 makes a fuss about proving that if P is independent of Q, so is Q of P. It is because in the proportion

(PQ) : (PQ̅) = (P̅Q) : (P̅Q̅) (PQ) (P̅Q)
we can transpose the means, giving
(PQ) : (P̅Q) = (PQ̅) : (P̅Q̅).		 (PQ̅) (P̅Q̅)

Now in our collection of denumeral colored things and denumeral white things, let F signify a particular generating relation, so that when the objects are numbered, according to that relation, the object numbered n + 1 is F of the object numbered n. Then, I say that a fortuitous distribution of color and whiteness in the collection consists in this, that any object of the collection being colored or not is independent of its being an F of a colored thing, and is also independent of its being an F of an F of a colored thing, and is also independent of its being at once an F of a colored thing and an F of an F of a white thing; and in short that an object's being colored or not is independent of its having or not having any character definable in terms of F, color, and whiteness. That satisfactorily defines a fortuitous distribution when the colored things and white things are both denumeral. †2

76. When either or both the two subcollections of colored things and white things are enumerable, that is, finite in number, such independence, as the definition requires, becomes impossible. Nevertheless, if both are large enumerable collections, there may be an approximation to the fulfillment of the definition, and then we loosely call the distribution fortuitous. If, for example, there are 500,000 colored things and 500,000 white things, then of all possible modes of sequences of 20 successive objects as to their being colored or white there will be only about one of each example. Therefore we cannot say that an object's being colored or not is independent of the sequence of color and whiteness among the twenty objects that precede it, for one of the four terms of the proportion that defines independence will probably be zero. On the other hand there will be about a thousand occurrences of each possible mode of sequence of 10 objects as to being colored or white and if, from 1 object up to 10 objects, the required proportionality is nearly fulfilled, there will be no harm in calling the distribution fortuitous.

77. In comparing two infinite collections we have to distinguish between one being inclusive of more or less than the other and one being more or less multitudinous than the other. I call a collection inclusive of more than another if it includes all the objects of the latter and others besides; but to say that one collection, say the simpletons, is more multitudinous than another, say the sages, means that to every sage a distinct simpleton might be assigned, and assigned to no other sage, while it would be impossible to assign to every simpleton a distinct sage for him alone. Two collections may neither of them be inclusive of all the other includes, as for example the Buddhists and the Japanese; but they cannot each be inclusive of ALL the other includes unless they are identically the same. On the other hand, of any two collections whatsoever, one must be at least as multitudinous as the other, and each may be so. That is, they may be equal. Of equal collections one may be inclusive of more than the other; but the less multitudinous of two collections cannot be the more inclusive. All these propositions except one are easily proved; and that one is proved in the Monist. †1

78. If of the two subcollections, the colored things and the white things, one is denumeral while the other is more than denumeral, we may still speak, and sometimes do speak, of a fortuitous distribution. It is true that for a collection more than denumeral there can be no generating relation. But still, unless the total collection is a continuum of more than one dimension, with or without topical singularities, all the objects of it may be placed in a sequence, at any rate by means of a relatively insignificant multitude of ruptures and junctions. It must be understood that the fortuitousness refers to the particular way in which the objects are placed in sequence. It must furthermore be understood that by a definite mode the whole sequence is broken up into a denumeral collection of subcollections, and the fortuitousness is relative to that mode of breaking up, and moreover this mode of dissection must be capable of a particular mode of variation such that the subcollections may be made all at once inclusive of less and less without limit, and the fortuitousness is still further relative to that mode of shrinking. If, then, no matter how small these subcollections are taken, the character of a subcollection containing a blue thing or not containing a blue thing is independent of that subcollection having any character definable in terms of the generating relation of the denumeral collection, of containing a blue thing and of not containing a colored thing, then the distribution is fortuitous. For example, we may say that certain marked points are fortuitously distributed upon an infinitely long line, meaning that if that line is cut up into a denumeral series of lengths, no matter how small, the lengths containing marked points will be fortuitously distributed along the whole series of lengths.

We might speak of a finite number of points being fortuitously distributed upon the circumference of a circle, meaning an approximate fortuitous distribution. When we say that a finite number [of] points are distributed at random on the circumference, that is quite another matter. We then have in mind a fortuitous distribution, it is true, but it is a fortuitous distribution of the denumeral cases in which a man might, in the course of all time, throw points down upon the circumference.

I do not say that no sense could be attached to the term fortuitous distribution in case both the blue things and the white things were more than denumeral. On the contrary, the difficulty is that several senses might be attached to the phrase, and, having no experience in that line of thought, I am not prepared to say which one would be more appropriate. I therefore pass that case by.

79. We have now determined precisely what Chance, as an objective phenomenon, consists in. In works on probabilities (of which I particularly recommend that of Laurent †1 as being brief and clear and yet at the same time scientific) very beautiful and valuable properties of the fortuitous distribution will be found traced out, especially that which relates to the probability curve.

In the fortuitous distribution the colored things and the white things are mixed up together with an irregularity which is perfect. It is the very highest pitch of irregularity. Departures from this, or regularities, may tend in either of two directions. On the one hand they may mix the colored things and white things more perfectly and uniformly, as when colored things and white things alternate, or they may sift them out, as when all the colored things come in one series and all the white things in another. Even the alternation might be called a sifting, for it puts all the colored things into the odd places and all the white things into the even places, and these constitute two distinct series. Still, having the word regularity for that, we may as well restrict the word sifting so as to enable us to express the less fundamental, but still not altogether unimportant, distinction between leaving the two series mingled and separating them.

80. Let us glance for a moment at the ways in which the three states of things — siftedness, uniform combination, and fortuitous irregularity of mixture — are in fact brought about in nature; and then in the light of these examples we shall be able to see how they could conceivably be brought about.

Sifting is performed by any conservative force quite inevitably. For example, a ray of white light strikes upon a prism. The different colors have different refrangibilities and the light is decomposed. The action is conservative because it is reversible. For if the dispersed light were reflected back upon its course it would be recompounded. But this does not happen except in the laboratory and that only imperfectly, when it is due to the elaborate contrivance of the experimenter. Conservative force, left to itself, can produce no such result, because it depends on the purposeful exact adjustment of each pencil of light. Now one of the first things that the mechanical philosophy discovered was that there are no final causes in pure mechanical action. In the same way, were a great number of meteors to start from the same almost infinitely distant point, all moving in the same direction so as to bring them within the sun's strong attraction, but were they to move with various velocities, the sun's attraction would separate their motions so that when they departed again they would all be arranged in the order of their velocities; the one with no velocity returning just as it came, the one with infinite velocity proceeding in a right line unchecked, and all the rest in more or less bent paths.

inline image

81. So much for the sifting. Let us next consider how a state of fortuitous distribution is brought about. How, for example, is it that the throws of a dice occur in the utterly irregular way in which they do? It is because when we turn over the dice box, there are slight differences in the motion, and also when we put the dice into the box there are small differences in the motion; and no regularity connects the differences of one kind with those of the other. Still, these circumstances would not in themselves give the character of fortuitous distribution to the throws were there not a fortuitous distribution either in the differences of our motion in putting the dice into the box or else fortuitous distribution in the variations of motion in throwing them out. †1 We see, then, that in this case the fortuitous distribution arises from another fortuitous distribution in one or more of the conditions of the production of the phenomenon. All this has been carefully studied by various writers on the theory of errors. Suppose we put into a jar some hot nitrogen and then some cold oxygen. At first, the molecules of nitrogen will be moving with various vires vivae distributed according to a modification of the probability curve and therefore fortuitously, while the molecules of oxygen will likewise have vires vivae distributed according to the same general law, but on the average their motion will be much slower. In the first state of things, therefore, the distribution of vires vivae among all the molecules considered as one collection will not be fortuitous. But there will be continual encounters of molecules, which, in these encounters, will be governed by conservative forces, generally attractions. In consequence of the different modes of these encounters being distributed fortuitously, which is itself due to the fortuitous distribution of the molecules in space, and the fortuitous distribution of the directions and velocities of their motions, continual interchanges of vis viva will take place, so that as time goes on there will be a closer and closer approximation to one fortuitous distribution of vis viva among all the molecules. There we see a fortuitous distribution in process of being brought about. That which happens, happens entirely under the governance of conservative forces; but the character of fortuitous distribution toward which there is a tendency is entirely due to the various fortuitous distributions existing in the different initial conditions of the motion, with which conservative forces never have anything to do. This is the more remarkable because the peculiar distribution which characterized the initial distribution of vires vivae gradually dies out. True, traces of it always remain; but they become fainter and fainter and approach without limit toward complete disappearance. The fortuitous distributions, however, which equally have nothing but initial conditions to sustain them, not only hold their ground, but, wherever the conservative forces act, at once mark their character in the effects. Hence, it is that we find ourselves forced to speak of the "action of chance.". . . . †1

§5. Space

82. †2 Would not the human race, supposing that it could survive the shock at all, be pretty sure to develop a new form of intuition in which the things that now appear near would appear far? For what is the real truth of nearness? Who is my neighbor? Is it not he with whom I intimately react? In short, the suggested explanation is that space is that form of intuition in which is presented the law of the mutual reaction of those objects whose mode of existence consists in mutually reacting. Let us see how much this hypothesis will explain. What are its necessary consequences? I must abridge the reasoning to a mere sketch. In the first place space, as a presentation of law, must be continuous and without singularities. In the second place, since reaction is essentially hic et nunc, or anti-general, it follows that the reacting objects must be entirely independent of one another in their purely spatial determinations. That is, one object being in one particular place in no way requires another object to be in any particular place. From this again it necessarily follows that each object occupies a single point of space, so that matter must consist of Boscovichian atomicules, †1 whatever their multitude may be. On the same principle it furthermore follows that any law among the reactions must involve some other continuum than merely Space alone. Why Time should be that other continuum I shall hope to make clear when we come to consider Time. †2 In the third place, since Space has the mode of being of a law, not that of a reacting existent, it follows that it cannot be the law that, in the absence of reaction, a particle shall adhere to its place; for that would be attributing to it an attraction for that place. Whence it follows that in so far as a particle is not acted upon by another, that which it retains is a relation between space and time. Now it is not logically accurate to say that the law of motion prescribes that a particle, so far as it is not acted upon by forces, continues to move in a straight line, describing equal intervals in equal times. On the contrary the true statement is that straight lines are that family of lines which particles, so far as they are unacted upon, describe, and that equal spaces are such spaces as such a particle describes in equal times. There are some further consequences of this principle the statement of which it will be convenient to postpone for a few minutes.

In the fourth place, since Space presents a law whose prescriptions are nothing but conditions of reactions, and since reaction is Duality, it follows that the conditions of the prescriptions of space are necessarily Dual. Hence immediately follow five corollaries. The first is that all forces are between pairs of particles. The second is that, when two places of the path of an isolated particle are determined, the law determines all the other places; so that two different straight lines cannot have two different points in common. The third corollary is that when the places of an isolated body at two instants are given, the law prescribes its places at all other instants. That is, the first differential coefficient, or mere difference between the places at two instants, determines its places at all other instants. That is, the velocity remains constant. From these corollaries again, together with the general principle from which they are derived, it follows that when a body is acted upon by another body that which is directly affected is the uniform velocity in a straight line, and that in such a way that, in so far as the action of the active body remains the same, two velocities or, what comes to the same thing, three positions with their dates, determine all the velocities the particle will take. This explains, therefore, why the force should produce acceleration rather than any other differential coefficient of the space relatively to the time. Hence, it further follows that a force at each moment of time acts to impart to the body a new rectilinear motion; whence it follows that forces will necessarily be compounded according to a parallelogram of forces. In the non-Euclidean geometry this is only so far modified that the parallelograms must be drawn infinitely small. And it further follows that the line of the force is the straight line through the two particles. There is still another apparent consequence; but I am not satisfied with the reasoning, since it rests upon a principle I am unable abstractly to define. I will, however, state it for what it is worth. Namely, since the force acts to impart an acceleration and since the law presented in space is perfectly general and comprehensive, it follows that the acceleration imparted may be different in kind and not merely in amount from the acceleration the particle already possesses. That is the point I consider doubtful. If it be admitted, it certainly follows that space must have at least three dimensions. Moreover, it again follows as a fourth corollary from space being a law of reactive conditions that, except for the quality of the particles themselves, it is the pure spatial determination which prescribes what the reaction of one particular particle upon another shall be; that is, the force between two particles depends only upon their qualities and their places at the instant. Moreover, as a fifth corollary, it follows that the mechanical law only prescribes how a pair of particles will act. It does not generally prescribe any relation between the actions of different pairs of particles, nor even of the action of a particle upon particles of the same kind placed differently. Hence, not only may different kinds of pairs of particles act differently, but the law of the variation of the action with the relative positions is left to depend upon the qualities of the particles, and this so completely that there is nothing to prevent a particle exercising different forces on different sides of it.

In the fifth place, from the fact that space presents a law of reciprocal reactions, several corollaries follow, particularly these two. First, when one particle, A, acts on another, B, this latter, B, will likewise act on A; and moreover this action cannot impart to both the same acceleration, because the law is such as to affect their relative places. This follows by the aid of the third principle already enunciated, as we shall see. Hence, it can only impart opposite accelerations to A and B. Secondly, those two accelerations must be equal, so that the masses of all atomicules are equal. From this, again, it follows that the masses are unchangeable; and further that if two bodies, or aggregates of atomicules, react upon one another in a certain ratio to one another, in that same ratio they will also react upon any third body.

A sixth principle, concerning the necessity of which some doubt may be entertained, is that, the law presented by space being perfectly general, every motion must admit of receiving the same kind of changes as every other. From this, if it be admitted, it certainly follows, though the demonstration is far too long to give, that space has either 1, 2 or 4 dimensions. Hence, since 1 and 2 dimensionality have been already excluded, the number of dimensions ought to be just 4.

I will now mention the postponed corollaries from the third principle. Since space has only the being of a law, its places cannot have distinct identities in themselves, for distinct identity belongs only to existent things. Hence place is only relative. But since, at the same time, different motions must be comparable in quantity, and this comparison cannot be effected by the moving and reacting particles themselves, it follows that another object must be placed in space to which all motion is referred. And since this object compares generally and thus partakes of the nature of law, it must unlike the moving and reacting bodies be continuous. It is a corrected equivalent of that which has been called the body alpha. It is the firmament, or Cayley's absolute. †1 Since this is to determine every motion, it follows that it is a locus which every straight line cuts, and because space is a law of twoness only, and for other reasons, every straight line must cut it in two points. It is therefore a real quadratic locus, severing space into two parts, and the space of existence must be infinite and limited in every direction.

83. I have thus briefly stated one side of my theory of space. That is, without touching upon the question of the derivation of space and its properties, or how accurately it may be supposed to fulfill its ideal conditions, I have given a hypothesis from which those ideal properties may be deduced. Many of the properties so deduced are known to be true, at least approximately. Others, I am happy to say, are extremely doubtful. I say I am happy because this gives them the character of predictions and renders the hypothesis capable of experiential confirmation or refutation. One of the doubtful properties, the last mentioned, I have succeeded I think in proving to be true by calculations from the proper motions of the stars. Another, that about atoms attracting differently in different directions, I have succeeded in making highly probable, from chemical facts. Still others have some evidence in their favor. The consequence most opposed to observation is the doubtful one of 4 dimensions.

84. Endeavoring to generalize the results that have been obtained, we may say that the continuity of space so acts as to cause an object to be affected by modes of existence not its own, not as participating in them but as being opposite to them. For instance, an isolated particle is at any instant at one point; that is its actual state. But it is so affected by the state which is not actual, but belongs to it by a date differing from the actual [in] one way, that, at a date differing from the actual the other way, it takes a state differing in the opposite way from its actual state. So again, when a force acts upon a body the effect of it is that the mean of the states of the body not actual, but indefinitely approximating to the actual, differs from its actual state. So in the action and reaction of bodies, each body is affected by the other body's motion, not as participating in it but as being opposite to it. But if you carefully note the nature of this generalized formula you will see that it is but an imperfect, somewhat particularized restatement of the principle that space presents the law of the reciprocal reactions of existents. Various other such imperfect formulæ might be mentioned.

85. Let us now consider non-conservative actions. These are all distinguished by asymptotic approach to a definite state of relative rest. Conservative force can never bring about any state of rest except for an instant. It can only produce, I believe, three permanent changes. Namely, it can permanently change the direction [of] motion of a body, and this it does because the body moves away out of the range of the force, or it can cause one body to rotate round another in an inward spiral, more and more rapidly. And third, a planet like Jupiter may turn the motion of a small body and then move away and leave the small body performing permanently, or quasi-permanently, an orbit round the sun. In course of time, however, Jupiter will come round again in such a way as to throw it out. This is a very curious case. Chance is an important factor of it. But all the non-conservative quasiforces produce states of relative rest. Such, for example, is the effect of viscosity. These states of relative rest are states of uniform distribution which upon minuter inspection turn out to be really states of fortuitous distribution. They betray their real nature by the probability curve, or some modification of it, playing a part in the phenomenon. Such, for example, is the case in the conduction of heat.

§6. Time

86. When we ask why chance produces permanent effects, the natural answer which escapes from our lips is that it is because of the independence of different instants of time. A change having been made, there is no particular reason why it should ever be unmade. If a man has won a napoleon at a gaming table he is no more likely to lose it than he was to lose a napoleon at the outset. But we have no sooner let slip the remark about the independence of the instants of time than we are shocked by it. What can be less independent than the parts of the continuum par excellence, through the spectacles of which we envisage every other continuum? And although it may be said that continuity consists in a binding together of things that are different and remain different, so that they are in a measure dependent on one another and yet in a measure independent, yet this is only true of finite parts of the continuum, not of the ultimate elements nor even of the infinitesimal parts. Yet it undoubtedly is true that the permanence of chance effects is due to the independence of the instants of time. How are we to resolve this puzzle? The solution of it lies in this, that time has a point of discontinuity at the present. This discontinuity appears in one form in conservative actions where the actual instant differs from all other instants absolutely, while those others only differ in degree; and the same discontinuity appears in another form in all non-conservative action, where the past is broken off from the future as it is in our consciousness. Thus, although the other instants of time are not independent of one another, independence does appear at the actual instant. It is not an utter, complete independence, but it is absolute independence in certain respects. Perhaps all fortuitous distribution originates from a fortuitous distribution of events in time; and this alone has no other explanation than the Law of Sufficient Reason, that is, is an absolute First. It is a truth well worthy of rumination that all the intellectual development of man rests upon the circumstance that all our action is subject to error. Errare est humanum is of all commonplaces the most familiar. Inanimate things do not err at all; and the lower animals very little. Instinct is all but unerring; but reason in all vitally important matters is a treacherous guide. †1 This tendency to error, when you put it under the microscope of reflection, is seen to consist of fortuitous variations of our actions in time. But it is apt to escape our attention that on such fortuitous variation our intellect is nourished and grows. For without such fortuitous variation, habit-taking would be impossible; and intellect consists in a plasticity of habit.

87. What is time? †2 Shall we say that it is the form under which the law of logical dependence presents itself to intuition? But what is logical dependence objectively considered? It is nothing but a necessitation which, instead of being brute, is governed by law. Our hypothesis therefore amounts to this, that time is the form under which logic presents itself to objective intuition; and the signification of the discontinuity at the actual instant is that here new premisses, not logically derived by Firsts, are introduced.

Chapter 4: Variety and Uniformity

§1. Variety †1

88. . . . The question, what are the shares of uniformity and variety in the phenomena of the universe, is a question which has never been agitated in any public dispute that has attracted general attention. The consequence is that everybody in a semi-unconscious way forms his own opinion about it, usually a pretty vague opinion; and he has the impression that all his neighbors think as he does about it. But, on questioning people closely, it will be found that there are no less than five different opinions that are widely spread on this subject. †2 I will briefly state them and point out just how much arbitrariness each supposes.

89. Beginning with the middling one, in the degree of arbitrariness that it allows, which is, no doubt, the opinion of the largest party among those who know enough of dynamics to entertain such a conception, this view is that the material universe is composed of particles of some kind, each having at any one instant its position in space, and also its velocity, determinate in direction and in amount; and it is held that physical laws are of such a nature that according to the positions of the particles at any instant their velocities are, at that instant, changing at perfectly determinate rates and in perfectly determinate directions. This party holds that, if this statement were rendered definite by indicating just what these accelerations are in each position of the particles, it would be the perfect résumé of all the laws of nature. As for consciousness, these persons hold that its states are rigidly dependent upon the instantaneous states of the physical universe, and that it need not be taken into account in saying what will happen in that universe.

This theory makes the uniformity to be perfectly exact and inflexible. It is such that, given the positions and velocities of all the particles at any one instant, the positions and velocities at all other instants are precisely determined and with these the exact phenomena of all consciousness and feeling. But it supposes the positions and velocities of all the particles at one instant to be entirely arbitrary. It further regards the law itself, although as a law it is general, [as] yet arbitrary in respect to what its requirements are.

90. If we designate the five classes of minds who entertain the five opinions by the first five letters of the alphabet, the A's being the persons who admit the least arbitrariness and the E's being those who admit the most, then the opinion just formulated is that of the C's. If you should be out walking on a fine starlit night in company with a B and a C, and were to point up to the heavens and ask your companions whether they supposed there was any law determining the arrangement of the stars, C would smile and would remark that not a single law of that description had ever been discovered yet. Thereupon B would exclaim, "What! Do you mean to say there is no regularity in the arrangement of the stars when there is the Milky Way before your eyes!" "Oh," C would reply, "there is a rough and irregular compression of the cluster in which we happen to find ourselves. But, assuming the Nebular Hypothesis to be true, that could hardly escape coming about in consequence of the cluster being very much condensed from a former state in which its velocity happened to be a little greater on one side than on the other, which constituted a rotation. But however it came about, the fact that the arrangement is so excessively rough shows at once that it is due to some accident and not to law, since the effects of law are rigidly exact." To this B might perhaps reply, "I do not think your explanation very satisfactory. You suppose that a manifest regularity of arrangement among millions of stars is the effect of an accident. It seems much easier to suppose that the regularity of arrangement was once perfect, but that the motions of the separate stars have deranged it." While this dialogue has been going on an adherent of the sect of A's has joined the group. He now says, "But you surely will admit that if the original perfect symmetry of arrangement has been broken up, probably in its passage into some different form of symmetry, the present apparently irregular arrangement must have been fully intended by the Creator." B replies, "I do not quite know that I am prepared to admit that the world ever was created. But even if it was, while the positive intentions of the Creator must have been fulfilled, we need not suppose that he expressly intended every relation between facts. If the Dowager Empress of China happens to have a fit of coughing and just at that moment I, on the other side of the globe, happen to take a piece of hoarhound candy, we need not suppose that this coincidence was any part of the Creator's plan." A replies, "I believe that Providence overrules every fact and relation however trivial; and even if I were in your state of scepticism, I should still hold it to be inconceivable that any state of facts should fail to conform to some law. You cannot shuffle a pack of cards so that there is no mathematically exact relation between the arrangement before shuffling and the arrangement after shuffling."

So there you have the three commonest forms of necessitarianism. A holds that every feature of all facts conforms to some law. B holds that the law fully determines every fact, but thinks that some relations of facts are accidental. C holds that uniformity within its jurisdiction is perfect, but confines its application to certain elements of phenomena.

91. The party of the D's, of which I am myself a member, holds that uniformities are never absolutely exact, so that the variety of the universe is forever increasing. At the same time we hold that even these departures from law are subject to a certain law of probability, and that in the present state of the universe they are far too small to be detected by our observations. We adopt this hypothesis as the only possible escape from making the laws of nature monstrous arbitrary elements. We wish to make the laws themselves subject to law. For that purpose that law of laws must be a law capable of developing itself. Now the only conceivable law of which that is true is an evolutionary law. We therefore suppose that all law is the result of evolution, and to suppose this is to suppose it to be imperfect.

92. Finally, there are those who suppose nature to be subject to freaks, who believe in miracles not simply as manifestations of superhuman power but as downright violations of the laws of nature, absolutely abnormal. Professor Newcomb, for example, in a series of articles which he contributed to the Independent, suggests that the human will has a power of deflecting the motions of particles, in plain violation of the third law of motion. I do not think, by the way, that it is generally known that some of the early Fathers of the Church refused to believe in physical miracles; and apparently attributed them to a superhuman hypnotic power, reminding one of what the Hindoo jugglers have made British officers think they saw. St. Augustine, †1 on the contrary, while holding it impious to think them to be violations of Nature's Laws, regards them apparently as occurrences that are to us what the reading of a letter by a man might seem to a dog to be, namely, a manifestation of some higher mastery of things than would be compatible with his nature.

93. One fallacy into which the necessitarians of class C generally fall is that they imagine that they can disprove that anything happens by chance by showing that the event has a cause. Thus Boëthius, at the beginning of the fifth book of his Consolations, after citing Aristotle as a necessitarian, †2 which is enough to take one's breath away, so monstrous is the blunder or the impudence of it, has a little ode of twelve lines which Mr. Henry Rosher James translates in 24, †3 that imitate the swing of the original very well, but miss the point. By a geographical fiction Boëthius represents that the Tigris and the Euphrates flow from a common lake. Now suppose a boat to be wrecked in that lake and one part of it is carried down the Tigris, the other part down the Euphrates, and where these rivers, after being separate for hundreds of miles, flow together again those two parts of the boats are dashed against one another. There is a fortuitous event if there ever was one; and yet, says Boëthius, the currents forced them to move just as they did so that there was no chance about it. True, the existential events were governed by law. But when we speak of chance, it is a question of cause. Now it is the ineluctable blunder of a nominalist, as Boëthius was, to talk of the cause of an event. But it is not an existential event that has a cause. It is the fact, which is the reference of the event to a general relation, that has a cause. †1 The event, it is true, was governed by the law of the current. But the fact which we are considering is that the two pieces that were dashed together had long before belonged together. That is a fact that would not happen once in ten thousand times, although when you join to this fact various circumstances of the actual event, and so contemplate quite another fact, it would happen every time, no doubt. That is to say, nobody can doubt it but an adherent of the E's sect. The example is a very good one as showing that the causal necessitation of more concrete fact does not prevent a more prescinded, †2 or general, fact of the same event from being quite fortuitous. The position of Aristotle in this matter is altogether right, and not "veri propinqua ratione" as Boëthius says; but it is a position that nobody can understand who is completely immersed in the state of mind of modern philosophy. Zeller, †3 for example, does not seize it at all.

94. But let us drop metaphysics and return to logic. It was Hobbes †4 who first said, referring to and combating Aristotle's doctrine, "Men commonly call that casual whereof they do not perceive the necessary cause," for Hobbes was a typical stoic in his philosophy. Leibnitz †5 emphatically agrees with Hobbes. "Fort bien," he says. "J'y consens, si l'on entend parler d'un hasard réel. Car la fortune et le hasard ne sont que des apparences, qui viennent de l'ignorance des causes, ou de l'abstraction qu'on en fait." This has been said a thousand times since with an air as if it explained the whole thing. I do not doubt that that is the impression of almost everybody in this hall. But I am quite sure that most of you will be glad to reexamine the question with me. I will just give you the headings of some thoughts about it, which, if it is not too great a liberty, I would suggest that you take note of and carefully pursue by yourselves when you find leisure. I wish in the latter part of this lecture to make some remarks of great importance in many reasonings; and in order to get any time for those remarks I shall be obliged to make my statement of this part so brief that only the most thorough student of philosophy could fully grasp the meaning of it at the single hearing.

95. The first thing to be taken into consideration is the general upshot of Kant's Critic of the Pure Reason. The first step of Kant's thought — the first moment of it, if you like that phraseology — is to recognize that all our knowledge is, and forever must be, relative to human experience and to the nature of the human mind. That conception being well digested, the second moment of the reasoning becomes evident, namely, that as soon as it has been shown concerning any conception that it is essentially involved in the very forms of logic or other forms of knowing, from that moment there can no longer be any rational hesitation about fully accepting that conception as valid for the universe of our possible experience. To repeat an example I have given before, you look at an object and say "That is red." I ask you how you prove that. You tell me you see it. Yes, you see something; but you do not see that it is red; because that it is red is a proposition; and you do not see a proposition. What you see is an image and has no resemblance to a proposition, and there is no logic in saying that your proposition is proved by the image. For a proposition can only be logically based on a premiss and a premiss is a proposition. To this you very properly reply, with Kant's aid, that my objections allege what is perfectly true, but that instead of showing that you have no right to say the thing is red they conclusively prove that you are logically justified in doing so. At this point, the idealist appears before the tribunal of your reason with the suggestion that since these metaphysical conceptions, that repose upon their being involved in the forms of logic, are only valid for experience and since all our knowledge is relative to the human mind, they are not valid for things as they objectively are; and since the conception of existence is preeminently a conception of that description, it is a mere fairy tale to say that outward objects exist, the only objects of possible experience being our own ideas. Hereupon comes the third moment of Kant's thought, which was only made prominent in the second edition, not, as Kant truly says, that it was not already in the book, but that it was an idea in which Kant's mind was so completely immersed that he failed to see the necessity of making an explicit statement of it, until Fichte misinterpreted him. It is really a most luminous and central element of Kant's thought. I may say that it is the very sun round which all the rest revolves. This third moment consists in the flat denial that the metaphysical conceptions do not apply to things in themselves. Kant never said that. What he said is that these conceptions do not apply beyond the limits of possible experience. But we have direct experience of things in themselves. †1 Nothing can be more completely false than that we can experience only our own ideas. That is indeed without exaggeration the very epitome of all falsity. Our knowledge of things in themselves is entirely relative, it is true; but all experience and all knowledge is knowledge of that which is, independently of being represented. Even lies invariably contain this much truth, that they represent themselves to be referring to something whose mode of being is independent of its being represented. †2 This is true even if the proposition relates to an object of representation as such. At the same time, no proposition can relate, or even thoroughly pretend to relate, to any object otherwise than as that object is represented. These things are utterly unintelligible as long as your thoughts are mere dreams. But as soon as you take into account that Secondness that jabs you perpetually in the ribs, you become awake to their truth. Duns Scotus and Kant are the great assertors of this doctrine, for which Thomas Reid deserves some credit too. But Kant failed to work out all the consequences of this third moment of thought and considerable retractions are called for, accordingly, from some of the positions of his Transcendental Dialectic. Nor in other respects must it be supposed that I assent to everything either in Scotus or in Kant. We all commit our blunders.

96. To this first consideration, it is necessary to add, in the second place, that of the great difference in the logical status of the future and the past, which Aristotle †1 stated with great emphasis without finding anybody in modern times to comprehend what he said, not even Trendelenburg, †2 who comes the nearest to it. Aristotle is understood by modern critics to be in a childishly naive state of mind on this subject. Now it is quite true that Aristotle was almost the first pioneer in logic and just stood at its threshold. It is also true that there are some monumental follies in his physical books; but the worst of these may fairly be presumed to be insertions made by different students during the thirty years when his manuscripts lay on the shelves of his school for general use. But Aristotle was by many lengths the greatest intellect that human history has to show; and it was precisely in such fields of thought, as this distinction of past and future time, that his mind was the most thoroughly trained. So gigantic is his power of thought that those critics may almost be excused who hold it to be impossible that all of the books that have come down to us as his should all have been produced by one man. I am ashamed to have to confess that I shared the general opinion of Aristotle's childish naïveté in those passages, until the further progress of my own studies forced me to the very substance of what Aristotle says. The past is ended and done; the future is endless and can never have been done. To be sure, if we regard past time as having had no beginning, then, when we make general assertions concerning it, we can only be talking of it as an object of possible experience, that is, of what future researches may bring to light. Hence it might be inferred that the contrast Aristotle speaks of between the past and the future might be merely subjective, having to do with our different attitude toward them. But even a moderate appreciation of the Kantian argument will show that, besides being true in regard to our knowledge of time, it must also be regarded as true of real time; and time is real, whether we accept Kant's dubious view of it, which he is certainly far from making evident, as the form of the internal sense, or not. I do not question Time's being a form, that is, being of the nature of a Law, and not an Existence; nor its being an Intuition, that is, being at the same time a single object; nor its having a special connection with the internal world. But I doubt very much whether Kant has succeeded in rightly stating the connection between those three features of Time.

97. Now there are three characters which mark the universe of our experience in a way of their own. They are Variety, Uniformity, and the passage of Variety into Uniformity. By the Passage of Variety into Uniformity, I mean that variety upon being multiplied almost in every department of experience shows a tendency to form habits. These habits produce statistical uniformities. When the number of instances entering into the statistics are small compared with the degree of their variation, the law will be extremely rough, but when the number runs up into the trillions, that is to say cubes of millions, or much higher, as in the case of molecules, there are no departures from the law that our senses can take cognizance of.

§2. Uniformity †1

98. (1) A fact consisting in this: that, of a certain genus of facts, a proportion approaching unity (the whole) belongs, in the course of experience, to a certain species; so that, though of itself the knowledge of this uniformity gives no information concerning a certain thing or character, yet it will strengthen any inductive conclusion of a certain kind.

It is, therefore, a high objective probability concerning an objective probability. There are, in particular, four classes of uniformities, the knowledge of any of which, or of its falsity, may deductively strengthen or weaken an inductive conclusion. These four kinds of uniformity are as follows:

i. The members of a class may present an extraordinary resemblance to one another in regard to a certain line of characters. Thus, the Icelanders are said to resemble one another most strikingly in their opinions about general subjects. Knowing this, we should not need to question many Icelanders, if we found that the first few whom we met all shared a common superstition, in order to conclude with considerable confidence that nearly all Icelanders were of the same way of thinking. Philodemus †1 insists strongly upon this kind of uniformity as a support of induction.

ii. A character may be such that, in whatever genus it occurs at all, it almost always belongs to all the species of that genus; or this uniformity may be lacking. Thus, when only white swans were known, it would have been hazardous to assert that all swans were white, because whiteness is not usually a generic character. It is considerably more safe to assert that all crows are black, because blackness is oftener a generic character. This kind of uniformity is especially emphasized by J. S. Mill as important in inductive inquiries. †2

iii. A certain set of characters may be intimately connected so as to be usually all present or all absent from certain kinds of objects. Thus, the different chemical reactions of gold are so inseparable that a chemist need only to succeed in getting, say, the purple of Cassius to be confident that the body under examination will show every reaction of gold.

iv. Of a certain object it may be known that its characteristic is that when it possesses one of a set of characters within a certain group of such sets, it possesses the rest. Thus, it may be known of a certain man that to whatever party he belongs, he is apt to embrace without reserve the entire creed of that party. We shall not, then, need to know many of his opinions, say in regard to politics, in order to infer with great confidence his position upon other political questions.

99. (2) The word "uniformity" plays such a singular and prominent rôle in the logic of J. S. Mill that it is proper to note it. †3 He was apt to be greatly influenced by Ockham's razor in forming theories which he defended with great logical acumen; but he differed from other men of that way of thinking in that his natural candour led to his making many admissions without perceiving how fatal they were to his negative theories. In addition to that, perhaps more than other philosophers, in endeavouring to embrace several ideas under a common term, he often leaves us at a loss to find any other character common and peculiar to those notions except that of their having received from him that common designation. In one passage †1 of his System of Logic (1842), he declares, in reference to the difference in strength between two inductive conclusions, that whoever shall discover the cause of that difference will have discovered the secret of inductive reasoning. When, therefore, he shortly afterwards †2 points out that the distinction between those two inductions is that one of them is supported by a uniformity of the second of the above four classes, while the other is met by a distinct diversity of the same kind, and when he himself gives to that uniformity this designation when he afterwards declares that the validity of induction depends upon uniformity, his reader naturally supposes he means uniformity in that sense. But we find that he employs the word for quite another purpose. Namely, he does not like the word law, as applied to an inductive generalization of natural facts — such as the "law" of gravitation — because it implies an element in nature, the reality of a general, which no nominalist can admit. He, therefore, desires to call the reality to which a true universal proposition about natural phenomena corresponds a "uniformity." †3

The implication of the word, thus used, is that the facts are, in themselves, entirely disconnected, and that it is the mind alone which unites them. One stone dropping to the earth has no real connection with another stone dropping to the earth. It is, surely, not difficult to see that this theory of uniformities, far from helping to establish the validity of induction, would be, if consistently admitted, an insuperable objection to such validity. For if two facts, A and B, are entirely independent in their real nature, then the truth of B cannot follow, either necessarily or probably, from the truth of A. If I have tried the experiment with a million stones and have found that every one of them fell when allowed to drop, it may be very natural for me to believe that almost any stone will act in the same way. But if it can be proved that there is no real connection between the behaviour of different stones, then there is nothing for it but to say that it was a chance coincidence that those million stones all behaved in the same way; for if there was any reason for it, and they really dropped, there was a real reason, that is, a real general. Now, if it is mere chance that they all dropped, that affords no more reason for supposing that the next will drop than my throwing three double sixes successively with a pair of dice is a reason for thinking that the next throw will be double sixes.

100. (3) But now we find that Mill's good sense and candour will not allow him to take the course which a Hobbes would have taken, and utterly deny the validity of induction; and this leads to a new use of the word uniformity, in which he speaks of the "uniformity of nature." Before asking exactly what this phrase means, it may be noted that, whatever it means, the assertion of it is an assent to scholastic realism, except for a difference of emphasis. For to say that throughout the whole course of experience, events always, or even only usually, happen alike under the same conditions (what is usually called the "invariability" of nature) is to assert an agreement (complete or partial) which could not be ascribed to chance without self-contradiction. For chance is merely the possible discrepancy between the character of the limited experience to which it belongs and the whole course of experience. Hence, to say that of the real, objective facts some general character can be predicated, is to assert the reality of a general. It only differs from scholastic realism in that Mill and his followers treat this aspect of the matter lightly — that is to say, the objective reality of the general — while the Scholastics regarded it as a great and vital feature of the universe. Instead of "uniformity" now importing that what others call "laws" are fabrications of the human mind, this "uniformity of nature" is erected by Mill into the greatest of laws and absolutely objective and real.

Let us now inquire what the "uniformity of nature," with its synonymous expressions that "the future resembles the past," and so forth, can mean. Mill †1 says that it means that if all the circumstances attending two phenomena are the same, they will be alike. But taken strictly this means absolutely nothing, since no two phenomena ever can happen in circumstances precisely alike, nor are two phenomena precisely alike. It is, therefore, necessary to modify the statement in order to give it any meaning at all; and it will be found that, however it may be so modified, the moment it begins to carry a definite meaning, one of three things results: it becomes either, first, grossly false, or, second, an assertion which there is really no good reason to believe even approximately true, or, thirdly, it becomes a quasi-subjective truth, not lending any colour of validity to induction proper. If, for example, we were to say that, under any given species of circumstances presenting any similarity, phenomena of any given genus would be found to have a specific general resemblance in contrast with the specific character of phenomena of the same genus occurring under a different species of circumstances of the same genus, this would be monstrously false, whether intended as an absolutely universal proposition or merely as one approximately true. Let, for example, the genus of phenomena be the values of the throws of a pair of dice in a given series of successive throws indefinitely continued. Let the first species of circumstances be that the ordinal number of a throw in the series is prime. It is pretty certain that there would be no general character in the corresponding values of throws to distinguish them from those which would result when the ordinal number is divisible by 2, or by 3, or by any other prime. It thus appears that when we take any genus of circumstances, the law turns out false. Suppose, then, that we modify it by saying that, taking any genus of phenomena and separating this into two species, there will be found in the discoverable circumstances some general resemblance for all those attending phenomena of the same species in contrast to those attending phenomena of the other species. This is a proposition which there is not the slightest reason to believe. Take, for example, as the genus of phenomena, the many thousands of Latin descriptions of American species of plants by Asa Gray and his scholars. Now consider the species of this genus of phenomena which agree in this respect, that the two first words of the description have their first vowels the same. There is no reason to suppose that there was any general respect in which the circumstances of that species of the genus of phenomena agree with one another and differ from others, either universally or usually. It is a mere chance result. It is true that some persons will not be inclined to assent to this judgment; but they cannot prove it otherwise. It can afford no adequate basis for induction. We see, then, that when we consider all phenomena, there is no way of making the statement sufficiently definite and certain. Suppose, then, that we attempt still another modification of the law, that, of interesting resemblances and differences between phenomena, some considerable proportion are accompanied by corresponding resemblances and differences between those of the circumstances which appear to us to be pertinent. The proposition is now rather psychological than metaphysical. It would be impossible, with any evidentiary basis, to strengthen the expression "some considerable proportion"; and in other respects the statement is vague enough. Still, there is sufficient truth in it, perhaps, to warrant the presumptive adoption of hypotheses, provided this adoption merely means that they are taken as sufficiently reasonable to justify some expense in experimentation to test their truth by induction; but it gives no warrant at all to induction itself. For, in the first place, induction needs no such dubious support, since it is mathematically certain that the general character of a limited experience will, as that experience is prolonged, approximate to the character of what will be true in the long run, if anything is true in the long run. Now all that induction infers is what would be found true in the usual course of experience, if it were indefinitely prolonged. Since the method of induction must generally approximate to that truth, that is a sufficient justification for the use of that method, although no definite probability attaches to the inductive conclusion. In the second place, the law, as now formulated, neither helps nor hinders the validity of induction proper; for induction proper consists in judging of the relative frequency of a character among all the individuals of a class by the relative frequency of that character among the individuals of a random sample of that class. Now the law, as thus formulated, may tend to make our hypothesis approximately true; but that advantage has been gained before the operation of induction, which merely tests the hypothesis, begins. This inductive operation is just as valid when the hypothesis is bad as when it is good, when the character dealt with is trivial as when it is interesting. The ratio which induction ascertains may be nearer 1/2, and more remote from 1 or 0, when the characters are uninteresting; and in that case a larger number of instances will usually be requisite for obtaining the ratio with any given degree of precision (for if the ratio is really 1 or 0, it will be almost a miracle if in the sample it is far from that ratio, although this will not be impossible, if the whole class is infinite), but the essential validity of the process of induction remains unaffected by that circumstance.

What is usually meant by the uniformity of nature probably is that in proportion as the circumstances are alike or unlike, so are any phenomena connected with them alike or unlike. It may be asked to what degree nature is uniform in that sense. The only tenable answer is that it is as little uniform as it possibly could be imagined to be; for were any considerable proportion of existing uniformities, or laws, of nature destroyed, others would necessarily thereby result.

In fact, the great characteristic of nature is its diversity. For every uniformity known, there would be no difficulty in pointing out thousands of non-uniformities; but the diversities are usually of small use to us, and attract the attention of poets mainly, while the uniformities are the very staff of life. Hence, the higher and wider are our desires the greater will be the general impression of uniformity produced upon us by the contemplation of nature as it interests us.

101. (4) There are senses in which nature may not irrationally be held to be uniform; but opinions differ very widely as to the extent and nature of this uniformity. The chief of these are as follows:

(a) The majority of physicists, at least of the older generation, hold, with regard to the physical universe, that its elements are masses, their positions, and the variations of these positions with time. It is believed that every motion exactly obeys certain laws of attraction and repulsion; and there is no other kind of law, except that each atom or corpuscle is a centre of energy arranged in equipotential surfaces about it, which follow a regular law; and that this is a permanency. But the equations of motion are differential equations of the second order, involving, therefore, two arbitrary constants for each moving atom or corpuscle, and there is no uniformity connected with these constants. At least, no such uniformity is, with the least probability, discoverable. As for the distribution of potential about an atom or corpuscle, it is regular; but there is no ulterior reason for that regularity, or, at least, none is probably discoverable. What is absolutely beyond discovery, whether direct and specific or indirect and general, may be considered to be non-existent.

From this usual and in some sense standard opinion there are many divergences in both directions. First, in the direction of greater uniformity.

(b) Some hold that there is some exact uniformity in the arbitrary constants of the motion of the atoms, so that, for example, perhaps at some initial instant they all had some symmetrical or regular arrangement, like a pack of cards unshuffled; and that the velocities at that instant were regular also. But this regularity being of a purely aesthetic or formal kind, and the laws of motion equally formal and unrelated to any purpose, it follows that all kinds of arrangements will be produced, ungoverned by any uniformity, but mere effects of chance. Three stars may, for example, at some instant form an equilateral triangle; but there would be no particular reason for this: it would be merely a casual coincidence.

(c) Others go farther and maintain that the constants of position and velocity are subject to a law not merely formal, but are governed by final causes in such a way that there is no arrangement or coincidence whatever which was not specially intended by the Creator. To this theory, such words as providence and fore-knowledge are ill adapted; because the two constants which each atom or corpuscle has remain constant throughout all time, and ought not to be considered as having been fixed at any particular epoch. The very idea is that the arrangement is determined by what would be the result of different arrangements at each period of time. If, for example, a given prayer effects rain, it must be supposed that, in view of that prayer, and as its consequence, the different atoms had the appropriate constants; but that these were not given to the atoms at any particular epoch, being permanent values. Any intentional action on the part of a free agent is to be explained in the same way. If an agent is to be supposed really free, it is difficult to see what other physical explanation is compatible with the exactitude of law. This seems to be substantially the notion of most of those who have supported free will.

On the other hand, many philosophers suppose a less degree of uniformity in nature than is supposed in opinion (a). Of these the following have come to the present writer's notice as being actually defended.

(d) Some suppose that while law is absolute, yet there are constantly arising cases analogous to unstable equilibrium in which, owing to a passage of a velocity through infinity or otherwise, the law does not determine what the motion shall be. Thus if one Boscovichian point attracts another inversely as the square of the distance, and they move in one straight line, then when they come together they may move through one another, or move backwards on the same line, or may separate along any other line, without violating the differential equation. Such "singularities," as the mathematicians say, are theoretically possible; and may be supposed to occur very often. But to suppose that free action becomes possible in such a way is very illogical. In the first place, it supposes a direct interaction between "mind" and matter; infinitesimal, no doubt, but none the less real. Why not better suppose a slight but finite action of this kind, and so avoid the following objections? Namely, in the second place, this is to put faith, not scientific credence, in the inductive laws of matter infinitely beyond what induction can ever warrant. We know very well that mind, in some sense, acts on matter, and matter on mind: the question is how. It is not in speculations of this fanciful kind that the true answer is likely to be found. In the third place, although this speculation wanders so far beyond all present knowledge, it nevertheless comes into conflict with a legitimate induction, namely, the supposition of any real "singularity" or breach of continuity in nature is in as distinct conflict with all our knowledge as is a miracle.

(e) Sundry far less tenable hypotheses of lacunae between inviolable laws have often been proposed. One opinion frequently met with is that the law of energy does not prescribe the direction of velocity, but only its amount; so that the mind may cause atoms to "swerve," in regular Lucretian fashion. †1 This singular notion has even been embraced by mathematicians, who are thinking of a projectile shot into a curved tube, or other case of an equation of condition. Of course, if mind can construct absolute constraints, it can much easier exert force that is finite. Other writers suppose lacunae, without telling us of what particular description they are; they seem to think law is absolute as far as it goes, but that its jurisdiction is limited.

(f) Much more philosophical and less logically objectionable is the notion of St. Augustine and others (it is near to the opinion of Aristotle) that the only fundamental kind of causation is the action of final causes, and that efficient causation is, in all cases, secondary. Accordingly, when a miracle occurs there is no violation of the real cursus naturae, but only of the apparent course of things.

(g) The hypothesis suggested by the present writer is that all laws are results of evolution; that underlying all other laws is the only tendency which can grow by its own virtue, the tendency of all things to take habits. Now since this same tendency is the one sole fundamental law of mind, it follows that the physical evolution works towards ends in the same way that mental action works towards ends, and thus in one aspect of the matter it would be perfectly true to say that final causation is alone primary. Yet, on the other hand, the law of habit is a simple formal law, a law of efficient causation; so that either way of regarding the matter is equally true, although the former is more fully intelligent. Meantime, if law is a result of evolution, which is a process lasting through all time, it follows that no law is absolute. That is, we must suppose that the phenomena themselves involve departures from law analogous to errors of observation. But the writer has not supposed that this phenomenon had any connection with free will. In so far as evolution follows a law, the law of habit, instead of being a movement from homogeneity to heterogeneity, is growth from difformity to uniformity. But the chance divergences from law are perpetually acting to increase the variety of the world, and are checked by a sort of natural selection and otherwise (for the writer does not think the selective principle sufficient), so that the general result may be described as "organized heterogeneity," or, better, rationalized variety. In view of the principle of continuity, the supreme guide in framing philosophical hypotheses, we must, under this theory, regard matter as mind whose habits have become fixed so as to lose the powers of forming them and losing them, while mind is to be regarded as a chemical genus of extreme complexity and instability. It has acquired in a remarkable degree a habit of taking and laying aside habits. The fundamental divergences from law must here be most extraordinarily high, although probably very far indeed from attaining any directly observable magnitude. But their effect is to cause the laws of mind to be themselves of so fluid a character as to simulate divergences from law. All this, according to the writer, constitutes a hypothesis capable of being tested by experiment.

Literature: Besides most treatises on LOGIC (q.v., especially inductive) see Renouvier and Prat, La nouvelle Monadologie (1899).

B. Synechism and Agapism

Chapter 5: The Law of Mind †1

§1. INTRODUCTION E

102. In an article published in The Monist for January, 1891, †2 I endeavored to show what ideas ought to form the warp of a system of philosophy, and particularly emphasized that of absolute chance. In the number of April, 1892, †3 I argued further in favor of that way of thinking, which it will be convenient to christen tychism (from {tyché}, chance). A serious student of philosophy will be in no haste to accept or reject this doctrine; but he will see in it one of the chief attitudes which speculative thought may take, feeling that it is not for an individual, nor for an age, to pronounce upon a fundamental question of philosophy. That is a task for a whole era to work out. I have begun by showing that tychism must give birth to an evolutionary cosmology, in which all the regularities of nature and of mind are regarded as products of growth, and to a Schelling-fashioned idealism which holds matter to be mere specialized and partially deadened mind. I may mention, for the benefit of those who are curious in studying mental biographies, that I was born and reared in the neighborhood of Concord — I mean in Cambridge — at the time when Emerson, Hedge, and their friends were disseminating the ideas that they had caught from Schelling, and Schelling from Plotinus, from Boehm, or from God knows what minds stricken with the monstrous mysticism of the East. But the atmosphere of Cambridge held many an antiseptic against Concord transcendentalism; and I am not conscious of having contracted any of that virus. Nevertheless, it is probable that some cultured bacilli, some benignant form of the disease was implanted in my soul, unawares, and that now, after long incubation, it comes to the surface, modified by mathematical conceptions and by training in physical investigations.

103. The next step in the study of cosmology must be to examine the general law of mental action. In doing this, I shall for the time drop my tychism out of view, in order to allow a free and independent expansion to another conception signalized in my first Monist paper as one of the most indispensable to philosophy, though it was not there dwelt upon; I mean the idea of continuity †1 The tendency to regard continuity, in the sense in which I shall define it, as an idea of prime importance in philosophy may conveniently be termed synechism. The present paper is intended chiefly to show what synechism is, and what it leads to. I attempted, a good many years ago, to develop this doctrine in the Journal of Speculative Philosophy (Vol. II) †2; but I am able now to improve upon that exposition, in which I was a little blinded by nominalistic prepossessions. I refer to it, because students may possibly find that some points not sufficiently explained in the present paper are cleared up in those earlier ones.

§2. What the Law Is

104. Logical analysis applied to mental phenomena shows that there is but one law of mind, namely, that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas.

I set down this formula at the beginning, for convenience, and now proceed to comment upon it.

§3. Individuality of Ideas

105. We are accustomed to speak of ideas as reproduced, as passed from mind to mind, as similar or dissimilar to one another, and, in short, as if they were substantial things; nor can any reasonable objection be raised to such expressions. But taking the word "idea" in the sense of an event in an individual consciousness, it is clear that an idea once past is gone forever, and any supposed recurrence of it is another idea. These two ideas are not present in the same state of consciousness, and therefore cannot possibly be compared. To say, therefore, that they are similar can only mean that an occult power from the depths of the soul forces us to connect them in our thoughts after they are both no more. We may note, here, in passing, that of the two generally recognized principles of association, contiguity and similarity, the former is a connection due to a power without, the latter a connection due to a power within. †1

106. But what can it mean to say that ideas wholly past are thought of at all, any longer? They are utterly unknowable. What distinct meaning can attach to saying that an idea in the past in any way affects an idea in the future, from which it is completely detached? A phrase between the assertion and the denial of which there can in no case be any sensible difference is mere gibberish.

I will not dwell further upon this point, because it is a commonplace of philosophy.

§4. Continuity of Ideas †2

107. We have here before us a question of difficulty, analogous to the question of nominalism and realism. But when once it has been clearly formulated, logic leaves room for one answer only. How can a past idea be present? Can it be present vicariously? To a certain extent, perhaps, but not merely so; for then the question would arise how the past idea can be related to its vicarious representation. The relation, being between ideas, can only exist in some consciousness: now that past idea was in no consciousness but that past consciousness that alone contained it; and that did not embrace the vicarious idea.

108. Some minds will here jump to the conclusion that a past idea cannot in any sense be present. But that is hasty and illogical. How extravagant, too, to pronounce our whole knowledge of the past to be mere delusion! Yet it would seem that the past is as completely beyond the bounds of possible experience as a Kantian thing-in-itself. †1

109. How can a past idea be present? Not vicariously. Then, only by direct perception. In other words, to be present, it must be ipso facto present. That is, it cannot be wholly past; it can only be going, infinitesimally past, less past than any assignable past date. We are thus brought to the conclusion that the present is connected with the past by a series of real infinitesimal steps.

110. It has already been suggested by psychologists that consciousness necessarily embraces an interval of time. But if a finite time be meant, the opinion is not tenable. If the sensation that precedes the present by half a second were still immediately before me, then, on the same principle, the sensation preceding that would be immediately present, and so on ad infinitum. Now, since there is a time, say a year, at the end of which an idea is no longer ipso facto present, it follows that this is true of any finite interval, however short.

But yet consciousness must essentially cover an interval of time; for if it did not, we could gain no knowledge of time, and not merely no veracious cognition of it, but no conception whatever. We are, therefore, forced to say that we are immediately conscious through an infinitesimal interval of time.

111. This is all that is requisite. For, in this infinitesimal interval, not only is consciousness continuous in a subjective sense, that is, considered as a subject or substance having the attribute of duration, but also, because it is immediate consciousness, its object is ipso facto continuous. In fact, this infinitesimally spread-out consciousness is a direct feeling of its contents as spread out. This will be further elucidated below. In an infinitesimal interval we directly perceive the temporal sequence of its beginning, middle, and end — not, of course, in the way of recognition, for recognition is only of the past, but in the way of immediate feeling. Now upon this interval follows another, whose beginning is the middle of the former, and whose middle is the end of the former. Here, we have an immediate perception of the temporal sequence of its beginning, middle, and end, or say of the second, third, and fourth instants. From these two immediate perceptions, we gain a mediate, or inferential, perception of the relation of all four instants. This mediate perception is objectively, or as to the object represented, spread over the four instants; but subjectively, or as itself the subject of duration, it is completely embraced in the second moment. (The reader will observe that I use the word instant to mean a point of time, and moment to mean an infinitesimal duration.) If it is objected that, upon the theory proposed, we must have more than a mediate perception of the succession of the four instants, I grant it; for the sum of the two infinitesimal intervals is itself infinitesimal, so that it is immediately perceived. It is immediately perceived in the whole interval, but only mediately perceived in the last two-thirds of the interval. Now, let there be an indefinite succession of these inferential acts of comparative perception, and it is plain that the last moment will contain objectively the whole series. Let there be, not merely an indefinite succession, but a continuous flow of inference through a finite time, and the result will be a mediate objective consciousness of the whole time in the last moment. In this last moment, the whole series will be recognized, or known as known before, except only the last moment, which of course will be absolutely unrecognizable to itself. Indeed, even this last moment will be recognized like the rest, or, at least, be just beginning to be so. There is a little elenchus, or appearance of contradiction, here, which the ordinary logic of reflection quite suffices to resolve.

§5. Infinity and Continuity, In General

112. Most of the mathematicians who during the last two generations have treated the differential calculus have been of the opinion that an infinitesimal quantity is an absurdity; although, with their habitual caution, they have often added "or, at any rate, the conception of an infinitesimal is so difficult, that we practically cannot reason about it with confidence and security." Accordingly, the doctrine of limits has been invented to evade the difficulty, or, as some say, to explain the signification of the word "infinitesimal." †1 This doctrine, in one form or another, is taught in all the textbooks, though in some of them only as an alternative view of the matter; it answers well enough the purposes of calculation, though even in that application it has its difficulties.

113. The illumination of the subject by a strict notation for the logic of relatives had shown me clearly and evidently that the idea of an infinitesimal involves no contradiction, †2 before I became acquainted with the writings of Dr. Georg Cantor (though many of these had already appeared in the Mathematische Annalen and in Borchardt's Journal, if not yet in the Acta Mathematica, all mathematical journals of the first distinction), in which the same view is defended with extraordinary genius and penetrating logic. †3

114. The prevalent opinion is that finite numbers are the only ones that we can reason about, at least, in any ordinary mode of reasoning, or, as some authors express it, they are the only numbers that can be reasoned about mathematically. But this is an irrational prejudice. I long ago †4 showed that finite collections are distinguished from infinite ones only by one circumstance and its consequences, namely that to them is applicable a peculiar and unusual mode of reasoning called by its discoverer, De Morgan, the "syllogism of transposed quantity." †5

Balzac, in the introduction of his Physiologie du mariage, remarks that every young Frenchman boasts of having seduced some French woman. Now, as a woman can only be seduced once, and there are no more French women than Frenchmen, it follows, if these boasts are true, that no French women escape seduction. If their number be finite, the reasoning holds. But since the population is continually increasing, and the seduced are on the average younger than the seducers, the conclusion need not be true. In like manner, De Morgan, as an actuary, might have argued that if an insurance company pays to its insured on an average more than they have ever paid it, including interest, it must lose money. But every modern actuary would see a fallacy in that, since the business is continually on the increase. But should war, or other cataclysm, cause the class of insured to be a finite one, the conclusion would turn out painfully correct, after all. The above two reasonings are examples of the syllogism of transposed quantity.

The proposition that finite and infinite collections are distinguished by the applicability to the former of the syllogism of transposed quantity ought to be regarded as the basal one of scientific arithmetic.

115. If a person does not know how to reason logically, and I must say that a great many fairly good mathematicians — yea, distinguished ones — fall under this category, but simply uses a rule of thumb in blindly drawing inferences like other inferences that have turned out well, he will, of course, be continually falling into error about infinite numbers. The truth is such people do not reason at all. But for the few who do reason, reasoning about infinite numbers is easier than about finite numbers, because the complicated syllogism of transposed quantity is not called for. For example, that the whole is greater than its part is not an axiom, as that eminently bad reasoner, Euclid, made it to be. It is a theorem readily proved by means of a syllogism of transposed quantity, but not otherwise. Of finite collections it is true, of infinite collections false. Thus, a part of the whole numbers are even numbers. Yet the even numbers are no fewer than all the numbers; an evident proposition, since if every number in the whole series of whole numbers be doubled, the result will be the series of even numbers.

1,2,3,4,5,6,etc.

2,4,6,8,10,12,etc.

So for every number there is a distinct even number. In fact, there are as many distinct doubles of numbers as there are of distinct numbers. But the doubles of numbers are all even numbers.

116. In truth, of infinite collections there are but two grades of magnitude, the endless and the innumerable. †1 Just as a finite collection is distinguished from an infinite one by the applicability to it of a special mode of reasoning, the syllogism of transposed quantity, so, as I showed in the paper last referred to, †1 a numerable collection is distinguished from an innumerable one by the applicability to it of a certain mode of reasoning, the Fermatian inference, or, as it is sometimes improperly termed, "mathematical induction." †2

As an example of this reasoning, Euler's demonstration of the binomial theorem for integral powers may be given. The theorem is that (x+y)n, where n is a whole number, may be expanded into the sum of a series of terms of which the first is xny0 and each of the others is derived from the next preceding by diminishing the exponent of x by 1 and multiplying by that exponent and at the same time increasing the exponent of y by 1 and dividing by that increased exponent. Now, suppose this proposition to be true for a certain exponent, n = M, then it must also be true for n = M+1. For let one of the terms in the expansion of (x+y)M be written Axpyq. Then, this term with the two following will be

A xp yq + A (p/q+1)xp-1yq+1 + A(p/q+1)(p-1/q+2)xp-2 yq+2

Now, when (x+y)M is multiplied by x+y to give (x+y)M+1, we multiply first by x and then by y instead of by x and add the two results. When we multiply by x, the second of the above three terms will be the only one giving a term involving xpyq+1 and the third will be the only one giving a term in xp-1 yq+2; and when we multiply by y the first will be the only term giving a term in xp yq+1, and the second will be the only term giving a term in xp-1 yq+2. Hence, adding like terms, we find that the coefficient of xp yq+1 in the expansion of (x+y)M+1 will be the sum of the coefficients of the first two of the above three terms, and that the coefficient of xp-1 yq+2 will be the sum of the coefficients of the last two terms. Hence, two successive terms in the expansion of (x+y)M+1 will be

A[1+(p/q+1)]xp yq+1 + A(p/q+1)[1+(p-1/q+2)]xp-1 yq+2

= A((p+q+1)/(q+1))xp yq+1 + A((p+q+1)/(q+1))(p/(q+2))xp-1 yq+2.

It is thus seen that the succession of terms follows the rule. Thus if any integral power follows the rule, so also does the next higher power. But the first power obviously follows the rule. Hence, all powers do so.

Such reasoning holds good of any collection of objects capable of being ranged in a series which, though it may be endless, can be numbered so that each member of it receives a definite integral number. For instance, all the whole numbers constitute such a numerable collection. Again, all numbers resulting from operating according to any definite rule with any finite number of whole numbers form such a collection. For they may be arranged in a series thus. Let F be the symbol of operation. First operate on 1, giving F (1). Then, operate on a second 1, giving F (1,1). Next, introduce 2, giving 3d, F (2); 4th, F (2,1); 5th, F (1,2); 6th, F (2,2). Next use a third variable giving 7th, F (1,1,1); 8th, F (2,1,1); 9th, F (1,2,1); 10th, F (2,2,1); 11th, F (1,1,2); 12th, F (2,1,2); 13th, F (1,2,2); 14th, F (2,2,2). Next introduce 3, and so on, alternately introducing new variables and new figures; and in this way it is plain that every arrangement of integral values of the variables will receive a numbered place in the series. †P1

117. The class of endless but numerable collections (so called because they can be so ranged that to each one corresponds a distinct whole number) is very large. But there are collections which are certainly innumerable. Such is the collection of all numbers to which endless series of decimals are capable of approximating. It has been recognized since the time of Euclid that certain numbers are surd or incommensurable, and are not exactly expressible by any finite series of decimals, nor by a circulating decimal. Such is the ratio of the circumference of a circle to its diameter, which we know is nearly 3.1415926. The calculation of this number has been carried to over 700 figures without the slightest appearance of regularity in their sequence. The demonstrations that this and many other numbers are incommensurable are perfect. That the entire collection of incommensurable numbers is innumerable has been clearly proved by Cantor. †1 I omit the demonstration; †1 but it is easy to see that to discriminate one from some other would, in general, require the use of an endless series of numbers. Now if they cannot be exactly expressed and discriminated, clearly they cannot be ranged in a linear series.

118. It is evident that there are as many points on a line or in an interval of time as there are of real numbers, in all. These are, therefore, innumerable collections. Many mathematicians have incautiously assumed that the points on a surface or in a solid are more than those on a line. But this has been refuted by Cantor. †2 Indeed, it is obvious that for every set of values of coordinates there is a single distinct number. Suppose, for instance, the values of the coordinates all lie between 0 and +1. Then if we compose a number by putting in the first decimal place the first figure of the first coordinate, in the second the first figure of the second coordinate, and so on, and when the first figures are all dealt out go on to the second figures in like manner, it is plain that the values of the coordinates can be read off from the single resulting number, so that a triad or tetrad of numbers, each having innumerable values, has no more values than a single incommensurable number.

Were the number of dimensions infinite, this would fail; and the collection of infinite sets of numbers, having each innumerable variations, might, therefore, be greater than the simple innumerable collection, and might be called endlessly infinite. The single individuals of such a collection could not, however, be designated, even approximately, so that this is indeed a magnitude concerning which it would be possible to reason only in the most general way, if at all.

119. Although there are but two grades of magnitudes of infinite collections, yet when certain conditions are imposed upon the order in which individuals are taken, distinctions of magnitude arise from that cause. Thus, if a simply endless series be doubled by separating each unit into two parts, the successive first parts and also the second parts being taken in the same order as the units from which they are derived, this double endless series will, so long as it is taken in that order, appear as twice as large as the original series. In like manner the product of two innumerable collections, that is, the collection of possible pairs composed of one individual of each, if the order of continuity is to be maintained, is, by virtue of that order, infinitely greater than either of the component collections.

120. We now come to the difficult question, What is continuity? †1 Kant †2 confounds it with infinite divisibility, saying that the essential character of a continuous series is that between any two members of it a third can always be found. This is an analysis beautifully clear and definite; but, unfortunately, it breaks down under the first test. For according to this, the entire series of rational fractions arranged in the order of their magnitude would be an infinite series, although the rational fractions are numerable, while the points of a line are innumerable. Nay, worse yet, if from that series of fractions any two with all that lie between them be excised, and any number of such finite gaps be made, Kant's definition is still true of the series, though it has lost all appearance of continuity.

121. Cantor defines a continuous series as one which is concatenated and perfect. †3 By a concatenated series, he means such a one that if any two points are given in it, and any finite distance, however small, it is possible to proceed from the first point to the second through a succession of points of the series each at a distance, from the preceding one, less than the given distance. This is true of the series of rational fractions ranged in the order of their magnitude. By a perfect series, he means one which contains every point such that there is no distance so small that this point has not an infinity of points of the series within that distance of it. This is true of the series of numbers between 0 and 1 capable of being expressed by decimals in which only the digits 0 and 1 occur.

It must be granted that Cantor's definition includes every series that is continuous; nor can it be objected that it includes any important or indubitable case of a series not continuous. Nevertheless, it has some serious defects. In the first place, it turns upon metrical considerations; while the distinction between a continuous and a discontinuous series is manifestly non-metrical. In the next place, a perfect series is defined as one containing "every point" of a certain description. But no positive idea is conveyed of what all the points are: that is definition by negation, and cannot be admitted. If that sort of thing were allowed, it would be very easy to say, at once, that the continuous linear series of points is one which contains every point of the line between its extremities. Finally, Cantor's definition does not convey a distinct notion of what the components of the conception of continuity are. It ingeniously wraps up its properties in two separate parcels, but does not display them to our intelligence.

122. Kant's definition expresses one simple property of a continuum; but it allows of gaps in the series. To mend the definition, it is only necessary to notice how these gaps can occur. Let us suppose, then, a linear series of points extending from a point, A, to a point, B, having a gap from B to a third point, C, and thence extending to a final limit, D; and let us suppose this series conforms to Kant's definition. Then, of the two points, B and C, one or both must be excluded from the series; for otherwise, by the definition, there would be points between them. That is, if the series contains C, though it contains all the points up to B, it cannot contain B. What is required, therefore, is to state in non-metrical terms that if a series of points up to a limit is included in a continuum the limit is included. It may be remarked that this is the property of a continuum to which Aristotle's attention seems to have been directed when he defines a continuum as something whose parts have a common limit. †1 The property may be exactly stated as follows: If a linear series of points is continuous between two points, A and D, and if an endless series of points be taken, the first of them between A and D and each of the others between the last preceding one and D, then there is a point of the continuous series between all that endless series of points and D, and such that every other point of which this is true lies between this point and D. For example, take any number between 0 and 1, as 0.1; then, any number between 0.1 and 1, as 0.11; then any number between 0.11 and 1, as 0.111; and so on, without end. Then, because the series of real numbers between 0 and 1 is continuous, there must be a least real number, greater than every number of that endless series. This property, which may be called the Aristotelicity of the series, together with Kant's property, or its Kanticity, completes the definition of a continuous series. †1

123. The property of Aristotelicity may be roughly stated thus: a continuum contains the end point belonging to every endless series of points which it contains. An obvious corollary is that every continuum contains its limits. But in using this principle it is necessary to observe that a series may be continuous except in this, that it omits one or both of the limits.

124. Our ideas will find expression more conveniently if, instead of points upon a line, we speak of real numbers. Every real number is, in one sense, the limit of a series, for it can be indefinitely approximated to. Whether every real number is a limit of a regular series may perhaps be open to doubt. But the series referred to in the definition of Aristotelicity must be understood as including all series whether regular or not. Consequently, it is implied that between any two points an innumerable series of points can be taken.

125. Every number whose expression in decimals requires but a finite number of places of decimals is commensurable. Therefore, incommensurable numbers suppose an infinitieth place of decimals. The word infinitesimal is simply the Latin form of infinitieth; that is, it is an ordinal formed from infinitum, as centesimal from centum. Thus, continuity supposes infinitesimal quantities. †2 There is nothing contradictory about the idea of such quantities. In adding and multiplying them the continuity must not be broken up, and consequently they are precisely like any other quantities, except that neither the syllogism of transposed quantity, nor the Fermatian inference applies to them.

If A is a finite quantity and i an infinitesimal, then in a certain sense we may write A+i = A. That is to say, this is so for all purposes of measurement. But this principle must not be applied except to get rid of all the terms in the highest order of infinitesimals present. As a mathematician, I prefer the method of infinitesimals to that of limits, as far easier and less infested with snares. †1 Indeed, the latter, as stated in some books, involves propositions that are false; but this is not the case with the forms of the method used by Cauchy, †2 Duhamel, †3 and others. As they understand the doctrine of limits, it involves the notion of continuity, and therefore contains in another shape the very same ideas as the doctrine of infinitesimals.

126. Let us now consider an aspect of the Aristotelical principle which is particularly important in philosophy. Suppose a surface to be part red and part blue; so that every point on it is either red or blue, and, of course, no part can be both red and blue. What, then, is the color of the boundary line between the red and the blue? The answer is that red or blue, to exist at all, must be spread over a surface; and the color of the surface is the color of the surface in the immediate neighborhood †4 of the point. I purposely use a vague form of expression. Now, as the parts of the surface in the immediate neighborhood of any ordinary point upon a curved boundary are half of them red and half blue, it follows that the boundary is half red and half blue. In like manner, we find it necessary to hold that consciousness essentially occupies time; and what is present to the mind at any ordinary instant is what is present during a moment in which that instant occurs. Thus, the present is half past and half to come. Again, the color of the parts of a surface at any finite distance from a point has nothing to do with its color just at that point; and, in the parallel, the feeling at any finite interval from the present has nothing to do with the present feeling, except vicariously. Take another case: the velocity of a particle at any instant of time is its mean velocity during an infinitesimal instant in which that time is contained. Just so my immediate feeling is my feeling through an infinitesimal duration containing the present instant.

§6. Analysis of Time

127. One of the most marked features about the law of mind is that it makes time to have a definite direction of flow from past to future. The relation of past to future is, in reference to the law of mind, different from the relation of future to past. This makes one of the great contrasts between the law of mind and the law of physical force, where there is no more distinction between the two opposite directions in time than between moving northward and moving southward.

128. In order, therefore, to analyze the law of mind, we must begin by asking what the flow of time consists in. Now, we find that in reference to any individual state of feeling, all others are of two classes, those which affect this one (or have a tendency to affect it, and what this means we shall inquire shortly), †1 and those which do not. The present is affectible by the past but not by the future.

129. Moreover, if state A is affected by state B, and state B by state C, then A is affected by state C, though not so much so. It follows, that if A is affectible by B, B is not affectible by A.

130. If, of two states, each is absolutely unaffectible by the other, they are to be regarded as parts of the same state. They are contemporaneous.

131. To say that a state is between two states means that it affects one and is affected by the other. Between any two states in this sense lies an innumerable series of states affecting one another; and if a state lies between a given state and any other state which can be reached by inserting states between this state and any third state, these inserted states not immediately affecting or being affected by either, then the second state mentioned immediately affects or is affected by the first, in the sense that in the one the other is ipso facto present in a reduced degree.

These propositions involve a definition of time and of its flow. Over and above this definition they involve a doctrine, namely, that every state of feeling is affectible by every earlier state.

§7. That Feelings Have Intensive Continuity †1

132. Time with its continuity logically involves some other kind of continuity than its own. †2 Time, as the universal form of change, cannot exist unless there is something to undergo change and to undergo a change continuous in time there must be a continuity of changeable qualities. Of the continuity of intrinsic qualities of feeling we can now form but a feeble conception. The development of the human mind has practically extinguished all feelings, except a few sporadic kinds, sound, colors, smells, warmth, etc., which now appear to be disconnected and disparate. †3 In the case of colors, there is a tridimensional spread of feelings. Originally, all feelings may have been connected in the same way, and the presumption is that the number of dimensions was endless. For development essentially involves a limitation of possibilities. But given a number of dimensions of feeling, all possible varieties are obtainable by varying the intensities of the different elements. Accordingly, time logically supposes a continuous range of intensity in feeling. It follows, then, from the definition of continuity, that when any particular kind of feeling is present, an infinitesimal continuum of all feelings differing infinitesimally from that is present.

§8. That Feelings Have Spatial Extension †4

133. Consider a gob of protoplasm, say an amoeba or a slime-mould. It does not differ in any radical way from the contents of a nerve-cell, though its functions may be less specialized. There is no doubt that this slime-mould, or this amoeba, or at any rate some similar mass of protoplasm, feels. That is to say, it feels when it is in its excited condition. But note how it behaves. When the whole is quiescent and rigid, a place upon it is irritated. Just at this point, an active motion is set up, and this gradually spreads to other parts. In this action, no unity nor relation to a nucleus, or other unitary organ can be discerned. It is a mere amorphous continuum of protoplasm, with feeling passing from one part to another. Nor is there anything like a wave-motion. The activity does not advance to new parts just as fast as it leaves old parts. Rather, in the beginning, it dies out at a slower rate than that at which it spreads. And while the process is going on, by exciting the mass at another point, a second quite independent state of excitation will be set up. In some places, neither excitation will exist, in others each separately, in still other places, both effects will be added together. Whatever there is in the whole phenomenon to make us think there is feeling in such a mass of protoplasm — feeling, but plainly no personality — goes logically to show that that feeling has a subjective, or substantial, spatial extension, as the excited state has. This is, no doubt, a difficult idea to seize, for the reason that it is a subjective, not an objective, extension. It is not that we have a feeling of bigness; though Professor James, †1 perhaps rightly, teaches that we have. It is that the feeling, as a subject of inhesion, is big. Moreover, our own feelings are focused in attention to such a degree that we are not aware that ideas are not brought to an absolute unity; just as nobody not instructed by special experiment has any idea how very, very little of the field of vision is distinct. Still, we all know how the attention wanders about among our feelings; and this fact shows that those feelings that are not coordinated in attention have a reciprocal externality, although they are present at the same time. But we must not tax introspection to make a phenomenon manifest which essentially involves externality.

134. Since space is continuous, it follows that there must be an immediate community of feeling between parts of mind infinitesimally near together. Without this, I believe it would have been impossible for minds external to one another ever to become coordinated, and equally impossible for any coordination to be established in the action of the nerve-matter of one brain.

§9. Affections of Ideas

135. But we are met by the question, what is meant by saying that one idea affects another. The unravelment of this problem requires us to trace out phenomena a little further.

Three elements go to make up an idea. The first is its intrinsic quality as a feeling. The second is the energy with which it affects other ideas, an energy which is infinite in the here-and-nowness of immediate sensation, finite and relative in the recency of the past. The third element is the tendency of an idea to bring along other ideas with it.

136. As an idea spreads, its power of affecting other ideas gets rapidly reduced; but its intrinsic quality remains nearly unchanged. It is long years now since I last saw a cardinal in his robes; and my memory of their color has become much dimmed. The color itself, however, is not remembered as dim. I have no inclination to call it a dull red. Thus, the intrinsic quality remains little changed; yet more accurate observation will show a slight reduction of it. The third element, on the other hand, has increased. As well as I can recollect, it seems to me the cardinals I used to see wore robes more scarlet than vermillion is, and highly luminous. Still, I know the color commonly called cardinal is on the crimson side of vermillion and of quite moderate luminosity, and the original idea calls up so many other hues with it, and asserts itself so feebly, hat I am unable any longer to isolate it.

137. A finite interval of time generally contains an innumerable series of feelings; and when these become welded together in association, the result is a general idea. For we have just seen how by continuous spreading an idea becomes generalized.

138. The first character of a general idea so resulting is that it is living feeling. A continuum of this feeling, infinitesimal in duration, but still embracing innumerable parts, and also, though infinitesimal, entirely unlimited, is immediately present. And in its absence of boundedness a vague possibility of more than is present is directly felt.

139. Second, in the presence of this continuity of feeling, nominalistic maxims appear futile. There is no doubt about one idea affecting another, when we can directly perceive the one gradually modified and shaping itself into the other. Nor can there any longer be any difficulty about one idea resembling another, when we can pass along the continuous field of quality from one to the other and back again to the point which we had marked.

140. Third, consider the insistency of an idea. The insistency of a past idea with reference to the present is a quantity which is less the further back that past idea is, and rises to infinity as the past idea is brought up into coincidence with the present. Here we must make one of those inductive applications of the law of continuity which have produced such great results in all the positive sciences. We must extend the law of insistency into the future. Plainly, the insistency of a future idea with reference to the present is a quantity affected by the minus sign; for it is the present that affects the future, if there be any effect, not the future that affects the present. Accordingly, the curve of insistency is a sort of equilateral hyperbola.

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Such a conception is none the less mathematical, that its quantification cannot now be exactly specified.

141. Now consider the induction which we have here been led into. This curve says that feeling which has not yet emerged into immediate consciousness is already affectible and already affected. In fact, this is habit, by virtue of which an idea is brought up into present consciousness by a bond that had already been established between it and another idea while it was still in futuro.

142. We can now see what the affection of one idea by another consists in. It is that the affected idea is attached as a logical predicate to the affecting idea as subject. So when a feeling emerges into immediate consciousness, it always appears as a modification of a more or less general object already in the mind. The word suggestion is well adapted to expressing this relation. The future is suggested by, or rather is influenced by the suggestions of, the past.

§10. Ideas Cannot Be Connected Except by Continuity

143. That ideas can nowise be connected without continuity is sufficiently evident to one who reflects upon the matter. But still the opinion may be entertained that after continuity has once made the connection of ideas possible, then they may get to be connected in other modes than through continuity. Certainly, I cannot see how anyone can deny that the infinite diversity of the universe, which we call chance, may bring ideas into proximity which are not associated in one general idea. It may do this many times. But then the law of continuous spreading will produce a mental association; and this I suppose is an abridged statement of the way the universe has been evolved. But if I am asked whether a blind {ananké} cannot bring ideas together, first I point out that it would not remain blind. There being a continuous connection between the ideas, they would infallibly become associated in a living, feeling, and perceiving general idea. Next, I cannot see what the mustness or necessity of this {ananké} would consist in. In the absolute uniformity of the phenomenon, says the nominalist. Absolute is well put in; for if it merely happened so three times in succession, or three million times in succession, in the absence of any reason, the coincidence could only be attributed to chance. But absolute uniformity must extend over the whole infinite future; and it is idle to talk of that except as an idea. No, I think we can only hold that wherever ideas come together they tend to weld into general ideas; and wherever they are generally connected, general ideas govern the connection; and these general ideas are living feelings spread out.

§11. Mental Law Follows the Forms of Logic †1

144. The three main classes of logical inference are Deduction, Induction, and Hypothesis. These correspond to three chief modes of action of the human soul. In deduction the mind is under the dominion of a habit or association by virtue of which a general idea suggests in each case a corresponding reaction. But a certain sensation is seen to involve that idea. Consequently, that sensation is followed by that reaction. That is the way the hind legs of a frog, separated from the rest of the body, reason, when you pinch them. It is the lowest form of psychical manifestation.

145. By induction, a habit becomes established. Certain sensations, all involving one general idea, are followed each by the same reaction; and an association becomes established, whereby that general idea gets to be followed uniformly by that reaction.

Habit is that specialization of the law of mind whereby a general idea gains the power of exciting reactions. But in order that the general idea should attain all its functionality, it is necessary, also, that it should become suggestible by sensations. That is accomplished by a psychical process having the form of hypothetic inference. By hypothetic inference, I mean, as I have explained in other writings, †2 an induction from qualities. For example, I know that the kind of man known and classed as a "mugwump" has certain characteristics. He has a high self-respect and places great value upon social distinction. He laments the great part that rowdyism and unrefined good fellowship play in the dealings of American politicians with their constituency. He thinks that the reform which would follow from the abandonment of the system by which the distribution of offices is made to strengthen party organizations and a return to the original and essential conception of office-filling would be found an unmixed good. He holds that monetary considerations should usually be the decisive ones in questions of public policy. He respects the principle of individualism and of laissez-faire as the greatest agency of civilization. These views, among others, I know to be obtrusive marks of a "mugwump." Now, suppose I casually meet a man in a railway train, and falling into conversation find that he holds opinions of this sort; I am naturally led to suppose that he is a "mugwump." That is hypothetic inference. That is to say, a number of readily verifiable marks of a mugwump being selected, I find this man has these, and infer that he has all the other characters which go to make a thinker of that stripe. Or let us suppose that I meet a man of a semi-clerical appearance and a sub-pharisaical sniff, who appears to look at things from the point of view of a rather wooden dualism. He cites several texts of Scripture and always with particular attention to their logical implications; and he exhibits a sternness, almost amounting to vindictiveness, towards evil doers in general. I readily conclude that he is a minister of a certain denomination. Now the mind acts in a way similar to this, every time we acquire a power of coördinating reactions in a peculiar way, as in performing any act requiring skill. Thus, most persons have a difficulty in moving the two hands simultaneously and in opposite directions through two parallel circles nearly in the medial plane of the body. To learn to do this, it is necessary to attend, first, to the different actions in different parts of the motion, when suddenly a general conception of the action springs up and it becomes perfectly easy. We think the motion we are trying to do involves this action, and this, and this. Then the general idea comes which unites all those actions, and thereupon the desire to perform the motion calls up the general idea. The same mental process is many times employed whenever we are learning to speak a language or are acquiring any sort of skill.

146. Thus, by induction, a number of sensations followed by one reaction become united under one general idea followed by the same reaction; while, by the hypothetic process, a number of reactions called for by one occasion get united in a general idea which is called out by the same occasion. By deduction, the habit fulfills its function of calling out certain reactions on certain occasions.

§12. Uncertainty of Mental Action

147. The inductive and hypothetic forms of inference are essentially probable inferences, not necessary; while deduction may be either necessary or probable.

148. But no mental action seems to be necessary or invariable in its character. In whatever manner the mind has reacted under a given sensation, in that manner it is the more likely to react again; were this, however, an absolute necessity, habits would become wooden and ineradicable and, no room being left for the formation of new habits, intellectual life would come to a speedy close. Thus, the uncertainty of the mental law is no mere defect of it, but is on the contrary of its essence. The truth is, the mind is not subject to "law" in the same rigid sense that matter is. It only experiences gentle forces which merely render it more likely to act in a given way than it otherwise would be. There always remains a certain amount of arbitrary spontaneity in its action, without which it would be dead.

149. Some psychologists think to reconcile the uncertainty of reactions with the principle of necessary causation by means of the law of fatigue. Truly for a law, this law of fatigue is a little lawless. I think it is merely a case of the general principle that an idea in spreading loses its insistency. Put me tarragon into my salad, when I have not tasted it for years, and I exclaim, "What nectar is this!" But add it to every dish I taste for week after week, and a habit of expectation has been created; and in thus spreading into habit, the sensation makes hardly any more impression upon me; or, if it be noticed, it is on a new side, from which it appears as rather a bore. The doctrine that fatigue is one of the primordial phenomena of mind I am much disposed to doubt. †1 It seems a somewhat little thing to be allowed as an exception to the great principle of mental uniformization. For this reason, I prefer to explain it in the manner here indicated, as a special case of that great principle. To consider it as something distinct in its nature, certainly somewhat strengthens the necessitarian position; but even if it be distinct, the hypothesis that all the variety and apparent arbitrariness of mental action ought to be explained away in favor of absolute determinism does not seem to me to recommend itself to a sober and sound judgment, which seeks the guidance of observed facts and not that of prepossessions.

§13. Restatement of the Law

150. Let me now try to gather up all these odds and ends of commentary and restate the law of mind, in a unitary way.

First, then, we find that when we regard ideas from a nominalistic, individualistic, sensualistic way, the simplest facts of mind become utterly meaningless. That one idea should resemble another or influence another, or that one state of mind should so much as be thought of in another, is, from that standpoint, sheer nonsense.

151. Second, by this and other means we are driven to perceive, what is quite evident of itself, that instantaneous feelings flow together into a continuum of feeling, which has in a modified degree the peculiar vivacity of feeling and has gained generality. And in reference to such general ideas, or continua of feeling, the difficulties about resemblance and suggestion and reference to the external cease to have any force.

152. Third, these general ideas are not mere words, nor do they consist in this, that certain concrete facts will every time happen under certain descriptions of conditions; but they are just as much, or rather far more, living realities than the feelings themselves out of which they are concreted. And to say that mental phenomena are governed by law does not mean merely that they are describable by a general formula; but that there is a living idea, a conscious continuum of feeling, which pervades them, and to which they are docile.

153. Fourth, this supreme law, which is the celestial and living harmony, does not so much as demand that the special ideas shall surrender their peculiar arbitrariness and caprice entirely; for that would be self-destructive. It only requires that they shall influence and be influenced by one another.

154. Fifth, in what measure this unification acts, seems to be regulated only by special rules; or, at least, we cannot in our present knowledge say how far it goes. But it may be said that, judging by appearances, the amount of arbitrariness in the phenomena of human minds is neither altogether trifling nor very prominent.

§14. Personality

155. Having thus endeavored to state the law of mind, in general, I descend to the consideration of a particular phenomenon which is remarkably prominent in our own consciousnesses, that of personality. A strong light is thrown upon this subject by recent observations of double and multiple personality. The theory, which at one time seemed plausible, that two persons in one body corresponded to the two halves of the brain will, I take it, now be universally acknowledged to be insufficient. But that which these cases make quite manifest is that personality is some kind of coordination or connection of ideas. Not much to say, this, perhaps. Yet when we consider that, according to the principle which we are tracing out, a connection between ideas is itself a general idea, and that a general idea is a living feeling, it is plain that we have at least taken an appreciable step toward the understanding of personality. This personality, like any general idea, is not a thing to be apprehended in an instant. It has to be lived in time; nor can any finite time embrace it in all its fullness. Yet in each infinitesimal interval it is present and living, though specially colored by the immediate feelings of that moment. Personality, so far as it is apprehended in a moment, is immediate self-consciousness.

156. But the word coordination implies somewhat more than this; it implies a teleological harmony in ideas, and in the case of personality this teleology is more than a mere purposive pursuit of a predeterminate end; it is a developmental teleology. This is personal character. A general idea, living and conscious now, it is already determinative of acts in the future to an extent to which it is not now conscious.

157. This reference to the future is an essential element of personality. Were the ends of a person already explicit, there would be no room for development, for growth, for life; and consequently there would be no personality. The mere carrying out of predetermined purposes is mechanical. This remark has an application to the philosophy of religion. It is that a genuine evolutionary philosophy, that is, one that makes the principle of growth a primordial element of the universe, is so far from being antagonistic to the idea of a personal creator that it is really inseparable from that idea; †1 while a necessitarian religion is in an altogether false position and is destined to become disintegrated. But a pseudo-evolutionism which enthrones mechanical law above the principle of growth is at once scientifically unsatisfactory, as giving no possible hint of how the universe has come about, and hostile to all hopes of personal relations to God.

§15. Communication

158. Consistently with the doctrine laid down in the beginning of this paper, I am bound to maintain that an idea can only be affected by an idea in continuous connection with it. By anything but an idea, it cannot be affected at all. This obliges me to say, as I do say, on other grounds, that what we call matter is not completely dead, but is merely mind hidebound with habits. It still retains the element of diversification; and in that diversification there is life. When an idea is conveyed from one mind to another, it is by forms of combination of the diverse elements of nature, say by some curious symmetry, or by some union of a tender color with a refined odor. To such forms the law of mechanical energy has no application. If they are eternal, it is in the spirit they embody; and their origin cannot be accounted for by any mechanical necessity. They are embodied ideas; and so only can they convey ideas. Precisely how primary sensations, as colors and tones, are excited, we cannot tell, in the present state of psychology. But in our ignorance, I think that we are at liberty to suppose that they arise in essentially the same manner as the other feelings, called secondary. As far as sight and hearing are in question, we know that they are only excited by vibrations of inconceivable complexity; and the chemical senses are probably not more simple. Even the least psychical of peripheral sensations, that of pressure, has in its excitation conditions which, though apparently simple, are seen to be complicated enough when we consider the molecules and their attractions. The principle with which I set out requires me to maintain that these feelings are communicated to the nerves by continuity, so that there must be something like them in the excitants themselves. If this seems extravagant, it is to be remembered that it is the sole possible way of reaching any explanation of sensation, which otherwise must be pronounced a general fact, absolutely inexplicable and ultimate. Now absolute inexplicability is a hypothesis which sound logic refuses under any circumstances to justify.

159. I may be asked whether my theory would be favorable or otherwise to telepathy. †1 I have no decided answer to give to this. At first sight, it seems unfavorable. Yet there may be other modes of continuous connection between minds other than those of time and space.

160. The recognition by one person of another's personality takes place by means to some extent identical with the means by which he is conscious of his own personality. The idea of the second personality, which is as much as to say that second personality itself, enters within the field of direct consciousness of the first person, and is as immediately perceived as his ego, though less strongly. At the same time, the opposition between the two persons is perceived, so that the externality of the second is recognized.

161. The psychological phenomena of intercommunication between two minds have been unfortunately little studied. So that it is impossible to say, for certain, whether they are favorable to this theory or not. But the very extraordinary insight which some persons are able to gain of others from indications so slight that it is difficult to ascertain what they are is certainly rendered more comprehensible by the view here taken.

162. A difficulty which confronts the synechistic philosophy is this. In considering personality, that philosophy is forced to accept the doctrine of a personal God; but in considering communication, it cannot but admit that if there is a personal God, we must have a direct perception of that person and indeed be in personal communication with him. Now, if that be the case, the question arises how it is possible that the existence of this being should ever have been doubted by anybody. The only answer that I can at present make is that facts that stand before our face and eyes and stare us in the face are far from being, in all cases, the ones most easily discerned. That has been remarked from time immemorial.

§16. Conclusion

163. I have thus developed as well as I could in a little space the synechistic philosophy, as applied to mind. I think that I have succeeded in making it clear that this doctrine gives room for explanations of many facts which without it are absolutely and hopelessly inexplicable; and further that it carries along with it the following doctrines: first, a logical realism of the most pronounced type; second, objective idealism; third, tychism, with its consequent thorough-going evolutionism. We also notice that the doctrine presents no hindrances to spiritual influences, such as some philosophies are felt to do.

Chapter 6: The Continuum

§1. Kant's Definition †1

164. [Continuous means] in mathematics and philosophy a connection of points (or other elements) as intimate as that of the instants or points of an interval of time: thus, the continuity of space consists in this, that a point can move from any one position to any other so that at each instant it shall have a definite and distinct position in space. This statement is not, however, a proper definition of continuity, but only an exemplification drawn from time. The old definitions — the fact that adjacent parts have their limits in common (Aristotle), infinite divisibility (Kant), the fact that between any two points there is a third (which is true of the system of rational numbers) — are inadequate. †2 The less unsatisfactory definition is that of G. Cantor, that continuity is the perfect concatenation of a system of points — words which must be understood in special senses. †3 Cantor calls a system of points concatenated when any two of them being given, and also any finite distance, however small, it is always possible to find a finite number of other points of the system through which by successive steps, each less than the given distance, it would be possible to proceed from one of the given points to the other. He terms a system of points perfect when, whatever point belonging to the system be given, it is not possible to find a finite distance so small that there are not an infinite number of points of the system within that distance of the given point. As examples of a concatenated system not perfect, Cantor gives the rational and also the irrational numbers in any interval. As an example of a perfect system not concatenated, he gives all the numbers whose expression in decimals, however far carried out, would contain no figures except 0 and 9.

165. Cantor's definition of continuity is unsatisfactory as involving a vague reference to all the points, and one knows not what that may mean. It seems to me to point to this: that it is impossible to get the idea of continuity without two dimensions. An oval line is continuous, because it is impossible to pass from the inside to the outside without passing a point of the curve.

166. Subsequent to writing the above [164] I made a new definition, according to which continuity consists in Kanticity and Aristotelicity. †1 The Kanticity is having a point between any two points. The Aristotelicity is having every point that is a limit to an infinite series of points that belong to the system.

167. I here slightly modify Cantor's definition of a perfect system. Namely, he defines it as such that it contains every point in the neighborhood of an infinity of points and no other. But the latter is a character of a concatenated system; hence I omit it as a character of a perfect system.

168. But further study of the subject has proved that this definition is wrong. It involves a misunderstanding of Kant's definition which he himself likewise fell into. Namely he defines a continuum as that all of whose parts have parts of the same kind. †2 He himself, and I after him, understood that to mean infinite divisibility, which plainly is not what constitutes continuity since the series of rational fractional values is infinitely divisible but is not by anybody regarded as continuous. Kant's real definition implies that a continuous line contains no points. Now if we are to accept the common sense idea of continuity (after correcting its vagueness and fixing it to mean something) we must either say that a continuous line contains no points or we must say that the principle of excluded middle does not hold of these points. The principle of excluded middle only applies to an individual (for it is not true that "Any man is wise" nor that "Any man is not wise" †3). But places, being mere possibles without actual existence, are not individuals. Hence a point or indivisible place really does not exist unless there actually be something there to mark it, which, if there is, interrupts the continuity. I, therefore, think that Kant's definition correctly defines the common sense idea, although there are great difficulties with it. I certainly think that on any line whatever, on the common sense idea, there is room for any multitude of points however great. If so, the analytical continuity of the theory of functions, which implies there is but a single point for each distance from the origin, defined by a quantity expressible to indefinitely close approximation by a decimal carried out to an indefinitely great number of places, is certainly not the continuity of common sense, since the whole multitude of such quantities is only the first abnumeral multitude, and there is an infinite series of higher grades. †1 On the whole, therefore, I think we must say that continuity is the relation of the parts of an unbroken space or time. The precise definition is still in doubt; but Kant's definition, that a continuum is that of which every part has itself parts of the same kind, seems to be correct. This must not be confounded (as Kant himself confounded it) with infinite divisibility, but implies that a line, for example, contains no points until the continuity is broken by marking the points. In accordance with this it seems necessary to say that a continuum, where it is continuous and unbroken, contains no definite parts; that its parts are created in the act of defining them and the precise definition of them breaks the continuity. In the calculus and theory of functions it is assumed that between any two rational points (or points at distances along the line expressed by rational fractions) there are rational points and that further for every convergent series of such fractions (such as 3.1, 3.14, 3.141, 3.1415, 3.14159, etc.) there is just one limiting point; and such a collection of points is called continuous. But this does not seem to be the common sense idea of continuity. It is only a collection of independent points. Breaking grains of sand more and more will only make the sand more broken. It will not weld the grains into unbroken continuity.

§2. Synechism †1

169. [Synechism is] that tendency of philosophical thought which insists upon the idea of continuity as of prime importance in philosophy and, in particular, upon the necessity of hypotheses involving true continuity.

170. A true continuum is something whose possibilities of determination no multitude of individuals can exhaust. Thus, no collection of points placed upon a truly continuous line can fill the line so as to leave no room for others, although that collection had a point for every value towards which numbers, endlessly continued into the decimal places, could approximate; nor if it contained a point for every possible permutation of all such values. It would be in the general spirit of synechism to hold that time ought to be supposed truly continuous in that sense. The term was suggested and used by C. S. Peirce in 1892. †2 (Cf. Pragmatism, passim. †3)

171. The general motive is to avoid the hypothesis that this or that is inexplicable. For the synechist maintains that the only possible justification for so much as entertaining a hypothesis is that it affords an explanation of the phenomena. Now, to suppose a thing inexplicable is not only to fail to explain it, and so to make an unjustifiable hypothesis, but, much worse, it is to set up a barrier across the road of science, and to forbid all attempt to understand the phenomenon.

172. To be sure, the synechist cannot deny that there is an element of the inexplicable and ultimate, because it is directly forced upon him; nor does he abstain from generalizing from this experience. True generality is, in fact, nothing but a rudimentary form of true continuity. Continuity is nothing but perfect generality of a law of relationship.

173. It would, therefore, be most contrary to his own principle for the synechist not to generalize from that which experience forces upon him, especially since it is only so far as facts can be generalized that they can be understood; and the very reality, in his way of looking at the matter, is nothing else than the way in which facts must ultimately come to be understood. There would be a contradiction here, if this ultimacy were looked upon as something to be absolutely realized; but the synechist cannot consistently so regard it. Synechism is not an ultimate and absolute metaphysical doctrine; it is a regulative principle of logic, prescribing what sort of hypothesis is fit to be entertained and examined. The synechist, for example, would never be satisfied with the hypothesis that matter is composed of atoms, all spherical and exactly alike. If this is the only hypothesis that the mathematicians are as yet in condition to handle, it may be supposed that it may have features of resemblance with the truth. But neither the eternity of the atoms nor their precise resemblance is, in the synechist's view, an element of the hypothesis that is even admissible hypothetically. For that would be to attempt to explain the phenomena by means of an absolute inexplicability. In like manner, it is not a hypothesis fit to be entertained that any given law is absolutely accurate. It is not, upon synechist principles, a question to be asked, whether the three angles of a triangle amount precisely to two right angles, but only whether the sum is greater or less. So the synechist will not believe that some things are conscious and some unconscious, unless by consciousness be meant a certain grade of feeling. He will rather ask what are the circumstances which raise this grade; nor will he consider that a chemical formula for protoplasm would be a sufficient answer. In short, synechism amounts to the principle that inexplicabilities are not to be considered as possible explanations; that whatever is supposed to be ultimate is supposed to be inexplicable; that continuity is the absence of ultimate parts in that which is divisible; and that the form under which alone anything can be understood is the form of generality, which is the same thing as continuity.

§3. Continuity Redefined †1 E

174. I feel that I ought to make amends for my blundering treatment of Continuity in a paper entitled "The Law of Mind," in Vol. II of The Monist, †2 by here redefining it after close and long study of the question. Whatever is continuous has material parts.

I begin by defining these thus: The material parts of a thing or other object, W, that is composed of such parts, are whatever things are, firstly, each and every one of them, other than W; secondly, are all of some one internal nature (for example, are all places, or all times, or all spatial realities, or are all spiritual realities, or are all ideas, or are all characters, or are all relations, or are all external representations, etc.); thirdly, form together a collection of objects in which no one occurs twice over and, fourthly, are such that the Being of each of them together with the modes of connexion between all subcollections of them, constitute the being of W. Almost everything which has material parts has different sets of such parts, often various ad libitum. Nothing which has an Essence (such as an essential purpose or use, like the jackknife of the celebrated poser) has any material parts in the strict sense just defined. But the term "material parts" may, without confusion (if a little care be exerted), be used in a somewhat looser sense. Namely, if the Being (generally, a Concept) of an object, T, essentially involves something C which prevents it from having any material parts in the strict sense, and if there be something, W, which differs from T only in the absence of C and of any other such hindrances, so that W has material parts, then the material parts of W may loosely be termed material parts of T; but in such case the concept of W so derived from T is nearly or quite always somewhat vague, so that either the material parts will be so too, or else they must be conceived as merely the parts of some state of it, and very likely of an instantaneous state that is an ens rationis closely approximating to the nature of a fiction. It will be seen that the definition of Material Parts involves the concept of Connexion, even if there be no other connexion between them than co-being; and in case no other connexion be essential to the concept of W, this latter is called a Collection, concerning which I have merely to say that my reflexions on Mr. Alfred Bray Kempe's invaluable, very profound, and marvellously strong contribution to the science of Logic in the Philosophical Transactions [of the Royal Society, v. 177] for 1886 (which, by the way, seems to have proved too strong food for the mewling, etc., creatures who write the treatises on the science) have led me to believe it to be indecomposable. But I dare not be positive thereanent.

175. I must here give the substance of a far-famed definition of equality in multitude which was originally due to Bernardo Bolzano. †1 This writer was a Catholic priest in Buda-Pesth who published a treatise on Logic in four volumes, and a work entitled Paradoxes of the Infinite. In one or other of these he certainly laid the foundations of the great modern exact logic of quantity, which has so far been developed under the lead of the immortal Dr. Georg Cantor. Though I have never seen either work I do not hesitate to say that Bolzano put Human Reason under an eternal debt by laying the foundation of this science, since his definition of equality sufficed of itself to do that; and I need hardly say that the Catholic Church, which carries consistency as far as is consistent with any life at all, visited condign punishment upon the priest for such outrageous violation of loyalty to Her as the giving of aid and comfort to Human Reason — and most traitorous of all to Reasoning about Infinity! — was felt to be by Her and by all the world except the poor simple soul who committed that foul offense. I gave the substance of the definition in a former paper, †2 going on to other matters of importance which I need not here touch upon. But owing to my having then a very imperfect understanding of graphs, I expressed the definition in the insufficiently analytic language of my Algebra of Dyadic Relations (the same that is mainly employed in Schröder's third volume). I am continually obliged to make elementary explanations owing to the disgracefully unscientific state of Logic, which is quite as much behind its condition six centuries ago in some particulars as it is in advance of that state in others. As for contemporary text-books in our language, they are the merest rubbish on the whole. The very best that can be said of them is that a few have merits in particular directions. They are all amateurish and encourage amateurish views of the universe and of life. In comparison with the state of all the non-philosophical sciences, they are downright puerile; and a green scum grows over them year by year. If our people were at all aware of this blot upon our civilization, it would be possible for a scientific student of the subject of some real strength to put forth at least a primer of the science. But it is a condition of the success of any such student in penetrating to the true science that he should make himself a recluse. He is thus out of the swim, and is crowded out of all opportunities to be of much service; whereby Spencerism, Agnosticism, and other amateurisms, whose professors lose precious little time in arduous research, are able to gain the exclusive ear of the ignorant persons whom they court. In the fourteenth century Nominalism was rendered a respectable opinion by the halting realism of Scotus and by the extravagant unpragmatism of his followers. But after physical science has discovered so many general principles in Nature, nominalism becomes a disgraceful habitude of thought.

176. But now I define a pseudo-continuum as that which modern writers on the theory of functions call a continuum. But this is fully represented by, and according to G. Cantor stands in one-to-one correspondence with, the totality of real values, rational and irrational; and these are iconized, in their turn, according to these writers [by the] entire body of decimal expressions carried out to the right to all finite powers of 1/10 without going on to Cantor's ωth place of decimals.

For it is a principle continually employed in the reasoning of the universally accepted "doctrine of limits" that two values, that differ at all, differ by a finite value, which would not be true if the ωth place of decimals were supposed to be included in their exact expressions; and indeed the whole purpose of the doctrine of limits is to avoid acknowledging that that place is concerned. Consequently the denumeral rows of figures which, by virtue of a simple general principle, are in one-to-one correspondence with the values, have relations among themselves, quite regardless of their denoting those values that perfectly agree in form with the relations between the values; and consequently these unlimited decimal fractions themselves, apart from their significations, constitute a pseudo-continuum. This consideration renders it easy to define a pseudo-continuum. It is in the first place a collection of objects absolutely distinct from one another. Now from the fact that Cantor and others call it a "continuum," as well as from other things they say about it, I am led to suspect that they do not regard the pseudo-continuum of unlimited decimal expressions as [having members] all absolutely distinct from any other, for the reason that, taking any one of them, it does not possess any one elementary and definite non-relative character which is not possessed by any other of them. But this is not what I mean, nor what is generally meant, by a collection of absolutely independent members. What I mean by that expression is that every member is distinguished from every other by possessing some one or another elementary and definite non-relative character which that other does not possess; and that this is the usual acceptation of the expression is evidenced by the fact that the majority of logicians are in the habit of conceiving of a universe of absolutely distinct individual objects, by which they only mean that every individual is in every respect, of a certain universe of respects, determined in one or other of two ways and that every individual is differently determined from every other in some of those respects; and they do not generally conceive that every individual object has a determination in any one elementary and definite respect, while all the other individuals are determined in the opposite way.

§4. Achilles and the Tortoise †1

177. . . . Three times in my life it has happened to me to receive visits from writers, each of them illustrious as compared with myself (and one of them was certainly one of the most famous men of his time), who came to talk with me about the paradox of Achilles and the Tortoise. Now since this ridiculous little catch presents no difficulty at all to a mind adequately trained in mathematics and in logic, but is one of those which is very apt to excite minds of a certain class to an obstinate determination to believe a given proposition — if a high degree of courtesy, not to say veneration (hard for an unsocial student to observe with veracity) has ever been found wanting in those who have endeavoured to set them right — I will make use of my experience gained in those three interviews to illustrate the danger of mistaking an accidental and temporary inability to doubt a proposition for such an absolute inability as can safely be considered an excuse for allowing oneself to become wedded to a belief.

178. All three of my interviewers entered upon the subject of the paradox by asking me to state my view of it; and I answered each of them more or less as follows: "A uniform speed is a quantity which multiplied into a time will give, as the product, the distance which an object moving uniformly with that speed will pass over in that time. So, if we use a capital L to denote the adopted unit of length, a capital T for that of time, and the lower case italics n, m, l, k, etc., for any abstract numbers whole or fractional, of which it may be convenient to speak without specifying their values, we can denote a uniform speed that would cover any number, n, of units of length, in any number, m, of units of time, by (n/m) (L/T), or (nL)/(mT), or L/((m/n)T), etc.

This speed kept up for the time kT will result in covering a space of (n/m)(L/T) × kT = ((n×k)/m)L; and the same speed will cover l units of length in the time lL/(n/m) (L/T) = (lm/n)T, or l ÷ (n/m) units of time.

Now the start, allowed to the tortoise before the race begins, may be measured, say, by sL or a number, s, of units of length. If we express the uniform speeds of the two runners during the race by the numbers of units of length they respectively run in each unit of time, writing their initials, a for Achilles and t for tortoise to express this number, their speeds will be aL/T and tL/T. It cannot be doubted that this famous race was run in southern Thessaly, say in latitude 39° where, by the rotation of the earth, everything is moving due east at a rate of nearly 6 3/4 miles a minute. Nevertheless, the point of the compass toward which they ran is not stated; so that it is to be assumed that it would make no difference, as, indeed, common sense would have testified that it could not, if that guide had not been dismissed in the very act of taking up the consideration of this problem. If, then, a velocity of 6.71 miles a minute makes no difference in the result, we may safely assume that it would make none if the race were run on a deck which was floating from the front to the back of the runners at the same rate as the tortoise was running forward. The effect of this would be to diminish the resultant velocity of each runner by tL/T, so that the resultant speed of Achilles would be (a-t)L/T, while that of the tortoise would disappear entirely: he would really be at rest. Since then at the instant when the race began Achilles was sL behind the tortoise, the time required for him to reach that stationary racer must have been sL/[(a-t)L/T]=(s/(a-t))T, or s/(a-t) units of time. Zeno's method of approximating to the time required for Achilles to overtake the tortoise manifests a want of arithmetical skill that was inevitable at his time. Yet, after all, it coincides in principle, and in many cases in the arithmetical result, with the method of long division. Namely, he calculates the quantity that is really s/(a-t), where t is much smaller than a, by taking as his first approximation (s/a), or the time which would be correct if t=0, that is, if the tortoise did not move. But since during this time the tortoise moves over the distance (s/a)t, he adds to his first approximation the time required for Achilles to run this distance, which is (s/a2)t, and so gets his second approximation s/a + (s/a)t. Proceeding in this way he obtains, as his final result, the endless series s/a + (s/a2)t + (s/a3)t2 + (s/a4)t3 + etc. . . . Now let us calculate s/(a-t) by long division.

Here is the work:

a - t) ((s/a) + (s/a2)t + (s/a3)t2 + (s/a4)t3 + etc.
s - (s/a)t
(s/a)t
(s/a)t - (s/a2)t2
(s/a2)t2
(s/a2)t2 - (s/a3)t3
(s/a3)t3

Arithmetically, of course, long division will come to an end, in case the divisor has no other factor, that the dividend has not, than such as are products of powers of factors of the base of numeration; and indeed, it may always be brought to an end in several ways. One of these is by adopting a smaller and appropriate unit of time. Another is by adopting a different and appropriate base of numeration. These devices show how entirely the nodus of the paradox of Achilles and the tortoise is a difficulty of the arithmetician who is awkward in finding an appropriate expression of that which Achilles does without the least embarrassment.

179. I now at length come to the ways in which different writers on this paradox have mistaken an impotence of thought, really due to their own insufficient study, for an impossibility of human thought universal. Zeno himself concluded that motion was altogether inconceivable, in spite of the fact that all men, himself included — the very babe in the cradle included — conceive it well enough, though they may become occasionally a little confused about it. Others have thought it inconceivable that Achilles should pass through a series of points essentially endless. One of my interviewers raised this point; and I am inclined to admit, though I do not feel absolutely sure of it, that a man could not, in a finite time, make an endless series of distinct volitions. But this does not embarrass Achilles the least in the world, for his final effort carries him through a whole infinity of the points into which Zeno's unskillful method would (could it be carried out) divide the space which that last bound of the hero covered. It seemed to me that when I showed my interviewer, by a comparison, that a series might be endless in respect to its succession of members and yet very short in another respect, that this simple reflexion took him by surprise and was quite a new idea to him, though he quickly exercized a will to continue believing in the inconceivability of passing over an endless succession in a finite time, and determined not to be shaken from it. My illustration was simply a succession of points on squared paper, so that the x-coördinates should be 4, 5, 6, 7, 8, 9, 10, etc., and supposed to extend endlessly while the y-coördinates were y = 16/x; and so the series would be endless, if it were completed, yet the whole measure of its ys would be only 4.

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180. The difficulty of another of my interviewers seemed to me less silly. He said, "Is not every one of the parts into which Zeno cuts up the time finite?" "Certainly," said I. "And are they not infinite in number?" "In multitude, yes." "Well, to me, it is perfectly inconceivable that an infinite multitude of objects, each finite, should not be infinite!" I told him it was next to inconceivable to me that the thing should remain inconceivable to him much longer. "Do you not fully agree that the sum of a lot of lengths is equal to their number multiplied into their average length?" I asked. "Yes," he said, "but what is the average length of these parts?" It was, however, easy to prove to him that fixing upon any definite value, however small, this value must be much greater than the average of all the successive terms of Zeno's series. For with each term of that series that is larger than the assumed value (the total number of which will be finite) one might associate a million less one of terms, each less than the quotient assumed value, divided by a billion times the number of all the terms greater than the assumed value; and this could evidently be done without using any term twice. Thus, we should find that, of each of the lots of terms each including one of terms larger than the assumed value, the average value would be less than the assumed value; and consequently the average value of all would be less than that value. So I proved that the average value of all the terms would be less than any assumed value; and consequently the fact that their multitude is infinite is no proof that their sum is infinite. It will be observed that I felt obliged to reason in the inelegant and awkward way I did, instead of directly proving the rule for the summation of a geometrical progression because I was dealing with one of those minds who, not detecting the fallacy (which always consists in their not being able to conceive of something which is, however, true) of a certain reasoning, directly opposed to a sound mathematical demonstration, passionately take the former to their bosoms, and not only regard all who trust to the latter as criminals, but think no act that tends to suppress such criminals is wrong. Those who have not had to do with this class of persons will think my statement exaggerated. I can only say to them, "Consult some other person who has had experience, before you rashly argue with these persons as you would with others." For that reason I felt I must avoid bringing in the rule for the summation of a geometrical series, and so condemned myself to the awkward argument I used. But all reasoning is quite thrown away upon a person who has once set his teeth and has resolved to believe in a definite proposition.

181. There is one intellectual habit which I have laboured very seriously to cultivate, and of which I have a number of times experienced advantages enough, each one of them, to repay all the work I have done toward acquiring it: I mean the habit, when I have been upon the point of assenting, in my own mind, to some conclusion, [and when] I knew that some other mind (whose ways of thinking were very unlike my own, but whom I had known to have reached, in his way, truths not easy to reach) had considered the matter and had reached a conclusion inconsistent with the one that was recommending itself to me, of pausing, endeavoring to put myself in that other's point of view, reconsidering more minutely my whole reasoning, seeking to weld it to other reasonings and reflexions which all sound thinkers would approve, and doing my best to find weak points in the reasoning I came so near to embracing. I should not venture to recommend the cultivation of this habit to any of those who set up their own accidental impossibility of conceiving, as a permanent and essential one, before which all other men ought to crook the knee; since the very essence of their mental malady consists in an exaggerated loyalty to their own principles, i.e. a heartfelt and rather intolerant religion whose divinity is their past mental selves. Those who are really acquainted with this folk will recognize the portrait.

182. No man could be closer to the antipode of their model than America's and the world's highest respected and closest beloved philosophic soul, William James. Nobody has a better right to testify to the morality of his attitude toward his own thoughts than I, who knew and loved him for forty-nine or fifty years. But owing to his almost unexampled incapacity for mathematical thought, combined with intense hatred for logic — probably for its pedantry, its insistence on minute exactitude — the gêne of its barbarous formulations, etc. rendered him an easy victim to Zeno and the Achilles; and he had, I fear, a right to be offended at the contemptuous language that I thought it my duty to use when talking of this paradox to the young men; though if he did feel offended, he never showed it to me. In what I have said here on the subject, I have endeavoured to substitute serious and courteous remonstrance for the tone I used at Harvard. †1

Although he is now gone from us, I thoroughly believe he is looking over my shoulder this minute as I write; and I hope he will be able to guide my pen to greater delicacy than I am capable of. He thought that the Achilles disproved Dedekind's theory of continuity, which I take to be generally believed by mathematicians, though it is beyond the jurisdiction of Pure Mathematics, which deals exclusively with the consequences deducible from hypotheses arbitrarily posited. †2 Personally, I agree entirely with James, against Dedekind's view; and hold that there would be no actually existent points in an existent continuum, and that if a point were placed in a continuum it would constitute a breach of the continuity. Of course, there is a possible, or potential, point-place wherever a point might be placed; but that which only may be is necessarily thereby indefinite, and as such, and in so far, and in those respects, as it is such, it is not subject to the principle of contradiction, just as the negation of a may-be, which is of course a must-be, (I mean that if "S may be P" is untrue, then "S must be non-P" is true), in those respects in which it is such, is not subject to the principle of excluded middle. †3 This renders may-be's and must-be's very delicate objects for thought to handle, and propositions concerning them that sound absurd sometimes express plain facts. This, however, is a matter that I cannot pretend to have got to the bottom of; and logic here seems to touch metaphysics. But while I am in full accord with James's conclusion, and indeed am inclined to think that it was I who first drew his attention to Kant's sometimes speaking, in the C. d. r. V., †1 as if this was his opinion, though other of his expressions are against it, I cannot in the least agree with him that the Achilles argument proves that it is so. What seems to me to prove that it cannot do so is that the whole state of things supposed in that paradox might perfectly well be true if, in place of time and space, there were a series of instants and a series of points corresponding to all the values of (mathematically speaking) real and rational quantities. That is to say, if all those places in space were abolished whose distances from a fixed point are not expressible as some fraction, proper or improper, of an inch — that is to say, whose distances from a selected point, the same for all, did not stand to the inch in the same ratio as that of one whole number to another — and the same work of destruction had been done to time (and we have absolutely no evidence, as far as I see, that such is not the actual truth as to space and time both), then the race between Achilles and Tortoise could have taken place exactly as it did, and no one the wiser. Yet it could not be said then that there were no points in space; for it would be nothing but points without the least continuity. In fact, in order to prove that such is not in fact the constitution of actual time, at least (for rotation might introduce strictly infinitesimal difficulties about space), it seems to me that we should be driven to considerations of the same nature as some I introduced in perhaps the crudest of my struggles with such subjects, a paper (regretted as soon as published) entitled "The Law of Mind." †2 William James, in one of his last talks with me, expressed the opinion that that paper was, perhaps, the best I had ever written. I mention this in the hope that it may lead to somebody's using what truth there may be in it, in new and far better treatment of the continuity of time and of consciousness. My notion is that we directly perceive the continuity of consciousness; and if anybody objects, that which is not really continuous may seem so, I reply, "Aye, but it could not seem so, if there were not some consciousness that is so." †1 I should like to see a good criticism of that reply.

I am not, at present, prepared to believe, as William James did, that he was, permanently and as a finality, incapable of conceiving that Achilles could traverse an infinite succession of points, [although Achilles] certainly would have no notion that there were any such points there. (There were doubtless a lot of pebbles and grains of sand along his path, judging from the little I saw, in passing in a braganza over a road in Phthiotis in the night. Now I do not think that if each pebble were broken into a million pieces the difficulty of getting over the road would necessarily have been increased; and I don't see why it should if one of those millions — or all of them — had been multiplied into an infinity.)

183. After studying William James on the intellectual side for half a century — for I was not acquainted with him as a boy — I must testify that I believe him to be, and always to have been during my acquaintance with him, about as perfect a lover of truth as it is possible for a man to be; and I do not believe there is any definite limit to man's capacity for loving the truth. If you ask me what that ugly word "about" signifies in my statement of James's love of truth, as I believe that love to have been, I reply that I conceive the imperfection of man's devotion to anything — at any rate to any such perfect ideal as Truth — to be very different from his incapacity to attain exactitude in reproducing a metre or a kilo, inasmuch as in these latter cases, what he is liable to do is to make his copy either too large or too small, with an equal liability — after making a constant allowance, one way or the other, for his tendency to make it a bit different from "nature" (as the artists call the real thing they aim to imitate, at least to a certain difference, près) — I repeat, after [we have made] such allowances [for] an equal liability, to err in excess and in defect, in such a case we are just as likely, and indeed a little likelier, to hit the truth as near as our last place of decimals goes, as we are to make a small error one way or the other. Indeed we are infinitesimally likelier to do so. But when it comes to efforts to attain an ideal that it would be an absurdity to talk of surpassing and an impossibility actually to reach, we ought to measure our shortcomings by the logarithms of [our] mechanical, blockhead, measures of those shortcomings. Exactly of what nature these "blockhead measures" would be, it would be a study to ascertain; but all measurement of the errors that are only known through those erroneous measurements are pretty rough; and a slight error in the mode of measuring is very unlikely to be of serious consequence.

184. In speaking, then, of William James as I do, I am saying the most that I could of any man's intellectual morality; and with him this was but one of a whole diadem of virtues. Though it is entirely out of place in this connexion, and I must beg the reader's pardon for so wandering from the point under consideration, I really lack the self-command to repress my reflexions when I have once set down his name. Though his lectures were delightful, they not at all exhibited the man at his best. It was his unstudied common behaviour that did so by the perfection of his manners, in their perfect freedom from expressing flattery or anything else false or inappropriate to the occasion. He did not express himself very easily, because rhetoric was his antipathy and logic an inconvenience to him. One always felt that the pencil, not the pen, was the lever with which he ought to have moved the world; and yet no! it was not the externals of things but their souls he could have pictured.

His comprehension of men to the very core was most wonderful. Who, for example, could be of a nature so different from his as I? He so concrete, so living; I a mere table of contents, so abstract, a very snarl of twine. Yet in all my life I found scarce any soul that seemed to comprehend, naturally, [not] my concepts, but the mainspring of my life better than he did. He was even greater [in the] practice than in the theory of psychology.

Chapter 7: The Logic of Continuity P †1

§1. Potential Aggregates

185. By the limit of an endless series of successive objects we mean an object which comes after all the objects of that series, but so that every other object which comes after all those objects comes after the limit also. When I say that the series of abnumeral multitudes has no limit, I mean that it has no limit among multitudes of distinct individuals. It will have a limit if there is properly speaking, any meaning in saying that something that is not a multitude of distinct individuals is more than every multitude of distinct individuals. But, you will ask, can there be any sense in that? I answer, yes, there can, in this way. That which is possible is in so far general and, as general, it ceases to be individual. Hence, remembering that the word "potential" means indeterminate yet capable of determination in any special case, there may be a potential aggregate of all the possibilities that are consistent with certain general conditions; and this may be such that given any collection of distinct individuals whatsoever, out of that potential aggregate there may be actualized a more multitudinous collection than the given collection. Thus the potential aggregate is, with the strictest exactitude, greater in multitude than any possible multitude of individuals. But being a potential aggregate only, it does not contain any individuals at all. It only contains general conditions which permit the determination of individuals.

186. The logic of this may be illustrated by considering an analogous case. You know very well that 2/3 is not a whole number. In the whole collection of whole numbers you will not find 2/3. That you know. Therefore, you know something about the entire collection of whole numbers. But what is the nature of your conception of this collection? It is general. It is potential. It is vague, but yet with such a vagueness as permits of its accurate determination in regard to any particular object proposed for examination. Very well, that being granted, I proceed to the analogy with what we have been saying. Every whole number considered as a multitude is capable of being completely counted. Nor does its being aggregated with or added to any other whole number in the least degree interfere with the completion of the count. Yet the aggregate of all whole numbers cannot be completely counted. For the completion would suppose the last whole number was included, whereas there is no last whole number. But though the aggregate of all whole numbers cannot be completely counted, that does not prevent our having a distinct idea of the multitude of all whole numbers. We have a conception of the entire collection of whole numbers. It is a potential collection, indeterminate yet determinable. And we see that the entire collection of whole numbers is more multitudinous than any whole number.

187. In like manner the potential aggregate of all the abnumeral multitudes is more multitudinous than any multitude. This potential aggregate cannot be a multitude of distinct individuals any more than the aggregate of all the whole numbers can be completely counted. But it is a distinct general conception for all that — a conception of a potentiality.

188. A potential collection, more multitudinous than any collection of distinct individuals can be, cannot be entirely vague. For the potentiality supposes that the individuals are determinable in every multitude. That is, they are determinable as distinct. But there cannot be a distinctive quality for each individual; for these qualities would form a collection too multitudinous for them to remain distinct. It must therefore be by means of relations that the individuals are distinguishable from one another. . . . No perfect continuum can be defined by a [asymmetrical] dyadic relation [since the origin and terminus would be points of discontinuity]. †1 But if we take instead a triadic relation, and say A is r to B for C, say, to fix our ideas, that proceeding from A in a particular way, say to the right, you reach B before C, it is quite evident that a continuum will result like a self-returning line with no discontinuity whatever. . . .

§2. The Logic of the Universe

189. Every attempt to understand anything — every research — supposes, or at least hopes, that the very objects of study themselves are subject to a logic more or less identical with that which we employ.

That the logic of the universe is more rudimentary than our subjective logic is a hypothesis which may be worth examination in some stage of culture, but it is too violently at war with all the lessons which this age has learned for any man nowadays to embrace it with that ardor with which a man must embrace the theory which he is to devote his best powers to developing and bringing to the test of experience. Whatever else may be said for or against that hypothesis, that which we of these times ought to try is rather the hypothesis that the logic of the universe is one to which our own aspires, rather than attains.

190. Now continuity is shown by the logic of relations to be nothing but a higher type of that which we know as generality. It is relational generality.

191. How then can a continuum have been derived? Has it for example been put together? Have the separated points become welded, or what?

Looking upon the course of logic as a whole we see that it proceeds from the question to the answer — from the vague to the definite. And so likewise all the evolution we know of proceeds from the vague to the definite. The indeterminate future becomes the irrevocable past. In Spencer's phrase the undifferentiated differentiates itself. The homogeneous puts on heterogeneity. However it may be in special cases, then, we must suppose that as a rule the continuum has been derived from a more general continuum, a continuum of higher generality.

192. From this point of view we must suppose that the existing universe, with all its arbitrary secondness, is an offshoot from, or an arbitrary determination of, a world of ideas, a Platonic world; not that our superior logic has enabled us to reach up to a world of forms to which the real universe, with its feebler logic, was inadequate.

193. If this be correct, we cannot suppose the process of derivation, a process which extends from before time and from before logic, we cannot suppose that it began elsewhere than in the utter vagueness of completely undetermined and dimensionless potentiality.

194. The evolutionary process is, therefore, not a mere evolution of the existing universe, but rather a process by which the very Platonic forms themselves have become or are becoming developed.

195. We shall naturally suppose, of course, that existence is a stage of evolution. This existence is presumably but a special existence. We need not suppose that every form needs for its evolution to emerge into this world, but only that it needs to enter into some theatre of reactions, of which this is one.

196. The evolution of forms begins or, at any rate, has for an early stage of it, a vague potentiality; and that either is or is followed by a continuum of forms having a multitude of dimensions too great for the individual dimensions to be distinct. It must be by a contraction of the vagueness of that potentiality of everything in general, but of nothing in particular, that the world of forms comes about.

197. We can hardly but suppose that those sense-qualities that we now experience, colors, odors, sounds, feelings of every description, loves, griefs, surprise, are but the relics of an ancient ruined continuum of qualities, like a few columns standing here and there in testimony that here some old-world forum with its basilica and temples had once made a magnificent ensemble. And just as that forum, before it was actually built, had had a vague underexistence in the mind of him who planned its construction, so too the cosmos of sense-qualities, which I would have you to suppose in some early stage of being was as real as your personal life is this minute, had in an antecedent stage of development a vaguer being, before the relations of its dimensions became definite and contracted.

198. The sense-quality is a feeling. Even if you say it is a slumbering feeling, that does not make it less intense; perhaps the reverse. For it is the absence of reaction — of feeling another — that constitutes slumber, not the absence of the immediate feeling that is all that it is in its immediacy. Imagine a magenta color. Now imagine that all the rest of your consciousness — memory, thought, everything except this feeling of magenta — is utterly wiped out, and with that is erased all possibility of comparing the magenta with anything else or of estimating it as more or less bright. That is what you must think the pure sense-quality to be. Such a definite potentiality can emerge from the indefinite potentiality only by its own vital Firstness and spontaneity. Here is this magenta color. What originally made such a quality of feeling possible? Evidently nothing but itself. It is a First.

199. Yet we must not assume that the qualities arose separate and came into relation afterward. It was just the reverse. The general indefinite potentiality became limited and heterogeneous. Those who express the idea to themselves by saying that the Divine Creator determined so and so may be incautiously clothing the idea in a garb that is open to criticism, but it is, after all, substantially the only philosophical answer to the problem. Namely, they represent the ideas as springing into a preliminary stage of being by their own inherent firstness. But so springing up, they do not spring up isolated; for if they did, nothing could unite them. They spring up in reaction upon one another, and thus into a kind of existence. This reaction and this existence these persons call the mind of God. I really think there is no objection to this except that it is wrapped up in figures of speech, instead of having the explicitness that we desire in science. For all you know of "minds" is from the actions of animals with brains or ganglia like yourselves, or at furthest like a cockroach. To apply such a word to God is precisely like the old pictures which show him like an aged man leaning over to look out from above a cloud. Considering the vague intention of it, as conceived by the non-theological artist, it cannot be called false, but rather ludicrously figurative.

200. In short, if we are going to regard the universe as a result of evolution at all, we must think that not merely the existing universe, that locus in the cosmos to which our reactions are limited, but the whole Platonic world, which in itself is equally real, is evolutionary in its origin, too. And among the things so resulting are time and logic. The very first and most fundamental element that we have to assume is a Freedom, or Chance, or Spontaneity, by virtue of which the general vague nothing-in-particular-ness that preceded the chaos took a thousand definite qualities. The second element we have to assume is that there could be accidental reactions between those qualities. The qualities themselves are mere eternal possibilities. But these reactions we must think of as events. Not that Time was. But still, they had all the here-and-nowness of events. I really do not see how the metaphysician can explain either of these elements as results, further than this, that it may be said that the accidental reaction was, at first, one of the special determinations that came about by pure spontaneity or chance.

201. Let me here say one word about Tychism, or the doctrine that absolute chance is a factor of the universe. There is one class of objectors to it who are so impressed with what they have read in popular books about the triumphs of science that they really imagine that science has proved that the universe is regulated by law down to every detail. Such men are theologians, perhaps, or perhaps they have been brought up in surroundings where everything was so minutely regulated that they have come to believe that every tendency that exists at all in Nature must be carried to its furthest limit. Or, there is I know not what other explanation of their state of mind; but I do know one thing: they cannot be real students of physical science — they cannot be chemists, for example. They are wrong in their logic. But there is another class of objectors for whom I have more respect. They are shocked at the atheism of Lucretius and his great master. They do not perceive that that which offends them is not the Firstness in the swerving atoms, because they themselves are just as much advocates of Firstness as the ancient Atomists were. But what they cannot accept is the attribution of this firstness to things perfectly dead and material. Now I am quite with them there. I think too that whatever is First is ipso facto sentient. If I make atoms swerve — as I do — I make them swerve but very very little, because I conceive they are not absolutely dead. And by that I do not mean exactly that I hold them to be physically such as the materialists hold them to be, only with a small dose of sentiency superadded. For that, I grant, would be feeble enough. But what I mean is, that all that there is, is First, Feelings; Second, Efforts; Third, Habits — all of which are more familiar to us on their psychical side than on their physical side; and that dead matter would be merely the final result of the complete induration of habit reducing the free play of feeling and the brute irrationality of effort to complete death. Now I would suppose that that result of evolution is not quite complete even in our beakers and crucibles. Thus, when I speak of chance, I only employ a mathematical term to express with accuracy the characteristics of freedom or spontaneity.

202. Permit me further to say that I object to having my metaphysical system as a whole called Tychism. For although tychism does enter into it, it only enters as subsidiary to that which is really, as I regard it, the characteristic of my doctrine, namely, that I chiefly insist upon continuity, or Thirdness, and, in order to secure to thirdness its really commanding function, I find it indispensable fully [to] recognize that it is a third, and that Firstness, or chance, and Secondness, or Brute reaction, are other elements, without the independence of which Thirdness would not have anything upon which to operate. Accordingly, I like to call my theory Synechism, because it rests on the study of continuity. I would not object to Tritism. And if anybody can prove that it is trite, that would delight me [in] the chiefest degree.

203. All that I have been saying about the beginnings of creation seems wildly confused enough. Now let me give you such slight indication, as brevity permits, of the clue to which I trust to guide us through the maze.

Let the clean blackboard be a sort of diagram of the original vague potentiality, or at any rate of some early stage of its determination. This is something more than a figure of speech; for after all continuity is generality. This blackboard is a continuum of two dimensions, while that which it stands for is a continuum of some indefinite multitude of dimensions. This blackboard is a continuum of possible points; while that is a continuum of possible dimensions of quality, or is a continuum of possible dimensions of a continuum of possible dimensions of quality, or something of that sort. There are no points on this blackboard. There are no dimensions in that continuum. I draw a chalk line on the board. This discontinuity is one of those brute acts by which alone the original vagueness could have made a step towards definiteness. There is a certain element of continuity in this line. Where did this continuity come from? It is nothing but the original continuity of the blackboard which makes everything upon it continuous. What I have really drawn there is an oval line. For this white chalk-mark is not a line, it is a plane figure in Euclid's sense — a surface, and the only line there, is the line which forms the limit between the black surface and the white surface. Thus the discontinuity can only be produced upon that blackboard by the reaction between two continuous surfaces into which it is separated, the white surface and the black surface. The whiteness is a Firstness — a springing up of something new. But the boundary between the black and white is neither black, nor white, nor neither, nor both. It is the pairedness of the two. It is for the white the active Secondness of the black; for the black the active Secondness of the white.

204. Now the clue, that I mentioned, consists in making our thought diagrammatic and mathematical, by treating generality from the point of view of geometrical continuity, and by experimenting upon the diagram.

We see the original generality like the ovum of the universe segmentated by this mark. However, the mark is a mere accident, and as such may be erased. It will not interfere with another mark drawn in quite another way. There need be no consistency between the two But no further progress beyond this can be made, until a mark will stay for a little while; that is, until some beginning of a habit has been established by virtue of which the accident acquires some incipient staying quality, some tendency toward consistency.

This habit is a generalizing tendency, and as such a generalization, and as such a general, and as such a continuum or continuity. It must have its origin in the original continuity which is inherent in potentiality. Continuity, as generality, is inherent in potentiality, which is essentially general.

205. The whiteness or blackness, the Firstness, is essentially indifferent as to continuity. It lends itself readily to generalization but is not itself general. The limit between the whiteness and blackness is essentially discontinuous, or antigeneral. It is insistently this here. The original potentiality is essentially continuous, or general.

206. Once the line will stay a little after it is marked, another line may be drawn beside it. Very soon our eye persuades us there is a new line, the envelope of those others.

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This rather prettily illustrates the logical process which we may suppose takes place in things, in which the generalizing tendency builds up new habits from chance occurrences. The new curve, although it is new in its distinctive character, yet derives its continuity from the continuity of the blackboard itself. The original potentiality is the Aristotelian matter or indeterminacy from which the universe is formed. The straight lines as they multiply themselves under the habit of being tangent to the envelope gradually tend to lose their individuality. They become in a measure more and more obliterated and sink into mere adjuncts to the new cosmos in which they are individuals.

207. Many such reacting systems may spring up in the original continuum; and each of these may itself act as a first line from which a larger system may be built, in which it in turn will merge its individuality.

208. At the same time all this, be it remembered, is not of the order of the existing universe, but is merely a Platonic world, of which we are, therefore, to conceive that there are many, both coordinated and subordinated to one another; until finally out of one of these Platonic worlds is differentiated the particular actual universe of existence in which we happen to be.

209. There is, therefore, every reason in logic why this here universe should be replete with accidental characters, for each of which, in its particularity, there is no other reason than that it is one of the ways in which the original vague potentiality has happened to get differentiated.

But, for all that, it will be found that if we suppose the laws of nature to have been formed under the influence of a universal tendency of things to take habits, there are certain characters that those laws will necessarily possess.

As for attempting to set forth the series of deductions I have made upon this subject, that would be out of the question. All that I have any thought of doing is to illustrate, by a specimen or two, chosen among those which need the least explanation, some of the methods by which such reasoning may be conducted.

§3. Circular Continua; Time and Space

210. Various continua, to which the inquirer's attention will be directed in the course of this investigation, must be assumed to be devoid of all topical singularities. For any such singularity is a locus of discontinuity; and from the nature of the continuum there may be no room to suppose any such secondness. But now, a continuum which is without singularities must, in the first place, return into itself. Here is a remarkable consequence.

Take, for example, Time. It makes no difference what singularities you may see reason to impose upon this continuum. You may, for example, say that all evolution began at this instant, which you may call the infinite past, and comes to a close at that other instant, which you may call the infinite future. But all this is quite extrinsic to time itself. Let it be, if you please, that evolutionary time, our section of time, is contained between those limits. Nevertheless, it cannot be denied that time itself, unless it be discontinuous, as we have every reason to suppose it is not, stretches on beyond those limits, infinite though they be, returns into itself, and begins again. †1 Your metaphysics must be shaped to accord with that.

211. Again, the lowest Listing number, †2 the number of separate pieces, cannot be zero; for such a hypothesis would annul the whole continuum. Nor can the highest Listing number †3 be zero, unless the continuum has singularities. But the intermediate Listing numbers †1 may be zero or almost any numbers. If metaphysics is really to be made a definite science, and not child's play, the first inquiry concerning any general must be, first, what its dimensionality is, and secondly, what these intermediate Listing numbers are; and whatever your answer is, it will generally be found to lead you into those difficult but definite questions out of which we are accustomed in inductive science to think that the true theory is pretty sure to grow. It is one of the great merits of the method of thought, that the logic of relatives inculcates, that it leads to such definite questions.

For example, take the continuum of all possible sense qualities after this has been so far restricted that the dimensions are distinct. This is a continuum in which firstness is the prevailing character. It is also highly primitive; and therefore we ought to suppose, till the contrary is proved, that the intermediate Listing numbers are all unity. For zero is distinctly a dualistic idea. It is mathematically A - A, i.e. the result of the inverse process of subtraction. Now an inverse process is a Second process. It is true that there is another sort of zero which is a limit. Such is the vague zero of indeterminacy. But a limit involves Secondness prominently, and besides that, Thirdness. In fact, the generality of indeterminacy marks its Thirdness. Accordingly, zero being an idea of Secondness, we find, as we should expect, that any continuum whose intermediate Listing numbers are zero is equivalent to a pair of continua whose Listing numbers are 1. For instance, a perspective plane has a cyclosis equal to 1, while a ball has a cyclosis equal to 0. Now a ball is, topically speaking, of the same shape as two planes after the singularity of the pair has been removed. I will show you that this is true. Let the one plane be that of the blackboard, and let the other be oblique to it. Let this mark represent their ray of intersection. This ray is a singular line upon the two planes considered as one surface. In order to remove this singularity, we must split it down, so as to leave the right-hand side of the blackboard plane joined along the right-hand parts of the split line to that part of the oblique plane that is in front, while the left-hand part of the blackboard plane is joined along the left-hand parts of the split line to the part of the oblique plane behind the blackboard. Thus the ray becomes two rays. But two rays intersect. So that a singular point still remains. We must, then, cut through that singular point, making two points of it; and leaving the right side of the blackboard plane joined to the forward part of the oblique plane and the left side joined to the other part. We now move apart those two hyperbolic branches, that the two rays have made, until they have made nearly a complete circuit of the plane. They no longer cut the ray at infinity, and we have an egg-shaped solid which is topically just like a ball. Thus I have shown how secondness enters into the zero cyclosis.

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It is the same with the other intermediate Listing numbers; and we must assume that all the Listing numbers of the continuum of sense-qualities are equal to 1. This is confirmed by carrying the evolution of the continuum and its definiteness a step further. Namely, we will now suppose that each quality has acquired a settled identity in all its different degrees, so that the continuum is ready for the application of measurement. This measurement is a network figure imposed upon the blank continuum. It is true that it is in large measure arbitrary. It is our creation. Nevertheless, we shall adapt our creation as far as possible to the real properties of the continuum itself. Besides, there are certain modes of measurement which are impossible without breach of continuity in certain shapes of continua. For example, anybody can see that the same system of coordinates which could be applied to defining positions of points on a sphere, say latitude and longitude, would have to be modified in order to apply it to the definition of positions on an anchor-ring. On the sphere, longitude returns into itself after every 360°, and there are two points, the poles, whose longitudes are indeterminate; while latitude extends through 180° and then stops. But on the ring there will be one series of lines which will go round the bar of the ring without ever cutting one another, and another series going round the hole of the ring without cutting one another. This is a much simpler system of measurement than any that is possible on the sphere. Now in the network figure of coordinates which conforms best to the properties of the continuum of pure quality there is a line for each quality, along which line that quality only varies in intensity. All these lines come together at the absolute zero of quality. For in the zero of intensity, quality is indistinguishable in its inmost nature. But those lines meet nowhere else. In the infinite degree qualities may dazzle our senses; but in themselves they are different. Hence, the continuum of quality is such that unlimited lines may cut one another an odd number of times; namely, once only. Now this would be impossible were the intermediate Listing numbers even, say zero. Our hypothesis that they are odd is therefore confirmed. (I must add that the measurement of quality is evidently hyperbolic, which weakens considerably the force of the last argument.)

212. As another example, consider the continuum of Space. In my lecture †1 on the subject I pointed out to you how though it is a continuum, and therefore a Thirdness, the whole nature and function of space refers to Secondness. It is the theatre of the reactions of particles, and reaction is Secondness in its purity. For this and other reasons, which I omit for the sake of brevity, we must, as our first retroduction, assume that the intermediate Listing numbers for space are all zero. When we come to consider the principles of hydrodynamics we find that view confirmed. I cannot enter into details; but the motions of a frictionless incompressible fluid is as though it were composed of interpenetrating parts, shot out in straight lines from sources and disappearing into sinks. But that implies that all the straight lines radiating from a single point will meet again in another single point which supposes the Cyclosis and Periphraxis of Space to be zero. There will be some difficulties connected with this view, but I do not think them serious; and at any rate this will serve as another illustration of the manner in which reasoning about continuity can be applied to give real vitality to metaphysical reasoning, and to cure it of its deathly impotency.

213. I should have been glad if I could have set forth all this in greater detail; but that would have required more mathematics. I should have liked to interest you in a number of my scientifically important and philosophically significant results which I have been obliged to leave altogether unmentioned. I wish I could also have expounded some theories of other thinkers which, although I cannot accept them, seem to me to be well worthy of the most careful consideration. But to treat a theory like this, the whole life of which lies in minute diagrammatic reasoning, in eight lectures was inevitably to make it seem excessively abstruse and, at the same time, to do no more than exhibit a fragment here and there selected as being comparatively easy of presentation. The subject of mathematical metaphysics, or Cosmology, is not so very difficult, provided it be properly expanded and displayed. It deeply concerns both physicist and psychist. The physicist ought to direct his attention to it, in order that he may be led to contemplate the intellectual side of his own science. Especially the chemist, whose attention is forced to theory, needs above all to study the theory of theorizing. Psychologists have not yet dropped their excellent habit of studying philosophy; but I venture to think that they are not fully alive to all the value for their science of certain higher mathematics and to the virtues of mathematical thinking. The failure of Herbart, whose attempt was made before either Mathematics or Psychology was ripe for it, does not argue that no success can be attained in that line. I have presented — or no, I have not presented anything in these lectures, but I have talked about the most abstract parts of Cosmology; but the subject embraces many topics which have not that character, such as the question of the present state of the evidences of the Conservation of Energy and the question of the nature of the influences which hold together the constituent elements of chemical compounds. In short, there is a great variety of different ways in which Cosmology is both curious and useful for widely different classes of minds. We all know the kind of man who is warranted never to be interested in it, the man who lays out a system of ideas in his youth and stands on his platform with stalwart constancy like Casabianca on the burning deck. But if a mind is not absolutely argon and helium, but is capable of being drawn by any means within an alien sphere of attraction, no study is more calculated to bring about that event than this. It is decidedly a difficult subject on which to break ground for oneself. Economy of time, avoidance of a terrible waste, requires the student to take counsel of the experience here of a mathematician, there of a logician, again of a physicist or chemist, and continually of a psychologist. It is, by the way, precisely in psychology where you are the strongest that I have to confess myself the weakest. For that reason, in these lectures I have touched as little as possible upon psychology, preferring to deal with topics of Cosmology where I should be more at home, although you were less so. Crabbed and confused as all these circumstances have caused these conferences to become, you have been kind enough to listen to them, and really I dare not acknowledge, as it is in my heart to do, the whole warmth of my thanks, for fear you might think it out of measure. But should it happen to any of you to select for his life's explorations a region very little trodden, he will, as a matter of course, have the pleasure of making a good many discoveries of more fundamental importance than at all remain to be made in any ground that has long been highly cultivated. But on the other hand, he will find that he has condemned himself to an isolation like that of Alexander Selkirk. He must be prepared for almost a lifetime of work with scarce one greeting, and I can assure him that if, as his day is sinking, a rare good fortune should bring a dozen men of real intellect, some men of great promise, others of great achievement, together to listen to so much of what he has learned as his long habit of silence shall have left him the power of expressing in the compass of eight lectures, he will know then an almost untasted joy and will comprehend then what gratitude I feel at this moment.

Chapter 8: Objective Logic

§1. The Origin of the Universe †1

214. Metaphysics has to account for the whole universe of being. It has, therefore, to do something like supposing a state of things in which that universe did not exist, and consider how it could have arisen. However, this statement needs amendment. For time is itself an organized something, having its law or regularity; so that time itself is a part of that universe whose origin is to be considered. We have therefore to suppose a state of things before time was organized. Accordingly, when we speak of the universe as "arising" we do not mean that literally. We mean to speak of some kind of sequence, say an objective logical sequence; but we do not mean in speaking of the first stages of creation before time was organized, to use "before," "after," "arising," and such words in the temporal sense. But for the sake of the commodity of speech we may avail ourselves of these words.

215. The initial condition, before the universe existed, was not a state of pure abstract being. On the contrary it was a state of just nothing at all, not even a state of emptiness, for even emptiness is something.

If we are to proceed in a logical and scientific manner, we must, in order to account for the whole universe, suppose an initial condition in which the whole universe was non-existent, and therefore a state of absolute nothing.

216. You must not let this interfere with or be interfered with by any religious belief. Religion is a practical matter. Its beliefs are formulae you will go upon. But a scientific proposition is merely something you take up provisionally as being the proper hypothesis to try first and endeavor to refute. The only belief you — as a purely scientific man — have about it is that it is adopted in accordance with a method which must lead to the truth in the long run. It is a damnable absurdity indeed to say that one thing is true in theology and another in science. But it is perfectly true that the belief which I shall do well to embrace in my practical affairs, such as my religion, may not accord with the proposition which a sound scientific method requires me provisionally to adopt at this stage of my investigation. Later, both the one proposition and the other may very likely be modified; but how, or which comes nearer to the ultimate conclusion, not being a prophet or a magician, I cannot yet say.

217. We start, then, with nothing, pure zero. But this is not the nothing of negation. For not means other than, and other is merely a synonym of the ordinal numeral second. As such it implies a first; while the present pure zero is prior to every first. The nothing of negation is the nothing of death, which comes second to, or after, everything. But this pure zero is the nothing of not having been born. There is no individual thing, no compulsion, outward nor inward, no law. It is the germinal nothing, in which the whole universe is involved or foreshadowed. As such, it is absolutely undefined and unlimited possibility — boundless possibility. There is no compulsion and no law. It is boundless freedom.

So of potential being there was in that initial state no lack.

218. Now the question arises, what necessarily resulted from that state of things? But the only sane answer is that where freedom was boundless nothing in particular necessarily resulted.

In this proposition lies the prime difference between my objective logic and that of Hegel. †1 He says, if there is any sense in philosophy at all, the whole universe and every feature of it, however minute, is rational, and was constrained to be as it is by the logic of events, so that there is no principle of action in the universe but reason. But I reply, this line of thought, though it begins rightly, is not exact. A logical slip is committed; and the conclusion reached is manifestly at variance with observation. It is true that the whole universe and every feature of it must be regarded as rational, that is as brought about by the logic of events. But it does not follow that it is constrained to be as it is by the logic of events; for the logic of evolution and of life need not be supposed to be of that wooden kind that absolutely constrains a given conclusion. The logic may be that of the inductive or hypothetic inference.

This may-be is at once converted into must-be when we reflect that among the facts to be accounted for are such as that, for example, red things look red and not blue and vice versa. It is obvious that that cannot be a necessary consequence of abstract being.

The effect of this error of Hegel is that he is forced to deny [the] fundamental character of two elements of experience which cannot result from deductive logic. What these elements are will appear in the sequel.

219. I say that nothing necessarily resulted from the Nothing of boundless freedom. That is, nothing according to deductive logic. But such is not the logic of freedom or possibility. The logic of freedom, or potentiality, is that it shall annul itself. For if it does not annul itself, it remains a completely idle and do-nothing potentiality; and a completely idle potentiality is annulled by its complete idleness.

220. I do not mean that potentiality immediately results in actuality. Mediately perhaps it does; but what immediately resulted was that unbounded potentiality became potentiality of this or that sort — that is, of some quality.

Thus the zero of bare possibility, by evolutionary logic, leapt into the unit of some quality. This was hypothetic inference. Its form was:

Something is possible,

Red is something;

∴ Red is possible.

221. Now a quality is a consciousness. I do not say a waking consciousness — but still, something of the nature of consciousness. A sleeping consciousness, perhaps.

A possibility, then, or potentiality, is a particular tinge of consciousness. I do not say the possibility is exactly a consciousness; but it is a tinge of consciousness, a potential consciousness. However, the distinction is little more than verbal.

But let us consider more closely what the quale-consciousness is.

§2. Quale-Consciousness †1

222. If a man is blind to the red and violet elements of light and only sees the green element, then all things appear of one color to him, and that color is a green of colorific intensity beyond anything that we with normal eyes can see or imagine. Such is the color that all things look to him. Yet since all things look alike in this respect, it never attracts his attention in the least. He may be said to be dead to it. If the man is at the same time deaf, without smell and taste, and devoid of skin sensations, then it is probable the green will be still more chromatic; for I suppose colors are for us somewhat diluted by skin sensations. But for the very reason that it is his own kind of sensation, he will only be the more completely oblivious of its quale. Yet for all that, that is the way things look to him, more intensely green than any scarlet or magenta is red to us.

This illustration puts into a high light the distinction between two kinds of consciousness, the quale-consciousness and that kind of consciousness which is intensified by attention, which objectively considered, I call vividness, †2 and as a faculty we may call liveliness.

223. The quale-consciousness is not confined to simple sensations. There is a peculiar quale to purple, though it be only a mixture of red and blue. There is a distinctive quale to every combination of sensations so far as it is really synthetized — a distinctive quale to every work of art — a distinctive quale to this moment as it is to me — a distinctive quale to every day and every week — a peculiar quale to my whole personal consciousness. I appeal to your introspection to bear me out in this.

224. Each quale is in itself what it is for itself, without reference to any other. It is absurd to say that one quale in itself considered is like or unlike another. Nevertheless, comparing consciousness does pronounce them to be alike. They are alike to the comparing consciousness, though neither alike nor unlike in themselves.

225. And now I enunciate a truth. It is this. In so far as qualia can be said to have anything in common, that which belongs to one and all is unity; and the various synthetical unities which Kant attributes to the different operations of the mind, as well as the unity of logical consistency, or specific unity, and also the unity of the individual object, all these unities †1 originate, not in the operations of the intellect, but in the quale-consciousness upon which the intellect operates.

226. But here the critic will interpose an objection based upon a dilemma. He will ask me whether I intend that "truth" which I have enunciated so pretentiously for a logical truth or a psychological truth. Because he will say, if you mean it for a logical truth then the only unity it can account for is the unity of non-contradiction, while if you intend it for a psychological truth it must depend upon the peculiar construction of the nervous system and consequently cannot be transferred to metaphysics, in general, which is the use to which you probably intend to put it.

This is a cunning objection. But it assumes that logic is purely subjective in a sense that is not only pre-Hegelian but pre-Kantian.

227. All those synthetic unities considered cerebrally are but the unity which comes out when association channels are closed and the inflowing excitation of a part of the brain is pent up and intensified.

But it ought to be evident that no unity can originate in concentration. If there is no unity in a mass of gas, it cannot acquire unity merely by being condensed to half its volume. But any unity there was there already may, in that way, be many times intensified.

If you say those unities are not all of this one species, then how unaccountable it is that so many different operations should give rise to one and the same character of unity.

228. Perhaps it may be thought that hypnotic phenomena show that subconscious feelings are not unified. But I maintain on the contrary that those phenomena exhibit the very opposite peculiarity. They are unified so far as they are brought into one quale-consciousness at all; and that is why different personalities are formed. Of course, each personality is based upon a "bundle of habits," as the saying is that a man is a bundle of habits. But a bundle of habits would not have the unity of self-consciousness. That unity must be given as a centre for the habits.

229. The brain shows no central cell. The unity of consciousness is therefore not of physiological origin. It can only be metaphysical. So far as feelings have any continuity, it is the metaphysical nature of feeling to have a unity.

230. I say then that this unity is logical in this sense, that to feel, to be immediately conscious, so far as possible, without any action and reaction nor any reflection, logically supposes one consciousness and not two nor more.

To be conscious of scarlet and magenta at the same time is either to compare them or set them over against one another and so to introduce another kind of consciousness than the mere quale-consciousness, or it is to merge them into one general feeling in which the scarlet and magenta are not separately recognized, and thus preserve the unity of quale-consciousness.

This is so true that it is next to impossible to express it in language without appearing to utter a tautologous sentence. If I were to say any quality considered in itself is considered apart from anything else and is therefore without parts, since the parts of a sensation are really other sensations, my auditors would object that this was a mere identical proposition, since in itself means nothing but "apart from anything else." But the illustration of color-blindness shows that there is such a thing as a quale-consciousness, and when I describe this consciousness as the idea of a quality in itself, I merely, by the laws of speech, am forced to seize upon the character of separateness in order to let another person know what sort of consciousness I have in view.

231. My speech may be tautologous, but I have a positive meaning; and the very fact that it is so difficult to express this meaning without tautology is a mark of its veraciousness. I may express myself thus:

In quale-consciousness there is but one quality, but one element. It is entirely simple.

There are evidences of this on every hand.

Thus consciousness, so far as it can be contained in an instant of time, is an example of quale-consciousness. Now everybody who has begun to think about consciousness at all has remarked that the present so conceived is absolutely severed from past and future. That is, the past and the future are utterly absent in the sense in which I am conscious of the now.

So I might express my truth by saying —

The Now is one, and but one.

The principle of contradiction may be regarded as a formalistic result of the same thing. Any object, A, cannot be blue and not blue at once.

It can be blue and hard, because blueness and hardness are not thought of as joined in quale-consciousness, one appealing to one experiment and the other to another. But A cannot be blue and yellow, because these would blend and so the color would cease to be blue or yellow either. Thus, the positive truth in the principle of contradiction is that quale-consciousness has but one element.

232. If quale-consciousness were double, it would be like a case of double consciousness. One might pronounce the object to be blue that the other said was not blue and the principle of contradiction would only assert that one judge must be set above those two. But where would be the strife requiring a judge if the quale-consciousness were double?

Our truth might therefore be expressed by saying:

The quale-consciousness is not a consciousness of strife, or duality.

The quality itself is nothing in the world but a quale-consciousness of a composite photograph or general average of experience.

And if the quality can be double, the principle of contradiction falls to the ground.

233. All the operations of the intellect consist in taking composite photographs of quale-consciousnesses. Instead of introducing any unity, they only introduce conflict that was not in the quale-consciousness itself.

Such unity as remains is nothing but the unity and simplicity of the quale-consciousness persisting in spite of all this multiplication and diversity.

234. Another expression of our truth is this:

Quality or quale-consciousness is all that it is in and for itself.

It is essentially solitary and celibate, a dweller in the desert.

235. Another expression of it is:

Quale-consciousness cannot blend with quale-consciousness without loss of its identity.

236. So much for the meaning of the proposition. I now call attention to a remarkable consequence of it. Namely it follows that there is no check upon the utmost variety and diversity of quale-consciousness as it appears to the comparing intellect. For if consciousness is to blend with consciousness, there must be common elements. But if it has nothing in itself but just itself, it is sui generis and is cut loose from all need of agreeing with anything. Whatever is absolutely simple must be absolutely free; for a law over it must apply to some common feature of it. And if it has no features, no law can seize upon it. It is totus, teres, atque rotundus.

And thus it is that that very same logical element of experience, the quale-element, which appears upon the inside as unity, when viewed from the outside is seen as variety.

237. This ought not to appear as a paradox. Suppose for example that one of you proposes to live by yourself and to suit yourself alone, away from all constraints of law and custom, according to your own whimseys, your simple plan of life being to do whatever came into your head. If you are disposed to do this, why should not thousands of others have similar views of life? They certainly will. Not by force of any logical necessity, but yet by a logic which is just as certain as if it were necessary, an analogical inference. If nothing prevents such a man as you from existing, nothing will prevent a million such men from existing.

Now if everyone acts really irrespective of all the rest, there will be no regularity nor common character in their behaviour. There will be a Babel of strange tongues and a Bedlam of strange deeds. The units, each totus, teres, atque rotundus will make a chaos of fortuitously wandering atoms.

This is the logic by which the unity of quale-consciousness, implying simplicity, and through simplicity, freedom, necessarily results in endless multiplicity and variety. All that is a perfectly ostensive result of logic and involves no paradox whatsoever. . . .

Chapter 9: Man's Glassy Essence †1

§1. The Constitution of Matter E

238. In The Monist for January, 1891 †2 I tried to show what conceptions ought to form the brick and mortar of a philosophical system. Chief among these was that of absolute chance †P1 for which I argued again in last April's number. †3 In July, †4 I applied another fundamental idea, that of continuity, to the law of mind. Next in order, I have to elucidate, from the point of view chosen, the relation between the psychical and physical aspects of a substance.

239. The first step towards this ought, I think, to be the framing of a molecular theory of protoplasm. But before doing that, it seems indispensable to glance at the constitution of matter in general. We shall, thus, unavoidably make a long detour; but, after all, our pains will not be wasted, for the problems of the papers that are to follow in the series will call for the consideration of the same question. †5

240. All physicists are rightly agreed the evidence is overwhelming which shows all sensible matter is composed of molecules in swift motion and exerting enormous mutual attractions, and perhaps repulsions, too. Even Sir William Thomson, †6 Lord Kelvin, who wishes to explode action at a distance and return to the doctrine of a plenum, not only speaks of molecules, but undertakes to assign definite magnitudes to them. The brilliant Judge Stallo, a man who did not always rightly estimate his own qualities in accepting tasks for himself, declared war upon the atomic theory in a book †1 well worth careful perusal. To the old arguments in favor of atoms which he found in Fechner's †2 monograph, he was able to make replies of considerable force, though they were not sufficient to destroy those arguments. But against modern proofs he made no headway at all. These set out from the mechanical theory of heat. Rumford's experiments †3 showed that heat is not a substance. Joule †4 demonstrated that it was a form of energy. The heating of gases under constant volume, and other facts instanced by Rankine, †5 proved that it could not be an energy of strain. This drove physicists to the conclusion that it was a mode of motion. Then it was remembered that John Bernoulli †6 had shown that the pressure of gases could be accounted for by assuming their molecules to be moving uniformly in rectilinear paths. The same hypothesis was now seen to account for Avogadro's law, that in equal volumes of different kinds of gases exposed to the same pressure and temperature are contained equal numbers of molecules. Shortly after, it was found to account for the laws of diffusion and viscosity of gases, and for the numerical relation between these properties. Finally, Crookes's radiometer †7 furnished the last link in the strongest chain of evidence which supports any physical hypothesis.

241. Such being the constitution of gases, liquids must clearly be bodies in which the molecules wander in curvilinear paths, while in solids they move in orbits or quasi-orbits. (See my definition solid II, 1, in the Century Dictionary.) †P1

242. We see that the resistance to compression and to interpenetration between sensible bodies is, by one of the prime propositions of the molecular theory, due in large measure to the kinetical energy of the particles, which must be supposed to be quite remote from one another, on the average, even in solids. This resistance is no doubt influenced by finite attractions and repulsions between the molecules. All the impenetrability of bodies which we can observe is, therefore, a limited impenetrability due to kinetic and positional energy. This being the case, we have no logical right to suppose that absolute impenetrability, or the exclusive occupancy of space, belongs to molecules or to atoms. It is an unwarranted hypothesis, not a vera causa. †P1 Unless we are to give up the theory of energy, finite positional attractions and repulsions between molecules must be admitted. Absolute impenetrability would amount to an infinite repulsion at a certain distance. No analogy of known phenomena exists to excuse such a wanton violation of the principle of continuity as such a hypothesis is. In short, we are logically bound to adopt the Boscovichian †1 idea that an atom is simply a distribution of component potential energy throughout space (this distribution being absolutely rigid) combined with inertia. The potential energy belongs to two molecules, and is to be conceived as different between molecules A and B from what it is between molecules A and C. The distribution of energy is not necessarily spherical. Nay, a molecule may conceivably have more than one center; it may even have a central curve, returning into itself. But I do not think there are any observed facts pointing to such multiple or linear centers. On the other hand, many facts relating to crystals, especially those observed by Voigt, †P1 go to show that the distribution of energy is harmonical but not concentric. We can easily calculate the forces which such atoms must exert upon one another by considering †P2 that they are equivalent to aggregations of pairs of electrically positive and negative points infinitely near to one another. About such an atom there would be regions of positive and of negative potential, and the number and distribution of such regions would determine the valency of the atom, a number which it is easy to see would in many cases be somewhat indeterminate. I must not dwell further upon this hypothesis, at present. In another paper, its consequences will be further considered. †2

243. I cannot assume that the students of philosophy who read this magazine are thoroughly versed in modern molecular physics, and therefore it is proper to mention that the governing principle in this branch of science is Clausius's law of the virial. I will first state the law, and then explain the peculiar terms of the statement. This statement is that the total kinetic energy of the particles of a system in stationary motion is equal to the total virial. By a system is here meant a number of particles acting upon one another. †P1 Stationary motion is a quasi-orbital motion among a system of particles so that none of them are removed to indefinitely great distances nor acquire indefinitely great velocities. The kinetic energy of a particle is the work which would be required to bring it to rest, independently of any forces which may be acting upon it. The virial of a pair of particles is half the work which the force which actually operates between them would do if, being independent of the distance, it were to bring them together. The equation of the virial is

1/2 Σm v2 = 1/2 ΣΣR r.

Here m is the mass of a particle, v its velocity, R is the attraction between two particles, and r is the distance between them. The sign Σ on the left-hand side signifies that the values of m v2 are to be summed for all the particles, and ΣΣ on the right-hand side signifies that the values of R r are to be summed for all the pairs of particles. If there is an external pressure P (as from the atmosphere) upon the system, and the volume of vacant space within the boundary of that pressure is V, then the virial must be understood as including 3/2 P V, so that the equation is

1/2 Σm v2 = 3/2 P V + 1/2 ΣΣR r.

There is strong (if not demonstrative) reason for thinking that the temperature of any body above the absolute zero (-273° C.) is proportional to the average kinetic energy of its molecules, or say αΘ, where α is a constant and Θ is the absolute temperature. Hence, we may write the equation

αΘ= 1/2 mv2 = 3/2 PV + 1/2 ΣRr

where the heavy lines above the different expressions signify that the average values for single molecules are to be taken. In 1872, a student in the University of Leyden, Van der Waals, †1 propounded in his thesis for the doctorate a specialization of the equation of the virial which has since attracted great attention. Namely, he writes it

αΘ=(P+c/V2)(V-b)

The quantity b is the volume of a molecule, which he supposes to be an impenetrable body, and all the virtue of the equation lies in this term which makes the equation a cubic in V, which is required to account for the shape of certain isothermal curves. †P1 But if the idea of an impenetrable atom is illogical, that of an impenetrable molecule is almost absurd. For the kinetical theory of matter teaches us that a molecule is like a solar system or star-cluster in miniature. Unless we suppose that in all heating of gases and vapors internal work is performed upon the molecules, implying that their atoms are at considerable distances, the whole kinetical theory of gases falls to the ground. As for the term added to P, there is no more than a partial and roughly approximative justification for it. Namely, let us imagine two spheres described round a particle as their center, the radius of the larger being so great as to include all the particles whose action upon the center is sensible, while the radius of the smaller is so large that a good many molecules are included within it. The possibility of describing such a sphere as the outer one implies that the attraction of the particles varies at some distances inversely as some higher power of the distance than the cube, or, to speak more clearly, that the attraction multiplied by the cube of the distance diminishes as the distance increases; for the number of particles at a given distance from any one particle is proportionate to the square of that distance and each of these gives a term of the virial which is the product of the attraction into the distance. Consequently, unless the attraction multiplied by the cube of the distance diminished so rapidly with the distance as soon to become insensible, no such outer sphere as is supposed could be described. However, ordinary experience shows that such a sphere is possible; and consequently there must be distances at which the attraction does thus rapidly diminish as the distance increases. The two spheres, then, being so drawn, consider the virial of the central particle due to the particles between them. Let the density of the substance be increased, say, N times. Then, for every term, Rr, of the virial before the condensation, there will be N terms of the same magnitude after the condensation. Hence, the virial of each particle will be proportional to the density, and the equation of the virial becomes

αΘ=PV + (c/V).

This omits the virial within the inner sphere, the radius of which is so taken that within that distance the number of particles is not proportional to the number in a large sphere. For Van der Waals this radius is the diameter of his hard molecules, which assumption gives his equation. But it is plain that the attraction between the molecules must to a certain extent modify their distribution, unless some peculiar conditions are fulfilled. The equation of Van der Waals can be approximately true, therefore, only for a gas. In a solid or liquid condition, in which the removal of a small amount of pressure has little effect on the volume, and where consequently the virial must be much greater than PV, the virial must increase with the volume. For suppose we had a substance in a critical condition in which an increase of the volume would diminish the virial more than it would increase 3/2 PV. If we were forcibly to diminish the volume of such a substance, when the temperature became equalized, the pressure which it could withstand would be less than before, and it would be still further condensed, and this would go on indefinitely until a condition were reached in which an increase of volume would increase 3/2 PV more than it would decrease the virial. In the case of solids, at least, P may be zero; so that the state reached would be one in which the virial increases with the volume or the attraction between the particles does not increase so fast with a diminution of their distance as it would if the attraction were inversely as the distance.

244. Almost contemporaneously with Van der Waals's paper, another remarkable thesis for the doctorate was presented at Paris by Amagat. It related to the elasticity and expansion of gases, and to this subject the superb experimenter, its author, has devoted his whole subsequent life. Especially interesting are his observations of the volumes of ethylene and of carbonic acid at temperatures from 20° to 100° and at pressures ranging from an ounce to five thousand pounds to the square inch. †1 As soon as Amagat had obtained these results, he remarked that the "coefficient of expansion at constant volume" as it is absurdly called, that is, the rate of variation of the pressure with the temperature, was very nearly constant for each volume. This accords with the equation of the virial, which gives

dp/dΘ = (α/V) - (dΣRr/dΘ)

Now, the virial must be nearly independent of the temperature, and therefore the last term almost disappears. The virial would not be quite independent of the temperature because, if the temperature (i.e. the square of the velocity of the molecules) is lowered, and the pressure correspondingly lowered, so as to make the volume the same, the attractions of the molecules will have more time to produce their effects, and consequently, the pairs of molecules the closest together will be held together longer and closer; so that the virial will generally be increased by a decrease of temperature. Now, Amagat's experiments do show an excessively minute effect of this sort, at least, when the volumes are not too small. However, the observations are well enough satisfied by assuming the "coefficient of expansion at constant volume" to consist wholly of the first term, a/V. Thus, Amagat's experiments enable us to determine the values of α and thence to calculate the virial; and this we find varies for carbonic acid gas nearly inversely to V0·9.There is, thus, a rough approximation to satisfying Van der Waals's equation. But the most interesting result of Amagat's experiments, for our purpose at any rate, is that the quantity α, though nearly constant for any one volume, differs considerably with the volume, nearly doubling when the volume is reduced fivefold. This can only indicate that the mean kinetic energy of a given mass of the gas for a given temperature is greater the more the gas is compressed. But the laws of mechanics appear to enjoin that the mean kinetic energy of a moving particle shall be constant at any given temperature. The only escape from contradiction, then, is to suppose that the mean mass of a moving particle diminishes upon the condensation of the gas. In other words, many of the molecules are dissociated, or broken up into atoms or sub-molecules. The idea that dissociation should be favored by diminishing the volume will be pronounced by physicists, at first blush, as contrary to all our experience. But it must be remembered that the circumstances we are speaking of, that of a gas under fifty or more atmospheres pressure, are also unusual. That the "coefficient of expansion under constant volume" when multiplied by the volumes should increase with a decrement of the volume is also quite contrary to ordinary experience; yet it undoubtedly takes place in all gases under great pressure. Again, the doctrine of Arrhenius †1 †P1 is now generally accepted, that the molecular conductivity of an electrolyte is proportional to the dissociation of ions. Now the molecular conductivity of a fused electrolyte is usually superior to that of a solution. Here is a case, then, in which diminution of volume is accompanied by increased dissociation.

245. The truth is that several different kinds of dissociation have to be distinguished. In the first place, there is the dissociation of a chemical molecule to form chemical molecules under the regular action of chemical laws. This may be a double decomposition, as when iodhydric acid is dissociated, according to the formula

HI+HI = HH+II

or it may be a simple decomposition, as when pentachloride of phosphorus is dissociated according to the formula

PCl5 = PCl3+ClCl.

All these dissociations require, according to the laws of thermo-chemistry, an elevated temperature. In the second place, there is the dissociation of a physically polymerous molecule, that is, of several chemical molecules joined by physical attractions. This I am inclined to suppose is a common concomitant of the heating of solids and liquids; for in these bodies there is no increase of compressibility with the temperature at all comparable with the increase of the expansibility. But, in the third place, there is the dissociation with which we are now concerned, which must be supposed to be a throwing off of unsaturated sub-molecules or atoms from the molecule. The molecule may, as I have said, be roughly likened to a solar system. As such, molecules are able to produce perturbations of one another's internal motions; and in this way a planet, i.e., a sub-molecule, will occasionally get thrown off and wander about by itself, till it finds another unsaturated sub-molecule with which it can unite. Such dissociation by perturbation will naturally be favored by the proximity of the molecules to one another.

§2. Protoplasm †1 E

246. Let us now pass to the consideration of that special substance, or rather class of substances, whose properties form the chief subject of botany and of zoölogy, as truly as those of the silicates form the chief subject of mineralogy: I mean the life-slimes, or protoplasm. Let us begin by cataloguing the general characters of these slimes. They one and all exist in two states of aggregation, a solid or nearly solid state and a liquid or nearly liquid state; but they do not pass from the former to the latter by ordinary fusion. They are readily decomposed by heat, especially in the liquid state; nor will they bear any considerable degree of cold. All their vital actions take place at temperatures very little below the point of decomposition. This extreme instability is one of numerous facts which demonstrate the chemical complexity of protoplasm. Every chemist will agree that they are far more complicated than the albumens. Now, albumen is estimated to contain in each molecule about a thousand atoms; so that it is natural to suppose that the protoplasms contain several thousands. We know that while they are chiefly composed of oxygen, hydrogen, carbon, and nitrogen, a large number of other elements enter into living bodies in small proportions; and it is likely that most of these enter into the composition of protoplasms. Now, since the numbers of chemical varieties increase at an enormous rate with the number of atoms per molecule, so that there are certainly hundreds of thousands of substances whose molecules contain twenty atoms or fewer, we may well suppose that the number of protoplasmic substances runs into the billions or trillions. Professor Cayley †1 has given a mathematical theory of "trees," with a view of throwing a light upon such questions; and in that light the estimate of trillions (in the English sense) seems immoderately moderate. It is true that an opinion has been emitted, and defended among biologists, that there is but one kind of protoplasm; †2 but the observations of biologists themselves have almost exploded that hypothesis, which from a chemical standpoint appears utterly incredible. The anticipation of the chemist would decidedly be that enough different chemical substances having protoplasmic characters might be formed to account, not only for the differences between nerve-slime and muscle-slime, between whale-slime and lion-slime, but also for those minuter pervasive variations which characterize different breeds and single individuals.

247. Protoplasm, when quiescent, is, broadly speaking, solid; but when it is disturbed in an appropriate way, or sometimes even spontaneously without external disturbance, it becomes, broadly speaking, liquid. A moner in this state is seen under the microscope to have streams within its matter; a slime-mould slowly flows by force of gravity. The liquefaction starts from the point of disturbance and spreads through the mass. This spreading, however, is not uniform in all directions; on the contrary, it takes at one time one course, at another another, through the homogeneous mass, in a manner that seems a little mysterious. The cause of disturbance being removed, these motions gradually (with higher kinds of protoplasm, quickly) cease, and the slime returns to its solid condition.

248. The liquefaction of protoplasm is accompanied by a mechanical phenomenon. Namely, some kinds exhibit a tendency to draw themselves up into a globular form. This happens particularly with the contents of muscle-cells. The prevalent opinion, founded on some of the most exquisite experimental investigations that the history of science can show, is undoubtedly that the contraction of muscle-cells is due to osmotic pressure; and it must be allowed that that is a factor in producing the effect. But it does not seem to me that it satisfactorily accounts even for the phenomena of muscular contraction; and besides, even naked slimes often draw up in the same way. In this case, we seem to recognize an increase of the surface-tension. In some cases, too, the reverse action takes place, extraordinary pseudopodia being put forth, as if the surface-tension were diminished in spots. Indeed, such a slime always has a sort of skin, due no doubt to surface-tension, and this seems to give way at the point where a pseudopodium is put forth.

249. Long-continued or frequently repeated liquefaction of the protoplasm results in an obstinate retention of the solid state, which we call fatigue. †1 On the other hand, repose in this state, if not too much prolonged, restores the liquefiability. These are both important functions.

250. The life-slimes have, further, the peculiar property of growing. Crystals also grow; their growth, however, consists merely in attracting matter like their own from the circumambient fluid. To suppose the growth of protoplasm of the same nature would be to suppose this substance to be spontaneously generated in copious supplies wherever food is in solution. Certainly, it must be granted that protoplasm is but a chemical substance, and that there is no reason why it should not be formed synthetically like any other chemical substance. Indeed, Clifford has clearly shown †2 that we have overwhelming evidence that it is so formed. But to say that such formation is as regular and frequent as the assimilation of food is quite another matter. It is more consonant with the facts of observation to suppose that assimilated protoplasm is formed at the instant of assimilation, under the influence of the protoplasm already present. For each slime in its growth preserves its distinctive characters with wonderful truth, nerve-slime growing nerve-slime and muscle-slime, muscle-slime, lion-slime growing lion-slime, and all the varieties of breeds and even individual characters being preserved in the growth. Now it is too much to suppose there are billions of different kinds of protoplasm floating about wherever there is food.

251. The frequent liquefaction of protoplasm increases its power of assimilating food; so much so, indeed, that it is questionable whether in the solid form it possesses this power.

252. The life-slime wastes as well as grows; and this too takes place chiefly if not exclusively in its liquid phases.

253. Closely connected with growth is reproduction; and though in higher forms this is a specialized function, it is universally true that wherever there is protoplasm, there is, will be, or has been a power of reproducing that same kind of protoplasm in a separated organism. Reproduction seems to involve the union of two sexes; though it is not demonstrable that this is always requisite.

254. Another physical property of protoplasm is that of taking habits. The course which the spread of liquefaction has taken in the past is rendered thereby more likely to be taken in the future; although there is no absolute certainty that the same path will be followed again.

255. Very extraordinary, certainly, are all these properties of protoplasm; as extraordinary as indubitable. But the one which has next to be mentioned, while equally undeniable, is infinitely more wonderful. It is that protoplasm feels. We have no direct evidence that this is true of protoplasm universally, and certainly some kinds feel far more than others. But there is a fair analogical inference that all protoplasm feels. It not only feels but exercises all the functions of mind.

256. Such are the properties of protoplasm. The problem is to find a hypothesis of the molecular constitution of this compound which will account for these properties, one and all.

Some of them are obvious results of the excessively complicated constitution of the protoplasm molecule. All very complicated substances are unstable; and plainly a molecule of several thousand atoms may be separated in many ways into two parts, in each of which the polar chemical forces are very nearly saturated. In the solid protoplasm, as in other solids, the molecules must be supposed to be moving as it were in orbits, or, at least, so as not to wander indefinitely. But this solid cannot be melted, for the same reason that starch cannot be melted; because an amount of heat insufficient to make the entire molecules wander is sufficient to break them up completely and cause them to form new and simpler molecules. But when one of the molecules is disturbed, even if it be not quite thrown out of its orbit at first, sub-molecules of perhaps several hundred atoms each are thrown off from it. These will soon acquire the same mean kinetic energy as the others, and therefore velocities several times as great. They will naturally begin to wander, and in wandering will perturb a great many other molecules and cause them in their turn to behave like the one originally deranged. So many molecules will thus be broken up that even those that are intact will no longer be restrained within orbits, but will wander about freely. This is the usual condition of a liquid, as modern chemists understand it; for in all electrolytic liquids there is considerable dissociation.

But this process necessarily chills the substance, not merely on account of the heat of chemical combination, but still more because the number of separate particles being greatly increased, the mean kinetic energy must be less. The substance being a bad conductor, this heat is not at once restored. Now the particles moving more slowly, the attractions between them have time to take effect, and they approach the condition of equilibrium. But their dynamic equilibrium is found in the restoration of the solid condition, which therefore takes place, if the disturbance is not kept up.

257. When a body is in the solid condition, most of its molecules must be moving at the same rate, or, at least, at certain regular sets of rates; otherwise the orbital motion would not be preserved. The distances of neighboring molecules must always be kept between a certain maximum and a certain minimum value. But if, without absorption of heat, the body be thrown into a liquid condition, the distances of neighboring molecules will be far more unequally distributed, and an effect upon the virial will result. The chilling of protoplasm upon its liquefaction must also be taken into account. The ordinary effect will no doubt be to increase the cohesion and with that the surface-tension, so that the mass will tend to draw itself up. But in special cases, the virial will be increased so much that the surface-tension will be diminished at points where the temperature is first restored. In that case, the outer film will give way and the tension at other places will aid in causing the general fluid to be poured out at those points, forming pseudopodia.

258. When the protoplasm is in a liquid state, and then only, a solution of food is able to penetrate its mass by diffusion. The protoplasm is then considerably dissociated; and so is the food, like all dissolved matter. If then the separated and unsaturated sub-molecules of the food happen to be of the same chemical species as sub-molecules of the protoplasm, they may unite with other sub-molecules of the protoplasm to form new molecules, in such a fashion that when the solid state is resumed there may be more molecules of protoplasm than there were at the beginning. It is like the jackknife whose blade and handle, after having been severally lost and replaced, were found and put together to make a new knife.

§3. The Physiology of Habit †1 E

259. We have seen that protoplasm is chilled by liquefaction, and that this brings it back to the solid state, when the heat is recovered. This series of operations must be very rapid in the case of nerve-slime and even of muscle-slime, and may account for the unsteady or vibratory character of their action. Of course, if assimilation takes place, the heat of combination, which is probably trifling, is gained. On the other hand, if work is done, whether by nerve or by muscle, loss of energy must take place. In the case of the muscle, the mode by which the instantaneous part of the fatigue is brought about is easily traced out. If when the muscle contracts it be under stress, it will contract less than it otherwise would do, and there will be a loss of heat. It is like an engine which should work by dissolving salt in water and using the contraction during the solution to lift a weight, the salt being recovered afterwards by distillation. But the major part of fatigue has nothing to do with the correlation of forces. A man must labor hard to do in a quarter of an hour the work which draws from him enough heat to cool his body by a single degree. Meantime, he will be getting heated, he will be pouring out extra products of combustion, perspiration, etc. and he will be driving the blood at an accelerated rate through minute tubes at great expense. Yet all this will have little to do with his fatigue. He may sit quietly at his table writing, doing practically no physical work at all, and yet in a few hours be terribly fagged. This seems to be owing to the deranged sub-molecules of the nerve-slime not having had time to settle back into their proper combinations. When such sub-molecules are thrown out, as they must be from time to time, there is so much waste of material.

260. In order that a sub-molecule of food may be thoroughly and firmly assimilated into a broken molecule of protoplasm, it is necessary not only that it should have precisely the right chemical composition, but also that it should be at precisely the right spot at the right time and should be moving in precisely the right direction with precisely the right velocity. If all these conditions are not fulfilled, it will be more loosely retained than the other parts of the molecule; and every time it comes round into the situation in which it was drawn in, relatively to the other parts of that molecule and to such others as were near enough to be factors in the action, it will be in special danger of being thrown out again. Thus, when a partial liquefaction of the protoplasm takes place many times to about the same extent, it will, each time, be pretty nearly the same molecules that were last drawn in that are now thrown out. They will be thrown out, too, in about the same way, as to position, direction of motion, and velocity, in which they were drawn in; and this will be in about the same course that the ones last before them were thrown out. Not exactly, however; for the very cause of their being thrown off so easily is their not having fulfilled precisely the conditions of stable retention. Thus, the law of habit is accounted for, and with it its peculiar characteristic of not acting with exactitude.

261. It seems to me that this explanation of habit, aside from the question of its truth or falsity, has a certain value as an addition to our little store of mechanical examples of actions analogous to habit. All the others, so far as I know, are either statical or else involve forces which, taking only the sensible motions into account, violate the law of energy. It is so with the stream that wears its own bed. Here, the sand is carried to its most stable situation and left there. The law of energy forbids this; for when anything reaches a position of stable equilibrium, its momentum will be at a maximum, so that it can, according to this law, only be left at rest in an unstable situation. In all the statical illustrations, too, things are brought into certain states and left there. A garment receives folds and keeps them; that is, its limit of elasticity is exceeded. This failure to spring back is again an apparent violation of the law of energy; for the substance will not only not spring back of itself (which might be due to an unstable equilibrium being reached) but will not even do so when an impulse that way is applied to it. Accordingly, Professor James says, "the phenomena of habit . . . are due to the plasticity of the . . . materials." †1 Now, plasticity of materials means the having of a low limit of elasticity. (See the Century Dictionary, under solid. †2) But the hypothetical constitution of protoplasm here proposed involves no forces but attractions and repulsions strictly following the law of energy. The action here, that is, the throwing of an atom out of its orbit in a molecule, and the entering of a new atom into nearly, but not quite the same orbit, is somewhat similar to the molecular actions which may be supposed to take place in a solid strained beyond its limit of elasticity. Namely, in that case certain molecules must be thrown out of their orbits, to settle down again shortly after into new orbits. In short, the plastic solid resembles protoplasm in being partially and temporarily liquefied by a slight mechanical force. But the taking of a set by a solid body has but a moderate resemblance to the taking of a habit, inasmuch as the characteristic feature of the latter, its inexactitude and want of complete determinacy, is not so marked in the former, if it can be said to be present there at all.

262. The truth is that, though the molecular explanation of habit is pretty vague on the mathematical side, there can be no doubt that systems of atoms having polar forces would act substantially in that manner, and the explanation is even too satisfactory to suit the convenience of an advocate of tychism. For it may fairly be urged that since the phenomena of habit may thus result from a purely mechanical arrangement, it is unnecessary to suppose that habit-taking is a primordial principle of the universe. But one fact remains unexplained mechanically, which concerns not only the facts of habit, but all cases of actions apparently violating the law of energy; it is that all these phenomena depend upon aggregations of trillions of molecules in one and the same condition and neighborhood; and it is by no means clear how they could have all been brought and left in the same place and state by any conservative forces. But let the mechanical explanation be as perfect as it may, the state of things which it supposes presents evidence of a primordial habit-taking tendency. For it shows us like things acting in like ways because they are alike. Now, those who insist on the doctrine of necessity will for the most part insist that the physical world is entirely individual. Yet law involves an element of generality. Now to say that generality is primordial, but generalization not, is like saying that diversity is primordial but diversification not. It turns logic upside down. At any rate, it is clear that nothing but a principle of habit, itself due to the growth by habit of an infinitesimal chance tendency toward habit-taking, is the only bridge that can span the chasm between the chance-medley of chaos and the cosmos of order and law.

263. I shall not attempt a molecular explanation of the phenomena of reproduction, because that would require a subsidiary hypothesis, and carry me away from my main object. Such phenomena, universally diffused though they be, appear to depend upon special conditions; and we do not find that all protoplasm has reproductive powers.

§4. Tychistic Idealism †1 E

264. But what is to be said of the property of feeling? If consciousness belongs to all protoplasm, by what mechanical constitution is this to be accounted for? The slime is nothing but a chemical compound. There is no inherent impossibility in its being formed synthetically in the laboratory, out of its chemical elements; and if it were so made, it would present all the characters of natural protoplasm. No doubt, then, it would feel. To hesitate to admit this would be puerile and ultra-puerile. By what element of the molecular arrangement, then, would that feeling be caused? This question cannot be evaded or pooh-poohed. Protoplasm certainly does feel; and unless we are to accept a weak dualism, the property must be shown to arise from some peculiarity of the mechanical system. Yet the attempt to deduce it from the three laws of mechanics, applied to never so ingenious a mechanical contrivance, would obviously be futile. It can never be explained, unless we admit that physical events are but degraded or undeveloped forms of psychical events. But once grant that the phenomena of matter are but the result of the sensibly complete sway of habits upon mind, and it only remains to explain why in the protoplasm these habits are to some slight extent broken up, so that, according to the law of mind, in that special clause of it sometimes called the principle of accommodation, †P1 feeling becomes intensified. Now the manner in which habits generally get broken up is this. Reactions usually terminate in the removal of a stimulus; for the excitation continues as long as the stimulus is present. Accordingly, habits are general ways of behaviour which are associated with the removal of stimuli. But when the expected removal of the stimulus fails to occur, the excitation continues and increases, and non-habitual reactions take place; and these tend to weaken the habit. If, then, we suppose that matter never does obey its ideal laws with absolute precision, but that there are almost insensible fortuitous departures from regularity, these will produce, in general, equally minute effects. But protoplasm is in an excessively unstable condition; and it is the characteristic of unstable equilibrium that near that point excessively minute causes may produce startlingly large effects. Here then, the usual departures from regularity will be followed by others that are very great; and the large fortuitous departures from law so produced will tend still further to break up the laws, supposing that these are of the nature of habits. Now, this breaking up of habit and renewed fortuitous spontaneity will, according to the law of mind, be accompanied by an intensification of feeling. The nerve-protoplasm is, without doubt, in the most unstable condition of any kind of matter; and consequently there the resulting feeling is the most manifest.

265. Thus we see that the idealist has no need to dread a mechanical theory of life. On the contrary, such a theory, fully developed, is bound to call in a tychistic idealism as its indispensable adjunct. Wherever chance-spontaneity is found, there in the same proportion feeling exists. In fact, chance is but the outward aspect of that which within itself is feeling. I long ago showed that real existence, or thing-ness, consists in regularities. †1 So, that primeval chaos in which there was no regularity was mere nothing, from a physical aspect. Yet it was not a blank zero; for there was an intensity of consciousness there, in comparison with which all that we ever feel is but as the struggling of a molecule or two to throw off a little of the force of law to an endless and innumerable diversity of chance utterly unlimited. †2

266. But after some atoms of the protoplasm have thus become partially emancipated from law, what happens next to them? To understand this we have to remember that no mental tendency is so easily strengthened by the action of habit as is the tendency to take habits. Now, in the higher kinds of protoplasm, especially, the atoms in question have not only long belonged to one molecule or another of the particular mass of slime of which they are parts; but before that, they were constituents of food of a protoplasmic constitution. During all this time they have been liable to lose habits and to recover them again; so that now, when the stimulus is removed, and the foregone habits tend to reassert themselves, they do so in the case of such atoms with great promptness. Indeed, the return is so prompt that there is nothing but the feeling to show conclusively that the bonds of law have ever been relaxed.

267. In short, diversification is the vestige of chance spontaneity; and wherever diversity is increasing, there chance must be operative On the other hand, wherever uniformity is increasing, habit must be operative. But wherever actions take place under an established uniformity, there, so much feeling as there may be, takes the mode of a sense of reaction. That is the manner in which I am led to define the relation between the fundamental elements of consciousness and their physical equivalents.

§5. The Nature of Personality †1 E

268. It remains to consider the physical relations of general ideas. It may be well here to reflect that if matter has no existence except as a specialization of mind, it follows that whatever affects matter according to regular laws is itself matter. But all mind is directly or indirectly connected with all matter, and acts in a more or less regular way; so that all mind more or less partakes of the nature of matter. Hence, it would be a mistake to conceive of the psychical and the physical aspects of matter as two aspects absolutely distinct. Viewing a thing from the outside, considering its relations of action and reaction with other things, it appears as matter. Viewing it from the inside, looking at its immediate character as feeling, it appears as consciousness. These two views are combined when we remember that mechanical laws are nothing but acquired habits, like all the regularities of mind, including the tendency to take habits, itself; and that this action of habit is nothing but generalization, and generalization is nothing but the spreading of feelings. But the question is, how do general ideas appear in the molecular theory of protoplasm?

269. The consciousness of a habit involves a general idea. In each action of that habit certain atoms get thrown out of their orbit, and replaced by others. Upon all the different occasions it is different atoms that are thrown off, but they are analogous from a physical point of view, and there is an inward sense of their being analogous. Every time one of the associated feelings recurs, there is a more or less vague sense that there are others, that it has a general character, and of about what this general character is. We ought not, I think, to hold that in protoplasm habit never acts in any other than the particular way suggested above. On the contrary, if habit be a primary property of mind, it must be equally so of matter, as a kind of mind. We can hardly refuse to admit that wherever chance motions have general characters, there is a tendency for this generality to spread and to perfect itself. In that case, a general idea is a certain modification of consciousness which accompanies any regularity or general relation between chance actions.

270. The consciousness of a general idea has a certain "unity of the ego," in it, which is identical when it passes from one mind to another. It is, therefore, quite analogous to a person; and, indeed, a person is only a particular kind of general idea. Long ago, in the Journal of Speculative Philosophy (Vol. II, p. 156), †1 I pointed out that a person is nothing but a symbol involving a general idea; but my views were, then, too nominalistic to enable me to see that every general idea has the unified living feeling of a person.

271. All that is necessary, upon this theory, to the existence of a person is that the feelings out of which he is constructed should be in close enough connection to influence one another. Here we can draw a consequence which it may be possible to submit to experimental test. Namely, if this be the case, there should be something like personal consciousness in bodies of men who are in intimate and intensely sympathetic communion. It is true that when the generalization of feeling has been carried so far as to include all within a person, a stopping-place, in a certain sense, has been attained; and further generalization will have a less lively character. But we must not think it will cease. Esprit de corps, national sentiment, sympathy, are no mere metaphors. None of us can fully realize what the minds of corporations are, any more than one of my brain cells can know what the whole brain is thinking. But the law of mind clearly points to the existence of such personalities, and there are many ordinary observations which, if they were critically examined and supplemented by special experiments, might, as first appearances promise, give evidence of the influence of such greater persons upon individuals. It is often remarked that on one day half a dozen people, strangers to one another, will take it into their heads to do one and the same strange deed, whether it be a physical experiment, a crime, or an act of virtue. When the thirty thousand young people of the society for Christian Endeavor were in New York, there seemed to me to be some mysterious diffusion of sweetness and light. If such a fact is capable of being made out anywhere, it should be in the church. The Christians have always been ready to risk their lives for the sake of having prayers in common, of getting together and praying simultaneously with great energy, and especially for their common body, for "the whole state of Christ's church militant here in earth," as one of the missals has it. This practice they have been keeping up everywhere, weekly, for many centuries. Surely, a personality ought to have developed in that church, in that "bride of Christ," as they call it, or else there is a strange break in the action of mind, and I shall have to acknowledge my views are much mistaken. Would not the societies for psychical research be more likely to break through the clouds, in seeking evidences of such corporate personality, than in seeking evidences of telepathy, which, upon the same theory, should be a far weaker phenomenon? †1

Chapter 10: Mind and Matter

§1. The Connection Between Mind and Matter P †1

272. Several different theories have been urged during the past months to account for the mutual action between mind and matter in volition and in sensation. Little positive evidence has been gathered as yet for any of them; yet three or four hint at some possible eventual solution of this famous, deeply interesting, and dark problem.

273. It will do no harm to glance, first, at Leibnitz's theory of Preëstablished Harmony, if only to serve as foil to the modern hypotheses. This was possibly evoked by the phenomena of the mutual influence of two pendulums. These phenomena are like the following. A clock with a heavy pendulum had been solidly fastened to a brick wall. About six feet away was a shelf attached to the same wall. A Hardy's noddy, or little inverted pendulum swinging by the bending of a spring, having been adjusted to the period of oscillation of the clock-pendulum, was placed upon that shelf, when it immediately began to swing in unmistakable synchronism with the clock; and this motion it kept up for months. Again, two pendulums exactly alike and weighing some twenty pounds each, were suspended from a two-inch plank which was supported all along its eighteen-inch ends by quarter-inch plates of vertically corrugated iron attached to the floor. The direction of swinging of both pendulums was that of the length of the plank. Both being at rest, one of them was started into oscillation. Almost immediately, the other began to swing, and at the end of about three minutes the one first started had come to rest, while the one that had not been touched was swinging with nearly the same amplitude that the first had in the beginning. But no sooner had the latter come to rest than it began to start up again, while the arcs of the other became less; and in three minutes more, substantially the original condition of things had been restored. Of course, the real explanation of these phenomena is that the support of the heavy pendulum — the brick wall in the one case, the corrugated iron in the other — yielded under the swaying of the pendulums, and so communicated an impulse from each to the other, increasing the motion of the one that was behind and diminishing that of the one that was ahead; and though this effect was in itself imperceptible, yet when it had been multiplied one or two hundredfold, or as many times as the repetitions of its cause, the total effect became great. Meantime (the pendulum-support in such experiments, not being seen to sway, and being recognized to be almost quite rigid) each pendulum always looks as if it were going through its curious succession of motions of its own accord, although in a sort of inverse sympathy with the other. Nor is this a mere ocular illusion; for when the differential equations which define the forces are integrated, it is found that the motion of each pendulum is simply the sum of two perfectly simple and regular funipendulous motions of slightly different periods, and is, in fact, exactly like that of a cork floating upon still water traversed by two series of waves of slightly different lengths. The remarkable thing is that the motion of each pendulum is expressed as perfectly regular, without reference to the other. And what is so manifest in regard to pendulums is equally true of any other dynamical phenomenon. Namely, the forces are expressed by differential equations; but those equations have their integrals, whether mathematicians have yet discovered them or not; and these integrals express the motion of each particle as perfectly regular and determinate, and express it independently of all other particles. Now, Leibnitz was a professed nominalist. For him, a law was nothing more than a regularity, a regularity nothing less than a law. Since, therefore, each atom was experiencing a series of motions (and, as he presumed, also a series of feelings) which were perfectly regular, independently of every other, it followed, for him, that such was the law of its being; and the action between the different atoms consisted merely in certain relations — a certain harmony — between the laws having been preestablished by the great Author of those laws; and from this point of view there was no more difficulty in actions between mind and matter than between matter and matter.

The fault of this explanation is the capital fault which attaches to all nominalistic explanations, namely that they merely restate the fact to be explained under another aspect; or, if they add anything to it, add only something from which no definite consequences can be deduced. A scientific explanation ought to consist in the assertion of some positive matter of fact, other than the fact to be explained, but from which this fact necessarily follows; and if the explanation be hypothetical, the proof of it lies in the experiential verification of predictions deduced from it as necessary consequences. Leibnitz's explanation merely comes to this, that the motions and changes of state of atoms are relative to one another, because God made them so in the beginning. But nothing can be deduced from this theory, since it is impossible for man to predict what God might see fit to do. This stamps the theory as one of those to which Auguste Comte applied the epithet metaphysical, that is, unverifiable. †1 To accept it as sufficient would be to block the road of inquiry.

274. Among the modern theories not open to this objection, the simplest is the materialistic hypothesis. According to this, nothing really exists but matter: feelings are nothing but the way matter appears to itself. The gist of this theory, be it remarked, is that the Whole is governed by mechanical forces that are determined by the state of things at the instant they act, without any reference to a purpose of bringing about any determinate state of things in the future. The distinguishing merits of this theory are its simplicity, together with its loyal adhesion to that wholesome maxim entia non sunt multiplicanda praeter necessitatem, which, though urged by an illustrious nominalist, nobody surely can deny. Nor can the theory be absolutely refuted. Still, there are so many facts which have all the appearance of being opposed to it, that, notwithstanding the strong bias in favor of it which Ockham's razor justly produces in the minds of scientific men, few of these who have duly considered the facts have been able to bring themselves to hold it for true. No doubt, all nervous physiology shows the dependence of mind upon body; but that is not in question. The question is whether mental phenomena are exclusively controlled by blind mechanical law, as they certainly must be if mind be but an aspect of matter and matter is governed by such a law. The very circumstance that we can foretell how we shall act seems to militate against the hypothesis; nor is it easy to divine how the hypothesis and this fact are to be reconciled. Then the fact that our knowledge of the future is of so different a kind [from] our knowledge of the past seems to be hopelessly in conflict with materialism; since the laws of mechanics, as they are now understood, make the dynamical relation of the past to the future exactly the same as that of the future to the past. For, given a system of forces, and the positions and velocities of all the particles at any one instant, and all the previous positions and velocities are determined in precisely the same manner as are the subsequent positions and velocities. These are among the more obvious objections to the theory; others even more fatal have been urged. †1

275. Another theory, which, though not new, has newly been revived, is that by a mental effort certain material particles can be made temporarily to attract and repel one another. One naturally asks why this would not result in perpetual motion contrary to the principle of the conservation of energy, in case, for example, of the repelling particles being made to do work till they were brought to rest, and then, after attraction between them had been induced, being made to do additional work until restored to their original positions and velocities. The only answer possible would be that fatigue would, in that case, set in; so that a certain amount of work having been done the power of making the particles attract and repel would be exhausted until restored by nutrition. But such exhaustion could not be identified with that fatigue of which we are sensible; for the latter has little relation to the amount of mechanical work performed. It must, then, be an exhaustion which is not otherwise manifested; so that, comparing this theory with that of the materialist, we see that, in regard to muscular exertion, the two almost coincide, the logical advantage, however, being altogether with the materialist. For, brought up against the fact of exhaustion, the materialist fetches out his microscopes and chemical apparatus and endeavors to verify his theory by detecting some histological or chemical facts on which exhaustion may depend; while the other theorist attributes it to a metaphysical agency out of the realm of verification. Note, by the way, this singular feature of the theory under examination, that though, according to it, the mind only sets up now an attraction and now a repulsion between a pair of atoms, yet the exhaustion is not all occasioned by this conversion of attraction into repulsion and of repulsion into attraction, but only arises when these atoms happen to meet with a physical force against which they can do work, or happen to be so moving that their velocities are increased. If to answer the objection that the exhaustion which the theory supposes is a metaphysical butterfly it be maintained that the energy can be traced throughout in its transformations, then not only are mechanical and mental energy correlated, and the latter made measurable in foot-pounds, but it is held that this can be exhibited as so measurable. Now, it is undeniable that mental energy may be expended in producing a purely intellectual result; and mental energy that might be expended in muscular effort may, if we choose, be devoted to thought instead. If, therefore, the mental energy expended in muscular work is really transformed into that work, as this theory has to suppose, in order to preserve any semblance of a conservation of energy, it is necessary to admit that the purely intellectual product upon which that mental energy may be expended has also its equivalent in foot-pounds. Supposing, for example, this energy to be expended in writing a newspaper article, that paper would have to be supposed to contain that energy. So, if the editor does not like it and throws it into the fire, the theorist must either hold that all those foot-pounds have been destroyed, or else that the fire burns hotter on account of the mental energy expended on the composition. In short, this hypothesis falls either into the Scylla of absurdity or into the Charybdis of unverifiable metaphysics. Besides, its application to the action of matter upon mind in sensation is unsatisfactory. For if the energy of the mind is exhausted in volition, sensation ought to share with nutrition the function of restoring it; but this we do not find to be the case.

276. For these and other obvious reasons, all the physicists who have examined into the question of an interchange of energy between mind and matter have come to the conclusion that no such phenomenon takes place. Hence the suggestion is often made that while mind creates a mechanical force between particles this force only acts at right angles to the directions of their motion, so as to leave the mechanical energy unaffected. If the motion of a mass were to be deflected, irrespective of any other, the law of action and reaction would be violated. But this is not what the advocates of this theory mean. Their true meaning will to a mathematician be most clearly expressed by saying that the effect of mind is supposed to be, not to alter the equation of motion, but only to add, at will, an equation of condition. The general reader will have to accept the statement that the theory comes to this, that the mind attaches at will, what it can at will remove, to certain pairs of portions of matter, pairs of absolutely rigid surfaces impenetrable to one another — a surface to each of the two portions of matter — so that these surfaces, being in contact, hamper the motions. But the theory may very advantageously be specialized a little, as follows. Atoms are usually assumed to be absolutely rigid bodies perfectly elastic. Let it be supposed that the mind has the power of altering the shape and size of certain of the atoms, with the proviso that their centers of gravity and inertia-properties be not disturbed in the act. No immediate dynamical result will take place, but only an indirect effect as soon as the atoms next impinge upon one another. This theory seems highly artificial, and is at present sadly in need of evidence to sustain it. Nevertheless, it fulfills the conditions of the problem, and is eminently deserving of being kept in view as one of the possibilities. The manner in which it applies to the action of matter upon mind in sensation is interesting. It is philosophical to presume that this action is analogous to the action of mind upon matter in volition. Upon this theory, then, it must be supposed that in sensation the action of the mental law of association goes on undisturbed, but that an absolute restraint is placed upon the ideas which may present themselves, so that the sensation is really a violent suggestion. But a further development of this idea would probably lead to another theory of the connection between soul and body, which has recently been advocated and which is the last that we shall mention.

277. †1 Observations upon living naked protoplasm seem to show that mind, or feeling, has a continuous extension in space. Nobody doubts that it has a continuity in time, nor that the consciousness in one instant directly influences, or spreads over into, the succeeding instant. In like manner, the feeling at any point of space appears to spread and to assimilate to its own quality, though with reduced intensity, the feelings in the closely surrounding places. In this way, feeling seems directly to act upon feeling continuous with it. Now, in obedience to the principle, or maxim, of continuity, that we ought to assume things to be continuous as far as we can, it has been urged that we ought to suppose a continuity between the characters of mind and matter, so that matter would be nothing but mind that had such indurated habits as to cause it to act with a peculiarly high degree of mechanical regularity, or routine. Supposing this to be the case, the reaction between mind and matter would be of no essentially different kind from the action between parts of mind that are in continuous union, and would thus come directly under the great law of mental association, just as the theory last mentioned makes sensation to do. This hypothesis might be called materialistic, since it attributes to mind one of the recognized properties of matter, extension, and attributes to all matter a certain excessively low degree of feeling, together with a certain power of taking habits. But it differs essentially from materialism, in that, instead of supposing mind to be governed by blind mechanical law, it supposes the one original law to be the recognized law of mind, the law of association, of which the laws of matter are regarded as mere special results. This theory has been ridiculed by theologians as the merest whimsey while philosophers have pronounced it to be absurd upon metaphysical grounds; but students of physical and natural science are somewhat more favorable to it. Its advocates maintain that it is a perfectly consistent and legitimate working hypothesis, that it unmistakably commits itself to certain predictions and predesignations, that its truth or falsity ought to be judged exclusively from the comparison of these consequences of it with observation, and that, as far as it has been carried, this comparison has been quite favorable to the theory.

§2. The Materialistic Aspect of Reasoning P †1

278. The class of chemical substances having the most complicated molecules is, without doubt, that of the protoplasms. †P1 This chemical complexity is, in my opinion, sufficient to account for the extraordinary properties of those substances by virtue of which they grow into animals and plants. In particular, the laws of nervous action are, as I think, traceable to the chemical characters of the protoplasms of which the contents of nerve-cells are composed. †2

279. When a group of nerves are stimulated, it is certain that the ganglions with which the group is most intimately connected on the whole are thrown into an active state. This in its turn usually occasions movements of the body. Those movements are often intelligent; that is to say, what is to be accomplished determines what is done. Now, as all mechanical action is determined by the conditions at the instant, the question arises how is the tendency of nervous reactions towards ends to be accounted for. Suppose, then, that in the beginning, the reflex movements were not intelligent. In that case, the stimulation continuing, the irritation would spread from ganglion to ganglion, while increasing in intensity. Meantime, the ganglions first excited would begin to be fatigued, and their action would flag; and thus for a double reason the bodily activity would be of a changing kind. This would happen again and again, until at last some motion would remove the stimulus; and as soon as this was withdrawn, the excitement would quickly subside.

280. †3 Now it seems to be a universal property of protoplasm, intimately connected with the property of growth, that it takes habits. That is to say, first, when a lump of protoplasm is disturbed, say by a prick, at a given point, a so-called excited state, in which the matter is more fluid, is brought on; and this condition spreads. But, second, it does not spread uniformly, but very differently in different directions, and precisely what direction the spreading will take seems to be as uncertain as a throw of dice. Nevertheless, third, there is a preponderance of cases in which the path of spreading is the same as it had been the last time a similar stimulation of the same point occurred, or as it had been in the majority of cases.

281. The nerves are particularly ready to take and to change their habits. Consequently, in the case we have been considering, if, after the withdrawal of the stimulus and the consequent cessation of the excitement, the stimulation should be repeated, the last mode of reflex action, which removed the stimulus, is more likely to occur at once than any other; and in case it does not occur at once, the action will as before go on until a reaction takes place which shall remove the stimulus. In this way, a habit is pretty certain to be speedily acquired of so reacting from any stimulation as to remove the stimulus.

282. In fact, the greater part of intelligent actions are directed toward causing the cessation of some irritation. We eat to get rid of hunger, etc. Even when the eye of an infant rolls to the light, the action is perhaps of this kind; for the field of distinct vision on the retina is less sensitive to light than other parts. When we stop and listen to a sound, there may be a different principle; but then, any sensation, when it is interpreted, is diminished in intensity in immediate consciousness.

283. But other principles of intelligent action may probably be deduced from the primitive characters of protoplasm. There are many circumstances which lead us to believe that habit-taking is intimately connected with nutrition. Protoplasm grows: and that not as a crystal in a supersaturated or highly concentrated solution grows, by simply attracting matter like itself. It grows by chemically transforming other substances into its own chemical kind. This I believe to be due to the excessive complexity of its molecule. Chemists have estimated that the number of atoms in ordinary egg-albumen is nearly a thousand; and there are several circumstances which show that it must be nearly that. The most conclusive of these is the fact that a solution of albumen may be enclosed in the merest film of coagulum, and will float in water without bursting its sac. †P1 But albumen is not protoplasm. Albumen is dead; protoplasm is essentially alive. Hence, it is not too much to suppose that protoplasm, even of a low order, has several thousands of atoms in each molecule; and any high order of protoplasm probably has ten thousand. Such a molecule must be excessively unstable; and I believe that in the excited condition a considerable percentage of the molecules of protoplasm are partially decomposed. The peripheral stimulus deranges one or more molecules (which must be imagined as something like little solar systems, only vastly more complex) and an errant fragment from one of these enters another such system and perturbs that. But after the stimulus is removed they gradually settle down again, some molecules being destroyed, but others being recomposed with groups of atoms coming from food, while still others take up fragments which had been thrown off from neighboring molecules. I think it is pretty clear that the new portions thus taken in would be a very long time in acquiring the ideally stable places in the molecule; and until they did so they would be more likely to be thrown out than other portions of the same molecules; and so a new excitation would be likely to repeat approximately the phenomena of the previous one; and the spreading of the disturbance would be likely to take the same course as before.

284. If this theory be true, different modes of spreading might differ greatly in regard to the amount of nutrition that would accompany them; and since the recomposed molecules would be the ones most likely to be deranged, those habits would be most likely to be formed which would result in the greatest nutritive gain. Thus, the animal would appear to exhibit a preference for modes of action involving the formation of new molecules of protoplasm. Were there a feeling of pain at every breaking of a molecule, and a pleasure at every recomposition of such a system, the animal would have a preference for pleasurable actions, and it would seem to him as if this pleasure, or the anticipation of it, were the cause of his acting in one way rather than in another.

285. This is a mode in which it would seem perhaps possible that a tendency to act intelligently, that is, so as to bring about a certain result, might arise in a mere mechanical system. Although it has not been shown that observed phenomena of intelligence could be thus accounted for, but only that they perhaps might be accounted for, and although the theory presents at one point a monstrous absurdity, that of supposing a piece of dead mechanism to feel pain and pleasure, yet, after all, this does not touch the main point, and I feel quite sure that the hypothesis affords an instructive point of view from which to contemplate the general question.

286. It is plain that intelligence does not consist in feeling in a certain way, but in acting in a certain way. Only, we must acknowledge that there are inward actions — what might be called potential actions, that is, actions which do not take place, but which somehow influence the formation of habits. †1 Certain stimuli, commonly visceral in their origin, throw the brain into an activity which simulates the effect of peripheral excitations of the senses. The reactions from such stimuli have the same internal character; an inward action removes the inward stimulus. A fancied conjuncture leads us to fancy an appropriate line of behaviour. Day-dreams are often spoken of as mere idleness; and so they would be, but for the remarkable fact that they go to form habits, by virtue of which when a similar real conjuncture arises we really behave in the manner we had dreamed of doing.

"Some say the soft Ideal that we wooed
Confronts us fiercely, foe-beset, pursued,
And cries reproachful, "Was it, then, my praise
And not myself was loved? Prove now thy truth;
I claim of thee the promise of thy youth;
Give me thy life, or cower in empty phrase,
The victim of thy genius, not its mate!"

People who build castles in the air do not, for the most part, accomplish much, it is true; but every man who does accomplish great things is given to building elaborate castles in the air and then painfully copying them on solid ground. Indeed, the whole business of ratiocination, and all that makes us intellectual beings, is performed in imagination. Vigorous men are wont to hold mere imagination in contempt; and in that they would be quite right if there were such a thing. How we feel is no matter; the question is what we shall do. But that feeling which is subservient to action and to the intelligence of action is correspondingly important; and all inward life is more or less so subservient. Mere imagination would indeed be mere trifling; only no imagination is mere. "More than all that is in thy custody, watch over thy phantasy," said Solomon, "For out of it are the issues of life." Omni custodia serva cor tuum, quia ex ipso vita procedit. †1

A decapitated frog almost reasons. †2 The habit that is in his cerebellum serves as a major premiss. The excitation of a drop of acid is his minor premiss. And his conclusion is the act of wiping it away. All that is of any value in the operation of ratiocination is there, except only one thing. What he lacks is the power of preparatory meditation.

Chapter 11: Evolutionary Love †1

§1. At First Blush. Counter-Gospels

287. Philosophy, when just escaping from its golden pupa-skin, mythology, proclaimed the great evolutionary agency of the universe to be Love. Or, since this pirate-lingo, English, is poor in such-like words, let us say Eros, the exuberance-love. Afterwards, Empedocles †2 set up passionate love and hate as the two coördinate powers of the universe. In some passages, kindness is the word. But certainly, in any sense in which it has an opposite, to be senior partner of that opposite, is the highest position that love can attain. Nevertheless, the ontological gospeller, in whose days those views were familiar topics, made the One Supreme Being, by whom all things have been made out of nothing, to be cherishing-love. What, then, can he say to hate? Never mind, at this time, what the scribe of the Apocalypse, if he were John, stung at length by persecution into a rage, unable to distinguish suggestions of evil from visions of heaven, and so become the Slanderer of God to men, may have dreamed. The question is rather what the sane John thought, or ought to have thought, in order to carry out his idea consistently. His statement that God is love seems aimed at that saying of Ecclesiastes that we cannot tell whether God bears us love or hatred. "Nay," says John, "we can tell, and very simply! We know and have trusted the love which God hath in us. God is love." There is no logic in this, unless it means that God loves all men. In the preceding paragraph, he had said, "God is light and in him is no darkness at all." We are to understand, then, that as darkness is merely the defect of light, so hatred and evil are mere imperfect stages of {agapé} and {agathon}, love and loveliness. This concords with that utterance reported in John's Gospel: "God sent not the Son into the world to judge the world; but that the world should through him be saved. He that believeth on him is not judged: he that believeth not hath been judged already. . . . And this is the judgment, that the light is come into the world, and that men loved darkness rather than the light." That is to say, God visits no punishment on them; they punish themselves, by their natural affinity for the defective. Thus, the love that God is, is not a love of which hatred is the contrary; otherwise Satan would be a coordinate power; but it is a love which embraces hatred as an imperfect stage of it, an Anteros — yea, even needs hatred and hatefulness as its object. For self-love is no love; so if God's self is love, that which he loves must be defect of love; just as a luminary can light up only that which otherwise would be dark. Henry James, the Swedenborgian, says: "It is no doubt very tolerable finite or creaturely love to love one's own in another, to love another for his conformity to one's self: but nothing can be in more flagrant contrast with the creative Love, all whose tenderness ex vi termini must be reserved only for what intrinsically is most bitterly hostile and negative to itself." This is from Substance and Shadow: An Essay on the Physics of Creation. †1 It is a pity he had not filled his pages with things like this, as he was able easily to do, instead of scolding at his reader and at people generally, until the physics of creation was well-nigh forgot. I must deduct, however, from what I just wrote: obviously no genius could make his every sentence as sublime as one which discloses for the problem of evil its everlasting solution.

288. The movement of love is circular, at one and the same impulse projecting creations into independency and drawing them into harmony. This seems complicated when stated so; but it is fully summed up in the simple formula we call the Golden Rule. This does not, of course, say, Do everything possible to gratify the egoistic impulses of others, but it says, Sacrifice your own perfection to the perfectionment of your neighbor. Nor must it for a moment be confounded with the Benthamite, or Helvetian, or Beccarian motto, Act for the greatest good of the greatest number. Love is not directed to abstractions but to persons; not to persons we do not know, nor to numbers of people, but to our own dear ones, our family and neighbors. "Our neighbor," we remember, is one whom we live near, not locally perhaps but in life and feeling.

289. Everybody can see that the statement of St. John is the formula of an evolutionary philosophy, which teaches that growth comes only from love, from I will not say self-sacrifice, but from the ardent impulse to fulfill another's highest impulse. Suppose, for example, that I have an idea that interests me. It is my creation. It is my creature; for as shown in last July's Monist, †1 it is a little person. I love it; and I will sink myself in perfecting it. It is not by dealing out cold justice to the circle of my ideas that I can make them grow, but by cherishing and tending them as I would the flowers in my garden. The philosophy we draw from John's gospel is that this is the way mind develops; and as for the cosmos, only so far as it yet is mind, and so has life, is it capable of further evolution. Love, recognizing germs of loveliness in the hateful, gradually warms it into life, and makes it lovely. That is the sort of evolution which every careful student of my essay "The Law of Mind" †2 must see that synechism calls for.

290. The nineteenth century is now fast sinking into the grave, and we all begin to review its doings and to think what character it is destined to bear as compared with other centuries in the minds of future historians. It will be called, I guess, the Economical Century; for political economy has more direct relations with all the branches of its activity than has any other science. Well, political economy has its formula of redemption, too. It is this: Intelligence in the service of greed ensures the justest prices, the fairest contracts, the most enlightened conduct of all the dealings between men, and leads to the summum bonum, food in plenty and perfect comfort. Food for whom? Why, for the greedy master of intelligence. I do not mean to say that this is one of the legitimate conclusions of political economy, the scientific character of which I fully acknowledge. But the study of doctrines, themselves true, will often temporarily encourage generalizations extremely false, as the study of physics has encouraged necessitarianism. What I say, then, is that the great attention paid to economical questions during our century has induced an exaggeration of the beneficial effects of greed and of the unfortunate results of sentiment, until there has resulted a philosophy which comes unwittingly to this, that greed is the great agent in the elevation of the human race and in the evolution of the universe.

291. I open a handbook of political economy †1 — the most typical and middling one I have at hand — and there find some remarks of which I will here make a brief analysis. I omit qualifications, sops thrown to Cerberus, phrases to placate Christian prejudice, trappings which serve to hide from author and reader alike the ugly nakedness of the greed-god. But I have surveyed my position. The author enumerates "three motives to human action: †2

The love of self;

The love of a limited class having common interests and feelings with one's self;

The love of mankind at large."

Remark, at the outset, what obsequious title is bestowed on greed — "the love of self." Love! The second motive is love. In place of "a limited class" put "certain persons," and you have a fair description. Taking "class" in the old-fashioned sense, a weak kind of love is described. In the sequel, there seems to be some haziness as to the delimitation of this motive. By the love of mankind at large, the author does not mean that deep, subconscious passion that is properly so called; but merely public-spirit, perhaps little more than a fidget about pushing ideas. The author proceeds to a comparative estimate of the worth of these motives. Greed, says he, but using, of course, another word, "is not so great an evil as is commonly supposed. . . . Every man can promote his own interests a great deal more effectively than he can promote any one else's, or than any one else can promote his." Besides, as he remarks on another page, the more miserly a man is, the more good he does. The second motive "is the most dangerous one to which society is exposed." Love is all very pretty: "no higher or purer source of human happiness exists." (Ahem!) But it is a "source of enduring injury," and, in short, should be overruled by something wiser. What is this wiser motive? We shall see.

As for public spirit, it is rendered nugatory by the "difficulties in the way of its effective operation." For example, it might suggest putting checks upon the fecundity of the poor and the vicious; and "no measure of repression would be too severe," in the case of criminals. The hint is broad. But unfortunately, you cannot induce legislatures to take such measures, owing to the pestiferous "tender sentiments of man towards man." It thus appears that public-spirit, or Benthamism, is not strong enough to be the effective tutor of love (I am skipping to another page) which must, therefore, be handed over to "the motives which animate men in the pursuit of wealth," in which alone we can confide, and which "are in the highest degree beneficent." †P1 Yes, in the "highest degree" without exception are they beneficent to the being upon whom all their blessings are poured out, namely, the Self, whose "sole object," says the writer, in accumulating wealth is his individual "sustenance and enjoyment." Plainly, the author holds the notion that some other motive might be in a higher degree beneficent, even for the man's self, to be a paradox wanting in good sense. He seeks to gloze and modify his doctrine; but he lets the perspicacious reader see what his animating principle is; and when, holding the opinions I have repeated, he at the same time acknowledges that society could not exist upon a basis of intelligent greed alone, he simply pigeon-holes himself as one of the eclectics of inharmonious opinions. He wants his mammon flavored with a soupçon of god.

292. The economists accuse those, to whom the enunciation of their atrocious villainies communicates a thrill of horror, of being sentimentalists. It may be so: I willingly confess to having some tincture of sentimentalism in me, God be thanked! Ever since the French Revolution brought this leaning of thought into ill repute — and not altogether undeservedly, I must admit, true, beautiful, and good as that great movement was — it has been the tradition to picture sentimentalists as persons incapable of logical thought and unwilling to look facts in the eyes. This tradition may be classed with the French tradition that an Englishman says godam at every second sentence, the English tradition that an American talks about "Britishers," and the American tradition that a Frenchman carries forms of etiquette to an inconvenient extreme; in short, with all those traditions which survive simply because the men who use their eyes and ears are few and far between. Doubtless some excuse there was for all those opinions in days gone by; and sentimentalism, when it was the fashionable amusement to spend one's evenings in a flood of tears over a woeful performance on a candle-litten stage, sometimes made itself a little ridiculous. But what after all is sentimentalism? It is an ism, a doctrine, namely, the doctrine that great respect should be paid to the natural judgments of the sensible heart. This is what sentimentalism precisely is; and I entreat the reader to consider whether to contemn it is not of all blasphemies the most degrading. Yet the nineteenth century has steadily contemned it, because it brought about the Reign of Terror. That it did so is true. Still, the whole question is one of how much. The Reign of Terror was very bad; but now the Gradgrind banner has been this century long flaunting in the face of heaven, with an insolence to provoke the very skies to scowl and rumble. Soon a flash and quick peal will shake economists quite out of their complacency, too late. The twentieth century, in its latter half, shall surely see the deluge-tempest burst upon the social order — to clear upon a world as deep in ruin as that greed-philosophy has long plunged it into guilt. No post-thermidorian high jinks then!

So a miser is a beneficent power in a community, is he? With the same reason precisely, only in a much higher degree, you might pronounce the Wall Street sharp to be a good angel, who takes money from heedless persons not likely to guard it properly, who wrecks feeble enterprises better stopped, and who administers wholesome lessons to unwary scientific men, by passing worthless checks upon them — as you did, the other day, to me, my millionaire Master in glomery, when you thought you saw your way to using my process without paying for it, and of so bequeathing to your children something to boast about of their father — and who by a thousand wiles puts money at the service of intelligent greed, in his own person. Bernard Mandeville, in his Fable of the Bees, †1 maintains that private vices of all descriptions are public benefits, and proves it, too, quite as cogently as the economist proves his point concerning the miser. He even argues, with no slight force, that but for vice civilization would never have existed. In the same spirit, it has been strongly maintained and is today widely believed that all acts of charity and benevolence, private and public, go seriously to degrade the human race.

293. The Origin of Species of Darwin merely extends politico-economical views of progress to the entire realm of animal and vegetable life. The vast majority of our contemporary naturalists hold the opinion that the true cause of those exquisite and marvelous adaptations of nature for which, when I was a boy, men used to extol the divine wisdom, is that creatures are so crowded together that those of them that happen to have the slightest advantage force those less pushing into situations unfavorable to multiplication or even kill them before they reach the age of reproduction. Among animals, the mere mechanical individualism is vastly reënforced as a power making for good by the animal's ruthless greed. As Darwin puts it on his title-page, it is the struggle for existence; and he should have added for his motto: Every individual for himself, and the Devil take the hindmost! Jesus, in his sermon on the Mount, expressed a different opinion.

294. Here, then, is the issue. The gospel of Christ says that progress comes from every individual merging his individuality in sympathy with his neighbors. On the other side, the conviction of the nineteenth century is that progress takes place by virtue of every individual's striving for himself with all his might and trampling his neighbor under foot whenever he gets a chance to do so. This may accurately be called the Gospel of Greed.

295. Much is to be said on both sides. I have not concealed, I could not conceal, my own passionate predilection. Such a confession will probably shock my scientific brethren. Yet the strong feeling is in itself, I think, an argument of some weight in favor of the agapastic theory of evolution — so far as it may be presumed to bespeak the normal judgment of the Sensible Heart. Certainly, if it were possible to believe in agapasm without believing it warmly, that fact would be an argument against the truth of the doctrine. At any rate, since the warmth of feeling exists, it should on every account be candidly confessed; especially since it creates a liability to one-sidedness on my part against which it behooves my readers and me to be severally on our guard.

§2. Second Thoughts. Irenica

296. Let us try to define the logical affinities of the different theories of evolution. †1 Natural selection, as conceived by Darwin, is a mode of evolution in which the only positive agent of change in the whole passage from moner to man is fortuitous variation. To secure advance in a definite direction chance has to be seconded by some action that shall hinder the propagation of some varieties or stimulate that of others. In natural selection, strictly so called, it is the crowding out of the weak. In sexual selection, it is the attraction of beauty, mainly.

297. The Origin of Species was published toward the end of the year 1859. The preceding years since 1846 had been one of the most productive seasons — or if extended so as to cover the great book we are considering, the most productive period of equal length in the entire history of science from its beginnings until now. The idea that chance begets order, which is one of the corner-stones of modern physics (although Dr. Carus †2 considers it "the weakest point in Mr. Peirce's system ") was at that time put into its clearest light. Quetelet had opened the discussion by his Letters on the Application of Probabilities to the Moral and Political Sciences, †3 a work which deeply impressed the best minds of that day, and to which Sir John Herschel †1 had drawn general attention in Great Britain. In 1857, the first volume of Buckle's History of Civilisation had created a tremendous sensation, owing to the use he made of this same idea. Meantime, the "statistical method" had, under that very name, been applied with brilliant success to molecular physics. Dr. John Herapath, an English chemist, had in 1847 outlined the kinetical theory of gases in his Mathematical Physics; and the interest the theory excited had been refreshed in 1856 by notable memoirs by Clausius †2 and Krönig. †3 In the very summer preceding Darwin's publication, Maxwell had read before the British Association the first and most important of his researches on this subject. †4 The consequence was that the idea that fortuitous events may result in a physical law, and further that this is the way in which those laws which appear to conflict with the principle of the conservation of energy are to be explained, had taken a strong hold upon the minds of all who were abreast of the leaders of thought. By such minds, it was inevitable that the Origin of Species, whose teaching was simply the application of the same principle to the explanation of another "non-conservative" †5 action, that of organic development, should be hailed and welcomed. The sublime discovery of the conservation of energy by Helmholtz in 1847, †6 and that of the mechanical theory of heat by Clausius †7 and by Rankine, †8 independently, in 1850, had decidedly overawed all those who might have been inclined to sneer at physical science. Thereafter a belated poet still harping upon "science peddling with the names of things" would fail of his effect. Mechanism was now known to be all, or very nearly so. All this time, utilitarianism — that improved substitute for the Gospel — was in its fullest feather; and was a natural ally of an individualistic theory. Dean Mansell's injudicious advocacy had led to mutiny among the bondsmen of Sir William Hamilton, and the nominalism of Mill had profited accordingly; and although the real science that Darwin was leading men to was sure some day to give a death-blow to the sham-science of Mill, yet there were several elements of the Darwinian theory which were sure to charm the followers of Mill. †1 Another thing: anæsthetics had been in use for thirteen years. Already, people's acquaintance with suffering had dropped off very much; and as a consequence, that unlovely hardness, by which our times are so contrasted with those that immediately preceded them, had already set in, and inclined people to relish a ruthless theory. The reader would quite mistake the drift of what I am saying if he were to understand me as wishing to suggest that any of those things (except perhaps Malthus) influenced Darwin himself. What I mean is that his hypothesis, while without dispute one of the most ingenious and pretty ever devised, and while argued with a wealth of knowledge, a strength of logic, a charm of rhetoric, and above all with a certain magnetic genuineness that was almost irresistible, did not appear, at first, at all near to being proved; and to a sober mind its case looks less hopeful now than it did twenty years ago; but the extraordinarily favorable reception it met with was plainly owing, in large measure, to its ideas being those toward which the age was favorably disposed, especially, because of the encouragement it gave to the greed-philosophy.

298. Diametrically opposed to evolution by chance are those theories which attribute all progress to an inward necessary principle, or other form of necessity. Many naturalists have thought that if an egg is destined to go through a certain series of embryological transformations, from which it is perfectly certain not to deviate, and if in geological time almost exactly the same forms appear successively, one replacing another in the same order, the strong presumption is that this latter succession was as predeterminate and certain to take place as the former. So, Nägeli, †1 for instance, conceives that it somehow follows from the first law of motion and the peculiar, but unknown, molecular constitution of protoplasm, that forms must complicate themselves more and more. Kölliker †2 makes one form generate another after a certain maturation has been accomplished. Weismann, †3 too, though he calls himself a Darwinian, holds that nothing is due to chance, but that all forms are simple mechanical resultants of the heredity from two parents. †P1 It is very noticeable that all these different sectaries seek to import into their science a mechanical necessity to which the facts that come under their observation do not point. Those geologists who think that the variation of species is due to cataclysmic alterations of climate or of the chemical constitution of the air and water are also making mechanical necessity chief factor of evolution.

299. Evolution by sporting and evolution by mechanical necessity are conceptions warring against one another. A third method, which supersedes their strife, lies enwrapped in the theory of Lamarck. †4 According to his view, all that distinguishes the highest organic forms from the most rudimentary has been brought about by little hypertrophies or atrophies which have affected individuals early in their lives, and have been transmitted to their offspring. Such a transmission of acquired characters is of the general nature of habit-taking, and this is the representative and derivative within the physiological domain of the law of mind. Its action is essentially dissimilar to that of a physical force; and that is the secret of the repugnance of such necessitarians as Weismann to admitting its existence. The Lamarckians further suppose that, although some of the modifications of form so transmitted were originally due to mechanical causes, yet the chief factors of their first production were the straining of endeavor and the overgrowth superinduced by exercise, together with the opposite actions. Now, endeavor, since it is directed toward an end, is essentially psychical, even though it be sometimes unconscious; and the growth due to exercise, as I argued in my last paper, †1 follows a law of a character quite contrary to that of mechanics.

300. Lamarckian evolution is thus evolution by the force of habit. — That sentence slipped off my pen while one of those neighbors whose function in the social cosmos seems to be that of an Interrupter was asking me a question. Of course, it is nonsense. Habit is mere inertia, a resting on one's oars, not a propulsion. Now it is energetic projaculation (lucky there is such a word, or this untried hand might have been put to inventing one) by which in the typical instances of Lamarckian evolution the new elements of form are first created. Habit, however, forces them to take practical shapes, compatible with the structures they affect, and, in the form of heredity and otherwise, gradually replaces the spontaneous energy that sustains them. Thus, habit plays a double part; it serves to establish the new features, and also to bring them into harmony with the general morphology and function of the animals and plants to which they belong. But if the reader will now kindly give himself the trouble of turning back a page or two, he will see that this account of Lamarckian evolution coincides with the general description of the action of love, to which, I suppose, he yielded his assent.

301. Remembering that all matter is really mind, remembering, too, the continuity of mind, let us ask what aspect Lamarckian evolution takes on within the domain of consciousness. Direct endeavor can achieve almost nothing. It is as easy by taking thought to add a cubit to one's stature as it is to produce an idea acceptable to any of the Muses by merely straining for it before it is ready to come. We haunt in vain the sacred well and throne of Mnemosyne; the deeper workings of the spirit take place in their own slow way, without our connivance. Let but their bugle sound, and we may then make our effort, sure of an oblation for the altar of whatsoever divinity its savour gratifies. Besides this inward process, there is the operation of the environment, which goes to break up habits destined to be broken up and so to render the mind lively. Everybody knows that the long continuance of a routine of habit makes us lethargic, while a succession of surprises wonderfully brightens the ideas. Where there is a motion, where history is a-making, there is the focus of mental activity, and it has been said that the arts and sciences reside within the temple of Janus, waking when that is open, but slumbering when it is closed. Few psychologists have perceived how fundamental a fact this is. A portion of mind, abundantly commissured to other portions, works almost mechanically. It sinks to a condition of a railway junction. But a portion of mind almost isolated, a spiritual peninsula, or cul-de-sac, is like a railway terminus. Now mental commissures are habits. Where they abound, originality is not needed and is not found; but where they are in defect spontaneity is set free. Thus, the first step in the Lamarckian evolution of mind is the putting of sundry thoughts into situations in which they are free to play. As to growth by exercise, I have already shown, in discussing "Man's Glassy Essence," †1 in last October's Monist, what its modus operandi must be conceived to be, at least, until a second equally definite hypothesis shall have been offered. Namely, it consists of the flying asunder of molecules, and the reparation of the parts by new matter. It is, thus, a sort of reproduction. It takes place only during exercise, because the activity of protoplasm consists in the molecular disturbance which is its necessary condition. Growth by exercise takes place also in the mind. Indeed, that is what it is to learn. But the most perfect illustration is the development of a philosophical idea by being put into practice. The conception which appeared, at first, as unitary splits up into special cases; and into each of these new thought must enter to make a practicable idea. This new thought, however, follows pretty closely the model of the parent conception; and thus a homogeneous development takes place. The parallel between this and the course of molecular occurrences is apparent. Patient attention will be able to trace all these elements in the transaction called learning.

302. Three modes of evolution have thus been brought before us: evolution by fortuitous variation, evolution by mechanical necessity, and evolution by creative love. We may term them tychastic evolution, or tychasm, anancastic evolution, or anancasm, and agapastic evolution, or agapasm. The doctrines which represent these as severally of principal importance we may term tychasticism, anancasticism, and agapasticism. On the other hand the mere propositions that absolute chance, mechanical necessity, and the law of love are severally operative in the cosmos may receive the names of tychism, anancism, and agapism.

303. All three modes of evolution are composed of the same general elements. Agapasm exhibits them the most clearly. The good result is here brought to pass, first, by the bestowal of spontaneous energy by the parent upon the offspring, and, second, by the disposition of the latter to catch the general idea of those about it and thus to subserve the general purpose. In order to express the relation that tychasm and anancasm bear to agapasm let me borrow a word from geometry. An ellipse crossed by a straight line is a sort of cubic curve; for a cubic is a curve which is cut thrice by a straight line; now a straight line might cut the ellipse twice and its associated straight line a third time. Still the ellipse with the straight line across it would not have the characteristics of a cubic. It would have, for instance, no contrary flexure, which no true cubic wants; and it would have two nodes, which no true cubic has. The geometers say that it is a degenerate cubic. Just so, tychasm and anancasm are degenerate forms of agapasm.

304. Men who seek to reconcile the Darwinian idea with Christianity will remark that tychastic evolution, like the agapastic, depends upon a reproductive creation, the forms preserved being those that use the spontaneity conferred upon them in such wise as to be drawn into harmony with their original, quite after the Christian scheme. Very good! This only shows that just as love cannot have a contrary, but must embrace what is most opposed to it, as a degenerate case of it, so tychasm is a kind of agapasm. Only, in the tychastic evolution, progress is solely owing to the distribution of the napkin-hidden talent of the rejected servant among those not rejected, just as ruined gamesters leave their money on the table to make those not yet ruined so much the richer. It makes the felicity of the lambs just the damnation of the goats, transposed to the other side of the equation. In genuine agapasm, on the other hand, advance takes place by virtue of a positive sympathy among the created springing from continuity of mind. This is the idea which tychasticism knows not how to manage.

305. The anancasticist might here interpose, claiming that the mode of evolution for which he contends agrees with agapasm at the point at which tychasm departs from it. For it makes development go through certain phases, having its inevitable ebbs and flows, yet tending on the whole to a fore-ordained perfection. Bare existence by this its destiny betrays an intrinsic affinity for the good. Herein, it must be admitted, anancasm shows itself to be in a broad acception a species of agapasm. Some forms of it might easily be mistaken for the genuine agapasm. The Hegelian philosophy is such an anancasticism. With its revelatory religion, with its synechism (however imperfectly set forth), with its "reflection," the whole idea of the theory is superb, almost sublime. Yet, after all, living freedom is practically omitted from its method. The whole movement is that of a vast engine, impelled by a vis a tergo, with a blind and mysterious fate of arriving at a lofty goal. I mean that such an engine it would be, if it really worked; but in point of fact, it is a Keely motor. †1 Grant that it really acts as it professes to act, and there is nothing to do but accept the philosophy. But never was there seen such an example of a long chain of reasoning — shall I say with a flaw in every link? — no, with every link a handful of sand, squeezed into shape in a dream. Or say, it is a pasteboard model of a philosophy that in reality does not exist. If we use the one precious thing it contains, the idea of it, introducing the tychism which the arbitrariness of its every step suggests, and make that the support of a vital freedom which is the breath of the spirit of love, we may be able to produce that genuine agapasticism at which Hegel was aiming.

§3. A Third Aspect. Discrimination

306. In the very nature of things, the line of demarcation between the three modes of evolution is not perfectly sharp. That does not prevent its being quite real; perhaps it is rather a mark of its reality. There is in the nature of things no sharp line of demarcation between the three fundamental colors, red, green, and violet. But for all that they are really different. The main question is whether three radically different evolutionary elements have been operative; and the second question is what are the most striking characteristics of whatever elements have been operative.

307. I propose to devote a few pages to a very slight examination of these questions in their relation to the historical development of human thought. I first formulate for the reader's convenience the briefest possible definitions of the three conceivable modes of development of thought, distinguishing also two varieties of anancasm and three of agapasm. The tychastic development of thought, then, will consist in slight departures from habitual ideas in different directions indifferently, quite purposeless and quite unconstrained whether by outward circumstances or by force of logic, these new departures being followed by unforeseen results which tend to fix some of them as habits more than others. The anancastic development of thought will consist of new ideas adopted without foreseeing whither they tend, but having a character determined by causes either external to the mind, such as changed circumstances of life, or internal to the mind as logical developments of ideas already accepted, such as generalizations. The agapastic development of thought is the adoption of certain mental tendencies, not altogether heedlessly, as in tychasm, nor quite blindly by the mere force of circumstances or of logic, as in anancasm, but by an immediate attraction for the idea itself, whose nature is divined before the mind possesses it, by the power of sympathy, that is, by virtue of the continuity of mind; and this mental tendency may be of three varieties, as follows. First, it may affect a whole people or community in its collective personality, and be thence communicated to such individuals as are in powerfully sympathetic connection with the collective people, although they may be intellectually incapable of attaining the idea by their private understandings or even perhaps of consciously apprehending it. Second, it may affect a private person directly, yet so that he is only enabled to apprehend the idea, or to appreciate its attractiveness, by virtue of his sympathy with his neighbors, under the influence of a striking experience or development of thought. The conversion of St. Paul may be taken as an example of what is meant. Third, it may affect an individual, independently of his human affections, by virtue of an attraction it exercises upon his mind, even before he has comprehended it. This is the phenomenon which has been well called the divination of genius; for it is due to the continuity between the man's mind and the Most High.

308. Let us next consider by means of what tests we can discriminate between these different categories of evolution. No absolute criterion is possible in the nature of things, since in the nature of things there is no sharp line of demarcation between the different classes. Nevertheless, quantitative symptoms may be found by which a sagacious and sympathetic judge of human nature may be able to estimate the approximate proportions in which the different kinds of influence are commingled.

309. So far as the historical evolution of human thought has been tychastic, it should have proceeded by insensible or minute steps; for such is the nature of chances when so multiplied as to show phenomena of regularity. For example, assume that of the native-born white adult males of the United States in 1880, one-fourth part were below 5 feet 4 inches in stature and one-fourth part above 5 feet 8 inches. Then by the principles of probability, among the whole population, we should expect

216 under 4 feet 6 inches 216 above 6 feet 6 inches
48 under 4 feet 5 inches 48 above 6 feet 7 inches
9 under 4 feet 5 inches 9 above 6 feet 8 inches
less than 2 under 4 feet 3 inches less than 2 above 6 feet 9 inches

I set down these figures to show how insignificantly few are the cases in which anything very far out of the common run presents itself by chance. Though the stature of only every second man is included within the four inches between 5 feet 4 inches and 5 feet 8 inches, yet if this interval be extended by thrice four inches above and below, it will embrace all our 8 millions odd of native-born adult white males (of 1880), except only 9 taller and 9 shorter.

310. The test of minute variation, if not satisfied, absolutely negatives tychasm. If it is satisfied, we shall find that it negatives anancasm but not agapasm. We want a positive test, satisfied by tychasm, only. Now wherever we find men's thought taking by imperceptible degrees a turn contrary to the purposes which animate them, in spite of their highest impulses, there, we may safely conclude, there has been a tychastic action.

311. Students of the history of mind there be of an erudition to fill an imperfect scholar like me with envy edulcorated by joyous admiration, who maintain that ideas when just started are and can be little more than freaks, since they cannot yet have been critically examined, and further that everywhere and at all times progress has been so gradual that it is difficult to make out distinctly what original step any given man has taken. It would follow that tychasm has been the sole method of intellectual development. I have to confess I cannot read history so; I cannot help thinking that while tychasm has sometimes been operative, at others great steps covering nearly the same ground and made by different men independently have been mistaken for a succession of small steps, and further that students have been reluctant to admit a real entitative "spirit" of an age or of a people, under the mistaken and unscrutinized impression that they should thus be opening the door to wild and unnatural hypotheses. I find, on the contrary, that, however it may be with the education of individual minds, the historical development of thought has seldom been of a tychastic nature, and exclusively in backward and barbarizing movements. I desire to speak with the extreme modesty which befits a student of logic who is required to survey so very wide a field of human thought that he can cover it only by a reconnaissance, to which only the greatest skill and most adroit methods can impart any value at all; but, after all, I can only express my own opinions and not those of anybody else; and in my humble judgment, the largest example of tychasm is afforded by the history of Christianity, from about its establishment by Constantine to, say, the time of the Irish monasteries, an era or eon of about 500 years. Undoubtedly the external circumstance, which more than all others at first inclined men to accept Christianity in its loveliness and tenderness, was the fearful extent to which society was broken up into units by the unmitigated greed and hard-heartedness into which the Romans had seduced the world. And yet it was that very same fact, more than any other external circumstance, that fostered that bitterness against the wicked world of which the primitive gospel of Mark contains not a single trace. At least, I do not detect it in the remark about the blasphemy against the Holy Ghost, †1 where nothing is said about vengeance, nor even in that speech †2 where the closing lines of Isaiah †3 are quoted, about the worm and the fire that feed upon the "carcasses of the men that have transgressed against me." But little by little the bitterness increases until, in the last book of the New Testament, its poor distracted author represents that all the time Christ was talking about having come to save the world, the secret design was to catch the entire human race, with the exception of a paltry 144,000, and souse them all in a brimstone lake, and as the smoke of their torment went up forever and ever, to turn and remark, "There is no curse any more." Would it be an insensible smirk or a fiendish grin that should accompany such an utterance? I wish I could believe St. John did not write it; but it is his gospel which tells about the "resurrection unto condemnation" — that is of men's being resuscitated just for the sake of torturing them — and at any rate, the Revelation is a very ancient composition. One can understand that the early Christians were like men trying with all their might to climb a steep declivity of smooth wet clay; the deepest and truest element of their life, animating both heart and head, was universal love; but they were continually, and against their wills, slipping into a party spirit, every slip serving as a precedent, in a fashion but too familiar to every man. This party feeling insensibly grew until by about A.D. 330 the luster of the pristine integrity that in St. Mark reflects the white spirit of light was so far tarnished that Eusebius (the Jared Sparks of that day), in the preface to his History, could announce his intention of exaggerating everything that tended to the glory of the church and of suppressing whatever might disgrace it. †1 His Latin contemporary Lactantius †2 is worse still; and so the darkling went on increasing until before the end of the century the great library of Alexandria was destroyed by Theophilus, †P1 until Gregory the Great, two centuries later, burnt the great library of Rome, †3 proclaiming that "Ignorance is the mother of devotion" (which is true, just as oppression and injustice is the mother of spirituality), until a sober description of the state of the church would be a thing our not too nice newspapers would treat as "unfit for publication." All this movement is shown by the application of the test given above to have been tychastic. Another very much like it on a small scale, only a hundred times swifter, for the study of which there are documents by the library-full, is to be found in the history of the French Revolution.

312. Anancastic evolution advances by successive strides with pauses between. The reason is that, in this process, a habit of thought, having been overthrown, is supplanted by the next strongest. Now this next strongest is sure to be widely disparate from the first, and as often as not is its direct contrary. It reminds one of our old rule of making the second candidate vice-president. This character, therefore, clearly distinguishes anancasm from tychasm. The character which distinguishes it from agapasm is its purposelessness. But external and internal anancasm have to be examined separately. Development under the pressure of external circumstances, or cataclasmine evolution, is in most cases unmistakable enough. It has numberless degrees of intensity, from the brute force, the plain war, which has more than once turned the current of the world's thought, down to the hard fact of evidence, or what has been taken for it, which has been known to convince men by hordes. The only hesitation that can subsist in the presence of such a history is a quantitative one. Never are external influences the only ones which affect the mind, and therefore it must be a matter of judgment for which it would scarcely be worth while to attempt to set rules, whether a given movement is to be regarded as principally governed from without or not. In the rise of medieval thought, I mean scholasticism and the synchronistic art developments, undoubtedly the crusades and the discovery of the writings of Aristotle were powerful influences. The development of scholasticism from Roscellin to Albertus Magnus closely follows the successive steps in the knowledge of Aristotle. Prantl thinks that that is the whole story, †1 and few men have thumbed more books than Carl Prantl. He has done good solid work, notwithstanding his slap-dash judgments. But we shall never make so much as a good beginning of comprehending scholasticism until the whole has been systematically explored and digested by a company of students regularly organized and held under rule for that purpose. But as for the period we are now specially considering, that which synchronized the Romanesque architecture, the literature is easily mastered. It does not quite justify Prantl's dicta as to the slavish dependence of these authors upon their authorities. Moreover, they kept a definite purpose steadily before their minds, throughout all their studies. I am, therefore, unable to offer this period of scholasticism as an example of pure external anancasm, which seems to be the fluorine of the intellectual elements. Perhaps the recent Japanese reception of western ideas is the purest instance of it in history. Yet in combination with other elements, nothing is commoner. If the development of ideas under the influence of the study of external facts be considered as external anancasm — it is on the border between the external and the internal forms — it is, of course, the principal thing in modern learning. But Whewell, whose masterly comprehension of the history of science critics have been too ignorant properly to appreciate, clearly shows that it is far from being the overwhelmingly preponderant influence, even there.

313. Internal anancasm, or logical groping, which advances upon a predestined line without being able to foresee whither it is to be carried nor to steer its course, this is the rule of development of philosophy. Hegel first made the world understand this; and he seeks to make logic not merely the subjective guide and monitor of thought, which was all it had been ambitioning before, but to be the very mainspring of thinking, and not merely of individual thinking but of discussion, of the history of the development of thought, of all history, of all development. This involves a positive, clearly demonstrable error. Let the logic in question be of whatever kind it may, a logic of necessary inference or a logic of probable inference (the theory might perhaps be shaped to fit either), in any case it supposes that logic is sufficient of itself to determine what conclusion follows from given premisses; for unless it will do so much, it will not suffice to explain why an individual train of reasoning should take just the course it does take, to say nothing of other kinds of development. It thus supposes that from given premisses, only one conclusion can logically be drawn, and that there is no scope at all for free choice. That from given premisses only one conclusion can logically be drawn is one of the false notions which have come from logicians' confining their attention to that Nantucket of thought, the logic of non-relative terms. In the logic of relatives, it does not hold good. †1

314. One remark occurs to me. If the evolution of history is in considerable part of the nature of internal anancasm, it resembles the development of individual men; and just as thirty-three years is a rough but natural unit of time for individuals, being the average age at which man has issue, so there should be an approximate period at the end of which one great historical movement ought to be likely to be supplanted by another. Let us see if we can make out anything of the kind. Take the governmental development of Rome as being sufficiently long and set down the principal dates.

B.C. 753, Foundation of Rome.
B.C. 510, Expulsion of the Tarquins.
B.C. 27, Octavius assumes title Augustus.
A.D. 476, End of Western Empire.
A.D. 962, Holy Roman Empire.
A.D. 1453, Fall of Constantinople.
The last event was one of the most significant in history, especially for Italy. The intervals are 243, 483, 502, 486 491, years. All are rather curiously near equal, except the first which is half the others. Successive reigns of kings would not commonly be so near equal. Let us set down a few dates in the history of thought.
B.C. 585, Eclipse of Thales. Beginning of Greek philosophy.
A.D. 30, The crucifixion.
A.D. 529, Closing of Athenian schools. End of Greek philosophy. A.D. 1125, (Approximate) Rise of the Universities of Bologna and Paris.
A.D. 1543, Publication of the De Revolutionibus of Copernicus. Beginning of Modern Science.
The intervals are 615, 499, 596, 418 years. In the history of metaphysics, we may take the following:
B.C. 322, Death of Aristotle.
A.D. 1274, Death of Aquinas.
A.D. 1804, Death of Kant.
The intervals are 1595 and 530 years. The former is about thrice the latter.

From these figures, no conclusion can fairly be drawn. At the same time, they suggest that perhaps there may be a rough natural era of about 500 years. Should there be any independent evidence of this, the intervals noticed may gain some significance.

315. The agapastic development of thought should, if it exists, be distinguished by its purposive character, this purpose being the development of an idea. We should have a direct agapic or sympathetic comprehension and recognition of it by virtue of the continuity of thought. I here take it for granted that such continuity of thought has been sufficiently proved by the arguments used in my paper on the "Law of Mind" in The Monist of last July [Chapter 5]. Even if those arguments are not quite convincing in themselves, yet if they are reënforced by an apparent agapasm in the history of thought, the two propositions will lend one another mutual aid. The reader will, I trust, be too well grounded in logic to mistake such mutual support for a vicious circle in reasoning. If it could be shown directly that there is such an entity as the "spirit of an age" or of a people, and that mere individual intelligence will not account for all the phenomena, this would be proof enough at once of agapasticism and of synechism. I must acknowledge that I am unable to produce a cogent demonstration of this; but I am, I believe, able to adduce such arguments as will serve to confirm those which have been drawn from other facts. I believe that all the greatest achievements of mind have been beyond the powers of unaided individuals; and I find, apart from the support this opinion receives from synechistic considerations, and from the purposive character of many great movements, direct reason for so thinking in the sublimity of the ideas and in their occurring simultaneously and independently to a number of individuals of no extraordinary general powers. The pointed Gothic architecture in several of its developments appears to me to be of such a character. All attempts to imitate it by modern architects of the greatest learning and genius appear flat and tame, and are felt by their authors to be so. Yet at the time the style was living, there was quite an abundance of men capable of producing works of this kind of gigantic sublimity and power. In more than one case, extant documents show that the cathedral chapters, in the selection of architects, treated high artistic genius as a secondary consideration, as if there were no lack of persons able to supply that; and the results justify their confidence. Were individuals in general, then, in those ages possessed of such lofty natures and high intellect? Such an opinion would break down under the first examination.

316. How many times have men now in middle life seen great discoveries made independently and almost simultaneously! The first instance I remember was the prediction of a planet exterior to Uranus by Leverrier †1 and Adams. †2 One hardly knows to whom the principle of the conservation of energy ought to be attributed, although it may reasonably be considered as the greatest discovery science has ever made. The mechanical theory of heat was set forth by Rankine †3 and by Clausius †4 during the same month of February, 1850; and there are eminent men who attribute this great step to Thomson. †P1 The kinetical theory of gases, after being started by John Bernoulli †1 and long buried in oblivion, was reinvented and applied to the explanation not merely of the laws of Boyle, Charles, and Avogadro, but also of diffusion and viscosity, by at least three modern physicists separately. It is well known that the doctrine of natural selection was presented by Wallace and by Darwin at the same meeting of the British Association; and Darwin in his "Historical Sketch" prefixed to the later editions of his book shows that both were anticipated by obscure forerunners. The method of spectrum analysis was claimed for Swan as well as for Kirchhoff, and there were others who perhaps had still better claims. The authorship of the Periodical Law of the Chemical Elements is disputed between a Russian, a German, and an Englishman; †2 although there is no room for doubt that the principal merit belongs to the first. These are nearly all the greatest discoveries of our times. It is the same with the inventions. It may not be surprising that the telegraph should have been independently made by several inventors, because it was an easy corollary from scientific facts well made out before. But it was not so with the telephone and other inventions. Ether, the first anæsthetic, was introduced independently by three different New England physicians †3. Now ether had been a common article for a century. It had been in one of the pharmacopoeias three centuries before. It is quite incredible that its anaesthetic property should not have been known; it was known. It had probably passed from mouth to ear as a secret from the days of Basil Valentine; but for long it had been a secret of the Punchinello kind. In New England, for many years, boys had used it for amusement. Why then had it not been put to its serious use? No reason can be given, except that the motive to do so was not strong enough. The motives to doing so could only have been desire for gain and philanthropy. About 1846, the date of the introduction, philanthropy was undoubtedly in an unusually active condition. That sensibility, or sentimentalism, which had been introduced in the previous century, had undergone a ripening process, in consequence of which, though now less intense than it had previously been, it was more likely to influence unreflecting people than it had ever been. All three of the ether-claimants had probably been influenced by the desire for gain; but nevertheless they were certainly not insensible to the agapic influences.

317. I doubt if any of the great discoveries ought, properly, to be considered as altogether individual achievements; and I think many will share this doubt. Yet, if not, what an argument for the continuity of mind, and for agapasticism is here! I do not wish to be very strenuous. If thinkers will only be persuaded to lay aside their prejudices and apply themselves to studying the evidences of this doctrine, I shall be fully content to await the final decision.

Chapter 12: Notes on Metaphysics

§1. Relations and Relationships †1

318. I have, since 1870, written much about the logic of relations. In those writings, I have usually restricted the terms "relations" and "relationships" to existential relations and relationships. By a relationship I understand the conception of a fact about a set of things abstracted from the representation of the things themselves or, in other words, a predicate which requires more than one subject to complete a proposition, or conception of a fact. A "relation" only differs from a "relationship" in that one of the subjects is regarded as being taken account of first, and is usually called the subject nominative, while the others are called the direct and indirect objects. †2 In other words a relation is a predicate requiring one subject nominative and one or more objects in a definite sequence. In my earlier papers [in Volume 3] I use the conception of relation chiefly; in my later ones that of relationship. The difference is little more than trifling. An existential relation or relationship is distinguished from others by two marks. †3 In the first place, its different subjects all belong to one universe; which distinguishes it very strikingly from such relations as that which subsists between a thing and its qualities, and that which subsists between portions of matter and the form into which they are built; as for example between the cells of a living body and the whole body, and often times between the different singulars of a plural and the plural itself. In the second place, an existential relation or relationship differs from some other relations and relationships in a respect which may be described in two ways, according as we employ collective or distributive forms of expression and thought. Speaking collectively, the one logical universe, to which all the correlates of an existential relationship belong, is ultimately composed of units, or subjects, none of which is in any sense separable into parts that are members of the same universe. For example, no relation between different lapses of time — say, between the age of Agamemnon and that of Homer — can be an existential relation, if we conceive every lapse of time to be made up of lapses of time, so that there are no indivisible units of time. To state the same thing distributively, every correlate of an existential relation is a single object which may be indefinite, or may be distributed; †1 that is, may be chosen from a class by the interpreter of the assertion of which the relation or relationship is the predicate, or may be designated by a proper name, but in itself, though in some guise or under some mask, it can always be perceived, yet never can it be unmistakably identified by any sign whatever, without collateral observation. Far less can it be defined. It is existent, in that its being does not consist in any qualities, but in its effects — in its actually acting and being acted on, so long as this action and suffering endures. Those who experience its effects perceive and know it in that action; and just that constitutes its very being. It is not in perceiving its qualities that they know it, but in hefting its insistency then and there, which Duns called its haecceitas — or, if he didn't, it was this that he was groping after. However, let me not lapse further into metaphysics just now.

319. My reasons for mostly limiting the scope of my logical studies of relations to the existential class were, firstly, that these are very tangible and are logically tractable; secondly that the great body of other sorts of relations differ from these merely in being indeterminate in some respects in which existential relations or some species of these are determinate, so that the logical theory of these virtually puts the student into possession of the logical theory of all but a very few recondite relations; thirdly, that when one takes up a virgin subject with a view to clearing the ground and erecting upon it a scientific structure, it is necessary to begin with some part of the work; and fourthly and finally, that to my perhaps dull apprehension it seemed that no sane mind could, after mature deliberation, make choice of another part of the whole task to begin with than that which I chose. I may add that it does not convince me that that seeming was illusory, that those who think it was so, instead of pointing out some better way of treating the problem, have been led to despair of the possibility of erecting any logic of relations at all. But while they have been occupying themselves with these doleful prognostications, I have taken hold of the work of erection itself and have brought it to a promising stage of advance. But just as there are many fogies nowadays — old and young — who with idle conservatism dispute the value of my work, so, unless the whole congregation of logicians experiences a regeneration, I expect the day will come when another generation of old and young fogies will be equally indisposed to admit that there is any corner of the whole field that I have not turned up, and put into the right condition. Yet I have faithfully tried to do my share in putting an end to all such unscientific attitudes among logicians, and am confident that the new blood that has been brought into our house is going to insure its modicum of scientific health to the logical stock of the next generation.

320. The intellectual life of thought resides in its forms — its patterns. Now there is one pattern which must always be supreme in thought, because it is essentially the pattern of reasoning itself. It ought to be called the Aristotelian pattern, because it was first formally emphasized in Aristotle's definition of universal predication — the dictum de omni, or "universal predication." †1 That definition runs thus: "We say that a term, P, is predicated universally, when there is nothing of which its subject is predicated of which the term P is not likewise predicated." †2 . . . The negative of an Aristotelian relationship is of a different pattern; and since Reasoning is essentially critical, it is almost as important to consider what does not follow as what does follow, consequently, the pattern of the negative of an Aristotelian — or of a neg-Aristotelian, as we may call it — has an importance second only to that of the Aristotelian pattern. This neg-Aristotelian pattern will be sufficiently illustrated in a single example: "A, even though he does not love B, may love something unloved by B." †1 Of special importance is such a combination of the Aristotelian and neg-Aristotelian patterns as not to produce a self-contradiction. Such is: "A loves whatever B may love and something besides." †2 This is the pattern of any transitive difference; that is, of any transitive relation in which nothing can stand to itself. It may be called the alio-transitive pattern. . . . The alio-transitive pattern may also be called the linear-pattern; since among points lying upon a line, if one, A, is further advanced — say, for example, further along the line from one end of it — than another, B, it will be further advanced than any point than which B may be further advanced, and is also further advanced than some (perhaps unactualized, i.e. unmarked) point than which B is not further advanced. This pattern is the logically simplest of any that is at once needful and sufficient as a basis for exact reasoning, and consequently is involved in all exact reasoning. This statement, faulty as it is in being vague, and inevident, is nevertheless a correct statement of the reason of the supreme importance of number.

321. That reasoning is of a triadic constitution has generally been perceived since Aristotle, though not generally quite definitely and accurately. In some external particulars this character has even been exaggerated by Kant and his school, who not only defines reasoning as "judgment by means of a mediate attribute," thus introducing the triadic character correctly enough, but also goes so far as to insist that a [Vernunft] Schluss must have two premisses; †3 giving a different title to what usually goes by the name of "immediate inference"; which is a purely verbal distinction. But even an immediate inference — if it really be an inference, and not a mere rewording, like, "No man is mortal," therefore "No mortal is man" †4 — involves a triadic relation. Take, for example, the inference from, "A certain woman is adored by all catholic men," and therefore, "Every catholic man adores some woman or other." †5 In order to show the structure of this reasoning, it should be stated in some such fashion as this: "I could name such a woman that you could not find a catholic man that did not adore her," and therefore, "Specify what catholic man you will and I can mention some woman whom he adores." This turns on a relation between, first, what you can designate, secondly, what I can designate, and thirdly, the result. If you choose to say that there are more than three correlates, that is a matter of indifference; for every relationship of more than three correlates is equivalent to a logical composite of two or more triadic relationships; but a triadic relationship cannot be built up from dyadic relationships. †1 Whoever thinks it can be so composed has overlooked the fact that composition is itself a triadic relationship, between the two (or more) components and the composite whole.

322. For forty years, that is, since the beginning of the year 1867, I have been constantly on the alert to find a genuine triadic relation — that is, one that does not consist in a mere collocation of dyadic relations, or the negative of such, etc. (I prefer not to attempt a perfectly definite definition) — which is not either an intellectual relation or a relation concerned with the less comprehensible phenomena of life. I have not met with one which could not reasonably be supposed to belong to one or other of these two classes. As a case as nearly brute and inorganic as any, I may mention the form of relationship involved in any screw-form which is definitely of the right-hand, or occidental, mode, or is definitely of the Japanese, or left-handed, mode. Such a relation exists in every carbon-atom whose four valencies are saturated by combination with four atoms of as many different kinds. But where the action of chance determines whether the screw be a right-handed or a left-handed one, the two forms will, in the long run, be produced in equal proportions, and the general result will not be definitely, or decisively, of either kind. We know no case of a definitely right-handed or left-handed screw-phenomenon, where the decision is not certainly due to the intervention of a definitely one-sided screw in the conditions of that decision, except in cases where the choice of a living being determines it; as when Pasteur picked out under the microscope the two kinds of crystals of a tartrate, and shoved those of one kind to the right and those of the other kind to the left. †1 We do not know the mechanism of such choice, and cannot say whether it be determined by an antecedent separation of left-handed screws from right-handed screws or not. No doubt, all that chance is competent to destroy, it may, once in a long, long time, produce; but it is a question whether absolute chance — pure tychism — ought not to be regarded as a product of freedom, and therefore of life, not necessarily physiological. It could not be caused, apparently, by the inorganic action of dynamical law. For the only way in which the laws of dynamics involve triadic relations is by their reference to second differentials of positions. †2 But though a second differential generally involves a triadic relation, yet owing to the law of the conservation of energy, which has been sufficiently proved for purely inorganic phenomena, the dynamic laws for such phenomena are expressible in terms of first differentials. It is, therefore, a non-genuine, or, as I phrase it, a "degenerate" form of triadic relationship †3 which is involved in such case. In short, the problem of how genuine triadic relationships first arose in the world is a better, because more definite, formulation of the problem of how life first came about; and no explanation has ever been offered except that of pure chance, which we must suspect to be no explanation, owing to the suspicion that pure chance may itself be a vital phenomenon. In that case, life in the physiological sense would be due to life in the metaphysical sense. Of course, the fact that a given individual has been persuaded of the truth of a proposition is the very slenderest possible argument for its truth; nevertheless, the fact that I, a person of the strongest possible physicistic prejudices, should, as the result of forty years of questionings, have been brought to the deep conviction that there is some essentially and irreducibly other element in the universe than pure dynamism may have sufficient interest to excuse my devoting a single sentence to its expression. For you may be sure that I had reasons that withstood severe, not to say hostile criticism; and if I live to do it, I shall embody them in a volume. †4

323. A tetradic, pentadic, etc. relationship is of no higher nature than a triadic relationship; in the sense that it consists of triadic relationships and is constituted of them. But a triadic relationship is of an essentially higher nature than a dyadic relationship, in the sense that while it involves three dyadic relationships, it is not constituted by them. If A gives B to C, he, A, acts upon B, and acts upon C; and B acts upon C. Perhaps, for example, he lays down B, whereupon C takes B up, and is benefited by A. But these three acts might take place without that essentially intellectual operation of transferring the legal right of possession, which axiomatically cannot be brought about by any pure dyadic relationships whatsoever. Just as much, but no more, is a dyadic relation — or the sort of fact expressed by a two-subject predicate — of a higher nature than any fact expressed by a one-subject predicate, such as "is blue." For the two-subject fact involves two one-subject facts, but is not constituted by them. If A acts upon B in any way, something analogous to a strain, or stress, takes place within A, and something of the same sort in B; but these two happenings might take place irrespectively of one another, without any action of A on B. In that sense the action is a higher sort of fact than the one-subject stress. A man cannot conceive of a one-subject fact otherwise than as more or less vaguely analogous to a feeling of his own. He cannot conceive of a two-subject fact otherwise than as analogous to an action of his own. A three-subject fact is comprehensible and is analogous to an utterance, a speech, a thought.

324. It is astonishing how human minds seem naturally to pervert the interrelations of these three categories of facts. The triadic fact takes place in thought. I do not say in anybody's thinking, but in pure abstract thought; while the dyadic fact is existential. With that comparison plainly before them, our minds perversely regard the dyadic fact as superior in reality to the "mere" relation of thought which is the triadic fact. We forget that thinking implies existential action, though it does not consist in that; or if we remember that thought implies the action of forces upon a brain or something like it, we still more perversely regard that as lowering the dignity of thought, and as making it a "mere" existential event; whereas the truth is just the opposite. In that thought requires existential acting, and further requires something else beside that, it ought to be plain enough that it exceeds the existential acting. The ruler of a nation depends upon his cook and his secretaries. That does not place him lower than they, but higher. Thought is higher than brute fact in much the same way that a statesman is higher than his secretaries: namely, it needs the existential facts, but regulates them. It is only imitation-thought to which the adjective "mere" is appropriate. . . .

§2. Mathematical and Real Time

325. If the pure mathematician speaks of "time," he by no means refers to the time of which we have experience, but to an arbitrarily imagined object whose characters are analogous to those of experiential time, so far as the characters of the latter are known. The mathematician's time is an arbitrarily supposed object in some respects analogous (this I insert to give a temporary support, or scaffolding, to the reader's conception) to the instantaneous condition of the water of some river whose water should be perfectly homogeneous and not composed of molecules, supposing however that we quite disregard the dimensions of depth and breadth of the river. But understand me: I mean this comparison with the river merely to afford a temporary support to your mind, Reader; a scaffolding that shall be convenient until the mathematical concept of Time has been erected in your field of thought; but being no part of that concept, it is afterward to be broken up and thrown away, unless its fragments should be serviceable in erecting some other concept. Analogies are never perfect, for an analogy that should be made perfect would be more than an analogy. The most important of the respects in which the ideal river differs from Time is that the former is the idea of a form that is imagined to exist, while the hypothesis of Time (for however closely it may agree with something in experience, which experience has indeed occasioned the hypothesis, nevertheless the mathematician's "time" is a purely arbitrary hypothesis, and makes no appeal to any evidences), the supposed "Time," far from being imagined to be anything existent, that is, anything that can react with the other existents, is imagined to be a mere possibleness — in forming which word I assume that "possible" is taken, not as relative to this or that condition, but as absolutely supposable in consistent thought. This point of contrast between the river and Time entrains consequences that it would be obviously fatal to sound thought to overlook. The chiefest of these, to my thinking, are the two I am going to mention. I will remark that although it is a Heraclitan river — is that river I am supposing to be supposed (i.e., one of those rivers that one can only cross once, because it is the water in its instantaneous place) — yet this does not prevent the recognition of its relation to other Heraclitan states of the same water; so that, notwithstanding that a quite instantaneous state composes this river, every drop has its temporal relation to the state of the water at another indefinitely near instant; so that while instantaneous, every part of it has a definite velocity. Now then, I might imagine that this flowing water comes into existence at a certain section of the stream, and is annihilated at another section, or I might, if I chose, imagine it to be sourceless and mouthless, an unlimited Heraclitan river. I might imagine that these creations and annihilations were many along the river. I might even imagine that the water never comes into complete existence, but [is] instantly annihilated at the very instant of its instantaneous creation, [so] that it consists of a series of lengthless cross sections; and so [that] the whole would have but an inchoate existence. All that is easily supposable in the case of the river, because the river is imagined to be existent, that is, to have a mode of being quite independent of any rationality, but consisting only in certain brute action. This gives room for supposing that a predicate is neither wholly true of it nor wholly false, nor has the limit between the true and the false parts at any definitely described cross sections. We can suppose those limits to be at some cross sections without saying what ones, nor even saying that it would be possible exactly to define them. But with mathematical Time all this is quite different, owing to its being a possibleness consisting in freedom from self-contradiction, without any supposed experience forcing ideas upon the mind from the external world.

326. If on a Monday an idea be possible, in the sense of involving no contradiction within itself regardless of all mere circumstances, then it will be possible on Tuesdays, on Wednesdays, and on Fridays; in short it will be possible forever and ever, unless the idea of the circumstance should come into definite rational contradiction to the idea in question. †1 Consequently, mathematical Time cannot have an arbitrary beginning nor end. For it is but a possibleness; and what is possible at all is possible without limit, unless there be some kind of a limit which comes into definite rational contradiction with the idea of Time. For the indefinite inhabits only the realm of experience, being, or having been, forced upon us brutally and without reason. That a certain idea may be existentially impossible may be a brute fact; but that it should be rationally impossible requires a definite reason. In like manner, if there be a "lapse," or determination of time, that is at once "after" one lapse B, and "before" another Y, then (but for a restriction which I shall insert before I reach the end of this statement) there must be any multitude you please of lapses that are at once "after" B and "before" Y; and since I long ago proved (Monist, Vol. 7, [3.548f]) that there is no maximum multitude of objects distinct from one another it will follow that in Time itself there is no such thing as an absolute instant, or absolutely definite before-and-afterness relatively to all other instants, and that an instant can only come about as the consequence of some brute existential fact related to time; but all this is subject to the following restriction: if it be true that some multitude — say, for example, the second abnumerable multitude, which is the multitude of all possible different collections of irrational quantities — is of such a nature that the idea of arranging the singulars of any plural of that multitude in a linear series would involve a self-contradiction, then the consequence falls to the ground, and it only remains that between B and Y there must be a plural of lapses whose multitude is the largest that is capable of linear arrangement. †P1 . . .

§3. Externality and Reality †1

327. What is meant by calling anything real? I can tell you in what sense I always use the word. According to my use of it, there is a certain resemblance between the Real and the External which renders the discrimination of each from the other important for right reason. Any object whose attributes, i.e. all that may truly be predicated, or asserted, of it, will, and always would, remain exactly what they are, unchanged, though you or I or any man or men should think or should have thought as variously as you please, I term external, in contradistinction to mental. For example, a dream is mental, because it depends upon what passed in the thoughts of the dreamer whether it be true that the dream was of a dog or was of the Round Table of King Arthur or of anything else. On the other hand, the colors of objects of human experience and in particular the contrast between the color of the petals of a Jaqueminot rose and that of the leaves of the bush, although it is relative to the sense of sight, is not mental, in my sense of that word. It is true that all colors are relative to the sense of sight. Yet there is a difference between a color and a sensation of color. For a color is a quality of a thing which remains the same whether it be exposed to one kind of illumination or to another, and whether it be seen by a normal or by a color-blind eye. Such is the established signification of the word "color." For we do not say that the petals and leaves of a rose-bush have the same color when they are viewed by color-blind people: on the contrary, we say that such people cannot distinguish those colors. Color is also something essentially vague; for the color of an object is the admixture of lights necessary to producing the same chromatic effect (1) upon a normal eye, in the absence of any perturbing cause, and (2) under a moderate white illumination. Now even normal eyes receive quite different chromatic sensations from the same objects; and two white illuminations may be quite indistinguishable and yet may be produced by two lights of such different compositions that it is possible to find two colored objects such that the one will to all normal eyes plainly appear to be of the warmer color under one of the two white illuminations, while the other object will as obviously appear to be of the warmer color under the other illumination; though the two illuminations are absolutely indistinguishable when viewed directly without being reflected. I once got up an apparatus to exhibit this, and showed the striking phenomenon to all visitors for months. Few persons are aware how very striking such phenomena can be made. Color, therefore, is a quite remarkably vague quality, as well as being relative to the normal sense of sight. If by "normal" were meant merely the average (or any other kind of mean) of actually occurring instances, say the average sensation of all the inhabitants of the globe on a certain date, then this might have been modified by some disease affecting a large part of the people who happened to be living at the time; and since "color" refers to normal chromatic sense, it would depend upon what passed in the minds of a certain body of men. But, in fact, the "normal" is not the average (or any other kind of mean) of what actually occurs, but of what would, in the long run, occur under certain circumstances. Now what would be, can, it is true, only be learned through observation of what happens to be; but nevertheless no collection of happenings can constitute one trillionth of one per cent of what might be, and would be under supposable conditions; and therefore, though it might conceivably prevent many generations from rightly determining what is normal, it could not affect the true — and ultimately ascertainable (provided there were anybody to ascertain it) — mean and normal; and thus, the result is that no such accident could affect the normal or the true color. So, in general, what I mean by the external might vary with how persons of a given general description would think under supposable circumstances; but it will not vary with how any finite body of individuals have thought, do now think, or will actually think.

328. So much for what I mean by the external. The main difference between the external, as I use the term, and the real, as I employ that term, seems to be that the question whether anything is external or not is the question of what a word or other symbol or concept (for thinking proper is always conducted in general signs of some sort) is, I say, a question of what a symbol signifies; while the question of whether anything is real or is a figment is the question what a word or other symbol or concept denotes. If the attributes of or possible true assertions about an object could vary according to the way in which you or I or any man or actual body of single men, living at any time or times, might think about that object, then that object is what I call a figment. But if even although its attributes, or what is true of it, should possibly vary according to what some man or men might think, yet if no attribute could vary between being true and being false, according to what any plural of single men could think about that thing, then, and though it were accordingly not external but mental, it would nevertheless be real, since precisely that is what I mean by calling an object real. . . . If two contradictory assertions about the same definite subject be true that subject cannot be real, is the principle of the reductio ad absurdum. If a subject of two assertions conflicting in form be indefinite (as, for example, "One might have one's pocket picked of real property" and "One cannot have one's pocket picked of real property") those assertions are not, properly speaking, contradictory, nor are they usually called so. They are, in logical parlance, subcontrary. (In the example, one assertion means "One can have one's pocket picked of real property in some sense," and "One cannot have one's pocket picked of real property in some sense.") That is, they are related like "Some S is P" and "Some S is not P." Such, then, is the sense to which I restrict the word "real"; and I believe that my definition comes as near to expressing the principal sense of our vernacular word in the mouths of the clearest-headed talkers as any definition could. Except in the legal sense, the vernacular word was derived from realis, which (except in the legal sense) was a vocable invented by medieval metaphysicians for their own purposes. Especially, it is a prominent word in the works of Duns Scotus, of which I have been an attentive and meditative student. Now Duns, generally believed to be the birthplace of this great thinker (and I have scarce a doubt of it), is less than ten statute miles north of the Tweed in Berwick, so that in the last quarter of the thirteenth century the logician was doubtless as almost genuinely an English boy as he would be if born there today. A northern dialect of Middle English was his mother tongue. No medieval logician influenced the present English of the market-place so much as he did; and my definition is thoroughly imbued with the spirit of Scotism. These considerations confirm my confidence that my definition not only, as that of a term of philosophy, best conforms to sound canons of terminology, †1 but that it expresses, as nearly as any definition could, the principal sense of the vernacular word, which, if this be true, is a supererogatory virtue. . . .

§4. Dyadic and Triadic Action

329. There has been during the nineteenth century a decided leaning of scientific opinion to discredit any other sort of action in the external world than that of dynamical force; to understand a dynamical force to be a purely brute force with no element of inherent reasonableness in it, but merely to be the only force that scientific research could discover. Especially, at a date about a generation after the enunciation of the doctrine of the conservation of energy (or "of forces," as the phrase was, until the conception of energy became widespread), and half a generation after the setting forth of the theory of natural selection, this current of opinion was mighty strong, wide, and deep in the scientific world. It has since sensibly abated. It certainly cannot be said that this conviction is, or was, quite without any sound reason to back it; for there were two such. The principal argument runs as follows: Scientific research has hitherto made plainly apparent no other cause of changes in the physical universe than brute force; and therefore it is presumable that there is no other. This is a sort of induction resting upon the principle that whatever error it may lead us into the very same argument will in time correct, if it be persisted in long enough. We still occasionally are obliged to take refuge in this argument; and doubtless always shall be so obliged; but it is the very weakest of all those forms of argumentation that have any validity at all. †1 It is good for nothing against the least sound objection; and in this case there is the conclusive objection that exact logical analysis shows dynamic causation (if every element of it be considered) is more than the mere brute force, the dyadic action, that it appears to superficial thinkers to be. For it is governed by law; and to him who bends his ear to that law it articulately testifies, though in a whisper, to the existential might of reasonableness. The secondary argument is therefore in truth somewhat the stronger of the two. It is that in all recent debate the contentions of the champions of spiritual force in Nature are pretty constantly marked with sophistries, exaggerations, unfairness, fogeyism, velleities of persecution; phenomena each of which is an infallible mark of a faith which is rotting in the breasts of its most insistent defenders. Except that "pretty constantly" is perhaps an exaggeration, this is entirely true. But it is no argument whatever against the reality of reasonableness: it only illustrates how the materialistic view recommends itself the more to those minds who are the further from sharing the spirit of science.

330. Any dynamic action — say, the attraction by one particle of another — is in itself dyadic. It is governed by a law; but that law no more furnishes a correlate to the relation than the vote of a legislator which insures a bill's becoming a statute makes him a participator in the blow of the swordsman who, in obedience to the warrant issued after conviction according to that statute, strikes off the head of a condemned man. In the law, per se, there is no physical force nor other compulsion. It is nothing but a formula, a maxim. The particles follow the law simply because, being sprung from the stock of reason, they naturally incline to obey reason. It is true that the attraction of one particle for another acts through continuous Time and Space, both of which are of triadic constitution. Yes; but this continuous Time and Space merely serve to weld together (while imparting form to the welded whole) instantaneous impulses in which there is neither continuous Time, Space, nor any third correlate; and it is such instantaneous impulse that I say is dyadic. However, the dyadic action is not the whole action; and the whole action is, in a way, triadic.

331. †1 Every triadic relationship involves three dyadic relationships and three monadic characters; just as every dyadic action involves two monadic characters. A monadic character involves nothing dyadic or triadic; nor does a dyadic action involve anything triadic. But a triad always involves three dyads and three monads; and a dyad involves two monads.

332. That whatever action is brute, unintelligent, and unconcerned with the result of it is purely dyadic is either demonstrable or is too evident to be demonstrable. But in case that dyadic action is merely a member of a triadic action, then so far from its furnishing the least shade of presumption that all the action in the physical universe is dyadic, on the contrary, the entire and triadic action justifies a guess that there may be other and more marked examples in the universe of the triadic pattern. No sooner is the guess made than instances swarm upon us amply verifying it, and refuting the agnostic position; while others present new problems for our study. With the refutation of agnosticism, the agnostic is shown to be a superficial neophyte in philosophy, entitled at most to an occasional audience on special points, yet infinitely more respectable than those who seek to bolster up what is really true by sophistical arguments — the traitors to truth that they are. . . .

§5. Essence and Existence

333. There are two grades or constituents of Being: the Essence, and the Existence. Each of these terms has an epistemological and metaphysical force. I consider Existence first, and to begin with, in its epistemological aspect. When a new image, optical, acoustical, or other, appears in the mind, one subjects it to various tests in order to ascertain whether it be of internal or of external provenance. These tests may be distributed into three classes, according to their strength when they testify to externality of origin (which I call being "affirmative") and according to their strength when they testify to internality of origin (which I call being "negative").

334. The following scheme shows the classes:

TESTS OF EXTERNALITY

Class I. Affirmatively, the strongest; negatively, the weakest.

Tests by physical concomitants; as by photography, phonography, seismography, chemical test-papers; and a great variety of other physical apparatus and observations.

Class II. Affirmatively and negatively of middling value.

Tests by the testified experience of other observers, or even of oneself at another time, placed in nearly the same circumstances.

Class III. Affirmatively, the weakest; negatively, the strongest.

Criticism of all the circumstances of the apparition, ending with the readiest and, in case its evidence should be negative, the most conclusive of all single tests, namely, that of making a direct inward effort to suppress the apparition.

335. The word "insistency," which I have used, wrongly conveys the suggestion of a more or less. But the above tests, critically applied, avail to separate apparitions into two discrete classes, with none of an intermediate character: those which are due to the normal action of the senses, and those which are due to some derangements of the health of the person to whom the appearance comes. The former are really experienced, the latter are deceptive hallucinations or illusions. All to which the senses normally testify without room for critical reasoning is usually and properly said to be "experienced"; and all that is truly experienced is, in the epistemological sense, existent. But experience only informs us that single objects exist, and that each of these at each single date exists only in a single place. These, no doubt, are what Aristotle meant by {to kath' hekaston} †1 and by {ai prötai ousiai} †2 in his earlier works, particularly the Predicaments. For {ousia} there plainly means existent, and {to ti einai} is existence. (I cannot satisfy myself that this was his meaning in his later writings; nor do I think it possible that Aristotle was such a dolt as never to modify his metaphysical opinions.) But {to atomon} †1 was, I think, the strict logical individual, determinate in every respect. †P1

336. In the metaphysical sense, existence is that mode of being which consists in the resultant genuine dyadic relation of a strict individual with all the other such individuals of the same universe. . . .

337. Coming to Essence, this in its epistemological force is that intelligible character which truly defines what a general or indefinite, that is, what an indeterminate monadic predicate primarily asserts, so that all else that it asserts is the necessary consequence of this epistemological essence. It is easy to state what the essences of artificial objects are: The essence of a stove is that it is intended to diffuse warmth. But as to the essence of natural objects, if they have any, we are unable as yet to give them. We are only able to state the essence of our common names for such things. The metaphysical essence is the intelligible element of the possibility of its Being, or so much of that as is not a mere consequence of the rest. . . .

§6. Modes of Being

338. All thinking is dialogic in form. Your self of one instant appeals to your deeper self for his assent. Consequently, all thinking is conducted in signs that are mainly of the same general structure as words; those which are not so, being of the nature of those signs of which we have need now and then in our converse with one another to eke out the defects of words, or symbols. †2 These non-symbolic thought-signs are of two classes: first, pictures or diagrams or other images (I call them Icons †2) such as have to be used to explain the significations of words; and secondly, signs more or less analogous to symptoms (I call them Indices †2) of which the collateral observations, by which we know what a man is talking about, are examples. The Icons chiefly illustrate the significations of predicate-thoughts, the Indices the denotations of subject-thoughts. The substance of thoughts consists of these three species of ingredients.

339. The next step consists in considering why it is that thoughts should take those three different forms. You will observe that each kind of sign serves to bring before the mind objects of a different kind from those revealed by the other species of signs. The key to the solution of this question is that what we think of cannot possibly be of a different nature from thought itself. For the thought thinking and the immediate thought-object are the very same thing regarded from different points of view. Therefore, Berkeley †1 was, so far, entirely in the right; although he blundered when from that manifest truth he inferred his idealism — and it was a blunder for just the reason pointed out by Kant in the second edition of the Kritik der Reinen Vernunft. †2 We must conclude, then, that the reason why different things have to be differently thought of is that their modes of metaphysical being are different.

340. Aristotle, however, failed to strike the nail squarely on the head when he said that generals are known by reason and singulars by sense. †3 Generals are predicates. Now while the structure, not only of predicates, but of all kinds of thought, is known by reason, that is, by symbols, like words, the matter of predicates, simple predicates, is not known by reason, but by the senses and by other feelings. A subject of every judgment — and it is the subject par excellence — is a singular; †4 and every singular, as Aristotle †5 himself says, is a subject. But to say that a singular is known by sense is a confusion of thought. It is not known by the feeling-element of sense, but by the compulsion, the insistency, that characterizes experience. For the singular subject is real; and reality is insistency. That is what we mean by "reality." It is the brute irrational insistency that forces us to acknowledge the reality of what we experience, that gives us our conviction of any singular.

341. The mode of being of the composition of thought, which is always of the nature of the attribution of a predicate to a subject, is the living intelligence which is the creator of all intelligible reality, as well as of the knowledge of such reality. It is the entelechy, or perfection of being.

342. So, then, there are these three modes of being: first, the being of a feeling, in itself, unattached to any subject, which is merely an atmospheric possibility, a possibility floating in vacuo, not rational yet capable of rationalization; secondly, there is the being that consists in arbitrary brute action upon other things, not only irrational but anti-rational, since to rationalize it would be to destroy its being; and thirdly, there is living intelligence from which all reality and all power are derived; which is rational necessity and necessitation.

343. A feeling is what it is, positively, regardless of anything else. Its being is in it alone, and it is a mere potentiality. A brute force, as, for example, an existent particle, on the other hand, is nothing for itself; whatever it is, it is for what it is attracting and what it is repelling: its being is actual, consists in action, is dyadic. That is what I call existence. A reason has its being in bringing other things into connexion with each other; its essence is to compose: it is triadic, and it alone has a real power.

344. Signs, the only things with which a human being can, without derogation, consent to have any transaction, being a sign himself, †1 are triadic; since a sign denotes a subject, and signifies a form of fact, which latter it brings into connexion with the former. †2 "But what," some listener, not you, dear Reader, may say, "are we not to occupy ourselves at all with earthquakes, droughts, and pestilence?" To which I reply, if those earthquakes, droughts, and pestilences are subject to laws, those laws being of the nature of signs, then, no doubt being signs of those laws they are thereby made worthy of human attention; but if they be mere arbitrary brute interruptions of our course of life, let us wrap our cloaks about us, and endure them as we may; for they cannot injure us, though they may strike us down. "But," some other peerer over the fence may continue — yet no! I will pursue the argument no further; for such cobwebs will not hold them prisoners, once they really desire the liberty of truth.

345. The division of modes of Being needs, for our purposes, to be carried a little further. A feeling so long as it remains a mere feeling is absolutely simple. For if it had parts, those parts would be something different from the whole, in the presence of which the being of the whole would consist. Consequently, the being of the feeling would consist of something beside itself, and in a relation. Thus it would violate the definition of feeling as that mode of consciousness whose being lies wholly in itself and not in any relation to anything else. In short, a pure feeling can be nothing but the total unanalyzed impression of the tout ensemble of consciousness. Such a mode of being may be called simple monadic Being.

346. Blind existential being may possibly not occur at all; since we know nothing with absolute certainty of existent things, and are especially in the dark as to their modes of being, and above all know extremely little about the ultimate parts of matter, beyond the fact that electricity, itself a most mysterious sort of existent, is an ingredient of them. In the book about God and religion upon which I have been at work for several years, and hope to write, one of the questions which will come up for fair consideration is whether either the monotheistic, absolute God or the polytheistic, finite God of the pseudo-pragmatists could know the nature of blind existence, as He must, if he had created it. It is an unexplored passage in the mammoth cave of metaphysics; and various questions concerning it suggest themselves. This much, however, seems clear about such existence; namely, that there ought to be two grades of it; a lower kind, approximating to the inner being of a simple quality, yet existential, instead of being merely potential, consisting in the action of the thing upon itself, a sort of embryonic self-consciousness; and a higher grade consisting in the action of a thing upon all the other things of the same universe, and measuring by its intensity its remoteness from each of them. A whole universe of such existents can only have the lower, or internal grade of existence.

347. Of triadic Being the multitude of forms is so terrific that I have usually shrunk from the task of enumerating them; and for the present purpose such an enumeration would be worse than superfluous: it would be a great inconvenience. In another paper, I intend to give the formal definition of a sign, which I have worked out by arduous and long labour. †1 I will omit the explanation of it here. Suffice it to say that a sign endeavours to represent, in part at least, an Object, which is therefore in a sense the cause, or determinant, of the sign even if the sign represents its object falsely. But to say that it represents its Object implies that it affects a mind, and so affects it as, in some respect, to determine in that mind something that is mediately due to the Object. That determination of which the immediate cause, or determinant, is the Sign, and of which the mediate cause is the Object may be termed the Interpretant. . . .

348. Modern thought has been extravagantly Ockhamistic, owing to the accidental circumstance that, at the revival of learning, the obscurantists, the fogeys, were adherents of Duns, of whom the politician Ockham was the typical opponent. But this had come about because, in those days of precise, if shallow, thinking, the Scotistic doctrine had emerged triumphant from all the scholastic disputations, of which the reformers of learning had but the dimmest idea. Get rid, thoughtful Reader, of the Ockhamistic prejudice of political partizenship that in thought, in being, and in development the indefinite is due to a degeneration from a primary state of perfect definiteness. The truth is rather on the side of the scholastic realists that the unsettled is the primal state, and that definiteness and determinateness, the two poles of settledness, are, in the large, approximations, developmentally, epistemologically, and metaphysically.

§7. Reality and Existence †2

349. C. S. P. In the first place, I call your attention to the fact that reality and existence are two different things.

VELIAN. How, then, would you define existence?

C. S. P. It will not be necessary to go into that question, which is one of great delicacy. It will be sufficient to point out certain respects in which reality and existence differ. Let us suppose two seeds to be exactly alike. I do not say that two seeds ever are so; but we are now merely considering the meanings of two words, and, therefore, we are free to imagine any state of things we can. We will suppose, then, that not merely to our senses, but to any conceivable senses, those seeds are precisely alike, except that they are in different places. But now we will suppose that I am really resolved to plant those two seeds in such different soil, and to treat them so differently, that they will grow into plants whose flowers will have different colors. They really will be different, whatever anybody may say or think. I have made certain dispositions, so that I myself could not now have it otherwise. Their future difference is then a reality, already. For the time has already passed at which anybody's dictum could make the fact otherwise. Yet I have not decided what the colors of the flowers of each are to be; for one of the two seeds will be taken at random, and placed in one soil and the other in another. Now, when it comes to the existence of those flowers, the colors will be absolutely what they will be. There can be no uncertainty or ambiguity about existence. The reality, however, of my determination of the colors is not altogether certain. Existence, then, is a special mode of reality, which, whatever other characteristics it possesses, has that of being absolutely determinate. Reality, in its turn, is a special mode of being, the characteristic of which is that things that are real are whatever they really are, independently of any assertion about them. If Man is the measure of things, as Protagoras said, then there is no complete reality; but being there certainly is, even then.

My dear Velian, some god suggests to me that, thousands of years after you and I have left this earth, a physicist by the name of Thomson †1 will prove that all matter consists of corpuscles. Now each of those corpuscles must, I suppose, have a center of mass, which is an absolute point. But no matter how infinite the multitude of those centers, they cannot in all time pass through every place. There must, then, remain places where no center has been or ever will be. Yet, for my part, I believe that the laws of motion, the law of gravitation, etc. are as real in those places as anywhere. I may be wrong; but we are considering only the meanings of words; and if my belief has any sense or meaning, although no matter ever exists in those places, those laws are real there. There are many other kinds of reality distinct from existence. But have I not said enough to show that the meanings of the three terms, being, reality, and existence, are distinguishable? VELIAN. More than enough.

§8. Truth, Being, and Nothing

350. C. S. P. Now let us consider the nature of truth. Before anything can be true or false, it is necessary, is it not, that something should be said, whether by writing, by speech, or in thought?

VELIAN. Undoubtedly.

C. S. P. And this must be said concerning something, some subject, must it not?

VELIAN. Yes.

C. S. P. And something definite must be said of that subject, some predicate, must it not?

VELIAN. Yes.

C. S. P. The subject must be designated by a word or other sign, must it not?

VELIAN. Yes.

C. S. P. And the predicate must be signified by some word or other sign, must it not?

VELIAN. Yes.

C. S. P. If it is said that the predicate-sign is [in-]applicable to something to which the subject-sign is applicable, that must be true or false, must it not?

VELIAN. Yes.

C. S. P. If this is false, then whatever there may be to which the subject-sign is applicable the predicate-sign is also applicable, is this not so?

VELIAN. Yes.

C. S. P. While if the former is true, the latter is false?

VELIAN. Yes.

C. S. P. Thus, if it is said that to whatever there may be to which the subject-sign is applicable the predicate-sign is also applicable, this must be either true or false.

VELIAN. Yes.

C. S. P. Now is there anything which is true or false which is not of one or other of those forms of assertion, or else of a form a mixture of those two?

VELIAN. What of the assertion "It rains"?

C. S. P. In order to be true or false, this assertion must refer to some time and place, and the circumstances under which the assertation was made must have indicated a time and place. That indicating circumstance, of which speaker and auditor had experience, was the subject-sign; and we may presume that the assertion was in meaning equivalent to these two: first, there is some time and place indicated by these circumstances to which the description "it rains" is applicable; and secondly, whatever time and place these circumstances indicate is an occasion to which the description "it rains" is applicable.

VELIAN. That will do; but what of the assertion "If I had upset my inkstand I should have spoiled my manuscript"?

C. S. P. The first clause suggests that a certain past occasion or series of past occasions have been otherwise indicated to which the meaning is limited, and it further calls to mind the proposition "I upset my inkstand"; and now it asserts positively one thing and virtually asserts another. The first is that whatever connected series of occurrences there may be among the series of occurrences alluded to, to which the description "I upset my inkstand" would be applicable, is a series of occurrences to which "I spoiled my Ms." is applicable. But the second virtual assertion modifies this by adding that whatever series of past occurrences there may be is a series to which the description "I did not upset my inkstand" is applicable.

351. VELIAN. Let your analysis of that which is true or false be granted, provisionally, what then?

C. S. P. Then it follows that that which can be true or false must be one or the other.

VELIAN. How so?

C. S. P. In order that my explanation may be fully understood, a little preface is desirable. Suppose that this is true: "Under some circumstances, every possible course of action will prove fatal." If that is true, then it is true that every possible course of action will prove fatal, is it not?

VELIAN. Only under some very peculiar circumstances.

C. S. P. Yes; but I wish my description of what is true or false, to apply to what is not only true or false generally, but also to what is true or false under conditions already assumed. Whatever may be the limitations previously imposed, that to which the truth or falsity is limited may be called the universe of discourse. †1 For example, at the mention of a certain name, every person initiated into the Eleusinian mysteries invariably experiences a feeling of awe. This is true. It is therefore true that every person initiated into the Eleusinian mysteries always experiences a sentiment of awe; not universally, but only under the limitations already understood before this is said.

VELIAN. That is clear.

C. S. P. Another point to be noticed is that given any sign whatever, which we may call P, we can always frame a sign which shall be applicable to every object of the universe of discourse to which P is inapplicable and which shall be inapplicable to every object to which P is applicable. If P is a word, this sign may be formed by simply prefixing not, {mé}; as man, not-man; righteous, not-righteous; I, not-I. The relation between P and not-P, therefore, is that that to which P and not-P both apply is not in the universe of discourse, and that to everything in the universe of discourse either P or not-P is applicable.

VELIAN. I do not know that that is true.

C. S. P. But you must allow me to define my own terms as I choose. I propose to define not-P as such a sign that it is applicable to everything in the universe of discourse unless P is applicable to it; while it shall be inapplicable to everything in the universe of discourse to which P is applicable. That is not a statement of fact, but simply of my use of the word "not." If you dispute it, you must show that I do not so use the word "not.". . . †2

Now, S and P being any two signs, I propose, in case there really is something in the universe of discourse to which both S and P are applicable, that is, something to which S is applicable but not-P inapplicable, to use the word true in such a sense that it is "true" that to something to which S is applicable P is applicable; and to use the phrase particularly true in such a sense that in this case P shall be said to be "particularly true" of S; while I propose to use the word false in such a sense that under the same circumstances it shall be "false" that to whatever there may be to which S is applicable [not-]P is applicable. But if there is not really any object of the universe of discourse to which S and P are both applicable, that is, if there is nothing to which S is applicable unless not-P be also applicable to it, then I propose to use the word false in such a sense that it shall be "false" that to something to which S is applicable P is applicable, and I propose to use the word true in such a sense that in that case it shall be "true" that to whatever there may be to which S is applicable, not-P is applicable; and I propose to use the phrase universally true in such a sense that not-P shall be said to be "universally true" of S. Furthermore, if A and B are two assertions, and if there is a third assertion C which is equivalent to asserting both A and B, then I say that the copulative assertion, C, is true in case both A is true and B is true, but is false in every other case, whether A is false or B is false; but if D is equivalent to asserting that C is false, then I say that the disjunctive assertion, D, is false in case both not-A and not-B are false, but is true in every other case whether not-A or not-B be true.

VELIAN. What next?

352. C. S. P. Now let us suppose that in the whole universe of discourse there is not really a single black tulip. In that case, according to the rules just laid down, green, blue, white, reality, non-existence, and anything else you please are universally true of black tulip, while not even being black or being a tulip is particularly true of black tulip. Everything is universally true of it, but universally nothing is false of it. Nothing is particularly true of it, but particularly everything is false of it. You assent?

VELIAN. Yes.

C. S. P. All this is so, because in the case supposed a black tulip is nothing. Therefore, instead of nothing being unutterable, and all that, as you say, universally it is real and non-real, utterable and unutterable, etc. But particularly it is none of these.

VELIAN. In that case, of Being everything should be universally false, and particularly true.

C. S. P. My dear Velian, leave rattles to babes, and jingles of words to Germans; for to an Italian and a Greek, reason is more becoming. Since of nothing, everything is true, it follows that of everything, being is true universally, but not at all that everything is universally true of being. †1 Moreover being is particularly true of everything of which anything is particularly true; but not of everything. But if you choose to extend the name being to everything which can be invented or suggested or cannot, you will have the notion of a non-notion, which is not even universally itself, and of which what you say may be feigned to be true. For the whole thing does not even rise to the level of a figment. It is a dream within a dream.

VELIAN. Why, Pure Being is the very foundation of all wisdom.

C. S. P. Say rather of that love which winds itself up in needless and senseless paradoxes. But to return to nothing. Good father Parmenides was quite right when he said "You will never get over this, that nothing is." Why should we wish to? Whatever is nothing is, of course. But when he adds the advice to keep your mind from the path of a certain inquiry, that is bad advice for a philosopher, no matter what the inquiry is.

VELIAN. But to say that nothing is, is a contradiction in terms!

C. S. P. Of course, why should it not be?

VELIAN. But [it] is absurd!

C. S. P. It is certainly absurd that nothing should be. Being nothing, it is not adequately described until it is shown to be absurd. But there is nothing absurd in saying so. In geometry we often prove the non-existence of something by showing that it would have contrary attributes. That proved, it follows that it is nothing, because nothing, and nothing alone, possesses contrary attributes. It is, therefore, an important truth, and not absurd, that nothing is absurd.

VELIAN. You astonish me.

C. S. P. You say that the name "nothing," {mé on}, is not applicable to anything that is. I grant you that, with pleasure. Particularly, everything is false of it. Moreover, you say, the word "something" refers exclusively to existing things. You are quite right there. It is the same thing, otherwise expressed. But when you conclude that the word "nothing" expresses nothing, you are entirely wrong. What a thing "expresses," {legei}, is whatever is universally true of it. Thus, to say that something is a man is to say that it is an animal and that it reasons. And it is still more absurd to say that he who uses the word "nothing" does not speak. It would be far truer to say that he who uses the word "being" does not speak; for to say that whatever may be a man is, may be said, exactly or approximately, to convey no information, true or false; so that it is all the same as if nothing were said.

VELIAN. As if nothing were said! So you confess that saying nothing is saying nothing.

C. S. P. My dear Velian, does your whole stock in trade consist of such bagatelles as that? Or are you really upon such an intellectual level as to think there is anything in such a confusion?

VELIAN. No; I admit that having nothing as what was uttered and having nothing as one's meaning may be different.

C. S. P. You do not draw the distinction accurately; but let it go. You proceeded to say that nothing which exists is in a relation to a thing that does not exist. Understood in a "particular" sense, that is true. For example, loving is a relation, and lovers of females are fewer than lovers of animals; because there are other animals besides females who are loved. Lovers of women are still fewer; and of lovers of pea-green women there are none, because whatever there may be which is a pea-green woman is nothing. But taking what you say in a "universal" sense, it is not true. Thus, there are many men each of whom loves all women; but those who love all females, including female mosquitoes, are much fewer, and when it comes to loving whatever pea-green woman there may be, this may be said of every object in the universe. For since there is no falsity in it, and every assertion not false is true, this is true. Again, you say number is the totality of things that exist. You can use number in that sense, if you like. Only in that sense, number is not a sign but a collection of things. In the sense in which number is an attribute, it is a sign, and, like other signs, it does not prove that a thing exists because this sign would be applicable to it if it did exist. But even if it did, that would not prevent number from being true of "nothing," since existence and everything else is true of nothing. Thus, your proof, that whatever be said of nothing is not true, utterly fails. Whatever is said universally of nothing is true: whatever is said particularly of nothing is false.

VELIAN. But let us take an object, say an inkstand. Take away from it its visibility, its impenetrability, and every character by which it could manifest itself to any sentient being with our senses or with any conceivable senses; so that the very gods could not perceive it or any effects of it. It would be reduced to nothing; and it would be false and not true that it was visible and impenetrable, and equally false that it was invisible or penetrable.

C. S. P. Yes; I grant that. But this is because you are making those assertions in the particular sense. In the very act of denying that these things are true in that sense, you are asserting them universally. To say that it is not true that there is an invisible nothing, and not true that there is a visible nothing, is just the same as to say that it is true that whatever there may be that is nothing is both visible and invisible.

VELIAN. But it is nonsense to say that it is false that the inkstand deprived of existence is invisible and at the same time that it is false to say that it is visible. For everything is either visible or invisible.

C. S. P. Everything is either visible or invisible, and every nothing there may be is both visible and invisible. The rule only applies to things of which it is true that they exist and false that they do not exist. There are even realities, if we admit the reality of generals (which is, at least, not to be refuted by mere definition), which are indeterminate in respect to the applicability of many signs. †1

§9. Matter and Form †1

353. The word matter (Lat. materia, which was used to translate the Gr. {hylé}) is often employed where the more appropriate Greek word would be {söma} corpus, body; or {to hypokeimenon}, subjectum, or even {hé hypostasis}, translated person in theology. Form (Lat. forma, used to translate the Gr. {morphé} and {eidos}, though the latter is more exactly represented by species) is often employed where {schéma} figure, or {typos}, shape, would be near equivalents. The Greek expressions {morphé, paradeigma, eidos, idea, to ti esti, to ti en einai} are pretty nearly synonymous.

354. The distinction of matter and form was first made, apparently, by Aristotle. It almost involves his metaphysical doctrine; and as long as his reign lasted it was dominant. Afterwards it was in disfavour; but Kant applied the terms, as he did many others drawn from the same source, to an analogous but widely different distinction. In many special phrases the Aristotelian and Kantian senses almost coalesce, in others they are quite disconnected. It will, therefore, be convenient to consider: (1) the Aristotelian distinction; (2) the Kantian distinction; and (3) special applications.

355. The Aristotelian distinction. Not only was the distinction originated by Aristotle, but one of the two conceptions, that of matter, is largely due to him. Indeed, it is perhaps true that the Greek word for matter in the sense of material, {hylé}, was never understood in that general sense before Aristotle came to Athens. For the first unquestionable cases of that meaning occur in certain dialogues of Plato, concerning which — though there are no dates that are not open to dispute — it seems to the present writer that it is as certain as any such fact in the history of Greek philosophy that the earliest of them was written about the time of Aristotle's arrival. It is true that, as Aristotle himself says, matter was the earliest philosophical conception. †2 For the first Ionian philosophers directed their thoughts to the question what the world was made of. But the extreme vagueness of the notion with them is shown by their calling it {he arché} the beginning, by the nonsense of the question, and by many more special symptoms. If the philosophical conception of matter distinguished the metaphysics of Aristotle that of Plato had been no less marked by its extraordinary development of the notion of form, to which the mixed morality and questioning spirit of Socrates had naturally led up; the morality, because the form is the complex of characters that a thing ought to have; the questioning, because it drew attention to the difference between those elements of truth which experience brutally forces upon us, and those of which reason persuades us, which latter make up the form. But Aristotle's distinction set form, as well as matter, in a new light.

356. It must not be forgotten that Aristotle was an Asclepiad, that is, that he belonged to a family which for generation after generation, from prehistoric times, had had their attention turned to vital phenomena; and he is almost as remarkable for his capacity as a naturalist as he is for his incapacity in physics and mathematics. He must have had prominently before his mind the fact that all eggs are very much alike, and all seeds are very much alike, while the animals that grow out of the one, the plants that grow out of the other, are as different as possible. Accordingly, his dunamis is germinal being, not amounting to existence; while his entelechy is the perfect thing that ought to grow out of that germ. Matter, which he associates with stuff, timber, metal, is that undifferentiated element of a thing which it must possess to have even germinal being. Since matter is, in itself, indeterminate, it is also in itself unknowable; but it is both determinable by form and knowable, even sensible, through form. The notion that the form can antecede matter is, to Aristotle, perfectly ridiculous. †1 It is the result of the development of matter. He looks upon the problem from the point of view of a naturalist. In particular, the soul is an outgrowth of the body. †2

357. The scholastics, who regarded Aristotle as all but infallible, yet to whom the ideas of a naturalist were utterly foreign, who were thoroughly theological in their notions, admitted that the soul was a form. But then they had great difficulty with those opinions of their master which depended upon his conceiving of matter as more primitive than form. Their notions of form were rather allied to those of Plato. The mode of being that, in some sense, anteceded individual existence, they would have held to be one in which there was form without matter, if awe of Aristotle had not caused them to modify the proposition in one way or another. A question, for example, which exercised them greatly was, how the form was restricted to individual existence? For Aristotle there could not be any such question, because he did not conceive of a form taking on individuality, but of an undifferentiated matter taking on, or rather developing, form, and individuality, perhaps, with it (412a, 7).

358. The Kantian distinction. Aristotle refuses to consider any proposition as science which is not universal. He does not go so far as to say that all knowledge involves synthesis, but he often approaches doing so. In particular, he holds that matter is something in itself beyond our knowledge, but the existence of which has to be assumed in order to synthetize the opposites that are involved in all change. He expressly defines that as the function of the conception of matter. †1 With Kant, the view that all knowledge involves synthesis — various acts of synthesis one over another — is vastly more developed; and he, too, employs the terms matter and form as called for by such synthesis. But it is curious that while with Aristotle it is matter that is the quasi-hypothesis imported into the facts that the mind may synthetize, with Kant, on the other hand, it is form which performs this function. The matter of cognition consists of those elements which are brutally and severally forced upon us by experience. By the form he means the rational or intelligible elements of cognition, which he wishes, as far as possible, to regard as independent contributions of the mind itself, which we have no right to suppose are duplicated by anything corresponding to them in the thing. For the Aristotelian, all pure matter is exactly alike, equally devoid of all predicates, while the forms make all the variety of the universe. For the Kantian, on the other hand, matter is the manifold, while the pure forms are the few different modes of unity. Nevertheless, the Kantians — indeed, Kant himself (see the Critic of the Pure Reason, 1st ed., 266) — argued that they were using the terms in their old and accepted sense. What enabled them to give some speciousness to their contention was the circumstance that during the full century and more of neglect of the Aristotelian doctrine that had intervened, certain secondary senses of the term matter, especially that of corporeal matter, and that of a species of corporeal matter, had become relatively prominent.

359. Special senses. Although there is only one first or primary matter, absolutely indeterminate, yet Aristotle often uses the term in a modified sense as that which is relatively indeterminate; so that the last or second matter is the same as the form. But these phrases are also used in quite other senses, which need not here be specially noticed. Matter being taken relatively, the same thing can have this or that as its matter in different respects; and so matter is distinguished into materia ex qua, in qua, and circa quam. Materia ex qua is the material; silver is the materia ex qua of a dime. Materia in qua is the subject in which the form inheres; materia circa quam is the object. Aquinas †1 illustrates the distinction by virtue, which is a form, and, as such, has no materia ex qua; but it has a subject in which it inheres and an object upon which it is exercised. Aquinas introduced the term signate matter. †2 Matter of composition, or proximate matter, is that of which a thing consists; matter of generation, or remote matter, that from which it is developed, as a seed or egg.

360. The varieties of form are so numerous that they may best be taken in alphabetical order.

Absolute form: form abstracted from matter.

Accidental form: an accident, or that the presence of which constitutes an accident; as music is the accidental form of the musician.

Advenient form: a form subsequent to the final form.

Apprehended form = apprehended species.

Artificial form: a form superinduced by art.

Assistant form: an agent aiding in the realization of a form, especially of that whose essential character is to move; as the angel who turns the heavens round once every twenty-four hours, or the captain of a ship.

Astral form. According to Gilbert (De Magnete), phenomena of electricity are produced by a material effluvium, while the action of a magnet takes place directly at a distance. Whatever it may be then which constitutes the magnetic field, not being matter, must be called form. Gilbert names it forma prima radicalis et astralis.

Common form: a form belonging to a species.

Completive form: used by Aquinas †1 in the sense of the last of the series of forms which gradually bring a thing to fully developed existence. By Aristotle called last form. †2

Composite form: the form of a collective whole, so far as it is different from its parts.

Corporeal form: a form of a corporeal nature. This is used by Aquinas, Summa Theologica, pars I. qu. lxv. art. 4. See Material form.

Disponent form: a form rendering matter apt to receive another, principal, form. Thus, dryness in wood disposes it to receive combustibility.

Elementary form: one of the four combinations of hot and cold with moist and dry which were supposed to characterize the four elements.

Exemplar form: an idea.

Final form: see Completive form.

General form: the form of a genus; as we should now say a generic form.

Immaterial form: a form which neither depends upon matter while it is being made nor after it is made; a term employed in the theological doctrine of creation.

Incorruptible form: a form not subject to corruption.

Individual form: in one of the theories of individuation, was a form which by existing in matter acquired the power of individuating another form.

Informant form: a form which is a part of the thing of which it is the form.

Inherent form: a form which can only exist in a state of inherence in matter.

Intellective form: the mind as form.

Intelligible form: see Sensible form.

Intermediate form: a form having a middle position between an elementary and a completive form.

Material form: a term of Scotus, who defines it as follows: "Formam materialem dico esse omnem illam, quae ex natura sua necessario inclinatur naturaliter, ut sit actus materiae, sive sit substantialis, sive accidentalis." (Op. Oxon., IV, i, 1); "Ideo dici potest tertio modo." But elsewhere (ibid., I Post. qu. ii.) he distinguishes two senses of the term: "Forma materialis potest intelligi dupliciter. Uno modo dicitur, quae educitur de potentia materiae, vel quia utitur organo corporeo in operando: et isto modo forma intellectiva non est forma materialis. Alio modo dicitur forma materialis, quia perfectio materiae, et isto modo anima intellectiva est forma materialis, ideo aliquam variationem potest accipere a materia, quam perficit, quia ex materia et forma fit vere unum." Perhaps the most accessible book from which to gain a hint of the nature of the difficulty which gives rise to this distinction is Bridges' edition of what is called The Opus Majus of Roger Bacon, vol. II, pp. 507-511, cap. ii.

Mathematical form: an object of mathematical contemplation, and the result of mathematical abstraction.

Metaphysical form: form in the philosophical sense.

Native or natural form, forma in natura exsistens, forma naturae, form of a nature, is a term going back to John of Salisbury (Opera, ed. Giles, v. 92), and closely connected, if not synonymous, with material form. Certain questions started by Aristotle †1 in Book V of the Metaphysics (of which there is an admirable periphrastic translation by Grote, Aristotle, 2d ed., pp. 619 ff.) gave rise to discussions in which the doctrine was compared with Christian beliefs; and the natural form plays a considerable part in such discussions.

Bacon †2 adopted the term forma naturae. He did not grossly depart from the received meaning of the term but, owing to his occupying himself with inquiries quite antipodal to those of the scholastics, the two parties did not understand one another. Bacon means the physical explanation of a phenomenon, its occult modus operandi. Among the followers of Bacon we, at first, hear a great deal about forms. Boyle wrote whole books about them. But the distinction of matter and form was not calculated to further such inquiries as theirs. It is adapted to expressing phenomena of life. It might be twisted to such a purpose as Gilbert put it to (see Astral form), but it was not suited to the mechanical philosophy of Boyle, and only led to wordy and fruitless discussions.

Participate form: a form considered as it is united with matter.

Preparatory form: a term used by Boyle where disponent form would be more technical. He says, "The preparatory form is but (if I may so speak) a harbinger that disposes the matter to receive a more perfect form, which, if it be not to be succeeded by any other more noble, is entitled the specific form of that body; as in the embryo, the vegetative and the sensitive soul is but preparatory to the rational, which alone is said to be the specific form of man" (Free Considerations about Subordinate Forms).

Physical form: such forms as may form the object of physical inquiries. Of course, the term was very differently understood during scholastic times and in the 17th century. But the above definition covers both uses.

Primary form. There is no such well-recognized term of metaphysics; but a remark of William Gilbert leads us to suppose that medical men attached some meaning to it.

Principal form is that which per se constitutes a species. Called also specific form.

Radical form: see Astral form.

Sensible form. Though it chances that Aristotle nowhere distinguishes {morphé} into {aisphété} and {noété}, yet his followers did. Sensible forms are those which the outward senses distinguish; intelligible are those which the intellect alone can distinguish.

Significate form: a Thomistic term, a form distinguished by a name.

Simple form: form without matter. "Forma simplex, quae est purus actus, est solus deus," says St. Thomas. †1

Specific form: see Principal form.

Subsistent form: a form capable of existing separate from matter, as Aquinas †1 holds that the angels and departed spirits are.

361. Substantial form: a form which constitutes a nature, i.e. a species or genus. Thus, the accidental form of a musician is music; but his substantial form is the rational soul which makes him a man. When men's thoughts became turned from theology to the investigation of physics, those who were animated by the new spirit found themselves confronted with objections based upon allegations of substantial forms. That these substantial forms, so used, were merely a hindrance to the progress of science, was quite plain to them. But the objections were urged with a logical accuracy, born of centuries of study, with which the new men were utterly incapable of coping. Their proper course would have been quietly to pursue their own inquiries, and leave the theologians to square their results with philosophy as best they could. But circumstances did not permit this. The theologians had the popular intelligence and the arm of power on their side; and, when an apparent opposition arose, they naturally exerted themselves to put it down. Thus, the innovators were led to protest against these senseless and harmful substantial forms; and they had to formulate their objections to them — a business for which they were entirely unfitted. But since the discoveries of the physicists were plainly adding to man's knowledge and power, while their antagonists were simply obstructive, the former soon carried the day in the general opinion of mankind. The history proves that there was something vicious about the theological application of substantial forms; but it in no degree goes to show that the physicists accurately defined the objection to that application. In reviewing the arguments at the present day, when the position of the mechanical philosophers is becoming almost as obsolete as that of the scholastic doctors, we first note that when the new men denied that the substantial forms were "entities," what they really had in mind was that those forms had not such a mode of being as would confer upon them the power dynamical to react upon things. The Scotists, for it was they upon whom, as being in possession of the universities, the brunt of the battle fell, had in fact never called the substantial forms "entities," a word sounding like a Scotistic term, but in fact the mere caricature of such a term. But had they used the word, nothing more innocent than the only meaning it could bear for them could be imagined. To call a form an "entity" could hardly mean more than to call it an abstraction. If the distinction of matter and form could have any value at all, it was the substantial forms that were, properly speaking, forms. If the Scotists could really specify any natural class, say man — and physics was at that time in no condition to raise any just doubt upon that score — then they were perfectly justified in giving a name to the intelligible characteristic of that class, and that was all the substantial form made any pretension to being. But the Scotists were guilty of two faults. The first — great enough, certainly, but relatively inconsiderable — was often referred to, though not distinctly analyzed and brought home to them. It was that they were utterly uncritical in accepting classes as natural, and seemed to think that ordinary language was a sufficient guarantee in the matter. Their other and principal fault, which may with justice be called a sin, since it involved a certain moral delinquency, was that they set up their idle logical distinctions as precluding all physical inquiry. The physicists and Scotists, being intent upon widely discrepant purposes, could not understand one another. There was a tolerably good excuse for the physicist, since the intention of the Scotist was of an abstract and technical kind, not easily understood. But there was no other excuse for the Scotist than that he was so drugged with his metaphysics that ordinary human needs had lost all appeal to him. All through the eighteenth century and a large part of the nineteenth, exclamations against the monstrousness of the scholastic dogma that substantial forms were entities continued to be part of the stock-in-trade of metaphysicians, and it accorded with the prevalent nominalism. But nowadays, when it is clearly seen that physical science gives its assent much more to scholastic realism (limited closely to its formal statement) than it does to nominalism, a view of the history more like that here put forward is beginning to prevail.

362. In the following terms, mostly Kantian, prepositional phrases express the qualifications.

Form of corporeity: a very common term of scholasticism, originating with Avicenna, and used by Aquinas (Summa Theol., pars i. cap. lxvi. art. 2), but more particularly by Scotus (in his great discussion Opus Oxon., IV. dist. xi. 9.3, beginning "De secundo articulo dico") and by all his followers. The point is, that the rational soul, being purely spiritual, cannot confer corporeity upon the human body, but a special form, the form of corporeity, is requisite. Suarez and others, generally Thomists, as well as Henry of Ghent, denied this on the ground that a species has but one form. Thus a great metaphysical dispute arose. It sprung from the study of the doctrine of transubstantiation. See Cavellus, Suppl. ad quaest. Scoti in De Anima, disp. i, which is in the Lyons ed. of Scotus, tom. ii.

Form of cognition, in Kant's doctrine, is that element of knowledge which the matter of experience must assume in order to be apprehended by the mind. Kant seems to have been thinking of legal forms which must be complied with in order to give standing before a court. So an English sovereign, in order to be crowned, must, as a "matter of form," swear to an intensity of loathing for Romish dogmas which he probably regards with great coolness. Kant's definitions are chiefly the following:

"In the phenomenon, that which corresponds to the impression of sense, I call the matter of it; while that which constitutes the fact that manifoldness of the phenomenon is intuited as ordered in certain relations, I call the form of the phenomenon" (Krit. d. Reinen Vernunft, 1st ed., p. 20).

"All cognition requires a concept, be it as imperfect and dark as you will; and this, in respect to its form, is always a universal which serves as a rule" (ibid., p. 106).

"The transcendental unity of the synthesis of the imagination is the pure form of all possible cognition, through which, consequently, all objects of possible experience must a priori be represented" (ibid., p. 118).

"There are two factors in cognition: first, the concept by which any object is thought — that is, the category; and secondly, the intuition by which that object is given. For if the concept had had no corresponding intuition, it would be a thought, no doubt, as far as its form goes; but having no object, no cognition whatsoever [he means, whether true or false] of anything would be possible by it; since, so far as I should know, there would be nothing, and perhaps could be nothing, to which such a concept would be applicable" (2d ed. of the Deduction of the Categories, §22).

"It is not more surprising that the laws of phenomena in nature must agree with the understanding and its a priori form, i.e. with its power of combining any manifold, than that the phenomena themselves must agree with the a priori form of sensuous intuition. For just as phenomena have no existence in themselves, but are merely relative to the mind, as having senses, so laws do not exist in the phenomena, but are merely relative to the mind in which the phenomena inhere, that mind exercising understanding" (and see the rest of this passage, ibid., §26).

Form of forms. Francis Bacon says "the soul may be called the form of forms," which would be a pretty conceit, were it not plagiarized from the serious doctrine of Aristotle: {ho nous eidos eidön} (432 a, 2).

363. The terms matter and form are used in certain peculiar ways in logic. Speaking materialiter, the matter of a proposition is said to be its subject and predicate, while the copula is its form. But speaking formaliter, the matter of a proposition is, as we familiarly say, the "matter of fact" to which the proposition relates; or as defined by the scholastics, "habitudo extremorum adinvicem." The second tractate of the Summulae of Petrus Hispanus begins with the words: "Propositionum triplex est materia; scilicet, naturalis, contingens, et remota. Naturalis est illa in qua praedicatum essentia subiecti vel proprium eius; ut, homo est animal; vel, homo est risibilis. Contingens est illa in qua praedicatum potest adesse et abesse subiecto praeter subiecti corruptionem; ut, homo est albus, homo non est albus. Remota est illa in qua praedicatum non potest convenire cum subiecto; ut, homo est asinus."

Of a syllogism, the proximate matter is the three propositions; the remote, the three terms. The form, which ought to be the ergo, by the same right by which the copula is recognized as the form of the proposition, is said to be "apta trium propositionum dispositio ad conclusionem ex praemissis necessario colligendam." But Kant, in the Logik by Jäsche, §59, makes the premisses the matter, and the conclusion the form.

§10. Possibility, Impossibility, and Possible †1

364. The term is used to express a variety of meanings which, although distinct in themselves, yet flow readily into one another. These meanings may best be grouped according as they have (1) an ontological objective value, or a logical subjective value; and (2) according as they are used antithetically to actuality or necessity. The antithetical point of view is the most convenient from which to begin.

365. Possibility may mean that something is (1) not actual, or (2) that, while it possesses actual existence, that existence lacks causal or rational necessity.

(1) As opposed to the actual, the phrase has again a double meaning. (a) Taken objectively, it may mean something as yet undeveloped, since not presenting itself in actually objectified form, but capable of doing so at some future time, when all the conditions of its realization occur: latent, potential being. This implies capacity for realization; and, if this capacity be taken in an active sense, connotes some inherent tendency to actuality, which, if not thwarted, leads to final completeness of being. This involves the active sense of potentiality, of force, etc. It is close to the literal sense of the term (posse, can be). This is the dominating sense in Greek philosophy, being connected with Aristotle's teleological theory of development. (b) Taken logically, it denotes that there is some ground for asserting actuality, but not sufficient to justify a positive statement: may, as distinct from can, be. Thus, possibly it will rain tomorrow. It has to do with degrees of certainty in judging.

366. (2) As opposed to the necessary, the term has also a double sense. (a) It may mean chance, contingency, as an objective fact. Chance again, has a double meaning: (i) something not derivable or explainable causally by reference to antecedent facts. There are those who assert the reality of such chance. On this view there are many possibilities in store in the future which no amount of knowledge would enable us to foresee or forestall. Indeterministic theories of the will assert possibilities of this sort also. (ii) Chance may mean that which, while necessary causally, is not necessary teleologically; the unplanned, the fatalistic. From this point of view the "possible" is that which unexpectedly prevents the carrying-out of a purpose or intention. It leads up to the logical sense (b), according to which the possible, as opposed to the necessary, is anything whose existence cannot be derived from reason; that, the existence of which, rationally speaking, might be otherwise. It is opposed to mathematical or metaphysical necessity, where existence cannot be otherwise than as it is. In this sense the objective actual may be only (logically) possible; the present rain-storm is actual, but since it does not follow from a necessity of thought, but only from empirical antecedents, it is not necessary, and hence just a contingent possibility. This distinction goes back also to Aristotle, being found in his logical writings, †1 as the possible, as potential meaning, is found in his metaphysical. †2 It has played a large part in modern rationalism, especially in the philosophy of Leibnitz, †3 being identical with his distinction of "truths of reason" and "truths of fact." In the sphere of mathematics, logic, and metaphysics there is no possibility in the strict sense; all that exists exists of necessity. In the physical and practical spheres which deal with the space and time world the notion of possibility has full sway. Everything is possible which does not contradict the laws of reason; that which is inconceivable, which violates the law of reason, is impossible. The impossible is the self-contradictory. Kant's †4 criticism of rational conceivability as a criterion of truth, to the effect that it is only formal, resting upon the principle of identity and contradiction, and when applied to existence must be supplemented by appeal to sense, made Leibnitz's distinctions of hardly more than historic interest.

367. The nominalistic definition (nominalistic in its real character, though generally admitted by realists, as Scotus, i. dist. 7, qu. unica) that that is possible which is not known not to be true in a real or assumed state of information is, like many nominalistic definitions, extremely helpful up to a certain point, while in the end proving itself quite superficial. It is not that certain things are possible because they are not known not to be true, but that they are not known not to be true because they are, more or less clearly, seen to be possible.

For example, one collection may be said to be greater than another if, and only if, there is no possible relation in which every member of the former collection stands to a member of the latter, to which no other member of the former stands in the same relation. Now, the question arises — whether or not it is possible for two collections to be, under this definition, each greater than the other. In advance of an investigation, the proposition is possibly true, in the sense that we do not know that it is impossible. But is the fact possible? That is, can we in any way suppose such a state of things without involving ourselves in contradiction? It is that positive supposition which will constitute the possibility, not the mere ignorance of whether such a supposition can be made or not. In order to make two such collections possible, we must make some positive assumption in regard to the possibility of collections; while in order to make such a relation between two collections impossible, we have to make a positive assumption of the possibility of a certain description of relation. It is not a question of ignorance, since nothing but pure hypothesis is concerned. The question is whether it is possible in every case to suppose distinct pairs, each composed of a member of either collection and such as completely to exhaust one of the collections. If this is always possible, then two collections each greater than the other are impossible. It is evidently desirable to state the logical principles of this general kind of possibility, which does not consist in ignorance, but, as it would seem, in hypothetic indetermination or disjunctive determination.

368. Nominalists uniformly speak of Aristotle's view of future contingents as really absurd. It may be so; but it is certainly the only doctrine which their principles leave room for. A certain event either will happen or it will not. There is nothing now in existence to constitute the truth of its being about to happen, or of its being about not to happen, unless it be certain circumstances to which only a law or uniformity can lend efficacy. But that law or uniformity, the nominalists say, has no real being; it is only a mental representation. If so, neither the being about to happen nor the being about not to happen has any reality at present; and the most that we can say is that the disjunction is true, but neither of the alternatives. If, however, we admit that the law has a real being, not of the mode of being of an individual, but even more real, then the future necessary consequent of a present state of things is as real and true as that present state of things itself.

369. By the old logicians, possibility is usually defined as non-repugnancy to existence. Kant defines it as that which satisfies the formal conditions of experience (Krit. d. Reinen Vernunft, 1st ed., pp. 218, 234).

370. The possible proposition, or problematic judgment, as it is called by German logicians, is said by many logicians, especially Sigwart, not to be any proposition at all, because it does not draw a sharp line between truth and falsity. It seems to be necessary to distinguish between a proposition which asserts that under such and such general conditions a certain thing is possible, of which an example is the proposition that of any two collections one is not greater than the other, and a proposition which pretends to be no more than a conjecture. If a conjecture can be absolutely baseless, which may be doubted, a proposition which pretended to be no more than that may be said to be no proposition at all. But it can hardly be maintained that, when Poincaré says that there is no physical law whatever which will not be rendered more certain by every new confirmatory experiment, he is depriving those laws of all meaning as propositions.

371. Logical possibility: that of a hypothesis not involving any self-contradiction.

Mere possibility: that of a state of things which might come to pass, but, in point of fact, never will. In common language, exaggerated to the "merest possibility."

Metaphysical possibility ought to mean a possibility of existence, nearly a potentiality; but the phrase does not seem to be used in that sense, but rather in the sense of possibility by supernatural power.

Moral possibility one might expect should be the opposite of moral impossibility, meaning, therefore, something reasonably free from extreme improbability. But, in fact, it seems to be used to mean what is morally permissible.

Physical possibility: (1) that which a knowledge of the laws of nature would not enable a person to be sure was not true; (2) that which might be brought about if psychological and spiritual conditions did not prevent, such as the Pope's pronouncing ex cathedra as an article of faith the fallibility of all his own utterances.

Practical possibility: that which lies within the power of a person or combination of persons under external conditions likely to be fulfilled, and questionable chiefly because internal conditions may not be fulfilled.

Proximate possibility. It is very difficult to make out what is meant by this; but the phrase is evidently modelled on potentia proxima, which is a state of high preparedness for existence; so that proximate possibility would be a high grade of possibility in a proposition amounting almost to positive assertion.

Real possibility is possibility in the thing, as contradistinguished from mere logical possibility (Scotus, Opus Oxon., I. ii. 7, Ad secundam probationem maioris).

Remote possibility: the possibility of a proposition which is far from being positively asserted. Also used in common speech.

Substantive possibility: the admissibility of a pure hypothesis (as illustrated above).

§11. Virtual †1

372. (1) A virtual X (where X is a common noun) is something, not an X, which has the efficiency (virtus) of an X.

This is the proper meaning of the word; but (2) it has been seriously confounded with "potential," which is almost its contrary. For the potential X is of the nature of X, but is without actual efficiency. A virtual velocity is something not a velocity, but a displacement; but equivalent to a velocity in the formula, "what is gained in velocity is lost in power."

So virtual representation was the non-representation of the American colonies in the British Parliament, which was supposed to be replaced by something. So Milton asks whether the angels have virtual or immediate touch. So, too, the sun was said to be virtualiter on earth, that is, in its efficiency.

(3) Virtual is sometimes used to mean pertaining to virtue in the sense of an ethical habit.

Virtual knowledge: a term of Scotus defined by him (Opus Oxon., Pt. I. iii. 3). . . .

§12. Unity and Plurality †1

373. (1) A universally accepted understanding as to the formation of Latin words would require unity to mean that which is essential to the number one.

If we consider the number one, irrespective of the possibility of two, three, etc., it involves no idea of number (and therefore not of totality or collection), nor even any idea of relation. The idea would, therefore, be found in a pure state only in an immediate consciousness which should make no distinction of any kind, whether between subject and object, or of the parts of the object. But the term is never used in this sense, unless with an accompanying explanation.

(2) The oneness element of experience which involves a positive assignment of the number one, and which must be originally one, and not a total.

374. Much may be said for the opinion that we are thus brought to the event of acting and being acted upon; for that must be one, and is the only element of experience whose essential peculiarity is entirely lost in any generalization of it. The negative oneness of immediate consciousness — as, for example, it appears in the idea of any particular colour — does not resist generalization, the idea of redness in general having the same sort of unity as that of the scarlet of mercuric iodide or the colour of aniline red (magenta). But the moment I pass from the idea of a particular item of my experience, such as seeing a boat with a couple of men going over Niagara, to the slightest generalization of it, such as that of the memory of seeing the event, or the general conception of going over Niagara, the positive oneness entirely disappears.

375. Nevertheless, the word unity is seldom applied to this sort of oneness, which goes by the name of individuality. There is no individuality in a quality of immediate consciousness such as magenta or solferino, because there is no setting of object over against subject, which is requisite before oneness can be positively assigned to an idea (positive oneness thus involving duality); but neither is there any generality in the immediate consciousness, as long as it remains nothing more than what it first was. The purest oneness does not involve the least reference to plurality, and is therefore not positively opposed to generalization, and is not destroyed when generalization takes place. But positive and insistent oneness necessarily involves, or rather springs out of, the idea of duality, and distinctly denies it; so that generalization destroys it; it is the otherness of otherness, the negation of negation.

376. (3) The idea which the word unity is usually employed in philosophy to express is that of a general (in the most general sense) in its relation to particulars, which would be much more accurately called "totality."

Unity is thus used, not to express pure oneness, nor yet positive oneness, but to express the negation of multitude in the object to which it is attributed. Thus it involves a distinct reference to the possibility, not of duality merely, as positive unity does, but of plurality (in the sense of more than two). The first unity might be named simplicity or firstness; the second is very appropriately termed individuality; the third, which is nearly what Kant †1 terms synthetical unity, ought to have some better designation than totality or universality.

377. Unity in certain old books (as in the Institutiones Metaphysicae of Burgersdicius, 1647) is divided into singular and universal unity, the former belonging to singulars, the latter to universals. Singular unity is either material (or numerical) or formal. Material unity is defined as that which belongs to the singulars in so far as they are considered as units with individualizing differences; which is an awkward attempt to define individuality. Formal unity is "the unity which belongs to singulars abstractedly from their individualizing differences." These definitions depend upon a particular theory of individuation. Universal unity is distinguished from communicability, which is the reference to the plurality of singulars; and these two elements together make up universality. Numerical unity implies repugnance to multiplication; formal unity, indifference to multiplication; universal unity, non-repugnance to multiplication. The nature of the fundamentum universalitatis distinguishes the mediaeval realist from the nominalist. The nominalists generally do not admit that there is any similarity in things apart from the mind; but they may admit that this exists, provided they deny that it constitutes any unity among the things apart from the mind. They cannot admit the latter and remain consistent nominalists. Thus, a nominalist may admit that there is in the events themselves an agreement consisting in the uniformity with which all stones dropped from the hand fall to the ground; but if he admits that there is anything at all, except the mere fact that they happen to do so, that should in any sense determine the different stones to fall every time they are dropped, he ceases to be a good nominalist and becomes a mediaeval realist. Unity is further divided (by Burgersdicius, whom we continue to follow) into unity of simplicity and unity of composition. Simplicity is said to be unity devoid of all multitude; composition is the union of a plurality of things. This definition of simplicity is confessedly defective in representing this mode of unity as having a reference to multitude. Composition is divided into real, rational, and modal. Real composition is the union of distinct entities in the real thing itself. It is either actual or potential. Actual composition is either per compositionem, as when water and alcohol are mixed, or per aggregationem (as in an army). Potential composition is when one thing is united in potentia to another. It is either per informationem or per inhaerentiam; a distinction peculiar to a certain kind of Aristotelianism. Rational composition is either of things which differ by reason alone, or of things brought together in one concept; it includes, firstly, genera, species, etc.; secondly, equality, similitude, etc.; thirdly, agreement in effects, external causes, etc. Modal composition is composition from a thing and a mode. Most of the above distinctions go back to Scotus, and a few are still earlier.

378. Unity is divided by Kant into analytical and synthetical. He never defines or explains these terms; but if we remember that, in his use of words, multiplicity of elements is essential to unity, it is easy to see that what he means by analytical unity is the unity of that which is given in its combined state and is analyzed by ordinary reflection. Thus we perceive a fact; and in order to express or think it we analyze it, and the relation of the percept to the elements resulting from this analysis is very inappropriately called analytical unity. But when in the formation of the percept different sense impressions are put together, so that ordinary thought cannot proceed from whole to parts, but an operation more or less subconscious is supposed to manufacture the whole out of the parts, the relation of the whole to the parts is called synthetical unity. Three kinds of transcendental synthesis are recognized in the first edition of the Krit. d. Reinen Vernunft, each resulting in a synthetical unity: they are the synthesis of apprehension in the intuition, which produces one representation; the synthesis of reproduction in the imagination; and the synthesis of recognition in the concept, which gives the unity of the rule. The transcendental unity of apperception is the unity which belongs to all my cognitions arising from a correlative unity of consciousness. It is transcendental, objective, and original. Besides these modes of transcendental unity, Kant recognizes other kinds of synthetical unity, some of which are empirical and contingent. There are also different modes of rational unity, some speculative, others moral.

That which the Scholastics meant by transcendental unity was unity in the sense in which it is said Quodlibet ens est unum, that is, is self-consistent.

379. We must not forget the three dramatic unities of time, place, and action, requiring the events represented to be included in one day, in one scene, and all to relate to one plot. Unity of action is set forth by Aristotle (Poetics, chaps. viii, ix, xviii). Unity of time is mentioned by him. That is, the action of a tragedy should, when convenient, be compressed into one day (Poetics, chap. v). The unity of place was remarked by French critics to have been observed by the Greek tragedians.

380. A unity in mathematics is a quantity which multiplied by any other gives that other. There can thus be but one unity in an algebra, although there may be many units.

§13. Whole and Parts †1

381. The old definition is: "Totum est quod constat plurium rerum unione." Psychologically, whatever is treated as a single object, though capable of treatment as two or more objects (parts of the whole): by "treated" meaning "thought of," "attended to," or otherwise "acted upon." †2

382. We may say that a whole is an ens rationis whose being consists in the copulate being of certain other things, either not entia rationis or not so much so as the whole; so that a whole is analogous to a collection, which is, in fact, a special kind of whole. There can be no doubt that the word whole always brings before the mind the image of a collection, and that we interpret the word whole by analogy with collection. The idea of a collection is itself, however, by no means an easy one to analyze. It is an ens rationis, abstraction, or fictitious subject (but the adjective must be understood in a broad sense, to be considered below), which is individual, and by means of which we are enabled to transform universal propositions into singular propositions. Thus, the proposition "all men are mortal," with a new subject and new predicate, appears as "The collection of men is a collection of mortals"; just as, for other purposes, and by means of other abstractions, we transform the same proposition into "The character of mortality is possessed by every man"; and the members of the collection are regarded as less fictitious than the collection. It very often happens that an object given indirect perception as an individual is, on closer scrutiny, seen to be identifiable with a collection of parts. But it does not seem to be strictly accurate to say that the larger object of perception is identical with that abstraction, the collection of the smaller objects. It is rather something perceived which agrees in its relations with the abstraction so well that, for convenience, it is regarded as the same thing. No doubt the parts of a perceived object are virtually objects of consciousness in the first percept; but it is useless to try to extend logical relations to the sort of thought which antecedes the completion of the percept. By the time we conceive an object as a collection, we conceive that the first reality belongs to the members of the collection and that the collection itself is a mere intellectual aspect, or way of regarding these members, justified, in ordinary cases, by certain facts. We may, therefore, define a collection as a fictitious (thought) individual, whose being consists in the being of certain less fictitious individuals. †1

383. Many adjectives are used to distinguish different kinds of wholes. Certain of the phrases may be defined.

Actual whole: any whole which cannot exist without the existence of its parts. Usually identified with the Constitute whole. Monboddo's definition (Ancient Met., i. 479) is not quite accurate.

Collective whole, or aggregate whole: defined by Chauvin as "that which has material parts separate and accidentally thrown together into one, as an army," etc. But the example shows that organization does not disqualify a whole from being called collective, although the term totum per aggregationem will no longer be applied to it, in that case. In so far as a whole is collective, any other relation between its parts is put out of view.

Composite whole: a term of Burgersdicius, who (Inst. Met., I. xxii. §7) defines it as "quod ex duabus partibus constat quarum una est in potentia ad alterum et altera vice versa actus est alterius." It includes the whole by information and the whole by inherence.

Comprehensive whole: a whole of logical comprehension.

Constituent whole: a whole which is essential to its parts.

Constitute whole: a whole whose parts are essential to it. See Actual whole (above).

Continuous whole: a continuum regarded as a whole. In order to define it, it would first be necessary to define continuity. Now we have, perhaps, not yet succeeded in analyzing the conception of continuity; for what the mathematicians call by that name, such as the relations of all real quantities capable of being designated to an indefinite degree of approximation by means of a whole number and a decimal, does not answer the requisites of the problem.

Copulative whole: a whole consisting of a sign which is essentially applicable to whatever certain signs, called its parts, are all applicable, but is essentially inapplicable to anything to which any one of these signs is inapplicable.

Definite whole: a whole constituted by genus and difference.

Definitive whole: see Definite whole (above).

Discrete whole: the same as a Collective whole (above).

Disjunctive whole: a whole consisting of a sign which is essentially applicable to whatever any one of certain signs, called its parts, is applicable, but is essentially inapplicable to anything to which none of these parts is applicable.

Dissimilar whole: same as Heterogeneous whole (below).

Essential whole: great confusion exists in the use of this very common expression. Aquinas (Summa Theol., Pt. I. lxxvi. 8) uses it in a broad sense which would make it about equivalent to Burgersdicius' composite whole, or perhaps broader. On the other hand, it is sometimes restricted to the whole per informationem, and this is perhaps the best settled use. But others make it include the physical and the metaphysical whole as its two species.

Extensive whole: a whole of logical extension, usually called a subjective or logical whole.

Formal whole: a comprehensive whole, especially of essential comprehension. See Actual whole (above).

Heterogeneous whole: a term of Aquinas; a whole whose parts are dissimilar from the whole.

Homogeneous whole: a term of Aquinas; a whole whose parts are similar to the whole, as the parts of a whole of water are.

Integral whole (a term in common use since Abélard's time): Blundevile (1599) says, "Whole integral is that which consisteth of integral parts, which though they cleave together, yet they are distinct and severall in number, as man's body, consisting of head, brest, belly, legs, etc." The usual definition is "quod habet partem extra partem," which restricts it to space. Burgersdicius, however, says that parts which differ in their ordinal places are partes extra partes.

Integrate whole: a pedantic variant of Integral whole (above).

Logical whole: same as Universal whole (below).

Mathematical whole: same as Integral whole (above).

Metaphysical whole: a whole in that respect in which a species is the whole of its genus and difference. See Formal whole (above).

Natural whole: a term proposed by Hamilton †1 to replace Comprehensive or Metaphysical whole; as if that were not sufficiently provided with aliases under which to hide itself.

Negative whole: a unit regarded as a whole, as in the phrases "deus totus est ubique," and "anima est tota in toto corpore."

Physical whole: a whole compounded of substance and accident; but some say of matter and form; and some that both come to the same thing. In the peripatetic view, however, substance is form, not matter.

Positive whole: a whole consisting of parts. See Negative whole (above).

Potential whole: same as Universal whole (below); so called because the genus does not actually, but only potentially, contain the species, etc.

Potestative whole: a term of Aquinas; equivalent to Potential whole (above).

Predicative whole: a whole of logical depth.

Quantitative whole: same as Integral whole (above).

Similar whole: see Homogeneous whole (above).

Subject whole: same as Subjective whole (below).

Subjective whole: a very venerable name for Universal whole (below).

Substantial whole: a whole of logical breadth.

Universal whole: see Universal.

Whole by accident: such a whole as neither essentially belongs to the parts nor the parts to it.

Whole by aggregation or aggregative whole: same as Collective whole (above) in an exclusive sense.

Whole by information: a compound of act and power in the same kind, such as man, according to the Aristotelian theory of the soul.

Whole by inherence: same as Physical whole (above).

Whole by itself or per se: a whole which essentially belongs to its parts or its parts to it.

§14. Kind †1

384. Before "class" acquired its logical signification in Queen Anne's reign, kind was sometimes used for any collection of objects having a common and peculiar general character, simple or complex.

Thus, in Blundevile's Arte of Logicke, we read: "Genus is a generall kind which may be spoken of many things differing in speciall kind." At other times, and more accurately, it was restricted to the species, or narrowest recognized class, or that which was supposed to be derived from one stock. Thus Wilson's Rule of Reason (1551) has: "Genus is a generall woorde vnder the whiche diuerse kindes or sortes of thinges are comprehended."

But before persons who picked their words had become ready to use "class" as a mere logical extension, they had begun to avoid "kind," except when the emphasis of attention was placed upon the logical depth rather than the breadth. †1 Watts's Logick (1724) illustrates this. This last is the ordinary popular sense of the word today; so that "of this kind," "of this nature," "of this character" are interchangeable phrases. J. S. Mill, however, in his System of Logic, Bk. I, chap. vii, §4, erected the word into a technical term of logic, at the same time introducing the term "real kind." His meaning, so far as it was determinate, was that classes are of two orders, the first comprising those which, over and above the characters which are involved in their definitions and which serve to delimit their extension, have, at most, but a limited number of others, and those following as "consequences, under laws of nature," of the defining characters; and the second, the real kinds, comprising those each of which has innumerable common properties independent of one another. As instances of real kinds, he mentions the class of animals and the class of sulphur; as an instance of a kind not real, the class of white things. It is important for the understanding of Mill's thought here, as throughout his work, to note that when he talks of "properties," he has in mind, mainly, characters interesting to us. Otherwise, it would not be true that all white things have few properties in common. By a "law of nature" he means any absolute uniformity; so that it is hardly enough to assert that if all white things had any property P, this would be a "consequence, under a law of nature," of their whiteness; for it would be itself an absolute and ultimate uniformity. Mill says that if the common properties of a class thus follow from a small number of primary characters "which, as the phrase is, account for all the rest," it is not a real kind. He does not remark that the man of science is bent upon ultimately thus accounting for each and every property that he studies. The following definition might be proposed: Any class which, in addition to its defining character, has another that is of permanent interest and is common and peculiar to its members, is destined to be conserved in that ultimate conception of the universe at which we aim, and is accordingly to be called "real."

§15. Perseity and Per Se †1

385. Scotus says there are two kinds of "perseity," that of a demonstration and that of a predicate which belongs immediately to its subject.

Per se translates {kath' auto, kath' auton}, etc. Similar phrases occur in ordinary Greek. Plato, for example, in the Theaetetus, †2 speaks of {epistémé en ekeinö tö onomati, ho ti pot' echei hé psyché hotan auté kath' autén pragmateuétai peri ta onta}. But in Aristotle it first becomes a term of art (see Bonitz under {heautou}). He enumerates four or five different meanings of it, from which we are led to infer that he did not himself invent it. Two such passages are Met., Δ. xviii. 2, and Anal. Post., iv. There are others, but they are less clear. Per se cannot very well be understood without some understanding of the phrase secundum quid ({kath' ho}). Aristotle †3 says:

"Secundum quid is said in several senses. In one sense it is the species ({eidos}) and essence of anything; thus, that secundum quid a man is good is itself good. Another sense is in what anything first comes into existence, as colour in a surface. In the first sense the secundum quid is the form ({eidos}); in the second it is the matter and first subject of anything. And, generally speaking, secundum quid refers to a cause. 'Secundum quid comes a man' is 'on what account comes he?' and 'secundum quid does he paralogize,' or 'does he syllogize,' is 'what is the cause of the paralogism' or 'the syllogism?' Furthermore, secundum quid is said in reference to position in space; as 'secundum quid stands he,' or 'secundum quid is he walking.' In such phrases it denotes position and place.

"Consequently, per se is necessarily said in different senses. In one sense, per se refers to the essence ({to ti én einai}) of anything; as 'Callias is per se Callias,' that is, the very essence of Callias. It also refers to whatever is involved in the definition of anything ({hosa en töi ti estin hyparchei}), as 'Callias is per se an animal'; that is, that he is an animal is implied in the word, or animal is what Callias is. The phrase is further applied in case anything in its origin assumes any character in itself or in what belongs to it ({ei en autöi dedektai prötöi é tön auton tini}); thus white is per se a surface, and man is per se alive, since the soul, which is part of man, receives life in its very origin. Further, that is per se which has nothing else as its cause. Thus there are many causes of man, such as being an animal, being biped, etc.; yet still man is per se man. Further, whatever belongs to one thing alone, and in so far as it is alone, is per se; so that what is abstract ({kechörismenon}) is per se."

These five senses are, then: (1) that a substance exists per se and not per accidens; (2) that an analytical proposition is true per se, or formally, and not as matter of fact; (3) that any character which a thing necessarily assumes by virtue of existing, belongs to it per se, and not secundum quid; (4) that which a thing causes of itself it does per se, and not per aliud; and (5) that which any abstraction, qua that which it is, is, does, or suffers, is per se and not secundum quid.

The second of the above senses is called per se primo modo; the third is called per se secundo modo; but a different explanation from the above is often given. In reliance particularly on a passage in Aristotle's Met., {Z}. v, it is said that a predication is per se secundo modo where the definition of the predicate contains the subject.

Another important expression is "known per se." A proposition is known per se if, and only if, it is cognoscible from its own terms but not cognoscible in any other way. For instance, that the letters on this page are black is not known per se, because it may be proved by testimony. Nor, on the other hand, is the doctrine of the Trinity per se, though it cannot be proved; for it is not self-evident. It has to be received on faith. But there was a great controversy between the Thomists on the one hand and the Scotists with the Nominalists on the other, as to whether, in the above definition, the word "terms" was to be taken objective or formaliter. See the Conimbricenses in I. Anal. Post., iii.

§16. Priority, Prior, and Prius †1

386. These words are used in about a dozen different senses in philosophy, although only five are specially recognized. They are enumerated in the mnemonic verses,

"Tempore, Natura, prius Ordine, dic et Honore,
Effecto Causam dicimus esse prius."

387. (1) Priority in time is considered by Kant to be dependent upon the peculiar constitution of the internal sense (though he does not attempt any inquiry into the constitution further than that it places objects in time). Now, so far as effects in the outer world are due to forces, it seems to be proved that they follow the law of energy. In that case, though connection and continuity in time are important, yet the flow of time one way rather than in the reverse way is unmeaning. There is no effect that follows after its cause. The law of energy amounts to this, that the instantaneous accelerations of the motions of particles depend solely upon the relative positions of those particles at that same instant; and what follows after depends upon what now is, in the same way precisely, and is calculated by the same laws, as what went before depends upon what now is. Thus, in respect to the direction of its flow, time seems to be, if not purely a psychological affair, at any rate not purely a dynamical affair. Those physical phenomena which proceed in one direction and not in the reverse direction, and which seem to be well explained, such as the viscosity, diffusion, and conduction of gases, may all be explained by principles of probability.

From the point of view of causality exercised by our ideas and upon our ideas, the relations of prius and posterius present a different problem. Our wishes and endeavors cannot change the past in the least degree; and the future cannot affect our senses. The past affects the senses, and more and more strongly the nearer it is; our will can affect the future, and more and more strongly the nearer it is. The consequence is that the whole procedure of investigating the past and the future is different from the problem as regards real time.

This kind of priority is divided by the schoolmen into priority quoad existentiam and quoad generationem (that is, the older of two is the prior).

388. (2) In a meaning allied to temporal priority, Aristotle sometimes speaks of sense as prior to reason. †1

(3) That which is at an earlier stage of development is also called prior to that which is more matured; boyhood is said by Aristotle †2 to be prior to manhood.

(4) So matter is prior to form; and potency to energy.

(5) The simple is prior to the complex; as a point to a line, a line to a surface, a surface to a solid.

(6) The rudimentary is prior to the recondite in order of exposition.

(7) In order of arrangement, the thing reached sooner is prior to that reached later.

(8) The relatively independent is prior to the relatively dependent, as substance to accident, and parts to whole.

(9) That caused thing which is nearer the cause, in any of the four senses of cause, is prior to that which is further from the cause.

(10) That is "prior in illation" from which the posterior follows as a rational consequence.

(11) The more general is prior to the more special.

(12) That which is more honorable or higher in rank or dignity is prior to that which is less so.

389. Prius natura, as practically used by Aristotle, †3 seems often to convey no clear notion. But he certainly calls the prius dignitate and prius causalitate both prius natura. The usage of the Aristotelians is to call that prius natura which is prior in consecution or in causality. That is prior in consecution which is such that if something else is supposed it is supposed, but which being supposed something else is not thereby supposed. Thus, if two are supposed, one is supposed; but one being supposed, two is not thereby supposed. Hence, one is prior to two. Prius causalitate is either prius natura generantis or prius natura intendente. Prius natura generantis is the priority of the simple to the complex, as of the parts to the whole; prius natura intendente is the priority of the perfect to the imperfect, as of the whole to the parts. But this hardly seems to agree with Aristotle (646 a 25). Prius nobis ({pros hémas proteron}) is what is prior in the order of learning, or more easily known.

§17. Proximate †1

390. Lat. past participle of proximare, to approach, but it is used to translate proximus, next. The word occurs in Glanvil's Vanity of Dogmatizing, but in no English treatise on logic before Watts. In philosophy, synonymous with IMMEDIATE, though not so strong.

391. Proximate cause and effect: an obscure term, like most of the terms of Aristotelianism, which acquired some practical importance owing to the courts holding that a man was responsible for the proximate effects of his actions, not for their remote effects. This ought to determine what should be meant by proximate cause and effect; namely, that that which a man ought to have foreseen might result from his action is its proximate effect. The idea of making the payment of considerable damages dependent upon a term of Aristotelian logic or metaphysics is most shocking to any student of those subjects, and well illustrates the value of PRAGMATISM. Burgersdicius, who is one of the clearest of the Aristotelians, says: "Proximate cause is taken in two senses, to wit in suo genere and absolutely. An absolutely proximate cause is one which constitutes its effect, not merely immediately, but by its mere existence; so that, if it exists, its effect (causatum, for Burgersdicius is not limiting his remarks to efficient causes) necessarily exists. The proximate cause in suo genere is that which immediately constitutes its effect, that is to say, without the intervention of anything else of the same order concurring to produce the effect." Interpreting this in the light of pragmatism, the man should be held responsible for what might naturally be expected, or feared, as the result of his action; but not for effects depending upon subsequent occurrences which he could not anticipate. Burgersdicius continues: "One thing may have many causes, proximate in suo genere, but only one absolutely proximate. . . . So the proximate material cause of man is his body; the efficient, his father; the formal, his rational soul; the final, bene esse."

392. Proximate knowledge is direct knowledge of a thing, not knowledge through something else. Better called direct knowledge.

Proximate matter is matter in a state in which it is prepared for the reception of a form. The proximate matter of a syllogism consists in its propositions, as distinct from the remote matter, which consists in the terms.

Proximate object of a directive (as we now say, normative) science is a certain one of the objects of practice, as distinguished from the object of doctrine. In speculative sciences there is only one object, the object of doctrine. In practical sciences there is besides an object of practice, which is that upon which it is designed to produce an effect. In a normative science, such as logic, there are two objects of practice — the proximate, which is the operation or action which is regulated, such as reasoning, and the remote, which is that in which that action takes place, such as a mind or a science conducted by many minds.

Proximate witness, testimony. There is hardly any such thing in English law. It is the witness who testifies, not to his own experience, but to facts which he knows by the immediate testimony of others.

§18. Sufficient Reason †1

393. (1) This phrase was made a term of philosophy, if not invented, by Leibnitz. In the Principes de la Nature et de la Grâce, he says (but this is far from being the first time in which he signalizes the principle): "It is necessary to resort to metaphysics and to make use of a great principle, not much employed, to the effect that nothing takes place without reason (rien ne se fait sans raison suffisante); that is to say, that nothing occurs for which one having sufficient knowledge might not be able to give a reason sufficient to determine why it is as it is and not otherwise."

It is impossible to understand what Leibnitz means by this, without careful study of his works. There are two difficulties. In the first place, Leibnitz confounded under this phrase two entirely different ideas which he failed to discriminate. In the second place, in order to understand Leibnitz's position here, it is necessary to take into account, on the one hand, the thorough individualistic nominalism, with which he began his philosophical life and never consciously surrendered, and on the other hand his recognition of intellectual relations in the universe of which that nominalistic metaphysics involves the denial. His singular and complicated metaphysics is the outcome of his struggle to reconcile those two incompatible positions.

His sufficient reason is not an efficient cause, but a utility, or, in a broad sense, a final cause. But a nominalist cannot admit that an immediate final cause exists. Leibnitz, however, makes it true. For a realist, the real is nothing but the immediate object of that which is true. But Leibnitz has another notion of truth. Thus, in a letter to Arnauld (quoted in Latta's accurate and convenient exposition, p. 61, note beginning p. 60), he says: "Always in every true affirmative proposition, whether necessary or contingent, universal or singular, the notion of the predicate is in some way comprehended in that of the subject, praedicatum inest subiecto; otherwise I know not what truth is"; and in other passages he shows that for him truth is a relation between notions. Yet, as a nominalist, he could not hold that those notions immediately correspond to anything real. Consequently, he does not say that there really is a sufficient reason, but that anybody favorably situated would be able to render a sufficient reason. There is nothing real that corresponds to it immediately. Remotely, the purpose of God may correspond to it. Thus, the world of reality and the world of truth are completely sundered; for the former, Leibnitz is a pure individualistic nominalist; for the latter, on the contrary, he is an intellectualist. When he says, for example, that that which has no sufficient reason is "necessarily" non-existent, he uses the adverb of logical not of metaphysical modality. He does not hold that real things are either emanations or entelechies of anything corresponding to a sufficient reason, but that is how the mind is affected. But when he comes to the ultimate sufficient reason of contingent truths, which is God, he ceases to draw the distinction between the world of thought and the world of being; and this exception introduces difficulties into his system. But Leibnitz confounds two things under his word "reason." The idea which principally governs his doctrine is that a reason is an explanation of the utility of that of which it is a reason; but he includes under the same word any explanation of the logical necessity of the object, the why it follows from a general law. Hence, in many cases, his sufficient reason fulfills the function of an efficient cause. It would be quite possible to quote passages from Leibnitz which conflict with this account of his conception. In order that the reader should apprehend it as he did, it would be requisite that his mind should be in the same unclear condition, which is not possible after one has once attained a superior grade of clearness. We can account for his implicit contradictions, but cannot reproduce his apprehension of them when we once see them to be contradictions.

It is to be remarked that Renouvier and Prat, in their rehabilitation of Leibnitzianism, reject the principle of sufficient reason (La Nouvelle Monadologie, p. 41, note 29).

394. The principle of sufficient reason may very well be understood to express our natural expectation or hope to find each unexpected phenomenon to be subject to reason and so to be intelligible. But to entertain this hope for each is not necessarily to entertain it for all. At any rate, it is easy to see that, however strong the tendency may be, it does not amount to any such absolute and ineluctable necessity as attaches to the law of contradiction, by the side of which Leibnitz and many Germans have placed it. Moreover, however important this tendency of thought and this truth about the universe may be in reference to the development of science, nevertheless, like the principle of the uniformity of nature, its strictly logical application to add force to arguments is very limited indeed. The modus ponens and modus tollens stand in no need of any such general principle to be perfectly apodictic. It is essential to no broad division of reasoning. As a general rule, when we infer that a particular phenomenon, or set of phenomena, which seemed surprising at first, is to be explained as a consequence of a fact or law not directly observable, the argument is not appreciably strengthened by a separate assumption that the phenomenon has some explanation; although there are special cases in which it can be fortified by a similar, but more definite, premiss.

Book 2: Religion

Chapter 1: The Order of Nature †1

§1. The Significance of Order E

395. Any proposition whatever concerning the order of Nature must touch more or less upon religion. In our day, belief, even in these matters, depends more and more upon the observation of facts. If a remarkable and universal orderliness be found in the universe, there must be some cause for this regularity, and science has to consider what hypotheses might account for the phenomenon. One way of accounting for it, certainly, would be to suppose that the world is ordered by a superior power. But if there is nothing in the universal subjection of phenomena to laws, nor in the character of those laws themselves (as being benevolent, beautiful, economical, etc.), which goes to prove the existence of a governor of the universe, it is hardly to be anticipated that any other sort of evidence will be found to weigh very much with minds emancipated from the tyranny of tradition.

396. Nevertheless, it cannot truly be said that even an absolutely negative decision of that question could altogether destroy religion, inasmuch as there are faiths in which, however much they differ from our own, we recognize those essential characters which make them worthy to be called religions, and which, nevertheless, do not postulate an actually existing Deity. That one, for instance, which has had the most numerous and by no means the least intelligent following of any on earth, teaches that the Divinity in his highest perfection is wrapped away from the world in a state of profound and eternal sleep, which really does not differ from non-existence, whether it be called by that name or not. No candid mind who has followed the writings of M. Vacherot can well deny that his religion is as earnest as can be. He worships the Perfect, the Supreme Ideal; but he conceives that the very notion of the Ideal is repugnant to its real existence. †1 In fact, M. Vacherot finds it agreeable to his reason to assert that nonexistence is an essential character of the perfect, just as St. Anselm and Descartes found it agreeable to theirs to assert the extreme opposite. I confess that there is one respect in which either of these positions seems to me more congruous with the religious attitude than that of a theology which stands upon evidences; for as soon as the Deity presents himself to either Anselm or Vacherot, and manifests his glorious attributes, whether it be in a vision of the night or day, either of them recognizes his adorable God, and sinks upon his knees at once; whereas the theologian of evidences will first demand that the divine apparition shall identify himself, and only after having scrutinized his credentials and weighed the probabilities of his being found among the totality of existences will he finally render his circumspect homage, thinking that no characters can be adorable but those which belong to a real thing.

397. If we could find out any general characteristic of the universe, any mannerism in the ways of Nature, any law everywhere applicable and universally valid, such a discovery would be of such singular assistance to us in all our future reasoning that it would deserve a place almost at the head of the principles of logic. On the other hand, if it can be shown that there is nothing of the sort to find out, but that every discoverable regularity is of limited range, this again will be of logical importance. What sort of a conception we ought to have of the universe, how to think of the ensemble of things, is a fundamental problem in the theory of reasoning.

§2. Uniformities E

398. It is the legitimate endeavor of scientific men now, as it was twenty-three hundred years ago, to account for the formation of the solar system and of the cluster of stars which forms the galaxy, by the fortuitous concourse of atoms. The greatest expounder of this theory, when asked how he could write an immense book on the system of the world without one mention of its author, replied, very logically, "Je n'avais pas besoin de cette hypothèse-là." But, in truth, there is nothing atheistical in the theory, any more than there was in this answer. Matter is supposed to be composed of molecules which obey the laws of mechanics and exert certain attractions upon one another; and it is to these regularities (which there is no attempt to account for) that general arrangement of the solar system would be due, and not to hazard.

399. If anyone has ever maintained that the universe is a pure throw of the dice, the theologians have abundantly refuted him. "How often," says Archbishop Tillotson, "might a man, after he had jumbled a set of letters in a bag, fling them out upon the ground before they would fall into an exact poem, yea, or so much as make a good discourse in prose! And may not a little book be as easily made by chance as this great volume of the world?" †1 The chance-world, here shown to be so different from that in which we live, would be one in which there were no laws, the characters of different things being entirely independent; so that, should a sample of any kind of objects ever show a prevalent character, it could only be by accident, and no general proposition could ever be established. Whatever further conclusions we may come to in regard to the order of the universe, this much may be regarded as solidly established, that the world is not a mere chance-medley.

But whether the world makes an exact poem or not, is another question. When we look up at the heavens at night, we readily perceive that the stars are not simply splashed onto the celestial vault; but there does not seem to be any precise system in their arrangement either. It will be worth our while, then, to inquire into the degree of orderliness in the universe; and, to begin, let us ask whether the world we live in is any more orderly than a purely chance-world would be.

400. Any uniformity, or law of Nature, may be stated in the form, "Every A is B"; as, every ray of light is a non-curved line, every body is accelerated toward the earth's center, etc. This is the same as to say, "There does not exist any A which is not B"; there is no curved ray; there is no body not accelerated toward the earth; so that the uniformity consists in the non-occurrence in Nature of a certain combination of characters (in this case, the combination of being A with being non-B). †P1 And, conversely, every case of the non-occurrence of a combination of characters would constitute a uniformity in Nature. Thus, suppose the quality A is never found in combination with the quality C: for example, suppose the quality of idiocy is never found in combination with that of having a well-developed brain. Then nothing of the sort A is of the sort C, or everything of the sort A is of the sort non-C (or say, every idiot has an ill-developed brain), which, being something universally true of the A's, is a uniformity in the world. Thus we see that, in a world where there were no uniformities, no logically possible combination of characters would be excluded, but every combination would exist in some object. But two objects not identical must differ in some of their characters, though it be only in the character of being in such and such a place. Hence, precisely the same combination of characters could not be found in two different objects; and, consequently, in a chance-world every combination involving either the positive or negative of every character would belong to just one thing. Thus, if there were but five simple characters in such a world, †P2 we might denote them by A, B, C, D, E, and their negatives by a, b, c, d, e; and then, as there would be 25 or 32 different combinations of these characters, completely determinate in reference to each of them, that world would have just 32 objects in it, their characters being as in the following table:

TABLE I

ABCDE AbCDE aBCDE abCDE
ABCDe AbCDe aBCDe abCDe
ABCdE AbCdE aBCdE abCdE
ABCde AbCde aBCde abCde
ABcDE AbcDE aBcDE abcDE
ABcDe AbcDe aBcDe abcDe
ABcdE AbcdE aBcdE abcdE
ABcde Abcde aBcde abcde

For example, if the five primary characters were hard, sweet, fragrant, green, bright, there would be one object which reunited all these qualities, one which was hard, sweet, fragrant, and green, but not bright; one which was hard, sweet, fragrant, and bright, but not green; one which was hard, sweet, and fragrant, but neither green nor bright; and so on through all the combinations.

401. This is what a thoroughly chance-world would be like, and certainly nothing could be imagined more systematic. When a quantity of letters are poured out of a bag, the appearance of disorder is due to the circumstance that the phenomena are only partly fortuitous. The laws of space are supposed, in that case, to be rigidly preserved, and there is also a certain amount of regularity in the formation of the letters. The result is that some elements are orderly and some are disorderly, which is precisely what we observe in the actual world. Tillotson, in the passage of which a part has been quoted, goes on to ask, "How long might 20,000 blind men which should be sent out from the several remote parts of England, wander up and down before they would all meet upon Salisbury Plains, and fall into rank and file in the exact order of an army? And yet this is much more easy to be imagined than how the innumerable blind parts of matter should rendezvous themselves into a world." †1 This is very true, but in the actual world the blind men are, as far as we can see, not drawn up in any particular order at all. And, in short, while a certain amount of order exists in the world, it would seem that the world is not so orderly as it might be, and, for instance, not so much so as a world of pure chance would be.

402. But we can never get to the bottom of this question until we take account of a highly-important logical principle †P1 which I now proceed to enounce. This principle is that any plurality or lot of objects whatever have some character in common (no matter how insignificant) which is peculiar to them and not shared by anything else. The word "character" here is taken in such a sense as to include negative characters, such as incivility, inequality, etc., as well as their positives, civility, equality, etc. To prove the theorem, I will show what character any two things, A and B, have in common, not shared by anything else. The things, A and B, are each distinguished from all other things by the possession of certain characters which may be named A-ness and B-ness. Corresponding to these positive characters are the negative characters un-A-ness, which is possessed by everything except A, and un-B-ness, which is possessed by everything except B. These two characters are united in everything except A and B; and this union of the characters un-A-ness and un-B-ness makes a compound character which may be termed A-B-lessness. This is not possessed by either A or B, but it is possessed by everything else. This character, like every other, has its corresponding negative un-A-B-lessness, and this last is the character possessed by both A and B, and by nothing else. It is obvious that what has thus been shown true of two things is mutatis mutandis, true of any number of things. Q. E. D.

403. In any world whatever, then, there must be a character peculiar to each possible group of objects. If, as a matter of nomenclature, characters peculiar to the same group be regarded as only different aspects of the same character, then we may say that there will be precisely one character for each possible group of objects. Thus, suppose a world to contain five things, α, β, γ, δ ε. Then it will have a separate character for each of the 31 groups (with non-existence making up 32 or 25) shown in the following table:

TABLE II

αβ αβγ αβγδ αβγδε
α αγ αβδ αβγε
β αδ αβε αβδε
γ αε αγδ αγδε
δ βγ αγε βγδε
ε βδ αδε
βε βγδ
γδ βγε
γε βδε
δε γδε

404. This shows that a contradiction is involved in the very idea of a chance-world, for in a world of 32 things, instead of there being only 35 or 243 characters, as we have seen that the notion of a chance-world requires, there would, in fact, be no less than 232, or 4,294,967,296 characters, which would not be all independent, but would have all possible relations with one another.

405. We further see that so long as we regard characters abstractly, without regard to their relative importance, etc., there is no possibility of a more or less degree of orderliness in the world, the whole system of relationship between the different characters being given by mere logic; that is, being implied in those facts which are tacitly admitted as soon as we admit that there is any such thing as reasoning.

406. In order to descend from this abstract point of view, it is requisite to consider the characters of things as relative to the perceptions and active powers of living beings. Instead, then, of attempting to imagine a world in which there should be no uniformities, let us suppose one in which none of the uniformities should have reference to characters interesting or important to us. In the first place, there would be nothing to puzzle us in such a world. The small number of qualities which would directly meet the senses would be the ones which would afford the key to everything which could possibly interest us. The whole universe would have such an air of system and perfect regularity that there would be nothing to ask. In the next place, no action of ours, and no event of Nature, would have important consequences in such a world. We should be perfectly free from all responsibility, and there would be nothing to do but to enjoy or suffer whatever happened to come along. Thus there would be nothing to stimulate or develop either the mind or the will, and we consequently should neither act nor think. We should have no memory, because that depends on a law of our organization. Even if we had any senses, we should be situated toward such a world precisely as inanimate objects are toward the present one, provided we suppose that these objects have an absolutely transitory and instantaneous consciousness without memory — a supposition which is a mere mode of speech, for that would be no consciousness at all. We may, therefore, say that a world of chance is simply our actual world viewed from the standpoint of an animal at the very vanishing-point of intelligence. The actual world is almost a chance-medley to the mind of a polyp. The interest which the uniformities of Nature have for an animal measures his place in the scale of intelligence.

407. Thus, nothing can be made out from the orderliness of Nature in regard to the existence of a God, unless it be maintained that the existence of a finite mind proves the existence of an infinite one.

§3. Induction E

408. In the last of these papers †1 we examined the nature of inductive or synthetic reasoning. We found it to be a process of sampling. A number of specimens of a class are taken, not by selection within that class, but at random. These specimens will agree in a great number of respects. If, now, it were likely that a second lot would agree with the first in the majority of these respects, we might base on this consideration an inference in regard to any one of these characters. But such an inference would neither be of the nature of induction, nor would it (except in special cases) be valid, because the vast majority of points of agreement in the first sample drawn would generally be entirely accidental, as well as insignificant. To illustrate this, I take the ages at death of the first five poets given in Wheeler's Biographical Dictionary. They are:

Aagard, 48.

Abeille, 70.

Abulola, 84.

Abunowas, 48.

Accords, 45.

These five ages have the following characters in common:

1. The difference of the two digits composing the number, divided by three, leaves a remainder of one.

2. The first digit raised to the power indicated by the second, and divided by three, leaves a remainder of one.

3. The sum of the prime factors of each age, including one, is divisible by three.

409. It is easy to see that the number of accidental agreements of this sort would be quite endless. But suppose that, instead of considering a character because of its prevalence in the sample, we designate a character before taking the sample, selecting it for its importance, obviousness, or other point of interest. Then two considerable samples drawn at random are extremely likely to agree approximately in regard to the proportion of occurrences of a character so chosen. The inference that a previously designated character has nearly the same frequency of occurrence in the whole of a class that it has in a sample drawn at random out of that class is induction. If the character be not previously designated, then a sample in which it is found to be prevalent can only serve to suggest that it may be prevalent in the whole class. We may consider this surmise as an inference if we please — an inference of possibility; but a second sample must be drawn to test the question of whether the character actually is prevalent. Instead of designating beforehand a single character in reference to which we will examine a sample, we may designate two, and use the same sample to determine the relative frequencies of both. This will be making two inductive inferences at once; and, of course, we are less certain that both will yield correct conclusions than we should be that either separately would do so. What is true of two characters is true of any limited number. Now, the number of characters which have any considerable interest for us in reference to any class of objects is more moderate than might be supposed. As we shall be sure to examine any sample with reference to these characters, they may be regarded not exactly as predesignated, but as predetermined (which amounts to the same thing); and we may infer that the sample represents the class in all these respects if we please, remembering only that this is not so secure an inference as if the particular quality to be looked for had been fixed upon beforehand.

410. The demonstration of this theory of induction rests upon principles and follows methods which are accepted by all those who display in other matters the particular knowledge and force of mind which qualify them to judge of this. The theory itself, however, quite unaccountably seems never to have occurred to any of the writers who have undertaken to explain synthetic reasoning. The most widely-spread opinion in the matter is one which was much promoted by Mr. John Stuart Mill †1 — namely, that induction depends for its validity upon the uniformity of Nature — that is, on the principle that what happens once will, under a sufficient degree of similarity of circumstances, happen again as often as the same circumstances recur. The application is this: The fact that different things belong to the same class constitutes the similarity of circumstances, and the induction is good, provided this similarity is "sufficient." What happens once is, that a number of these things are found to have a certain character; what may be expected, then, to happen again as often as the circumstances recur consists in this, that all things belonging to the same class should have the same character.

411. This analysis of induction has, I venture to think, various imperfections, to some of which it may be useful to call attention. †2 In the first place, when I put my hand in a bag and draw out a handful of beans, and, finding three-quarters of them black, infer that about three-quarters of all in the bag are black, my inference is obviously of the same kind as if I had found any larger proportion, or the whole, of the sample black, and had assumed that it represented in that respect the rest of the contents of the bag. But the analysis in question hardly seems adapted to the explanation of this proportionate induction, where the conclusion, instead of being that a certain event uniformly happens under certain circumstances, is precisely that it does not uniformly occur, but only happens in a certain proportion of cases. It is true that the whole sample may be regarded as a single object, and the inference may be brought under the formula proposed by considering the conclusion to be that any similar sample will show a similar proportion among its constituents. But this is to treat the induction as if it rested on a single instance, which gives a very false idea of its probability.

412. In the second place, if the uniformity of Nature were the sole warrant of induction, we should have no right to draw one in regard to a character whose constancy we knew nothing about. Accordingly, Mr. Mill says †1 that, though none but white swans were known to Europeans for thousands of years, yet the inference that all swans were white was "not a good induction," because it was not known that color was a usual generic character (it, in fact, not being so by any means). But it is mathematically demonstrable that an inductive inference may have as high a degree of probability as you please independent of any antecedent knowledge of the constancy of the character inferred. Before it was known that color is not usually a character of genera, there was certainly a considerable probability that all swans were white. But the further study of the genera of animals led to the induction of their non-uniformity in regard to color. A deductive application of this general proposition would have gone far to overcome the probability of the universal whiteness of swans before the black species was discovered. When we do know anything in regard to the general constancy or inconstancy of a character, the application of that general knowledge to the particular class to which any induction relates, though it serves to increase or diminish the force of the induction, is, like every application of general knowledge to particular cases, deductive in its nature and not inductive.

413. In the third place, to say that inductions are true because similar events happen in similar circumstances — or, what is the same thing, because objects similar in some respects are likely to be similar in others — is to overlook those conditions which really are essential to the validity of inductions. When we take all the characters into account, any pair of objects resemble one another in just as many particulars as any other pair. If we limit ourselves to such characters as have for us any importance, interest, or obviousness, then a synthetic conclusion may be drawn, but only on condition that the specimens by which we judge have been taken at random from the class in regard to which we are to form a judgment, and not selected as belonging to any sub-class. The induction only has its full force when the character concerned has been designated before examining the sample. These are the essentials of induction, and they are not recognized in attributing the validity of induction to the uniformity of Nature. The explanation of induction by the doctrine of probabilities, given in the last of these papers, is not a mere metaphysical formula, but is one from which all the rules of synthetic reasoning can be deduced systematically and with mathematical cogency. But the account of the matter by a principle of Nature, even if it were in other respects satisfactory, presents the fatal disadvantage of leaving us quite as much afloat as before in regard to the proper method of induction. It does not surprise me, therefore, that those who adopt this theory have given erroneous rules for the conduct of reasoning, nor that the greater number of examples put forward by Mr. Mill in his first edition, as models of what inductions should be, proved in the light of further scientific progress so particularly unfortunate that they had to be replaced by others in later editions. One would have supposed that Mr. Mill might have based an induction on this circumstance, especially as it is his avowed principle that, if the conclusion of an induction turns out false, it cannot have been a good induction. Nevertheless, neither he nor any of his scholars seem to have been led to suspect, in the least, the perfect solidity of the framework which he devised for securely supporting the mind in its passage from the known to the unknown, although at its first trial it did not answer quite so well as had been expected.

§4. Mind and Nature E

414. When we have drawn any statistical induction — such, for instance, as that one-half of all births are of male children — it is always possible to discover, by investigation sufficiently prolonged, a class of which the same predicate may be affirmed universally; to find out, for instance, what sort of births are of male children. The truth of this principle follows immediately from the theorem that there is a character peculiar to every possible group of objects. The form in which the principle is usually stated is, that every event must have a cause.

415. But, though there exists a cause for every event, and that of a kind which is capable of being discovered, yet if there be nothing to guide us to the discovery; if we have to hunt among all the events in the world without any scent; if, for instance, the sex of a child might equally be supposed to depend on the configuration of the planets, on what was going on at the antipodes, or on anything else — then the discovery would have no chance of ever getting made.

416. That we ever do discover the precise causes of things, that any induction whatever is absolutely without exception, is what we have no right to assume. On the contrary, it is an easy corollary, from the theorem just referred to, that every empirical rule has an exception. But there are certain of our inductions which present an approach to universality so extraordinary that, even if we are to suppose that they are not strictly universal truths, we cannot possibly think that they have been reached merely by accident. The most remarkable laws of this kind are those of time and space. With reference to space, Bishop Berkeley first showed, in a very conclusive manner, that it was not a thing seen, but a thing inferred. †1 Berkeley chiefly insists on the impossibility of directly seeing the third dimension of space, since the retina of the eye is a surface. But, in point of fact, the retina is not even a surface; it is a conglomeration of nerve-needles directed toward the light and having only their extreme points sensitive, these points lying at considerable distances from one another compared with their areas. Now, of these points, certainly the excitation of no one singly can produce the perception of a surface, and consequently not the aggregate of all the sensations can amount to this. But certain relations subsist between the excitations of different nerve-points, and these constitute the premisses upon which the hypothesis of space is founded, and from which it is inferred. †2 That space is not immediately perceived is now universally admitted; and a mediate cognition is what is called an inference, and is subject to the criticism of logic. But what are we to say to the fact of every chicken as soon as it is hatched solving a problem whose data are of a complexity sufficient to try the greatest mathematical powers? It would be insane to deny that the tendency to light upon the conception of space is inborn in the mind of the chicken and of every animal. The same thing is equally true of time. That time is not directly perceived is evident, since no lapse of time is present, and we only perceive what is present. That, not having the idea of time, we should never be able to perceive the flow in our sensations without some particular aptitude for it, will probably also be admitted. The idea of force — at least, in its rudiments — is another conception so early arrived at, and found in animals so low in the scale of intelligence, that it must be supposed innate. But the innateness of an idea admits of degree, for it consists in the tendency of that idea to present itself to the mind. Some ideas, like that of space, do so present themselves irresistibly at the very dawn of intelligence, and take possession of the mind on small provocation, while of other conceptions we are prepossessed, indeed, but not so strongly, down a scale which is greatly extended. The tendency to personify every thing, and to attribute human characters to it, may be said to be innate; but it is a tendency which is very soon overcome by civilized man in regard to the greater part of the objects about him. Take such a conception as that of gravitation varying inversely as the square of the distance. It is a very simple law. But to say that it is simple is merely to say that it is one which the mind is particularly adapted to apprehend with facility. Suppose the idea of a quantity multiplied into another had been no more easy to the mind than that of a quantity raised to the power indicated by itself — should we ever have discovered the law of the solar system?

417. It seems incontestable, therefore, that the mind of man is strongly adapted to the comprehension of the world; at least, so far as this goes, that certain conceptions, highly important for such a comprehension, naturally arise in his mind; and, without such a tendency, the mind could never have had any development at all.

418. †1 How are we to explain this adaptation? The great utility and indispensableness of the conceptions of time, space, and force, even to the lowest intelligence, are such as to suggest that they are the results of natural selection. Without something like geometrical, kinetical, and mechanical conceptions, no animal could seize his food or do anything which might be necessary for the preservation of the species. He might, it is true, be provided with an instinct which would generally have the same effect; that is to say, he might have conceptions different from those of time, space, and force, but which coincided with them in regard to the ordinary cases of the animal's experience. But, as that animal would have an immense advantage in the struggle for life whose mechanical conceptions did not break down in a novel situation (such as development must bring about), there would be a constant selection in favor of more and more correct ideas of these matters. Thus would be attained the knowledge of that fundamental law upon which all science rolls; namely, that forces depend upon relations of time, space, and mass. When this idea was once sufficiently clear, it would require no more than a comprehensible degree of genius to discover the exact nature of these relations. Such an hypothesis naturally suggests itself, but it must be admitted that it does not seem sufficient to account for the extraordinary accuracy with which these conceptions apply to the phenomena of Nature, and it is probable that there is some secret here which remains to be discovered.

§5. Design E

419. Some important questions of logic depend upon whether we are to consider the material universe as of limited extent and finite age, or quite boundless in space and in time. In the former case, it is conceivable that a general plan or design embracing the whole universe should be discovered, and it would be proper to be on the alert for some traces of such a unity. In the latter case, since the proportion of the world of which we can have any experience is less than the smallest assignable fraction, it follows that we never could discover any pattern in the universe except a repeating one; any design embracing the whole would be beyond our powers to discern, and beyond the united powers of all intellects during all time. Now, what is absolutely incapable of being known is, as we have seen in a former paper, †1 not real at all. An absolutely incognizable existence is a nonsensical phrase. If, therefore, the universe is infinite, the attempt to find in it any design embracing it as a whole is futile, and involves a false way of looking at the subject. If the universe never had any beginning, and if in space world stretches beyond world without limit, there is no whole of material things, and consequently no general character to the universe, and no need or possibility of any governor for it. But if there was a time before which absolutely no matter existed, if there are certain absolute bounds to the region of things outside of which there is a mere void, then we naturally seek for an explanation of it, and, since we cannot look for it among material things, the hypothesis of a great disembodied animal, the creator and governor of the world, is natural enough.

420. The actual state of the evidence as to the limitation of the universe is as follows: As to time, we find on our earth a constant progress of development since the planet was a red-hot ball; the solar system seems to have resulted from the condensation of a nebula, and the process appears to be still going on. We sometimes see stars (presumably with systems of worlds) destroyed and apparently resolved back into the nebulous condition, but we have no evidence of any existence of the world previous to the nebulous stage from which it seems to have been evolved. All this rather favors the idea of a beginning than otherwise. As for limits in space, we cannot be sure that we see anything outside of the system of the Milky Way. Minds of theological predilections have therefore no need of distorting the facts to reconcile them with their views.

421. But the only scientific presumption is, that the unknown parts of space and time are like the known parts, occupied; that, as we see cycles of life and death in all development which we can trace out to the end, the same holds good in regard to solar systems; that as enormous distances lie between the different planets of our solar system, relatively to their diameters, and as still more enormous distances lie between our system relatively to its diameter and other systems, so it may be supposed that other galactic clusters exist so remote from ours as not to be recognized as such with certainty. I do not say that these are strong inductions; I only say that they are the presumptions which, in our ignorance of the facts, should be preferred to hypotheses which involve conceptions of things and occurrences totally different in their character from any of which we have had any experience, such as disembodied spirits, the creation of matter, infringements of the laws of mechanics, etc.

422. The universe ought to be presumed too vast to have any character. When it is claimed that the arrangements of Nature are benevolent, or just, or wise, or of any other peculiar kind, we ought to be prejudiced against such opinions, as being the offspring of an ill-founded notion of the finitude of the world. And examination has hitherto shown that such beneficences, justice, etc., are of a most limited kind — limited in degree and limited in range.

423. In like manner, if anyone claims to have discovered a plan in the structure of organized beings, or a scheme in their classification, or a regular arrangement among natural objects, or a system of proportionality in the human form, or an order of development, or a correspondence between conjunctions of the planets and human events, or a significance in numbers, or a key to dreams, the first thing we have to ask is whether such relations are susceptible of explanation on mechanical principles, and if not they should be looked upon with disfavor as having already a strong presumption against them; and examination has generally exploded all such theories.

424. There are minds to whom every prejudice, every presumption, seems unfair. It is easy to say what minds these are. They are those who never have known what it is to draw a well-grounded induction, and who imagine that other people's knowledge is as nebulous as their own. That all science rolls upon presumption (not of a formal but of a real kind) is no argument with them, because they cannot imagine that there is anything solid in human knowledge. These are the people who waste their time and money upon perpetual motions and other such rubbish.

425. But there are better minds who take up mystical theories (by which I mean all those which have no possibility of being mechanically explained). These are persons who are strongly prejudiced in favor of such theories. We all have natural tendencies to believe in such things; our education often strengthens this tendency; and the result is, that to many minds nothing seems so antecedently probable as a theory of this kind. Such persons find evidence enough in favor of their views, and in the absence of any recognized logic of induction they cannot be driven from their belief.

But to the mind of a physicist there ought to be a strong presumption against every mystical theory; and therefore it seems to me that those scientific men who have sought to make out that science was not hostile to theology have not been so clear-sighted as their opponents.

426. It would be extravagant to say that science can at present disprove religion; but it does seem to me that the spirit of science is hostile to any religion except such a one as that of M. Vacherot. Our appointed teachers inform us that Buddhism is a miserable and atheistical faith, shorn of the most glorious and needful attributes of a religion; that its priests can be of no use to agriculture by praying for rain, nor to war by commanding the sun to stand still. We also hear the remonstrances of those who warn us that to shake the general belief in the living God would be to shake the general morals, public and private. This, too, must be admitted; such a revolution of thought could no more be accomplished without waste and desolation than a plantation of trees could be transferred to new ground, however wholesome in itself, without all of them languishing for a time, and many of them dying. Nor is it, by the way, a thing to be presumed that a man would have taken part in a movement having a possible atheistical issue without having taken serious and adequate counsel in regard to that responsibility. But, let the consequences of such a belief be as dire as they may, one thing is certain: that the state of the facts, whatever it may be, will surely get found out, and no human prudence can long arrest the triumphal car of truth — no, not if the discovery were such as to drive every individual of our race to suicide!

427. But it would be folly to suppose that any metaphysical theory in regard to the mode of being of the perfect is to destroy that aspiration toward the perfect which constitutes the essence of religion. It is true that, if the priests of any particular form of religion succeed in making it generally believed that religion cannot exist without the acceptance of certain formulas, or if they succeed in so interweaving certain dogmas with the popular religion that the people can see no essential analogy between a religion which accepts these points of faith and one which rejects them, the result may very well be to render those who cannot believe these things irreligious. Nor can we ever hope that any body of priests should consider themselves more teachers of religion in general than of the particular system of theology advocated by their own party. But no man need be excluded from participation in the common feelings, nor from so much of the public expression of them as is open to all the laity, by the unphilosophical narrowness of those who guard the mysteries of worship. Am I to be prevented from joining in that common joy at the revelation of enlightened principles of religion which we celebrate at Easter and Christmas because I think that certain scientific, logical, and metaphysical ideas which have been mixed up with these principles are untenable? No; to do so would be to estimate those errors as of more consequence than the truth — an opinion which few would admit. People who do not believe what are really the fundamental principles of Christianity are rare to find, and all but these few ought to feel at home in the churches.

Chapter 2: A Religion of Science E

§1. The Marriage of Religion and Science †1

428. What is science? The dictionary will say that it is systematized knowledge. Dictionary definitions, however, are too apt to repose upon derivations; which is as much as to say that they neglect too much the later steps in the evolution of meanings. Mere knowledge, though it be systematized, may be a dead memory; while by science we all habitually mean a living and growing body of truth. We might even say that knowledge is not necessary to science. The astronomical researches of Ptolemy, though they are in great measure false, must be acknowledged by every modern mathematician who reads them to be truly and genuinely scientific. That which constitutes science, then, is not so much correct conclusions, as it is a correct method. But the method of science is itself a scientific result. It did not spring out of the brain of a beginner: it was a historic attainment and a scientific achievement. So that not even this method ought to be regarded as essential to the beginnings of science. That which is essential, however, is the scientific spirit, which is determined not to rest satisfied with existing opinions, but to press on to the real truth of nature. To science once enthroned in this sense, among any people, science in every other sense is heir apparent.

429. And what is religion? In each individual it is a sort of sentiment, or obscure perception, a deep recognition of a something in the circumambient All, which, if he strives to express it, will clothe itself in forms more or less extravagant, more or less accidental, but ever acknowledging the first and last, the Α and Ω, as well as a relation to that Absolute of the individual's self, as a relative being. But religion cannot reside in its totality in a single individual. Like every species of reality, it is essentially a social, a public affair. It is the idea of a whole church, welding all its members together in one organic, systemic perception of the Glory of the Highest — an idea having a growth from generation to generation and claiming a supremacy in the determination of all conduct, private and public.

430. Now, as science grows, it becomes more and more perfect, considered as science; and no religionist can easily so narrow himself as to deny this. But as religion goes through the different stages of its history, it has, I fear we must confess, seldom been seen so vitalized as to become more and more perfect, even as judged from its own standpoint. Like a plucked flower, its destiny is to wilt and fade. The vital sentiment that gave it birth loses gradually its pristine purity and strength, till some new creed treads it down. Thus it happens quite naturally that those who are animated with the spirit of science are for hurrying forward, while those who have the interests of religion at heart are apt to press back.

431. While this double change has been taking place, religion has found herself compelled to define her position; and, in doing so, has inevitably committed herself to sundry propositions, which, one by one, have been, first questioned, then assailed, and finally overthrown by advancing science. Seeing such a chasm open before her feet, religion has at first violently recoiled, and at last has leapt it; satisfying herself as best she might with an altered creed. In most cases the leap has not seemed to hurt her; yet internal injuries may have been sustained. Who can doubt that the church really did suffer from the discovery of the Copernican system, although infallibility, by a narrow loophole, managed to escape? In this way, science and religion become forced into hostile attitudes. Science, to specialists, may seem to have little or nothing to say that directly concerns religion; but it certainly encourages a philosophy which, if in no other respect, is at any rate opposed to the prevalent tendency of religion, in being animated by a progressive spirit. There arises, too, a tendency to pooh-pooh at things unseen.

432. It would be ridiculous to ask to whose fault this situation is chargeable. You cannot lay blame upon elemental forces. Religion, from the nature of things, refuses to go through her successive transformations with sufficient celerity to keep always in accord with the convictions of scientific philosophy. The day has come, however, when the man whom religious experience most devoutly moves can recognize the state of the case. While adhering to the essence of religion, and so far as possible to the church, which is all but essential, say, penessential, to it, he will cast aside that religious timidity that is forever prompting the church to recoil from the paths into which the Governor of history is leading the minds of men, a cowardice that has stood through the ages as the landmark and limit of her little faith, and will gladly go forward, sure that truth is not split into two warring doctrines, and that any change that knowledge can work in his faith can only affect its expression, but not the deep mystery expressed.

433. Such a state of mind may properly be called a religion of science. Not that it is a religion to which science or the scientific spirit has itself given birth; for religion, in the proper sense of the term, can arise from nothing but the religious sensibility. But it is a religion, so true to itself, that it becomes animated by the scientific spirit, confident that all the conquests of science will be triumphs of its own, and accepting all the results of science, as scientific men themselves accept them, as steps toward the truth, which may appear for a time to be in conflict with other truths, but which in such cases merely await adjustments which time is sure to effect. This attitude, be it observed, is one which religion will assume not at the dictate of science, still less by way of a compromise, but simply and solely out of a bolder confidence in herself and in her own destiny.

434. Meantime, science goes unswervingly its own gait. What is to be its goal is precisely what it must not seek to determine for itself, but let itself be guided by nature's strong hand. Teleological considerations, that is to say ideals, must be left to religion; science can allow itself to be swayed only by efficient causes; and philosophy, in her character of queen of the sciences, must not care, or must not seem to care, whether her conclusions be wholesome or dangerous.

§2. What Is Christian Faith? †1

435. It is easy to chop logic about matters of which you have no experience whatever. Men colour blind have more than once learnedly discussed the laws of colour-sensation, and have made interesting deductions from those laws. But when it comes to positive knowledge, such knowledge as a lawyer has of the practice of the courts, that can only rest on long experience, direct or indirect. So, a man may be an accomplished theologian without ever having felt the stirring of the spirit; but he cannot answer the simple question at the head of this article except out of his own religious experience.

436. There is in the dictionary a word, solipsism, meaning the belief that the believer is the only existing person. Were anybody to adopt such a belief, it might be difficult to argue him out of it. But when a person finds himself in the society of others, he is just as sure of their existence as of his own, though he may entertain a metaphysical theory that they are all hypostatically the same ego. In like manner, when a man has that experience with which religion sets out, he has as good reason — putting aside metaphysical subtilties — to believe in the living personality of God as he has to believe in his own. Indeed, belief is a word inappropriate to such direct perception.

437. Seldom do we pass a single hour of our waking lives away from the companionship of men (including books); and even the thoughts of that solitary hour are filled with ideas which have grown in society. Prayer, on the other hand, occupies but little of our time; and, of course, if solemnity and ceremony are to be made indispensable to it (though why observe manners toward the Heavenly Father that an earthly father would resent as priggish?) nothing more is practicable. Consequently, religious ideas never come to form the warp and woof of our mental constitution, as do social ideas. They are easily doubted, and are open to various reasons for doubt, which reasons may all be comprehended under one, namely, that the religious phenomenon is sporadic, not incessant.

438. This causes a degeneration in religion from a perception to a trust, from a trust to a belief, and a belief continually becoming more and more abstract. Then, after a religion has become a public affair, quarrels arise, to settle which watchwords are drawn up. This business gets into the hands of theologians: and the ideas of theologians aways appreciably differ from those of the universal church. They swamp religion in fallacious logical disputations. Thus, the natural tendency is to the continual drawing tighter and tighter of the narrowing bounds of doctrine, with less and less attention to the living essence of religion, until, after some symbolum quodcumque has declared that the salvation of each individual absolutely and almost exclusively depends upon his entertaining a correct metaphysics of the godhead, the vital spark of inspiration becomes finally quite extinct.

439. Yet it is absurd to say that religion is a mere belief. You might as well call society a belief, or politics a belief, or civilization a belief. Religion is a life, and can be identified with a belief only provided that belief be a living belief — a thing to be lived rather than said or thought.

440. The Christian religion, if it has anything distinctive — and must not aspire to be the necessary ultimate outcome of every path of religious progress — is distinguished from other religions by its precept about the Way of Life. I appeal to the typical Christian to answer out of the abundance of his spirit, without dictation from priests, whether this be not so. In the recently discovered book, The Teaching of the Twelve Apostles, †P1 which dates from about A.D. 100, we see that, long before the Apostles' or any other creed was insisted upon, or at all used, the teaching of the Lord was considered to consist in the doctrine of the Two Ways — the Way of Life and the Way of Death. This it was that at that date was regarded as the saving faith — not a lot of metaphysical propositions. This is what Jesus Christ taught; and to believe in Christ is to believe what he taught.

441. Now what is this way of life? Again I appeal to the universal Christian conscience to testify that it is simply love. As far as it is contracted to a rule of ethics, it is: Love God, and love your neighbour; "on these two commandments hang all the law and the prophets." It may be regarded in a higher point of view with St. John as the universal evolutionary formula. But in whatever light it be regarded or in whatever direction developed, the belief in the law of love is the Christian faith.

442. "Oh," but it may be said, "that is not distinctive of Christianity! That very idea was anticipated by the early Egyptians, by the Stoics, by the Buddhists, and by Confucius." So it was; nor can the not insignificant difference between the negative and the positive precept be properly estimated as sufficient for a discrimination between religions. Christians may, indeed, claim that Christianity possesses that earmark of divine truth — namely, that it was anticipated from primitive ages. The higher a religion the more catholic.

443. Man's highest developments are social; and religion, though it begins in a seminal individual inspiration, only comes to full flower in a great church coextensive with a civilization. This is true of every religion, but supereminently so of the religion of love. Its ideal is that the whole world shall be united in the bond of a common love of God accomplished by each man's loving his neighbour. Without a church, the religion of love can have but a rudimentary existence; and a narrow, little exclusive church is almost worse than none. A great catholic church is wanted.

444. The invisible church does now embrace all Christendom. Every man who has been brought up in the bosom of Christian civilization does really believe in some form of the principle of love, whether he is aware of doing so, or not.

445. Let us, at any rate, get all the good from the vital element in which we are all at one that it can yield: and the good that it can yield is simply all that is anyway possible, and richer than is easily conceivable. Let us endeavour, then, with all our might to draw together the whole body of believers in the law of love into sympathetic unity of consciousness. Discountenance as immoral all movements that exaggerate differences, or that go to make fellowship depend on formulas invented to exclude some Christians from communion with others.

446. A sapient critic has recently blamed me for defective cocksureness in my metaphysical views. That is no less than an indictment for practicing just as I have aways preached. Absurd was the epithet ever coming to my tongue for persons very confident in opinions which other minds, as good as they, denied. Can you induce the philosophic world to agree upon any assignable creed, or in condemning any specified item in the current creeds of Christendom? I believe not; though doubtless you can gather a sequacious little flock, quite disposed to follow their bell-bearer into every vagary — if you will be satisfied so. For my part, I should think it more lovely to patch up such peace as might be with the great religious world. This happens to be easy to an individual whose unbiased study of scientific logic has led him to conclusions not discordant with traditional dogmas. Unfortunately, such a case is exceptional; and guilt rests on you who insist on so tautening the lines of churches as to close them against the great body of educated and thinking men, pure and undefiled though the religion of many of them (you are obliged to acknowledge it) be. Surely another generation will witness a sweeping reform in this respect. You will not be permitted to make of those churches a permanent laughing-stock for coming ages. Many things are essential to religion which yet ought not to be insisted on: the law of love is not the rule of angry and bullying insistence. Thus, it seems plain to me, I confess, that miracles are intrinsic elements of a genuine religion. †1 But it is not half so important to emphasize this as it is to draw into our loving communion almost the entire collection of men who unite clear thought with intellectual integrity. And who are you, anyway, who are so zealous to keep the churches small and exclusive? Do you number among your party the great scholars and the great saints? Are you not, on the other hand, egged on by all the notorious humbugs — votaries of Mammon or of Ward McAllister — who deem the attitude of a church-caryatid to be a respectable or a genteel thing? Your voting-power, too, is repleted with many who, as soon as they are a little better informed and educated, will drop away from you; and in these days that education will come speedily.

447. To those who for the present are excluded from the churches, and who, in the passionate intensity of their religious desire, are talking of setting up a church for the scientifically educated, a man of my stripe must say, Wait, if you can; it will be but a few years longer; but if you cannot wait, why then Godspeed! Only, do not, in your turn, go and draw lines so as to exclude such as believe a little less — or, still worse, to exclude such as believe a little more — than yourselves. Doubtless, a lot of superstition clings to the historical churches; but superstition is the grime upon the venerable pavement of the sacred edifice, and he who would wash that pavement clean should be willing to get down on his knees to his work inside the church.

448. A religious organization is a somewhat idle affair unless it be sworn in as a regiment of that great army that takes life in hand, with all its delights, in grimmest fight to put down the principle of self-seeking, and to make the principle of love triumphant. It has something more serious to think about than the phraseology of the articles of war. Fall into the ranks then; follow your colonel. Keep your one purpose steadily and alone in view, and you may promise yourself the attainment of your sole desire, which is to hasten the chariot wheels of redeeming love!

§3. The Church †1

449. Many a scientific man and student of philosophy recognizes that it is the Christian church which has made him a man among men. To it he owes consolations, enjoyments, escapes from great perils, and whatever rectitude of heart and purpose may be his. To the monks of the medieval church he owes the preservation of ancient literature; and without the revival of learning he can hardly see how the revival of science would have been possible. To them he owes the framework of his intellectual system, and if he speaks English, a most important part of his daily speech. The law of love which, however little it be obeyed, he holds to be the soul of civilization, came to Europe through Christianity. Besides, religion is a great, perhaps the greatest, factor of that social life which extends beyond one's own circle of personal friends. That life is everything for elevated, and humane, and democratic civilization; and if one renounces the Church, in what other way can one as satisfactorily exercise the faculty of fraternizing with all one's neighbours?

450. On the other hand, owe what one may to the Church, the truth claims paramount allegiance; and above the importance of any particular truth, or body of truths, is that of the right methods of reaching the truth. Now the Church requires subscription to a platform — a Creed. And how has that platform been made? With strict party regularity, no doubt. Yet whether it be that of Trent, Lambeth, Geneva, or what, there is not one plank in it that has not, as a matter of historical fact, been inserted with a view of proclaiming the damnation and of procuring the persecution of some body of convinced Christians. Hence it is that the central doctrine of love is not to be found in any one of them. Granting for a moment that exact theology is a vital matter, as all creeds agree to make it (though had it been so deemed by the founder of Christianity he would have laid down his own formula in set terms), can anybody who understands the procedure of science, or has so much as read the first book of Bacon's Novum Organum, assent for a moment to the idea that any science, be it theology or any other, can be rightly developed under the impulses of ecclesiastical ambition and the odium of priests? Truth is the fruit of free inquiry and of such docility toward facts as shall make us always willing to acknowledge that we are wrong, and anxious to discover that we have been so.

451. The raison d'être of a church is to confer upon men a life broader than their narrow personalities, a life rooted in the very truth of being. To do that it must be based upon and refer to a definite and public experience. Fears of hell and hopes of paradise have no such reference; they are matters all sane men confess they know nothing about. Even for the greatest saints, the active motives were not such hopes and fears, but the prospect of leaving behind them fertile seeds of desirable fruits here on earth. It is not the question whether miracles and answers to prayer are abstractly possible. The question is whether they are appreciable constituents of human experiences, worth taking into account in comparison with those great facts of life that no man either doubts or ever will doubt.

Chapter 3: A Neglected Argument for the Reality of God †1

§1. Musement E

452. The word "God," so "capitalized" (as we Americans say), is the definable proper name, signifying Ens necessarium; in my belief Really creator of all three Universes of Experience.

Some words shall herein be capitalized when used, not as vernacular, but as terms defined. Thus an "idea" is the substance of an actual unitary thought or fancy; but "Idea," nearer Plato's idea of {idea}, denotes anything whose Being consists in its mere capacity for getting fully represented, regardless of any person's faculty or impotence to represent it.

453. "Real" is a word invented in the thirteenth century to signify having Properties, i.e. characters sufficing to identify their subject, and possessing these whether they be anywise attributed to it by any single man or group of men, or not. Thus, the substance of a dream is not Real, since it was such as it was, merely in that a dreamer so dreamed it; but the fact of the dream is Real, if it was dreamed; since if so, its date, the name of the dreamer, etc. make up a set of circumstances sufficient to distinguish it from all other events; and these belong to it, i.e. would be true if predicated of it, whether A, B, or C Actually ascertains them or not. The "Actual" is that which is met with in the past, present, or future.

454. An "Experience" is a brutally produced conscious effect that contributes to a habit, self-controlled, yet so satisfying, on deliberation, as to be destructible by no positive exercise of internal vigour. I use the word "self-controlled" for "controlled by the thinker's self," and not for "uncontrolled" except in its own spontaneous, i.e. automatic, self-development, as Professor J. M. Baldwin †2 uses the word. Take for illustration the sensation undergone by a child that puts its forefinger into a flame with the acquisition of a habit of keeping all its members out of all flames. A compulsion is "Brute," whose immediate efficacy nowise consists in conformity to rule or reason.

455. Of the three Universes of Experience familiar to us all †1, the first comprises all mere Ideas, those airy nothings to which the mind of poet, pure mathematician, or another might give local habitation and a name within that mind. Their very airy-nothingness, the fact that their Being consists in mere capability of getting thought, not in anybody's Actually thinking them, saves their Reality. The second Universe is that of the Brute Actuality of things and facts. I am confident that their Being consists in reactions against Brute forces, notwithstanding objections redoubtable until they are closely and fairly examined. The third Universe comprises everything whose being consists in active power to establish connections between different objects, especially between objects in different Universes. Such is everything which is essentially a Sign — not the mere body of the Sign, which is not essentially such, but, so to speak, the Sign's Soul, which has its Being in its power of serving as intermediary between its Object and a Mind. Such, too, is a living consciousness, and such the life, the power of growth, of a plant. Such is a living constitution — a daily newspaper, a great fortune, a social "movement."

456. An "Argument" is any process of thought reasonably tending to produce a definite belief. †2 An "Argumentation" is an Argument proceeding upon definitely formulated premisses.

457. If God Really be, and be benign, then, in view of the generally conceded truth that religion, were it but proved, would be a good outweighing all others, we should naturally expect that there would be some Argument for His Reality that should be obvious to all minds, high and low alike, that should earnestly strive to find the truth of the matter; and further, that this Argument should present its conclusion, not as a proposition of metaphysical theology, but in a form directly applicable to the conduct of life, and full of nutrition for man's highest growth. What I shall refer to as the N.A. — the Neglected Argument — seems to me best to fulfill this condition, and I should not wonder if the majority of those whose own reflections have harvested belief in God must bless the radiance of the N.A. for that wealth. Its persuasiveness is no less than extraordinary; while it is not unknown to anybody. Nevertheless, of all those theologians (within my little range of reading) who, with commendable assiduity, scrape together all the sound reasons they can find or concoct to prove the first proposition of theology, few mention this one, and they most briefly. They probably share those current notions of logic which recognize no other Arguments than Argumentations.

458. There is a certain agreeable occupation of mind which, from its having no distinctive name, I infer is not as commonly practiced as it deserves to be; for indulged in moderately — say through some five to six per cent of one's waking time, perhaps during a stroll — it is refreshing enough more than to repay the expenditure. Because it involves no purpose save that of casting aside all serious purpose, I have sometimes been half-inclined to call it reverie with some qualification; but for a frame of mind so antipodal to vacancy and dreaminess such a designation would be too excruciating a misfit. In fact, it is Pure Play. Now, Play, we all know, is a lively exercise of one's powers. Pure Play has no rules, except this very law of liberty. It bloweth where it listeth. It has no purpose, unless recreation. The particular occupation I mean — a petite bouchée with the Universes — may take either the form of aesthetic contemplation, or that of distant castle-building (whether in Spain or within one's own moral training), or that of considering some wonder in one of the Universes, or some connection between two of the three, with speculation concerning its cause. It is this last kind — I will call it "Musement" on the whole — that I particularly recommend, because it will in time flower into the N.A. One who sits down with the purpose of becoming convinced of the truth of religion is plainly not inquiring in scientific singleness of heart, and must aways suspect himself of reasoning unfairly. So he can never attain the entirety even of a physicist's belief in electrons, although this is avowedly but provisional. But let religious meditation be allowed to grow up spontaneously out of Pure Play without any breach of continuity, and the Muser will retain the perfect candour proper to Musement.

459. If one who had determined to make trial of Musement as a favorite recreation were to ask me for advice, I should reply as follows: The dawn and the gloaming most invite one to Musement; but I have found no watch of the nychthemeron that has not its own advantages for the pursuit. It begins passively enough with drinking in the impression of some nook in one of the three Universes. But impression soon passes into attentive observation, observation into musing, musing into a lively give and take of communion between self and self. If one's observations and reflections are allowed to specialize themselves too much, the Play will be converted into scientific study; and that cannot be pursued in odd half hours.

460. I should add: Adhere to the one ordinance of Play, the law of liberty. I can testify that the last half century, at least, has never lacked tribes of Sir Oracles, colporting brocards to bar off one or another roadway of inquiry; and a Rabelais would be needed to bring out all the fun that has been packed in their airs of infallibility. Auguste Comte, notwithstanding his having apparently produced some unquestionably genuine thinking, was long the chief of such a band. The vogue of each particular maxim of theirs was necessarily brief. For what distinction can be gained by repeating saws heard from all mouths? No bygone fashion seems more grotesque than a panache of obsolete wisdom. I remember the days when a pronouncement all the rage was that no science must borrow the methods of another; the geologist must not use a microscope, nor the astronomer a spectroscope. Optics must not meddle with electricity, nor logic with algebra. But twenty years later, if you aspired to pass for a commanding intellect, you would have to pull a long face and declare that "It is not the business of science to search for origins." This maxim was a masterpiece, since no timid soul, in dread of being thought naive, would dare inquire what "origins" were, albeit the secret confessor within his breast compelled the awful self-acknowledgment of his having no idea into what else than "origins" of phenomena (in some sense of that indefinite word) man can inquire. That human reason can comprehend some causes is past denial, and once we are forced to recognize a given element in experience, it is reasonable to await positive evidence before we complicate our acknowledgment with qualifications. Otherwise, why venture beyond direct observation? Illustrations of this principle abound in physical science. Since, then, it is certain that man is able to understand the laws and the causes of some phenomena, it is reasonable to assume, in regard to any given problem, that it would get rightly solved by man, if a sufficiency of time and attention were devoted to it. Moreover, those problems that at first blush appear utterly insoluble receive, in that very circumstance, as Edgar Poe remarked †1 in his "The Murders in the Rue Morgue," their smoothly-fitting keys. This particularly adapts them to the Play of Musement.

461. Forty or fifty minutes of vigorous and unslackened analytic thought bestowed upon one of them usually suffices to educe from it all there is to educe, its general solution. There is no kind of reasoning that I should wish to discourage in Musement; and I should lament to find anybody confining it to a method of such moderate fertility as logical analysis. Only, the Player should bear in mind that the higher weapons in the arsenal of thought are not playthings but edge-tools. In any mere Play they can be used by way of exercise alone; while logical analysis can be put to its full efficiency in Musement. So, continuing the counsels that had been asked of me, I should say, "Enter your skiff of Musement, push off into the lake of thought, and leave the breath of heaven to swell your sail. With your eyes open, awake to what is about or within you, and open conversation with yourself; for such is all meditation." It is, however, not a conversation in words alone, but is illustrated, like a lecture, with diagrams and with experiments.

462. Different people have such wonderfully different ways of thinking that it would be far beyond my competence to say what courses Musements might not take; but a brain endowed with automatic control, as man's indirectly is, is so naturally and rightly interested in its own faculties that some psychological and semi-psychological questions would doubtless get touched; such, in the latter class, as this: Darwinians, with truly surprising ingenuity, have concocted, and with still more astonishing confidence have accepted as proved, one explanation for the diverse and delicate beauties of flowers, another for those of butterflies, and so on; but why is all nature — the forms of trees, the compositions of sunsets — suffused with such beauties throughout, and not nature only, but the other two Universes as well? Among more purely psychological questions, the nature of pleasure and pain will be likely to attract attention. Are they mere qualities of feeling, or are they rather motor instincts attracting us to some feelings and repelling others? Have pleasure and pain the same sort of constitution, or are they contrasted in this respect, pleasure arising upon the forming or strengthening of an association by resemblance, and pain upon the weakening or disruption of such a habit or conception? †1

463. Psychological speculations will naturally lead on to musings upon metaphysical problems proper, good exercise for a mind with a turn for exact thought. It is here that one finds those questions that at first seem to offer no handle for reason's clutch, but which readily yield to logical analysis. But problems of metaphysics will inevitably present themselves that logical analysis will not suffice to solve. Some of the best will be motived by a desire to comprehend universe-wide aggregates of unformulated but partly experienced phenomena. I would suggest that the Muser be not too impatient to analyze these, lest some significant ingredient be lost in the process; but that he begin by pondering them from every point of view, until he seems to read some truth beneath the phenomena.

464. At this point a trained mind will demand that an examination be made of the truth of the interpretation; and the first step in such examination must be a logical analysis of the theory. But strict examination would be a task a little too serious for the Musement of hour fractions, and if it is postponed there will be ample remuneration even in the suggestions that there is not time to examine; especially since a few of them will appeal to reason as all but certain.

Let the Muser, for example, after well appreciating, in its breadth and depth, the unspeakable variety of each Universe, turn to those phenomena that are of the nature of homogeneities of connectedness in each; and what a spectacle will unroll itself! As a mere hint of them I may point out that every small part of space, however remote, is bounded by just such neighbouring parts as every other, without a single exception throughout immensity. The matter of Nature is in every star of the same elementary kinds, and (except for variations of circumstance), what is more wonderful still, throughout the whole visible universe, about the same proportions of the different chemical elements prevail. Though the mere catalogue of known carbon-compounds alone would fill an unwieldy volume, and perhaps, if the truth were known, the number of amino-acids alone is greater, yet it is unlikely that there are in all more than about 600 elements, of which 500 dart through space too swiftly to be held down by the earth's gravitation, coronium being the slowest-moving of these. This small number bespeaks comparative simplicity of structure. Yet no mathematician but will confess the present hopelessness of attempting to comprehend the constitution of the hydrogen-atom, the simplest of the elements that can be held to earth.

465. From speculations on the homogeneities of each Universe, the Muser will naturally pass to the consideration of homogeneities and connections between two different Universes, or all three. Especially in them all we find one type of occurrence, that of growth, itself consisting in the homogeneities of small parts. This is evident in the growth of motion into displacement, and the growth of force into motion. In growth, too, we find that the three Universes conspire; and a universal feature of it is provision for later stages in earlier ones. This is a specimen of certain lines of reflection which will inevitably suggest the hypothesis of God's Reality. It is not that such phenomena might not be capable of being accounted for, in one sense, by the action of chance with the smallest conceivable dose of a higher element; for if by God be meant the Ens necessarium, that very hypothesis requires that such should be the case. But the point is that that sort of explanation leaves a mental explanation just as needful as before. Tell me, upon sufficient authority, that all cerebration depends upon movements of neurites that strictly obey certain physical laws, and that thus all expressions of thought, both external and internal, receive a physical explanation, and I shall be ready to believe you. But if you go on to say that this explodes the theory that my neighbour and myself are governed by reason, and are thinking beings, I must frankly say that it will not give me a high opinion of your intelligence. But however that may be, in the Pure Play of Musement the idea of God's Reality will be sure sooner or later to be found an attractive fancy, which the Muser will develop in various ways. The more he ponders it, the more it will find response in every part of his mind, for its beauty, for its supplying an ideal of life, and for its thoroughly satisfactory explanation of his whole threefold environment.

§2. The Hypothesis of God E

466. The hypothesis of God is a peculiar one, in that it supposes an infinitely incomprehensible object, although every hypothesis, as such, supposes its object to be truly conceived in the hypothesis. This leaves the hypothesis but one way of understanding itself; namely, as vague yet as true so far as it is definite, and as continually tending to define itself more and more, and without limit. The hypothesis, being thus itself inevitably subject to the law of growth, appears in its vagueness to represent God as so, albeit this is directly contradicted in the hypothesis from its very first phase. But this apparent attribution of growth to God, since it is ineradicable from the hypothesis, cannot, according to the hypothesis, be flatly false. Its implications concerning the Universes will be maintained in the hypothesis, while its implications concerning God will be partly disavowed, and yet held to be less false than their denial would be. Thus the hypothesis will lead to our thinking of features of each Universe as purposed; and this will stand or fall with the hypothesis. Yet a purpose essentially involves growth, and so cannot be attributed to God. Still it will, according to the hypothesis, be less false to speak so than to represent God as purposeless.

467. Assured as I am from my own personal experience that every man capable of so controlling his attention as to perform a little exact thinking will, if he examines Zeno's argument about Achilles and the tortoise, come to think, as I do, that it is nothing but a contemptible catch, †1 I do not think that I either am or ought to be less assured, from what I know of the effects of Musement on myself and others, that any normal man who considers the three Universes in the light of the hypothesis of God's Reality, and pursues that line of reflection in scientific singleness of heart, will come to be stirred to the depths of his nature by the beauty of the idea and by its august practicality, even to the point of earnestly loving and adoring his strictly hypothetical God, and to that of desiring above all things to shape the whole conduct of life and all the springs of action into conformity with that hypothesis. Now to be deliberately and thoroughly prepared to shape one's conduct into conformity with a proposition is neither more nor less than the state of mind called Believing that proposition, however long the conscious classification of it under that head be postponed. †2

§3. The Three Stages of Inquiry E

468. There is my poor sketch of the Neglected Argument, greatly cut down to bring it within the limits assigned to this article. Next should come the discussion of its logicality; but nothing readable at a sitting could possibly bring home to readers my full proof of the principal points of such an examination. I can only hope to make the residue of this paper a sort of table of contents, from which some may possibly guess what I have to say; or to lay down a series of plausible points through which the reader will have to construct the continuous line of reasoning for himself. In my own mind the proof is elaborated, and I am exerting my energies to getting it submitted to public censure. My present abstract will divide itself into three unequal parts. The first shall give the headings of the different steps of every well-conducted and complete inquiry, without noticing possible divergencies from the norm. I shall have to mention some steps which have nothing to do with the Neglected Argument in order to show that they add no jot nor tittle to the truth which is invariably brought just as the Neglected Argument brings it. The second part shall very briefly state, without argument (for which there is no room), just wherein lies the logical validity of the reasoning characteristic of each of the main stages of inquiry. The third part shall indicate the place of the Neglected Argument in a complete inquiry into the Reality of God, and shall show how well it would fill that place, and what its logical value is supposing the inquiry to be limited to this; and I shall add a few words to show how it might be supplemented.

469. Every inquiry whatsoever takes its rise in the observation, in one or another of the three Universes, of some surprising phenomenon, some experience which either disappoints an expectation, or breaks in upon some habit of expectation of the inquisiturus; and each apparent exception to this rule only confirms it. There are obvious distinctions between the objects of surprise in different cases; but throughout this slight sketch of inquiry such details will be unnoticed, especially since it is upon such that the logic-books descant. The inquiry begins with pondering these phenomena in all their aspects, in the search of some point of view whence the wonder shall be resolved. At length a conjecture arises that furnishes a possible Explanation, by which I mean a syllogism exhibiting the surprising fact as necessarily consequent upon the circumstances of its occurrence together with the truth of the credible conjecture, as premisses. †1 On account of this Explanation, the inquirer is led to regard his conjecture, or hypothesis, with favor. As I phrase it, he provisionally holds it to be "Plausible"; this acceptance ranges in different cases — and reasonably so — from a mere expression of it in the interrogative mood, as a question meriting attention and reply, up through all appraisals of Plausibility, to uncontrollable inclination to believe. The whole series of mental performances between the notice of the wonderful phenomenon and the acceptance of the hypothesis, during which the usually docile understanding seems to hold the bit between its teeth and to have us at its mercy, the search for pertinent circumstances and the laying hold of them, sometimes without our cognizance, the scrutiny of them, the dark laboring, the bursting out of the startling conjecture, the remarking of its smooth fitting to the anomaly, as it is turned back and forth like a key in a lock, and the final estimation of its Plausibility, I reckon as composing the First Stage of Inquiry. Its characteristic formula of reasoning I term Retroduction, †1 i.e. reasoning from consequent to antecedent. In one respect the designation seems inappropriate; for in most instances where conjecture mounts the high peaks of Plausibility — and is really most worthy of confidence — the inquirer is unable definitely to formulate just what the explained wonder is; or can only do so in the light of the hypothesis. In short, it is a form of Argument rather than of Argumentation.

470. Retroduction does not afford security. The hypothesis must be tested.

This testing, to be logically valid, must honestly start, not as Retroduction starts, with scrutiny of the phenomena, but with examination of the hypothesis, and a muster of all sorts of conditional experiential consequences which would follow from its truth. This constitutes the Second Stage of Inquiry. For its characteristic form of reasoning our language has, for two centuries, been happily provided with the name Deduction.

471. Deduction has two parts. For its first step must be by logical analysis to Explicate the hypothesis, i.e. to render it as perfectly distinct as possible. This process, like Retroduction, is Argument that is not Argumentation. But unlike Retroduction, it cannot go wrong from lack of experience, but so long as it proceeds rightly must reach a true conclusion. Explication is followed by Demonstration, or Deductive Argumentation. Its procedure is best learned from Book I of Euclid's Elements, a masterpiece which in real insight is far superior to Aristotle's Analytics; and its numerous fallacies render it all the more instructive to a close student. It invariably requires something of the nature of a diagram; that is, an "Icon," or Sign that represents its Object in resembling it. It usually, too, needs "Indices," or Signs that represent their Objects by being actually connected with them. But it is mainly composed of "Symbols," or Signs that represent their Objects essentially because they will be so interpreted. Demonstration should be Corollarial when it can. An accurate definition of Corollarial Demonstration would require a long explanation; but it will suffice to say that it limits itself to considerations already introduced or else involved in the Explication of its conclusion; while Theorematic Demonstration resorts to a more complicated process of thought. †1

472. The purpose of Deduction, that of collecting consequents of the hypothesis, having been sufficiently carried out, the inquiry enters upon its Third Stage, that of ascertaining how far those consequents accord with Experience, and of judging accordingly whether the hypothesis is sensibly correct, or requires some inessential modification, or must be entirely rejected. Its characteristic way of reasoning is Induction. This stage has three parts. For it must begin with Classification, which is an Inductive Non-argumentational kind of Argument, by which general Ideas are attached to objects of Experience; or rather by which the latter are subordinated to the former. Following this will come the testing-argumentations, the Probations; and the whole inquiry will be wound up with the Sentential part of the Third Stage, which, by Inductive reasonings, appraises the different Probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result.

473. The Probations, or direct Inductive Argumentations, are of two kinds. The first is that which Bacon ill described as "inductio illa quæ procedit per enumerationem simplicem." So at least he has been understood. For an enumeration of instances is not essential to the argument that, for example, there are no such beings as fairies, or no such events as miracles. The point is that there is no well-established instance of such a thing. I call this Crude Induction. †2 It is the only Induction which concludes a logically Universal Proposition. It is the weakest of arguments, being liable to be demolished in a moment, as happened toward the end of the eighteenth century to the opinion of the scientific world that no stones fall from the sky. The other kind is Gradual Induction, †1 which makes a new estimate of the proportion of truth in the hypothesis with every new instance; and given any degree of error there will sometime be an estimate (or would be, if the probation were persisted in) which will be absolutely the last to be infected with so much falsity. Gradual Induction is either Qualitative or Quantitative and the latter either depends on measurements, or on statistics, or on countings.

§4. The Validity of the Three Stages E

474. Concerning the question of the nature of the logical validity possessed by Deduction, Induction, and Retroduction, which is still an arena of controversy, I shall confine myself to stating the opinions which I am prepared to defend by positive proofs. The validity of Deduction was correctly, if not very clearly, analyzed by Kant. †2 This kind of reasoning deals exclusively with Pure Ideas attaching primarily to Symbols and derivatively to other Signs of our own creation; and the fact that man has a power of Explicating his own meaning renders Deduction valid. Induction is a kind of reasoning that may lead us into error; but that it follows a method which, sufficiently persisted in, will be Inductively Certain (the sort of certainty we have that a perfect coin, pitched up often enough, will sometime turn up heads) to diminish the error below any predesignate degree, is assured by man's power of perceiving Inductive Certainty. In all this I am inviting the reader to peep through the big end of the telescope; there is a wealth of pertinent detail that must here be passed over.

475. Finally comes the bottom question of logical Critic, †3 What sort of validity can be attributed to the First Stage of inquiry? Observe that neither Deduction nor Induction contributes the smallest positive item to the final conclusion of the inquiry. They render the indefinite definite; Deduction Explicates; Induction evaluates: that is all. Over the chasm that yawns between the ultimate goal of science and such ideas of Man's environment as, coming over him during his primeval wanderings in the forest, while yet his very notion of error was of the vaguest, he managed to communicate to some fellow, we are building a cantilever bridge of induction, held together by scientific struts and ties. Yet every plank of its advance is first laid by Retroduction alone, that is to say, by the spontaneous conjectures of instinctive reason; and neither Deduction nor Induction contributes a single new concept to the structure. Nor is this less true or less important for those inquiries that self-interest prompts.

476. The first answer we naturally give to this question is that we cannot help accepting the conjecture at such a valuation as that at which we do accept it; whether as a simple interrogation, or as more or less Plausible, or, occasionally, as an irresistible belief. But far from constituting, by itself, a logical justification such as it becomes a rational being to put forth, this pleading, that we cannot help yielding to the suggestion, amounts to nothing more than a confession of having failed to train ourselves to control our thoughts. It is more to the purpose, however, to urge that the strength of the impulse is a symptom of its being instinctive. Animals of all races rise far above the general level of their intelligence in those performances that are their proper function, such as flying and nest-building for ordinary birds; and what is man's proper function if it be not to embody general ideas in art-creations, in utilities, and above all in theoretical cognition? To give the lie to his own consciousness of divining the reasons of phenomena would be as silly in a man as it would be in a fledgling bird to refuse to trust to its wings and leave the nest, because the poor little thing had read Babinet, †1 and judged aerostation to be impossible on hydrodynamical grounds. Yes; it must be confessed that if we knew that the impulse to prefer one hypothesis to another really were analogous to the instincts of birds and wasps, it would be foolish not to give it play, within the bounds of reason; especially since we must entertain some hypothesis, or else forego all further knowledge than that which we have already gained by that very means. But is it a fact that man possesses this magical faculty? Not, I reply, to the extent of guessing right the first time, nor perhaps the second; but that the well-prepared mind has wonderfully soon guessed each secret of nature is historical truth. All the theories of science have been so obtained. But may they not have come fortuitously, or by some such modification of chance as the Darwinian supposes? I answer that three or four independent methods of computation show that it would be ridiculous to suppose our science to have so come to pass. Nevertheless, suppose that it can be so "explained," just as that any purposed act of mine is supposed by materialistic necessitarians to have come about. Still, what of it? Does that materialistic explanation, supposing it granted, show that reason has nothing to do with my actions? Even the parallelists will admit that the one explanation leaves the same need of the other that there was before it was given; and this is certainly sound logic. There is a reason, an interpretation, a logic, in the course of scientific advance, and this indisputably proves to him who has perceptions of rational or significant relations, that man's mind must have been attuned to the truth of things in order to discover what he has discovered. It is the very bedrock of logical truth.

477. Modern science has been builded after the model of Galileo, who founded it, on il lume naturale. That truly inspired prophet had said that, of two hypotheses, the simpler is to be preferred; †1 but I was formerly one of those who, in our dull self-conceit fancying ourselves more sly than he, twisted the maxim to mean the logically simpler, the one that adds the least to what has been observed, in spite of three obvious objections: first, that so there was no support for any hypothesis; secondly, that by the same token we ought to content ourselves with simply formulating the special observations actually made; and thirdly, that every advance of science that further opens the truth to our view discloses a world of unexpected complications. It was not until long experience forced me to realize that subsequent discoveries were every time showing I had been wrong, while those who understood the maxim as Galileo had done, early unlocked the secret, that the scales fell from my eyes and my mind awoke to the broad and flaming daylight that it is the simpler Hypothesis in the sense of the more facile and natural, the one that instinct suggests, that must be preferred; for the reason that, unless man have a natural bent in accordance with nature's, he has no chance of understanding nature at all. Many tests of this principal and positive fact, relating as well to my own studies as to the researches of others, have confirmed me in this opinion; and when I shall come to set them forth in a book, their array will convince everybody. Oh, no! I am forgetting that armour, impenetrable by accurate thought, in which the rank and file of minds are clad! They may, for example, get the notion that my proposition involves a denial of the rigidity of the laws of association: it would be quite on a par with much that is current. I do not mean that logical simplicity is a consideration of no value at all, but only that its value is badly secondary to that of simplicity in the other sense.

If, however, the maxim is correct in Galileo's sense, whence it follows that man has, in some degree, a divinatory power, primary or derived, like that of a wasp or a bird, then instances swarm to show that a certain altogether peculiar confidence in a hypothesis, not to be confounded with rash cocksureness, has a very appreciable value as a sign of the truth of the hypothesis. I regret I cannot give an account of certain interesting and almost convincing cases. The N.A. excites this peculiar confidence in the very highest degree.

§5. Pragmaticism †1 E

478. We have now to apply these principles to the evaluation of the N.A. Had I space I would put this into the shape of imagining how it is likely to be esteemed by three types of men: the first of small instruction with corresponding natural breadth, intimately acquainted with the N.A., but to whom logic is all Greek; the second, inflated with current notions of logic, but prodigiously informed about the N.A.; the third, a trained man of science who, in the modern spirit, has added to his specialty an exact theoretical and practical study of reasoning and the elements of thought, so that psychologists account him a sort of psychologist, and mathematicians a sort of mathematician.

479. I should, then, show how the first would have learned that nothing has any kind of value in itself — whether æsthetic, moral, or scientific — but only in its place in the whole production to which it appertains; and that an individual soul with its petty agitations and calamities is a zero except as filling its infinitesimal place, and accepting his little futility as his entire treasure. He will see that though his God would not really (in a certain sense) adapt means to ends, it is nevertheless quite true that there are relations among phenomena which finite intelligence must interpret, and truly interpret, as such adaptations; and he will macarize himself for his own bitterest griefs, and bless God for the law of growth with all the fighting it imposes upon him — Evil, i.e. what it is man's duty to fight, being one of the major perfections of the Universe. In that fight he will endeavour to perform just the duty laid upon him and no more. Though his desperate struggles should issue in the horrors of his rout, and he should see the innocents who are dearest to his heart exposed to torments, frenzy and despair, destined to be smirched with filth, and stunted in their intelligence, still he may hope that it be best for them, and will tell himself that in any case the secret design of God will be perfected through their agency; and even while still hot from the battle, will submit with adoration to His Holy will. He will not worry because the Universes were not constructed to suit the scheme of some silly scold.

480. The context of this I must leave the reader to imagine. I will only add that the third man, considering the complex process of self-control, will see that the hypothesis, irresistible though it be to first intention, yet needs Probation; and that though an infinite being is not tied down to any consistency, yet man, like any other animal, is gifted with power of understanding sufficient for the conduct of life. This brings him, for testing the hypothesis, to taking his stand upon Pragmaticism, which implies faith in common sense and in instinct, though only as they issue from the cupel-furnace of measured criticism. In short, he will say that the N.A. is the First Stage of a scientific inquiry, resulting in a hypothesis of the very highest Plausibility, whose ultimate test must lie in its value in the self-controlled growth of man's conduct of life.

481. †1 Since I have employed the word Pragmaticism, and shall have occasion to use it once more, it may perhaps be well to explain it. About forty years ago, my studies of Berkeley, Kant, and others led me, after convincing myself that all thinking is performed in Signs, and that meditation takes the form of a dialogue, so that it is proper to speak of the "meaning" of a concept, to conclude that to acquire full mastery of that meaning it is requisite, in the first place, to learn to recognize the concept under every disguise, through extensive familiarity with instances of it. But this, after all, does not imply any true understanding of it; so that it is further requisite that we should make an abstract logical analysis of it into its ultimate elements, or as complete an analysis as we can compass. But, even so, we may still be without any living comprehension of it; and the only way to complete our knowledge of its nature is to discover and recognize just what general habits of conduct a belief in the truth of the concept (of any conceivable subject, and under any conceivable circumstances) would reasonably develop; that is to say, what habits would ultimately result from a sufficient consideration of such truth. It is necessary to understand the word "conduct," here, in the broadest sense. If, for example, the predication of a given concept were to lead to our admitting that a given form of reasoning concerning the subject of which it was affirmed was valid, when it would not otherwise be valid, the recognition of that effect in our reasoning would decidedly be a habit of conduct.

482. In 1871, in a Metaphysical Club in Cambridge, Massachusetts, I used to preach this principle as a sort of logical gospel, representing the unformulated method followed by Berkeley, and in conversation about it I called it "Pragmatism." †2 In December [November] 1877 and January 1878 I set forth the doctrine in the Popular Science Monthly; and the two parts of my essay were printed in French in the Revue Philosophique, volumes vi and vii. †1 Of course, the doctrine attracted no particular attention, for, as I had remarked in my opening sentence, very few people care for logic. But in 1897 Professor James remodelled the matter, and transmogrified it into a doctrine of philosophy, †2 some parts of which I highly approved, while other and more prominent parts I regarded, and still regard, as opposed to sound logic. About the time Professor Papini †3 discovered, to the delight of the Pragmatist school, that this doctrine was incapable of definition, which would certainly seem to distinguish it from every other doctrine in whatever branch of science, I was coming to the conclusion that my poor little maxim should be called by another name; and accordingly, in April, 1905 I renamed it Pragmaticism. †4 I had never before dignified it by any name in print, except that, at Professor Baldwin's request, I wrote a definition of it for his Dictionary of Psychology and Philosophy. †5 I did not insert the word in the Century Dictionary, though I had charge of the philosophical definitions of that work; †6 for I have a perhaps exaggerated dislike of réclame.

483. It is that course of meditation upon the three Universes which gives birth to the hypothesis and ultimately to the belief that they, or at any rate two of the three, have a Creator independent of them, that I have throughout this article called the N.A., because I think the theologians ought to have recognized it as a line of thought reasonably productive of belief. This is the "humble" argument, the innermost of the nest. †7 In the mind of a metaphysician it will have a metaphysical tinge; but that seems to me rather to detract from its force than to add anything to it. It is just as good an argument, if not better, in the form it takes in the mind of the clodhopper.

484. The theologians could not have presented the N.A.; because that is a living course of thought of very various forms. But they might and ought to have described it, and should have defended it, too, as far as they could, without going into original logical researches, which could not be justly expected of them. They are accustomed to make use of the principle that that which convinces a normal man must be presumed to be sound reasoning; and therefore they ought to say whatever can truly be advanced to show that the N.A., if sufficiently developed, will convince any normal man. Unfortunately, it happens that there is very little established fact to show that this is the case. I have not pretended to have any other ground for my belief that it is so than my assumption, which each one of us makes, that my own intellectual disposition is normal. I am forced to confess that no pessimist will agree with me. I do not admit that pessimists are, at the same time, thoroughly sane, and in addition are endowed in normal measure with intellectual vigour; and my reasons for thinking so are two. The first is, that the difference between a pessimistic and an optimistic mind is of such controlling importance in regard to every intellectual function, and especially for the conduct of life, that it is out of the question to admit that both are normal, and the great majority of mankind are naturally optimistic. Now, the majority of every race depart but little from the norm of that race. In order to present my other reason, I am obliged to recognize three types of pessimists. The first type is often found in exquisite and noble natures of great force of original intellect whose own lives are dreadful histories of torment due to some physical malady. Leopardi is a famous example. We cannot but believe, against their earnest protests, that if such men had had ordinary health, life would have worn for them the same colour as for the rest of us. Meantime, one meets too few pessimists of this type to affect the present question. The second is the misanthropical type, the type that makes itself heard. It suffices to call to mind the conduct of the famous pessimists of this kind, Diogenes the Cynic, Schopenhauer, Carlyle, and their kin with Shakespeare's Timon of Athens, to recognize them as diseased minds. The third is the philanthropical type, people whose lively sympathies, easily excited, become roused to anger at what they consider the stupid injustices of life. Being easily interested in everything, without being overloaded with exact thought of any kind, they are excellent raw material for littérateurs: witness Voltaire. No individual remotely approaching the calibre of a Leibnitz is to be found among them.

485. The third argument, enclosing and defending the other two, consists in the development of those principles of logic according to which the humble argument is the first stage of a scientific inquiry into the origin of the three Universes, but of an inquiry which produces, not merely scientific belief, which is always provisional, but also a living, practical belief, logically justified in crossing the Rubicon with all the freightage of eternity. The presentation of this argument would require the establishment of several principles of logic that the logicians have hardly dreamed of, and particularly a strict proof of the correctness of the maxim of Pragmaticism. My original essay, having been written for a popular monthly, assumes, for no better reason than that real inquiry cannot begin until a state of real doubt arises and ends as soon as Belief is attained, that "a settlement of Belief," or, in other words, a state of satisfaction, is all that Truth, or the aim of inquiry, consists in. †1 The reason I gave for this was so flimsy, while the inference was so nearly the gist of Pragmaticism, that I must confess the argument of that essay might with some justice be said to beg the question. The first part of the essay, †2 however, is occupied with showing that, if Truth consists in satisfaction, it cannot be any actual satisfaction, but must be the satisfaction which would ultimately be found if the inquiry were pushed to its ultimate and indefeasible issue. This, I beg to point out, is a very different position from that of Mr. Schiller and the pragmatists of today. †3 I trust I shall be believed when I say that it is only a desire to avoid being misunderstood in consequence of my relations with pragmatism, and by no means as arrogating any superior immunity from error which I have too good reason to know that I do not enjoy, that leads me to express my personal sentiments about their tenets. Their avowedly undefinable position, if it be not capable of logical characterization, seems to me to be characterized by an angry hatred of strict logic, and even some disposition to rate any exact thought which interferes with their doctrines as all humbug. At the same time, it seems to me clear that their approximate acceptance of the Pragmaticist principle, and even that very casting aside of difficult distinctions (although I cannot approve of it), has helped them to a mightily clear discernment of some fundamental truths that other philosophers have seen but through a mist, and most of them not at all. Among such truths — all of them old, of course, yet acknowledged by few — I reckon their denial of necessitarianism; their rejection of any "consciousness" different from a visceral or other external sensation; their acknowledgment that there are, in a Pragmatistical sense, Real habits (which Really would produce effects, under circumstances that may not happen to get actualized, and are thus Real generals); and their insistence upon interpreting all hypostatic abstractions in terms of what they would or might (not actually will) come to in the concrete. It seems to me a pity they should allow a philosophy so instinct with life to become infected with seeds of death in such notions as that of the unreality of all ideas of infinity †1 and that of the mutability of truth, †2 and in such confusions of thought as that of active willing (willing to control thought, to doubt, and to weigh reasons) with willing not to exert the will (willing to believe). †3

§6. Additament †4 P

486. A nest of three arguments for the Reality of God has now been sketched, though none of them could, in the limits of a single article, be fairly presented. The first is that entirely honest, sincere and unaffected, because unprepense, meditation upon the Idea of God, into which the Play of Musement will inevitably sooner or later lead, and which, by developing a deep sense of the adorability of that Idea, will produce a truly religious Belief in His Reality and His nearness. It is a reasonable argument, because it naturally results in the most intense and living determination (Bestimmung) of the soul toward shaping the Muser's whole conduct into conformity with the Hypothesis that God is Real and very near; and such a determination of the soul in regard to any proposition is the very essence of a living Belief in such proposition. This is that "humble argument," open to every honest man, which I surmise to have made more worshippers of God than any other.

487. The second of the nest is the argument which seems to me to have been "neglected" by writers upon natural theology, consisting in showing that the humble argument is the natural fruit of free meditation, since every heart will be ravished by the beauty and adorability of the Idea, when it is so pursued. Were the theologians able to perceive the force of this argument, they would make it such a presentation of universal human nature as to show that a latent tendency toward belief in God is a fundamental ingredient of the soul, and that, far from being a vicious or superstitious ingredient, it is simply the natural precipitate of meditation upon the origin of the Three Universes. Of course, it could not, any more than any other theological argumentation, have the value or the religious vitality of the "Humble Argument"; for it would only be an apology — a vindicatory description — of the mental operations which the Humble Argument actually and actively lives out. Though this is properly the neglected argument, yet I have sometimes used the abbreviation "the N.A." for the whole nest of three.

488. The third argument of the nest consists in a study of logical methodeutic, illuminated by the light of a first-hand acquaintance with genuine scientific thought — the sort of thought whose tools literally comprise not merely Ideas of mathematical exactitude, but also the apparatus of the skilled manipulator, actually in use. The student, applying to his own trained habits of research the art of logical analysis — an art as elaborate and methodical as that of the chemical analyst, compares the process of thought of the Muser upon the Three Universes with certain parts of the work of scientific discovery, and finds that the "Humble Argument" is nothing but an instance of the first stage of all such work, the stage of observing the facts, or variously rearranging them, and of pondering them until, by their reactions with the results of previous scientific experience, there is "evolved" (as the chemists word it) an explanatory hypothesis. He will note, however, that this instance of Retroduction, undeniable as this character is, departs widely from the ordinary run of instances, especially in three respects. In the first place, the Plausibility of the hypothesis reaches an almost unparalleled height among deliberately formed hypotheses. So hard is it to doubt God's Reality, when the Idea has sprung from Musements, that there is great danger that the investigation will stop at this first stage, owing to the indifference of the Muser to any further proof of it. At the same time, this very Plausibility is undoubtedly an argument of no small weight in favor of the truth of the hypothesis.

489. In the second place, although it is a chief function of an explanatory hypothesis (and some philosophers say the only one) to excite a clear image in the mind by means of which experiential consequences of ascertainable conditions may be predicted, yet in this instance the hypothesis can only be apprehended so very obscurely that in exceptional cases alone can any definite and direct deduction from its ordinary abstract interpretation be made. How, for example, can we ever expect to be able to predict what the conduct would be, even of [an] omniscient being, governing no more than one poor solar system for only a million years or so? How much less if, being also omnipotent, he be thereby freed from all experience, all desire, all intention! Since God, in His essential character of Ens necessarium, is a disembodied spirit, and since there is strong reason to hold that what we call consciousness is either merely the general sensation of the brain or some part of it, or at all events some visceral or bodily sensation, God probably has no consciousness. Most of us are in the habit of thinking that consciousness and psychic life are the same thing and otherwise greatly to overrate the functions of consciousness. (See James's paper "Does 'Consciousness' Exist?" in Jour. Phil., Psy., and Sci. Meth. I, 477; 1904, Sep. 1. But the negative reply is, in itself, no novelty.)

490. The effects of the second peculiarity of the hypothesis are counteracted by a third, which consists in its commanding influence over the whole conduct of life of its believers. According to that logical doctrine which the present writer first formulated in 1873 †1 and named Pragmatism, the true meaning of any product of the intellect lies in whatever unitary determination it would impart to practical conduct under any and every conceivable circumstance, supposing such conduct to be guided by reflexion carried to an ultimate limit. It appears to have been virtually the philosophy of Socrates. But although it is "an old way of thinking," in the sense that it was practiced by Spinoza, Berkeley, and Kant, I am not aware of its having been definitely formulated, whether as a maxim of logical analysis or otherwise, by anybody before my publication of it in 1878. Naturally, nobody ever heard of pragmatism. People don't care for methods! they want results. Give them all the diamonds you make, and you may have the method of making them for your own. So it was not until in 1898 †2 — Professor James took hold of the old thing, dignified it by calling it by its name in print (which I had never done even when I was in charge of the philosophical part of the Century Dictionary), furbished it up, and turned it into a philosophical doctrine — that it had any vogue at all. It did not, however, shine with its present effulgence until Professor Papini †3 made the discovery that it cannot be defined — a circumstance which, I believe, distinguishes it from all other doctrines, of whatsoever natures they may be, that were ever promulgated. Thereupon I thought it high time to give my method a less distinguished designation; and I rechristened it pragmaticism. †4 Pragmaticism, then, is a theory of logical analysis, or true definition; and its merits are greatest in its application to the highest metaphysical conceptions. At the same time, these merits can only be appreciated as the result of long training. A full exposition of the pragmaticistic definition of Ens necessarium would require many pages; but some hints toward it may be given. A disembodied spirit, or pure mind, has its being out of time, since all that it is destined to think is fully in its being at any and every previous time. But in endless time it is destined to think all that it is capable of thinking. Order is simply thought embodied in arrangement; and thought embodied in any other way appears objectively as a character that is a generalization of order, and that, in the lack of any word for it, we may call for the nonce, "Super-order." It is something like uniformity. The idea may be caught if it is described as that of which order and uniformity are particular varieties. Pure mind, as creative of thought, must, so far as it is manifested in time, appear as having a character related to the habit-taking capacity, just as super-order is related to uniformity. Now imagine, in such vague way as such a thing can be imagined, a perfect cosmology of the three universes. It would prove all in relation to that subject that reason could desiderate; and of course all that it would prove must, in actual fact, now be true. But reason would desiderate that that should be proved from which would follow all that is in fact true of the three universes; and the postulate from which all this would follow must not state any matter of fact, since such fact would thereby be left unexplained. That perfect cosmology must therefore show that the whole history of the three universes, as it has been and is to be, would follow from a premiss which would not suppose them to exist at all. Moreover, such premiss must in actual fact be true. But that premiss must represent a state of things in which the three universes were completely nil. Consequently, whether in time or not, the three universes must actually be absolutely necessary results of a state of utter nothingness. We cannot ourselves conceive of such a state of nility; but we can easily conceive that there should be a mind that could conceive it, since, after all, no contradiction can be involved in mere non-existence. A state in which there should be absolutely no super-order whatsoever would be such a state of nility. For all Being involves some kind of super-order. For example, to suppose a thing to have any particular character is to suppose a conditional proposition to be true of it, which proposition would express some kind of super-order, as any formulation of a general fact does. To suppose it to have elasticity of volume is to suppose that if it were subjected to pressure its volume would diminish until at a certain point the full pressure was attained within and without its periphery. This is a super-order, a law expressible by a differential equation. Any such super-order would be a super-habit. Any general state of things whatsoever would be a super-order and a super-habit. In that state of absolute nility, in or out of time, that is, before or after the evolution of time, there must then have been a tohu bohu of which nothing whatever affirmative or negative was true universally. There must have been, therefore, a little of everything conceivable. There must have been here and there a little undifferentiated tendency to take super-habits. But such a state must tend to increase itself. For a tendency to act in any way, combined with a tendency to take habits, must increase the tendency to act in that way. Now substitute in this general statement for "tendency to act in any way" a tendency to take habits, and we see that that tendency would grow. It would also become differentiated in various ways. But there are some habits that carried beyond a certain point eliminate their subjects from the universe. There are many ways in which this may happen. Thus a tendency to lose mass will end in a total loss of mass. A tendency to lose energy will end in removing its subject from perceptible existence. A tendency to gain energy will end in the body's shooting through the universe too rapidly to produce any effect, etc.

491. Among the many pertinent considerations which have been crowded out of this article, I may just mention that it could have been shown that the hypothesis of God's Reality is logically not so isolated a conclusion as it may seem. On the contrary, it is connected so with a theory of the nature of thinking that if this be proved so is that. Now there is no such difficulty in tracing experiential consequences of this theory of thinking as there are in attempting directly to trace out other consequences of God's reality. In so short an article, it could not be expected that I should take notice of objections. Yet objections, such as they are, are obvious enough, and a few of them wear at first sight a redoubtable aspect. For example, it may be said that since I compare man's power of guessing at the truth with the instincts of animals, I ought to have noticed that these are entirely explained by the action of natural selection in endowing animals with such powers as contribute to the preservation of their different stocks; and that there is evidence that man's power of penetrating the secrets of nature depends upon this, in the fact that all the successful sciences have been either mechanical in respect to their theories or psychological. Now, some notions of mechanics are needed by all animals to enable them to get food, and are needed most by man; while correct ideas of what passes in his neighbours' minds are needed for the existence of society, and therefore for the propagation of his kind. †1 Metaphysics, however, cannot adapt the human race to maintaining itself, and therefore the presumption [is] that man has no such genius for discoveries about God, Freedom, and Immortality, as he has for physical and psychical science.

§7. Knowledge of God †2

492. [We] can know nothing except what we directly experience. So all that we can anyway know relates to experience. All the creations of our mind are but patchworks from experience. So that all our ideas are but ideas of real or transposed experiences. A word can mean nothing except the idea it calls up. So that we cannot even talk about anything but a knowable object. The unknowable about which Hamilton and the agnostics talk can be nothing but an Unknowable Knowable. The absolutely unknowable is a non-existent existence. †3 The Unknowable is a nominalistic heresy. The nominalists in giving their adherence to that doctrine which is really held by all philosophers of all stripes, namely, that experience is all we know, understand experience in their nominalistic sense as the mere first impressions of sense. These "first impressions of sense" are hypothetical creations of nominalistic metaphysics: I for one deny their existence. But anyway even if they exist, it is not in them that experience consists. By experience must be understood the entire mental product. Some psychologists whom I hold in respect will stop me here to say that, while they admit that experience is more than mere sensation, they cannot extend it to the whole mental product, since that would include hallucinations, delusions, superstitious imaginations and fallacies of all kinds; and that they would limit experience to sense-perceptions. But I reply that my statement is the logical one. Hallucinations, delusions, superstitious imaginations, and fallacies of all kinds are experiences, but experiences misunderstood; while to say that all our knowledge relates merely to sense perception is to say that we can know nothing — not even mistakenly — about higher matters, as honor, aspirations, and love.

493. Where would such an idea, say as that of God, come from, if not from direct experience? Would you make it a result of some kind of reasoning, good or bad? Why, reasoning can supply the mind with nothing in the world except an estimate of the value of a statistical ratio, that is, how often certain kinds of things are found in certain combinations in the ordinary course of experience. And scepticism, in the sense of doubt of the validity of elementary ideas — which is really a proposal to turn an idea out of court and permit no inquiry into its applicability — is doubly condemned by the fundamental principle of scientific method — condemned first as obstructing inquiry, and condemned second because it is treating some other than a statistical ratio as a thing to be argued about. No: as to God, open your eyes — and your heart, which is also a perceptive organ — and you see him. But you may ask, Don't you admit there are any delusions? Yes: I may think a thing is black, and on close examination it may turn out to be bottle-green. But I cannot think a thing is black if there is no such thing to be seen as black. Neither can I think that a certain action is self-sacrificing, if no such thing as self-sacrifice exists, although it may be very rare. It is the nominalists, and the nominalists alone, who indulge in such scepticism, which the scientific method utterly condemns.

Chapter 4: Answers to Questions concerning My Belief in God †1 P

§1. The Reality of God

494. The questions can be answered without very long explanations. "Do you believe in the existence of a Supreme Being?" Hume, in his Dialogues Concerning Natural Religion, †2 justly points out that the phrase "Supreme Being" is not an equivalent of "God," since it neither implies infinity nor any of the other attributes of God, excepting only Being and Supremacy. This is important; and another distinction between the two designations is still more so. Namely, "God" is a vernacular word and, like all such words, but more than almost any, is vague. No words are so well understood as vernacular words, in one way; yet they are invariably vague; and of many of them it is true that, let the logician do his best to substitute precise equivalents in their places, still the vernacular words alone, for all their vagueness, answer the principal purposes. This is emphatically the case with the very vague word "God," which is not made less vague by saying that it imports "infinity," etc., since those attributes are at least as vague. I shall, therefore, if you please, substitute "God," for "Supreme Being" in the question.

495. I will also take the liberty of substituting "reality" for "existence." This is perhaps overscrupulosity; but I myself always use exist in its strict philosophical sense of "react with the other like things in the environment." †3 Of course, in that sense, it would be fetichism to say that God "exists." The word "reality," on the contrary, is used in ordinary parlance in its correct philosophical sense. It is curious that its legal meaning, in which we speak of "real estate," is the earliest, occurring early in the twelfth century. Albertus Magnus, who, as a high ecclesiastic, must have had to do with such matters, imported it into philosophy. †1 But it did not become at all common until Duns Scotus, in the latter part of the thirteenth century began to use it freely. †2 I define the real as that which holds its characters on such a tenure that it makes not the slightest difference what any man or men may have thought them to be, or ever will have thought them to be, here using thought to include, imagining, opining, and willing (as long as forcible means are not used); but the real thing's characters will remain absolutely untouched.

496. Of any kind of figment, this is not true. So, then, the question being whether I believe in the reality of God, I answer, Yes. I further opine that pretty nearly everybody more or less believes this, including many of the scientific men of my generation who are accustomed to think the belief is entirely unfounded. The reason they fall into this extraordinary error about their own belief is that they precide †3 (or render precise) the conception, and, in doing so, inevitably change it; and such precise conception is easily shown not to be warranted, even if it cannot be quite refuted. Every concept that is vague is liable to be self-contradictory in those respects in which it is vague. †4 No concept, not even those of mathematics, is absolutely precise; and some of the most important for everyday use are extremely vague. Nevertheless, our instinctive beliefs involving such concepts are far more trustworthy than the best established results of science, if these be precisely understood. For instance, we all think that there is an element of order in the universe. Could any laboratory experiments render that proposition more certain than instinct or common sense leaves it? It is ridiculous to broach such a question. But when anybody undertakes to say precisely what that order consists in, he will quickly find he outruns all logical warrant. Men who are given to defining too much inevitably run themselves into confusion in dealing with the vague concepts of common sense.

497. They generally make the matter worse by erroneous, not to say absurd, notions of the function of reasoning. Every race of animals is provided with instincts well adapted to its needs, and especially to strengthening the stock. It is wonderful how unerring these instincts are. Man is no exception in this respect; but man is so continually getting himself into novel situations that he needs, and is supplied with, a subsidiary faculty of reasoning for bringing instinct to bear upon situations to which it does not directly apply. This faculty is a very imperfect one in respect to fallibility; but then it is only needed to bridge short gaps. Every step has to be reviewed and criticized; and indeed this is so essential that it is best to call an uncriticized step of inference by another name. If one does not at all know how one's belief comes about, it cannot be called even by the name of inference. If, with St. Augustine, †1 we draw the inference "I think; therefore, I am," but, when asked how we justify this inference, can only say that we are compelled to think that, since we think, we are, this uncriticized inference ought not to be called reasoning, which at the very least conceives its inference to be one of a general class of possible inferences on the same model, and all equally valid. But one must go back and criticize the premisses and the principles that guide the drawing of the conclusions. If it could be made out that all the ultimate (or first) premisses were percepts; and that all the ultimate logical principles were as clear as the principle of contradiction, then one might say that one's conclusion was perfectly rational. Strictly speaking, it would not be quite so, because it is quite possible for perception itself to deceive us, and it is much more possible for us to be mistaken about the indubitableness of logical principles. But as a matter of fact, as far as logicians have hitherto been able to push their analyses, we have in no single case, concerning a matter of fact, as distinguished from a matter of mathematical conditional possibility, been able to reach this point. We are in every case either forced by the inexorable critic, sooner or later, to declare, "such and such a proposition or mode of inference I cannot doubt; it seems perfectly clear that it is so, but I can't say why," or else the critic himself tires before the criticism has been pushed to its very end.

498. If you absolutely cannot doubt a proposition — cannot bring yourself, upon deliberation, to entertain the least suspicion of the truth of it, it is plain that there is no room to desire anything more. †1 Many and many a philosopher seems to think that taking a piece of paper and writing down "I doubt that" is doubting it, or that it is a thing he can do in a minute as soon as he decides what he wants to doubt. Descartes convinced himself that the safest way was to "begin" by doubting everything, and accordingly he tells us he straightway did so, except only his je pense, which he borrowed from St. Augustine. Well I guess not; for genuine doubt does not talk of beginning with doubting. The pragmatist knows that doubt is an art which has to be acquired with difficulty; and his genuine doubts will go much further than those of any Cartesian. What he does not doubt, about ordinary matters of everybody's life, he is apt to find that no well matured man doubts. They are part of our instincts. Instincts are now known not to be nearly so unchangeable as used to be supposed; and the present "mutation"-theory, which I have always insisted must be the way in which species have arisen, †2 is, I am confident, the first beginning of the correct theory, and shows that it is no disproof of the instinctive character of a belief that it relates to concepts which the primitive man cannot be supposed to have had. Now, this is no confirmation of what one does not doubt. For what one does not doubt cannot be rendered more satisfactory than it already is. Yet while I may entertain, as far as I can search my mind, no perceptible doubt whatever of any one of a hundred propositions, I may suspect that, among so many, some one that is not true may have slipped in; and, if so, the marvellous inerrancy of instinct may perhaps add a little to my general confidence in the whole lot. However, I am far from insisting upon the point. I think the consideration is better adapted to helping us to detect the counterfeit paper doubts, of which so many are in circulation.

499. All the instinctive beliefs, I notice, are vague. The moment they are precided, the pragmatist will begin to doubt them.

500. The fourth part of the first book of Hume's Treatise of Human Nature affords a strong argument for the correctness of my view that reason is a mere succedaneum to be used where instinct is wanting, by exhibiting the intensely ridiculous way in which a man winds himself up in silly paper doubts if he undertakes to throw common sense, i.e. instinct, overboard and be perfectly rational. Bradley's Appearance and Reality is another example of the same thing, although Bradley is at the opposite pole from Hume in what he does admit. But Bradley is in no way as good a case as Hume. Hume endeavours to modify his conclusion by not stating it in the extreme length to which it ought to carry him. But a careful reader will see that if he proves anything at all by all his reasoning, it is that reasoning, as such, is ipso facto and essentially illogical, "illegitimate," and unreasonable. And the reason it is so is that either it is bad reasoning, or rests on doubtful premisses, or else that those premisses have not been thoroughly criticized. Of course not. The moment you come to a proposition which is perfectly satisfactory, so that you can entertain not the smallest suspicion of it, this fact debars you from making any genuine criticism of it. So that what Hume's argument would lead him to is that reasoning is "illegitimate" because its premisses are perfectly satisfactory. He candidly confesses that they are satisfactory to himself. But he seems to be dissatisfied with himself for being satisfied. It is easy to see, however, that he pats himself on the back, and is very well satisfied with himself for being so dissatisfied with being satisfied. Bradley's position is equally ridiculous. Another circumstance which goes toward confirming my view that instinct is the great internal source of all wisdom and of all knowledge is that all the "triumphs of science," of which that poor old nineteenth century used to be so vain, have been confined to two directions. They either consist in physical — that is, ultimately, dynamical — explanations of phenomena, or else in explaining things on the basis of our common sense knowledge of human nature. Now dynamics is nothing but an elaboration of common sense; its experiments are mere imaginary experiments. So it all comes down to common sense in these two branches, of which the one is founded on those instincts about physical forces that are required for the feeding impulsion and the other upon those instincts about our fellows that are required for the satisfaction of the reproductive impulse. Thus, then all science is nothing but an outgrowth from these two instincts. †1

You will see that all I have been saying is not preparatory to any argument for the reality of God. It is intended as an apology for resting the belief upon instinct as the very bedrock on which all reasoning must be built.

501. I have often occasion to walk at night, for about a mile, over an entirely untravelled road, much of it between open fields without a house in sight. The circumstances are not favorable to severe study, but are so to calm meditation. If the sky is clear, I look at the stars in the silence, thinking how each successive increase in the aperture of a telescope makes many more of them visible than all that had been visible before. The fact that the heavens do not show a sheet of light proves that there are vastly more dark bodies, say planets, than there are suns. They must be inhabited, and most likely millions of them with beings much more intelligent than we are. For on the whole, the solar system seems one of the simplest; and presumably under more complicated phenomena greater intellectual power will be developed. What must be the social phenomena of such a world! How extraordinary are the minds even of the lower animals. We cannot appreciate our own powers any more than a writer can appreciate his own style, or a thinker the peculiar quality of his own thought. I don't mean that a Dante did not know that he expressed himself with fewer words than other men do, but he could not admire himself as we admire him; nor can we wonder at human intelligence as we do at that of wasps. Let a man drink in such thoughts as come to him in contemplating the physico-psychical universe without any special purpose of his own; especially the universe of mind which coincides with the universe of matter. The idea of there being a God over it all of course will be often suggested; and the more he considers it, the more he will be enwrapt with Love of this idea. He will ask himself whether or not there really is a God. If he allows instinct to speak, and searches his own heart, he will at length find that he cannot help believing it. I cannot tell how every man will think. I know the majority of men, especially educated men, are so full of pedantries — especially the male sex — that they cannot think straight about these things. But I can tell how a man must think if he is a pragmatist. Now the shower of communications that I have been getting during the last two months causes me to share the expectation that I find so many good judges are entertaining, that pragmatism is going to be the dominant philosophical opinion of the twentieth century. . . .

502. If a pragmaticist is asked what he means by the word "God," he can only say that just as long acquaintance with a man of great character may deeply influence one's whole manner of conduct, so that a glance at his portrait may make a difference, just as almost living with Dr. Johnson enabled poor Boswell to write an immortal book and a really sublime book, just as long study of the works of Aristotle may make him an acquaintance, so if contemplation and study of the physico-psychical universe can imbue a man with principles of conduct analogous to the influence of a great man's works or conversation, then that analogue of a mind — for it is impossible to say that any human attribute is literally applicable — is what he means by "God." Of course, various great theologians explain that one cannot attribute reason to God, nor perception (which always involves an element of surprise and of learning what one did not know), and, in short, that his "mind" is necessarily so unlike ours, that some — though wrongly — high in the church say that it is only negatively, as being entirely different from everything else, that we can attach any meaning to the Name. This is not so; because the discoveries of science, their enabling us to predict what will be the course of nature, is proof conclusive that, though we cannot think any thought of God's, we can catch a fragment of His Thought, as it were.

503. Now such being the pragmaticist's answer to the question what he means by the word "God," the question whether there really is such a being is the question whether all physical science is merely the figment — the arbitrary figment — of the students of nature, and further whether the one lesson the Gautama Boodha, Confucius, Socrates, and all who from any point of view have had their ways of conduct determined by meditation upon the physico-psychical universe, be only their arbitrary notion or be the Truth behind the appearances which the frivolous man does not think of; and whether the superhuman courage which such contemplation has conferred upon priests who go to pass their lives with lepers and refuse all offers of rescue is mere silly fanaticism, the passion of a baby, or whether it is strength derived from the power of the truth. Now the only guide to the answer to this question lies in the power of the passion of love which more or less overmasters every agnostic scientist and everybody who seriously and deeply considers the universe. But whatever there may be of argument in all this is as nothing, the merest nothing, in comparison to its force as an appeal to one's own instinct, which is to argument what substance is to shadow, what bed-rock is to the built foundations of a cathedral.

504. Caldecott's Philosophy of Religion explains thirteen different types of reasons for believing in God, with different varieties of several of them. †1 I have examined them all with care, and think each one proves something. But I do not think their conclusions always have much to do with religion.

§2. Creation

505. "Do you believe this Supreme Being to have been the creator of the universe?" Not so much to have been as to be now creating the universe, concerning which see my articles in the first three volumes of The Monist; †2 and much the same opinion has been entertained by others, especially by Renouvier, †3 the French protagonist of [the monadistic] philosophy. But I object to Renouvier's philosophy as nominalistic and otherwise not thorough. Still, his Essais de Critique and particularly his Nouvelle Monadologie are very strong books in many respects, which no thoughtful reader can forget. I think that, vain as it is to attempt to bring to light any definite meaning from the idea, it is nevertheless true that all reality is due to the creative power of God.

506. I am inclined to think (though I admit that there is no necessity of taking that view) that the process of creation has been going on for an infinite time in the past, and further, during all past time, and, further, that past time had no definite beginning, yet came about by a process which in a generalized sense, of which we cannot easily get much idea, was a development. †1 I believe Time to be a reality, and not the figment which Kant's nominalism proposes to explain it as being. As reality, it is due to creative power. People who have had no practice in higher logical analysis are apt to be sceptical as to anybody's being able to attach any idea to such propositions. They are even dumbfounded to hear one say that a part is not necessarily less than its whole; while after one has learned how to think of such things, the marvel is that anybody should ever have deliberately said that the part is necessarily less than the whole or ever should have said "so fast eternity comes on," meaning by "eternity" the infinitely distant future, as if the part of the future that will remain future tomorrow were not just as long as today's or yesterday's future.

I think we must regard Creative Activity as an inseparable attribute of God.

§3. God's Purpose

507. "What do you imagine the present functions of this Supreme Being toward the universe to be?" Creation, as just said; and much may also be learned from the book Substance and Shadow (1863) by Henry James, the father. The book was presented to me, by the way, by Miss Maria Fay, a very interesting and spiritual lady. In particular, the obvious solution of the problem of evil is there pointed out. †2 Columbus's egg was not simpler. In general, God is perpetually creating us, that is developing our real manhood, our spiritual reality. Like a good teacher, He is engaged in detaching us from a False dependence upon Him.

§4. Omniscience

508. "Do you believe Him to be omniscient?" Yes, in a vague sense. Of course, God's knowledge is something so utterly unlike our own that it is more like willing than knowing. †1 I do not see why we may not assume that He refrains from knowing much. For this thought is creative. But perhaps the wisest way is to say that we do not know how God's thought is performed and that [it] is simply vain to attempt it. We cannot so much as frame any notion of what the phrase "the performance of God's mind" means. Not the faintest! The question is gabble.

§5. Omnipotence

509. "Do you believe Him to be Omnipotent?" Undoubtedly He is so, vaguely speaking; but there are many questions that might be put of no profit except to the student of logic. Some of the scholastic commentaries consider them. Leibnitz thought that this was the best of "all possible" worlds. That seems to imply some limitation upon Omnipotence. Unless the others were created too, it would seem that, all things considered, this universe was the only possible one. Perhaps others do exist. But we only wildly gabble about such things.

§6. Infallibility

510. "Do you believe Him to be infallible?" If omniscient, how not? But perhaps this is a slip of the typewriter for impeccable. Theologians insist upon sundry questions which are in the highest degree displeasing to me, not to say offensive. I do not presume to know anything about it, but it seems to me that the very meaning of the word "God" implies, not surely morality, for He seems to me to be above all self-restraint or law, but to imply aesthetic spiritual perfection.

§7. Miracles

511. "Do you believe that He ever modifies or changes the laws of nature or interferes with the course of events in individual cases?" I call your attention to the circumstance that some of the most respected theologians, such as St. Augustine, †2 and others before him, St. Thomas Aquinas, †3 Bishop Joseph Butler, †1 are decidedly of the opinion that God never interfered with what they call the cursus naturæ, which is what we call the operations of the laws of nature, "laws of nature" meaning with them the items of the jus naturae, or something which my unlegal ignorance is unable to distinguish from that. Miracles are for them simply what no man can do without special aid from on high, or which at least are signs of some special authority, without being in reality deviations from the regular uniformities of the world. However, my own doctrine of Tychism, †2 like Renouvier's somewhat similar theory, †3 and those of Fouillée, †4 Delboeuf, †5 and others, must, in so far as it is accepted, somewhat weaken that view.

512. I also call your attention to the fact that Hume's †6 argument against miracles †7 has nothing at all to do with whether they are or are not violations of the laws of nature. The argument is based upon a misunderstanding of the doctrine of probabilities, of which some of the early treatises had appeared in his day. It might be corrected, but it would still rest on a complete misunderstanding of the true logic of the criticism of ancient history. †8

513. But the German critics (I speak only of those who treat of the history of philosophy, for I have never looked into the Biblical criticisms) are as illogical as Hume and in much the same way. †9 Hence, whenever their conclusions have been tested by the spade of the archeologist it has been to their complete discomfiture. Hume's argument is in no particularly intimate relation to the rest of his book, and was evidently inserted as a bid for popularity. For while he was a young fellow of fifteen to seventeen, miracles had been vehemently attacked by a clergyman of the name of Woolston, †10 who took the ground of Origen †1 and other early fathers of the church that the stories in the gospel were simply allegorical. His books had the most stupendous sale in England, completely demonstrating the general disbelief in miracles at that day. In point of fact, there never was a period of history in which the general tone of thought was so absolutely contrary to the supernatural. The state of opinion about the [time of the] French Revolution, and that about 1875, when "agnosticism" was at its [crudest], were pious in comparison with 1730. Therefore, Hume who sacrificed the best parts of his system to make his Inquiry popular, undoubtedly stuck in his argument against miracles for that purpose.

514. For my part, I do not see how we can ascertain a priori whether miracles (be they violations of the laws of nature or not) and special providences take place or not. In so far Hume is entirely in the right. It is simply a question of evidence. His argument has a certain weight. If there are no miracles nowadays, there is a strong presumption against those which took place amidst a rabble of Galileans. But are there no miracles nowadays? I do not feel so sure of it. There is Mrs. Piper and Perry. I do not think it rational not [to] think, for us who know Perry, that that case is of tremendous, almost conclusive, weight. There is the blood of St. Januarius which Sir Humphrey Davy — of his own motion, and not forced into it at all — undertook to investigate and was given every facility he could think of, and who declared he could not find the least symptom of fraud about the thing. Take such men as Sir William Crookes †2 and Lord Rayleigh †3 — well even Hodgson †4 — one must confess the case is very strong; so strong that but for one circumstance I should unhesitatingly accept it. That circumstance is that every surprising discovery of science — as for example when Becquerel found those photographic plates which he had put away in a drawer to be affected by the uranium salt that was wrapped up in black paper and accidentally laid upon them — every such event, is soon followed by others closely connected with it, so that all possible doubt is swept away together with all surprise at the occurrence. Miracles, on the contrary, are always sui generis. The only ones that were not so, the falling of stones out of the heavens, lost all their prestige when it was found how common the occurrence was. The isolatedness of the miracle is really no argument against its reality. It is nearly the same with works of great genius. You have Rafael and Michelangelo together, and then for a long time nothing surprising. Dante stands all alone. Byron was unparalleled before or since; for A. de Musset is surely not to be compared with him. Indeed every branch of art and science can furnish such examples. The isolation, then, is no argument against miracles, but it effectively prevents our ever having sufficient evidence of them. I must confess that the gospel miracles appear at this date very far from impressive. It is curious that Origen, no further from Jesus in history than we from the expulsion of James II from England, should have found them so difficult to believe.

§8. Prayer

515. "Do you believe in the efficacy of prayer?" The only thing connected with that, that I am quite satisfied about, is that the clergy do not believe in it. I mean the influential clergy. The conclusive proof of that is that when Tyndall †1 proposed to put the matter to the test of experiment, although they had the record of the somewhat similar proposal of the King of Samaria and Elijah's †2 perfectly frank response, they backed down and pretended that it would be blasphemous. So it is blasphemy to inquire into the truth of religion, is it? No living man thinks it disrespectful to inquire into the authenticity of his signature; and the higher clergy are far more sensitive to their own dignity than God's, and very justly so, since it is quite possible to be disrespectful to an ecclesiastic, while it is absolutely impossible really to think of God without awe mingled with love.

516. But what business is it of mine whether my prayers are to be efficacious or not? We, one and all of us, have an instinct to pray; and this fact constitutes an invitation from God to pray. And in fact there is found to be not only soulagement in prayer, but great spiritual good and moral strength. I do not see why prayer may not be efficacious, or if not the prayer exactly, the state of mind of which the prayer is nothing more than the expression, namely the soul's consciousness of its relation to God, which is nothing more than precisely the pragmatistic meaning of the name of God; so that, in that sense, prayer is simply calling upon the name of the Lord. To pray for specific things, not merely for the {epioution}, bread, but that it may be better baked than yesterday's, is childish, of course; yet innocent.

517. "Why does not this Omniscient Being see the need and interpose the Omnipotent and Supreme Authority to meet the needs prayed for? Is it because of a vanity which is one of the attributes of fallible man?" I remember two passages in my writings in which I made as much fun as politeness would allow of writers who undertook to tell us what was "conducive to our welfare." Once it was Simon Newcomb who was talking like that in his book on Political Economy; †1 and I remarked that an economist, far from having any qualifications for exploring this most occult of all matters, was particularly unfit for the task owing to his habit of taking it for granted that wealth was desirable. †2 The other time it was Karl Pearson, who wanted to found the rules of logic upon that, and I remarked †3 that, for my part, if ever I undertook the supremely difficult inquiry of what was conducive to our welfare I should feel that I needed to arm myself beforehand with whatever resources logic could afford, to speak of no others. What are our "needs"? We know what we have an impulse to seek, and if we have considered the matter deliberately we are convinced that those things are far from being the same as our true needs. Yet if we are going to pray for anything specific, which is once in a long time, on some supreme occasion, a permissible frailty, surely we shall add something like, "Fulfill now, O Lord, the desires and petitions of Thy servants, as may be most expedient for them." Not to do so, would, as you seem to suggest, be vanity indeed.

518. "Do you believe that the prayers of several persons for one end are more potent than those of one?" I know of no experiments to ascertain how this may be; but I certainly think that common prayers have some peculiar virtues of their own. As I say, the inquiry into efficacity is distasteful to me because that is not the motive of my prayers. Still, I should like to have an inquiry instituted into the matter.

§9. Immortality †1

519. "Do you believe in a future life?" Some kind of a future life there can be no doubt of. A man of character leaves an influence living after him. It is living: it is personal. In my opinion, it is quite proper to call that a future life. Jesus so spoke of it when he said he would always be with us. It is in some respects more fit to be made the subject of a promise than any other kind of future life. For it is something we all desire; while other kinds present nothing alluring that is not excessively vague or else unwholesome and antipractical. In the next place its vivacity and endurance are proportional to the spirituality of the man. How many instances have we seen of that! Beyond that, I simply am content to be in God's hands. If I am in another life it is sure to be most interesting; but I cannot imagine how it is going to be me. At the same time, I really don't know anything about it.

520. "Is not every act of memory in the human being the result of the action of that being's material brain. . . . ? If this is true, on the death of the material body . . . does not the memory cease?" †2

This is commonly assumed to be the case; and owing to my slight interest in the matter it may well be that there are some facts bearing upon the question that I am not aware of. But my impression is that there is no positive reason for believing it except the general facts of the dependence of mental action on the brain. For instance, when Broca's convolution is much diseased we always find the use of language is greatly affected. But I am sure this is not a strong positive reason for an affirmative answer to the first of the two questions. It undoubtedly warrants the assumption in science, until facts to the contrary appear. But your questions are not scientific, but practical questions. From that standpoint I think I must say that the matter is open to some doubt. When a part of the brain is extirpated we find the result is that certain faculties are lost. But after a time they are recovered. How can this be? The answer given is that other parts of the brain learn to perform these functions. But after all, we do not know more than that if anything happens to the hemispheres, memory is deranged. It is a most wonderful thing if all we remember is really preserved in the cells of the cerebrum. However, there can be no doubt, I think, that upon death we soon lose consciousness, at least for the time being.

You will observe that the essential immortality of the soul is not exactly the Christian doctrine, which is that the body is reproduced, and with it presumably the memory. There is nothing at all to prove it except that it was a belief clung to by St. Paul and founded by him upon the resurrection of Jesus.

521. "If the power to remember dies with the material body, has the question of any single person's future life after death any particular interest for him?" As you put the question, it is not whether the matter ought rationally to have an interest, but whether as a fact it has; and perhaps this is the proper question, trusting as it seems to do, rather to instinct, than to reason. Now if we had a drug which would abolish memory for a while, and you were going to be cut for the stone, suppose the surgeon were to say, "You will suffer damnably, but I will administer this drug so that you will during that suffering lose all memory of your previous life. Now you have of course no particular interest in your sufferings as long as you will not remember your present and past life, you know, have you?" †1

Chapter 5: Hume on Miracles †1 P

§1. The Nature of Hypotheses

522. The science of legitimate inference can only be of practical value provided its propositions are proved with absolute completeness. For they have to carry weight enough to override our instinctive judgments of what is good reasoning. If they cannot do that, they are of no use. But even apparently convincing proofs may be mistaken; and the maxims of this science may be suspected of being so, if they conflict with our instinctive logic. †2 They must, therefore, not only come to us supported by full proofs, but also by the recommendation of those who have had long experience in the use of them.

In a brief article it is impossible to make the proofs clearly evident; and it would be unjust to them to attempt such a thing, which could only convey the idea that they were of an unintelligible and unconvincing nature. Yet to discuss the legitimacy of inferences on any other than the true scientific grounds is mere trifling. The difficulty is insuperable. All that can be done is to lay down the correct principles, and postpone the proofs to another occasion. It may perhaps be permissible to give some hints as to what the general nature of the proofs is.

All our knowledge may be said to rest upon observed facts. It is true that there are psychological states which antecede our observing facts as such. Thus, it is a fact that I see an inkstand before me; but before I can say that I am obliged to have impressions of sense into which no idea of an inkstand, or of any separate object, or of an "I," or of seeing, enter at all; and it is true that my judging that I see an inkstand before me is the product of mental operations upon these impressions of sense. But it is only when the cognition has become worked up into a proposition, or judgment of a fact, that I can exercize any direct control over the process; and it is idle to discuss the "legitimacy" of that which cannot be controlled. Observations of fact have, therefore, to be accepted as they occur.

523. But observed facts relate exclusively to the particular circumstances that happened to exist when they were observed. They do not relate to any future occasions upon which we may be in doubt how we ought to act. They, therefore, do not, in themselves, contain any practical knowledge.

Such knowledge must involve additions to the facts observed. The making of those additions is an operation which we can control; and it is evidently a process during which error is liable to creep in.

524. Any proposition added to observed facts, tending to make them applicable in any way to other circumstances than those under which they were observed, may be called a hypothesis. A hypothesis ought, at first, to be entertained interrogatively. Thereupon, it ought to be tested by experiment so far as practicable. There are two distinct processes, both of which may be performed rightly or wrongly. We may go wrong and be wasting time in so much as entertaining a hypothesis, even as a question. That is a subject for criticism in every case. There are some hypotheses which are of such a nature that they never can be tested at all. Whether such hypotheses ought to be entertained at all, and if so in what sense, is a serious question; but it hardly concerns our present inquiry. The hypotheses with which we shall have in this paper to deal are capable of being put to the test. How this is to be done is a question of extreme importance; but my intention is to consider it only in a very cursory manner, at present. There are, moreover, many hypotheses in regard to which knowledge already in our possession may, at once, quite justifiably either raise them to the rank of opinions, or even positive beliefs, or cause their immediate rejection. This also is a matter to be considered. But it is the first process, that of entertaining the question, which will here be of foremost importance.

525. Before we go further, let us get the points stated above quite clear. By a hypothesis, I mean, not merely a supposition about an observed object, as when I suppose that a man is a Catholic priest because that would explain his dress, expression of countenance, and bearing, but also any other supposed truth from which would result such facts as have been observed, as when van't Hoff, having remarked that the osmotic pressure of one per cent solutions of a number of chemical substances was inversely proportional to their atomic weights, thought that perhaps the same relation would be found to exist between the same properties of any other chemical substance. The first starting of a hypothesis and the entertaining of it, whether as a simple interrogation or with any degree of confidence, is an inferential step which I propose to call abduction. This will include a preference for any one hypothesis over others which would equally explain the facts, so long as this preference is not based upon any previous knowledge bearing upon the truth of the hypotheses, nor on any testing of any of the hypotheses, after having admitted them on probation. I call all such inference by the peculiar name, abduction, because its legitimacy depends upon altogether different principles from those of other kinds of inference.

§2. The Testing of Hypotheses †1

526. The operation of testing a hypothesis by experiment, which consists in remarking that, if it is true, observations made under certain conditions ought to have certain results, and then causing those conditions to be fulfilled, and noting the results, and, if they are favorable, extending a certain confidence to the hypothesis, I call induction. For example, suppose that I have been led to surmise that among our colored population there is a greater tendency toward female births than among our whites. I say, if that be so, the last census must show it. I examine the last census report and find that, sure enough, there was a somewhat greater proportion of female births among colored births than among white births in that census year. To accord a certain faith to my hypothesis on that account is legitimate. It is a strong induction. I have taken all the births of that year as a sample of all the births of years in general, so long as general conditions remain as they were then. It is a very large sample, quite unnecessarily so, were it not that the excess of the one ratio over the other is quite small. All induction whatever may be regarded as the inference that throughout a whole class a ratio will have about the same value that it has in a random sample of that class, provided the nature of the ratio for which the sample is to be examined is specified (or virtually specified) in advance of the examination. †1 So long as the class sampled consists of units, and the ratio in question is a ratio between counts of occurrences, induction is a comparatively simple affair. But suppose we wish to test the hypothesis that a man is a Catholic priest, that is, has all the characters that are common to Catholic priests and peculiar to them. Now characters are not units, nor do they consist of units, nor can they be counted, in such a sense that one count is right and every other wrong. Characters have to be estimated according to their significance. The consequence is that there will be a certain element of guess-work in such an induction; so that I call it an abductory induction. †2 I might say to myself, let me think of some other character that belongs to Catholic priests, beside those that I have remarked in this man, a character which I can ascertain whether he possesses or not. All Catholic priests are more or less familiar with Latin pronounced in the Italian manner. If, then, this man is a Catholic priest, and I make some remark in Latin which a person not accustomed to the Italian pronunciation would not at once understand, and I pronounce it in that way, then if that man is a Catholic priest he will be so surprised that he cannot but betray his understanding of it. I make such a remark; and I notice that he does understand it. But how much weight am I to attach to that test? After all, it does not touch an essential characteristic of a priest or even of a Catholic. It must be acknowledged that it is but a weak confirmation, and all the more so, because it is quite uncertain how much weight should be attached to it. Nevertheless, it does and ought to incline me to believe that the man is a Catholic priest. It is an induction, because it is a test of the hypothesis by means of a prediction, which has been verified. But it is only an abductory induction, because it was a sampling of the characters of priests to see what proportion of them this man possessed, when characters cannot be counted, nor even weighed, except by guess-work. It also partakes of the nature of abduction in involving an original suggestion; while typical induction has no originality in it, but only tests a suggestion already made.

527. In induction, it is not the fact predicted that in any degree necessitates the truth of the hypothesis or even renders it probable. It is the fact that it has been predicted successfully and that it is a haphazard specimen of all the predictions which might be based on the hypothesis and which constitute its practical truth. But it frequently happens that there are facts which, merely as facts, apart from the manner in which they have presented themselves, necessitate the truth, or the falsity, or the probability in some definite degree, of the hypothesis. For example, suppose the hypothesis to be that a man believes in the infallibility of the Pope. Then, if we ascertain in any way that he believes in the immaculate conception, in the confessional, and in prayers for the dead, or on the other hand that he disbelieves all or some of these things, either fact will be almost decisive of the truth or falsity of the proposition. Such inference is deduction. So if we ascertain that the man in question is a violent partisan in politics and in many other subjects. If, then, we find that he has given money toward a Catholic institution, we may fairly reason that such a man would not do that unless he believed in the Pope's infallibility. Or again, we might learn that he is one of five brothers whose opinions are identical on almost all subjects. If, then, we find that the other four all believe in the Pope's infallibility or all disbelieve it, this will affect our confidence in the hypothesis. This consideration will be strengthened by our general experience that while different members of a large family usually differ about most subjects, yet it mostly happens that they are either all Catholics or all Protestants. Those are four different varieties of deductive considerations which may legitimately influence our belief in a hypothesis.

528. These distinctions are perfectly clear in principle, which is all that is necessary, although it might sometimes be a nice question to say to which class a given inference belongs. It is to be remarked that, in pure abduction, it can never be justifiable to accept the hypothesis otherwise than as an interrogation. But as long as that condition is observed, no positive falsity is to be feared; and therefore the whole question of what one out of a number of possible hypotheses ought to be entertained becomes purely a question of economy.

529. Let us suppose that there are thirty-two different possible ways of explaining a set of phenomena. Then, thirty-one hypotheses must be rejected. The most economical procedure, when it is practicable, will be to find some observable fact which, under conditions easily brought about, would result from sixteen of the hypotheses and not from any of the other sixteen. Such an experiment, if it can be devised, at once halves the number of hypotheses. Or if the experiment might give any one of four results each of which would be the necessary consequence of the truth of any one of eight of the hypotheses, the single experiment would divide the number of admissible hypotheses by four. When such an experiment, or anything approaching such an experiment, is possible, it is clear that it is unwise to adopt any other course. But unfortunately, it commonly happens that this method becomes exhausted before the hypotheses are reduced to a single one, so that nothing remains but to test the remainder each by itself.

530. Now the testing of a hypothesis is usually more or less costly. Not infrequently the whole life's labor of a number of able men is required to disprove a single hypothesis and get rid of it. Meantime the number of possible hypotheses concerning the truth or falsity of which we really know nothing, or next to nothing, may be very great. In questions of physics there is sometimes an infinite multitude of such possible hypotheses. The question of economy is clearly a very grave one. †1

In very many questions, the situation before us is this: We shall do better to abandon the whole attempt to learn the truth, however urgent may be our need of ascertaining it, unless we can trust to the human mind's having such a power of guessing right that before very many hypotheses shall have been tried, intelligent guessing may be expected to lead us to the one which will support all tests, leaving the vast majority of possible hypotheses unexamined. Of course, it will be understood that in the testing process itself there need be no such assumption of mysterious guessing-powers. It is only in selecting the hypothesis to be tested that we are to be guided by that assumption.

531. If we subject the hypothesis, that the human mind has such a power in some degree, to inductive tests, we find that there are two classes of subjects in regard to which such an instinctive scent for the truth seems to be proved. One of these is in regard to the general modes of action [of] mechanical forces, including the doctrine of geometry; the other is in regard to the ways in which human beings and some quadrupeds think and feel. In fact, the two great branches of human science, physics and psychics, are but developments of that guessing-instinct under the corrective action of induction. †1

532. In those subjects, we may, with great confidence, follow the rule that that one of all admissible hypotheses which seems the simplest to the human mind ought to be taken up for examination first. Perhaps we cannot do better than to extend this rule to all subjects where a very simple hypothesis is at all admissible.

This rule has another advantage, which is that the simplest hypotheses are those of which the consequences are most readily deduced and compared with observation; so that, if they are wrong, they can be eliminated at less expense than any others. †2

533. This remark at once suggests another rule, namely, that if there be any hypothesis which we happen to be well provided with means for testing, or which, for any reason, promises not to detain us long, unless it be true, that hypothesis ought to be taken up early for examination. Sometimes, the very fact that a hypothesis is improbable recommends it for provisional acceptance on probation.

534. On the other hand, if one of the admissible hypotheses presents a marked probability of the nature of an objective fact, it may in the long run promote economy to give it an early trial. By an objective probability I mean one which could be used to guarantee an insurance company or gamester against loss, because it expresses the real fact that among occurrences of a certain genus a certain proportion are of a certain species. Such is the probability of one/six that a die will turn up any particular face. Such a probability must be distinguished from a mere likelihood †1 which is nothing better than the expression of our preconceived ideas. The confusion between those two kinds of probability is one of the main sources of human errors, especially in abduction, in which yielding to judgments of likelihood is a fertile source of waste of time and energy.

535. In some departments of science, where experimentation is easy, the testing of hypotheses may be performed with some promptitude. In other departments, especially in ancient history, it will extend beyond a human life, so that for the individual the result of the abduction is all that he can hope to live to see. So long as the scientific hypothesis does not offer any particular dangers to the individual, he will do well to content himself with that hypothesis which the wise application of principles of economy recommends to undying scientific research. On the other hand, if there are such dangers, the individual may, as a scientific man, entertain one hypothesis for probation, while he allows probabilities greater weight in deciding upon what hypothesis he shall base his individual behaviour. Thus, in metaphysics, the maxim called Ockham's razor, to the effect that more elements must not be introduced into a hypothesis until it is absolutely proved that fewer are not sufficient, is a sound economic principle which ought to guide the scientific metaphysician. But centuries before it is absolutely proved that the simpler hypothesis is inadequate, it may have been made extremely probable that it is so, and the individual's behaviour may reasonably be based upon what the ultimate conclusion of science is likely to be.

536. In the department of ancient history, what is called "higher criticism" — that is to say, that particular color of non-textual criticism which has been dominant during the nineteenth century, especially in Germany — has placed, and though it has of late years retreated from many of its positions, still continues to place, great reliance upon likelihoods. To such a pitch is this carried that, although we can have no knowledge of ancient history independent of Greek (and Latin) authors, yet the critics do not hesitate utterly to reject narratives attested sometimes by as many as a dozen ancient authorities — all the testimony there is, at any rate — because the events narrated do not seem to persons living in modern Germany to be likely. I could write a whole book, †1 and not an unentertaining one, in illustration of this point. But scientific archaeology has, in our day, subjected those hypotheses to objective tests; and the uniform result has been to show that what seemed likelihoods to German professors were all but quite uniformly wrong and the ancient testimonies right. †2 Thus the maxim of exact logical analysis, that no regard at all, or very little indeed, ought to be paid to subjective likelihoods in abduction, has been fully confirmed by inductive tests.

§3. The Meaning of Miracles

537. Hume's argument against miracles is substantially based upon the assumption that we ought to judge of testimony by balancing the likelihood that the witnesses tell the truth against the likelihood that no such event as that to which they testify ever took place. †3 It is true that Hume gives a metaphysical definition of a miracle based upon the definition of Aquinas. †4 But his argument in no way turns upon that. The definition he virtually uses is that a miracle is something the like of which has never been known to happen. He has completely mistaken the nature of the true logic of abduction.

538. I beg to say that I go no farther than that. I do not assent to the contention of many theologians that the miracles of Jesus can properly convince a modern man of the divinity of Jesus. On the contrary, all the evidence which can now be presented for them is quite insufficient, unless the general divinity of the Christian religion be assumed. The evidence which may have been overwhelming for eye witnesses and persons near them is of a very different and inferior character to that which may weigh with a modern Christian.

539. Now, laying aside the question of how one ought to think, let us ask what effect was, in fact, produced upon Hume's contemporaries by his argument against miracles; and also, what effect was produced by Hume's introducing a definition of a miracle which introduced the idea of a Law of Nature. †1 For it is a fact that Hume defined a miracle as a violation of a law of nature, and that the great bulk of his contemporaries were not sufficiently at home in philosophy to see that he was giving the definition a metaphysical turn that was quite uncalled for.

540. The fathers of the church had introduced no more metaphysics into their definitions of a miracle than had the simple folks who had witnessed miracles, or thought they had witnessed them. For both classes a miracle was nothing more than a great wonder.

541. The miracle remained nothing more than a great wonder, until the scholastic doctors, in their desire to give exactitude to theology, began to define it metaphysically. Aquinas said that a miracle was an interruption of the order of nature; and that remained the regular definition for the scholastics. When Hume took up the subject of miracles, he endeavoured to conform to the definition of the theologians, although for the purposes of his argument it was a matter of indifference how a miracle should be defined. All he needed was that it should be something the like of which was perfectly unexampled in experience. He was perfectly willing to adopt whatever definition the theologians preferred. But Hume was a literary man, and one of the characteristics of his philosophical style was that he was continually endeavouring to clothe philosophical ideas in fresh and modern phraseology. He probably referred either to Aquinas or to some theologian influenced by Aquinas; but he thought the definition would come home to his readers more if, instead of defining a miracle as an interruption of the order of nature, he defined it as a violation of a law of nature; for "law of nature" had become a familiar phrase. There was nothing in this modification of language which was particularly favorable to Hume's argument.

542. Aquinas had not spoken of a violation of a law of nature, because the phrase "law of nature" bore, in his day, no such meaning as Hume attached to it. The phrase itself is very old. It occurs in the early Greek poet Pindar, †1 and in Plato. †2 In Latin it is met with in the early poet Lucretius. †3 But until modern times, it had meant a rule of natural morality. For a scholastic, therefore, it would have been simple nonsense to say that a violation of a law of nature would be a miracle. That is why he spoke of the "order of nature" which meant for him substantially what we mean by a "law of nature." If there was any difference, it lay in this, that to the majority of scholastics, the order of nature was something absolutely real, having a being in or behind the very essence of nature; while for the majority of modern thinkers a law of nature is relative to the human understanding. The medieval "order of nature" would, therefore, have been more inviolable than the modern "law of nature," were it not for the fact that the marvellous appealed to the childish mind of the Middle Ages, while the scientific regularity appeals to the modern mind. But after men had become generally pretty thoroughly disgusted with scholasticism, Descartes came forward with a new philosophy which answered their new wants. Now it was a part of this philosophy, not, it is true, much insisted on by Descartes †4 himself, but so much in the line of his ideas that his followers would be sure to insist upon it, as in fact they did, that nothing takes place in the world without the direct assistance of the Deity. There was no other force in causation, according to them, than that it is the will of God that events shall follow one another in certain definite ways. It was under the influence of this conception that Boyle, †5 a natural philosopher of strong theological tendencies, and at the same time of a decided physical turn of thought, began to speak of "laws of nature," very much in the modern sense, except that with him, no doubt, there was an implication that they were divine decrees. The phrase had met with favor and, by Hume's time, had become familiar to all English ears. He adopted it, therefore, in his definition of a miracle, although it rather suggested the possibility of miracles than otherwise. Still, as close a reasoner as Hume was could easily see that it would not materially affect the force of his argument to admit that miracles do, from time to time, occur; for in regard to any special miracle it would still remain more likely that the miracle had not occurred and that the witnesses had not given exact testimony than that the witnesses had been exact and that the particular miracle in question had occurred. The truth is that, as soon as it is granted that it is proper to judge of testimony by the balance of likelihoods and unlikelihoods, Hume's reasoning about miracles has been substantially admitted.

543. In estimating the effect of Hume's argument upon his contemporaries it should be remembered that attacks upon the miracles of Jesus presented no novelty whatever at the time when Hume's celebrated essay was written. For all through the period of Hume's boyhood the whole island of Great Britain had resounded with the violent attacks continually renewed upon them by Thomas Woolston, whose books had had a popular sale that was quite unprecedented. Woolston was a thoroughly sincere Christian; but he maintained that the fathers of the church had unanimously held the gospel miracles to be parables and types of the greater spiritual miracles that the religion of Christ was destined to accomplish. †1 He offered no general argument against miracles, but simply took up the narrative of each one and undertook to show, first, that the circumstances were such as to render its literal happening incredible, and secondly, that even if it did happen it would not tend to prove the divinity of Jesus. As an example of his style of reasoning we may take the miracle of casting out the devils into the herd of swine. Woolston said that it could not have happened, because it had for centuries been against the law in Judæa to keep swine; so that no herd of swine could have been on the public road. He added that if it had happened, so far from evidencing the divinity of Jesus, it would simply have evinced a total disregard for the rights of property, for which any jury in England would have awarded damages. Woolston kept up a hot fire of such arguments all his life, and after his death his follower Annet †1 had taken up the cudgels.

544. This discussion had been made familiar to every man in England and Scotland; and it is therefore safe to say that by the time Hume wrote, whoever was to [be] persuaded that the miracles of Jesus were unliteral had already been persuaded. But I must say that I cannot but believe that Woolston had carried substantially the whole population with him on his main contention, which was that whatever views are taken of the miracles they cannot suffice by themselves, in modern days, to prove the Christian religion. I believe that those who adhered to the literal miracles did so because they were inclined to believe in the Christian religion, and that they had, but for rare exceptions, failed to be brought to believe in the Christian religion because of an antecedent conviction of the reality of the gospel miracles.

545. What Hume mainly did was to supply those who were disposed to reject the miracles with an expeditious way of disposing of the evidence at one blow. At the same time, he probably shook the belief of some who had been accustomed to regard legal evidence as a matter to be discussed by the method of balancing likelihoods and unlikelihoods — a method which had met considerable favour among lawyers.

546. Of course, formalism was rife among the men of that generation. There was in many minds such a worship of obstinacy that they would naturally look upon the immutability of a divine decree as an attribute of Deity, regard[less] of the circumstances of any particular case. The extreme irrationality of many rules of law fostered such sentiments. It may have been, therefore, that as soon as some men of that description were credibly informed that a miracle was a violation of a law of nature, or divine decree, they would be unable to conceive that such a Deity as they could worship, the personification of obstinacy, would ever consent to such a thing; and they may perhaps have read that argument into Hume, although it is one which Hume himself could only look upon with contempt. I can, at any rate, imagine no other way in which Hume's definition of a miracle could have specially weakened faith in miracles.

§4. Butler's Analogy

547. It was while Hume was engaged in writing his first treatise, and long before he touched upon miracles, that Bishop Butler's Analogy of Reason with Nature was published. †1 This work contains an interesting application of the then current notion that the order of nature is a law to the doctrine of miracles. Butler †2 remarks that if we could know what the laws of nature really are it would perhaps be seen that they positively require the occurrence of miracles. For if there are any "laws" of nature, they must be supposed to be supremely reasonable. Now the supreme reasonableness of a "law" will consist in its advancing a rational purpose in every particular case. Hence, if there is really a need of an apparently exceptional phenomenon, it will not be contrary to real analogies, but on the contrary required by them, that that apparently exceptional phenomenon should occur. On the surface of it, at any rate, this view creates no objection to Hume's real argument; but it clearly does show that to look upon the order of nature as being of the nature of a "law" is to adopt a view which is really favorable to miracles, rather than the reverse.

But when we come to penetrate the spirit of Butler's remark, we recognize that it has, hidden in the depths of it, an idea which has only to be developed to refute all such reasonings as that of Hume about miracles, and the similar but far more extravagant conclusions of the "higher critics" of ancient history, and which is in remarkable consonance with the higher teachings of modern science.

Chapter 6: Science and Immortality †1

§1. Psychic Research E

548. What is the bearing of positively ascertained facts upon the doctrine of a future life? By the doctrine of a future life, I understand the proposition that after death we shall retain or recover our individual consciousness, feeling, volition, memory, and, in short (barring an unhappy contingency), all our mental powers unimpaired. The question is, laying aside all higher aspects of this doctrine, its sacredness and sentiment — concerning which a scientific man is not, as such, entitled to an opinion — and judging it in the same cold way in which a proposition in physics would have to be judged, what facts are there leading us to believe or to disbelieve it?

549. Under the head of direct positive evidence to the affirmative would be placed that of religious miracles, of spiritualistic marvels, and of ghosts, etc. I have little to say to all this. I take the modern Catholic miracles to be the best attested. Three members of the English Psychical Research Society have lately published a vast book of fourteen hundred pages, large octavo, under the title of Phantasms of the Living. This work gives some seven hundred cases of apparitions, etc. of a dying person to another person at a distance. The phenomenon of telepathy, or perception under conditions which forbid ordinary perception, though not fully established, is supported by some remarkable observations. But the authors of the book I am speaking of — Messrs. Gurney, Myers, and Podmore — think they have proved a kind of telepathy by which dying persons appear to others at great distances. Their most imposing arguments are based upon the doctrine of probabilities, and these I have examined with care. I am fully satisfied that these arguments are worthless, partly because of the uncertainty and error of the numerical data, and partly because the authors have been astonishingly careless in the admission of cases ruled out by the conditions of the argumentation.

550. But, granting all the ghost stories that ever were told, and the reality of all spiritual manifestation, what would they prove? These ghosts and spirits exhibit but a remnant of mind. Their stupidity is remarkable. They seem like the lower animals. If I believed in them, I should conclude that, while the soul was not always at once extinguished on the death of the body, yet it was reduced to a pitiable shade, a mere ghost, as we say, of its former self. Then these spirits and apparitions are so painfully solemn. I fancy that, were I suddenly to find myself liberated from all the trials and responsibilities of this life, my probation over, and my destiny put beyond marring or making, I should feel as I do when I find myself on an ocean steamer, and know that for ten days no business can turn up, and nothing can happen. I should regard the situation as a stupendous frolic, should be at the summit of gayety, and should only be too glad to leave the vale of tears behind. Instead of that, these starveling souls come mooning back to their former haunts, to cry over spilled milk.

551. Under the head of positive evidence apparently unfavorable to the doctrine, we may reckon ordinary observations of the dependence of healthy mind-action upon the state of the body. There are, also, those rare cases of double consciousness where personal identity is utterly destroyed or changed, even in this life. If a man or woman, who is one day one person, another day another, is to live hereafter, pray tell me which of the two persons that inhabit the one body is destined to survive?

552. There is certainly a large and formidable mass of facts, which, though not bearing directly upon the question of a future life, yet inclines us to a general conception of the universe which does not harmonize with that belief. We judge of the possibility of the unseen by its analogy with the seen. We smile at Aladdin's lamp or the elixir of life, because they are extremely unlike all that has come under our observation. Those of us who have never met with spirits, or any fact at all analogous to immortality among the things that we indubitably know, must be excused if we smile at that doctrine. As far as we see, forms of beauty, of sentiment, and of intelligence are the most evanescent of phenomena.

"The flower that once has bloomed forever dies."

Besides, scientific studies have taught us that human testimony, when not hedged about with elaborate checks, is a weak kind of evidence. In short, the utter unlikeness of an immortal soul to anything we cannot doubt, and the slightness of all the old arguments of its existence, appear to me to have tremendous weight.

§2. The Breakdown of the Mechanical Philosophy

553. On the other hand, the theory of another life is very likely to be strengthened, along with spiritualistic views generally, when the palpable falsity of that mechanical philosophy of the universe which dominates the modern world shall be recognized. It is sufficient to go out into the air and open one's eyes to see that the world is not governed altogether by mechanism, as Spencer, in accord with greater minds, would have us believe. The endless variety in the world has not been created by law. It is not of the nature of uniformity to originate variation, nor of law to beget circumstance. When we gaze upon the multifariousness of nature we are looking straight into the face of a living spontaneity. †1 A day's ramble in the country ought to bring that home to us.

554. Then there is the great fact of growth, of evolution. I know that Herbert Spencer endeavours to show that evolution is a consequence of the mechanical principle of the conservation of energy. But his chapter †2 on the subject is mathematically absurd, and convicts him of being a man who will talk pretentiously of what he knows nothing about. The principle of the conservation of energy may, as is well known, be stated in this form: whatever changes can be brought about by forces can equally happen in the reverse order (all the movements taking place with the same velocities, but in the reverse directions), under the government of the same forces. Now, the essential of growth is that it takes place in one determinate direction, which is not reversed. Boys grow into men, but not men into boys. It is thus an immediate corollary from the doctrine of the conservation of energy that growth is not the effect of force alone.

555. The world, then, is evidently not governed by blind law. Its leading characteristics are absolutely irreconcilable with that view. When scientific men first began to understand dynamics, and had applied it with great success to the explanation of some phenomena, they jumped to the anticipation that the universe could be explained in that way; and thus what was called the Mechanical Philosophy was set up. But a further study of the nature of force has shown that it has this conservative character, which absolutely refutes that mechanical notion of the universe. As well as I can read the signs of the times, the doom of necessitarian metaphysics is sealed. The world has done with it. It must now give place to more spiritualistic views, and it is very natural now to anticipate that a further study of nature may establish the reality of a future life.

556. For my part, I cannot admit the proposition of Kant — that there are certain impassable bounds to human knowledge; and, even if there are such bounds in regard to the infinite and absolute, the question of a future life, as distinct from the question of immortality, does not transcend them. The history of science affords illustrations enough of the folly of saying that this, that, or the other can never be found out. Auguste Comte said that it was clearly impossible for man ever to learn anything of the chemical constitution of the fixed stars, †1 but before his book had reached its readers the discovery which he announced as impossible had been made. Legendre said of a certain proposition in the theory of numbers that, while it appeared to be true, it was most likely beyond the powers of the human mind to prove it; yet the next writer on the subject gave six independent demonstrations of the theorem. I really cannot see why the dwellers upon earth should not, in some future day, find out for certain whether there is a future life or not. But at present I apprehend that there are not facts enough in our possession to warrant our building any practical conclusion upon them. If any one likes to believe in a future life, either out of affection for the venerable creed of Christendom or for his private consolation, he does well. But I do not think it would be wise to draw from that religious or sentimental proposition any practical deduction whatever — as, for instance, that human happiness and human rights are of little account, that all our thoughts ought to be turned away from the things of this world, etc. — unless such deduction has the independent sanction of good sense.

Chapter 7: Logic and Spiritualism

CHAPTER 7

LOGIC AND SPIRITUALISM †1P

557. Facts, new or newly published, rappings, table-turnings, with different predispositions opining differently, started controversy concerning Spiritualism. In course of time, other facts, planchette, public exhibitions, mind-reading, trances, apparitions, physical manifestations in great variety, many hundred well-attested strange experiences, attempts at scientific experimentation — contrariwise, important mediums and mind-readers detected rogues, new psychological laws explanatory of various illusions — all these facts doubtless had influence, one or other way, upon men's opinions. Meantime, a mighty flood, literature and talk, deluged the subject — observations highly judicious, delicious satire, ingenious speculations, a large part sadly rash, a very little too timorous. But doubted whether all this comment has changed one individual's mind.

558. In this impotence of argumentation, sole hope of contributing anything useful to the discussion lies in breathing into it spirit so candid, unsophisticated, direct, yielding, that the impartial mind, he who alone can get good from such reading, he who looks upon speculative opinions as so many objects of natural history, calculated to excite lively interest by curious relationships and affinities, more so perhaps being false than being true, but who lays them upon his dissection-table as things not calling for sympathy, as vivisection-subjects whose vehement logic-squirmings need excite no concern whatever — that this reader may be aided in picking to pieces, disentangling, studying, the intellectual component impulses urgent to the opinion in hand, in appreciating them, in considering their just limits of action, not so much himself to form definitive judgment pro or con (which mostly is not safe while controversy rages) as to assign it schematic place in the natural history of opinion.

559. First, I state plainly what I dispute. Hypnotism I question not, nor double and triple personality. That these things yet remain imperfectly classified is admitted, too; and not alone these phenomena, but much in everyday life, in communication of ideas in ordinary conversation. Only vague, doubtful explanations are deliverable for phenomena resembling clairvoyance. Not altogether improbably, unrecognized avenues of sense may exist. Possibly so the blind avoid trees and walls. Phenomena in abundance await explanation from future science about every stock and stone; how much more about mind? But here, with parting salutation, I diverge from spiritualistic paths, for I think no mind with which man can communicate can act or feel otherwise than through its residental nerve matter, which in turn can act and react upon external bodies only according to recognized laws of mechanics. Not that telepathy is absurd or in its nature impossible, but, in the coarse form it has been imagined impracticable as voyage to planet Mars. Belief in telepathy ought to be ranked as variation of spiritualism.

560. I run up my colors and confess myself scientific specialist. Spiritualists do not take kindly to scientific men, and never forego opportunities of instancing scientific follies. Though eminent scientists be their allies, they would not have spiritualism judged by the scientific kind of intelligence, surely anticipating disfavor from such judgment. For scientific men, we may as well acknowledge it, are, as such, mere specialists. That stigma! We are blind to our own blindness; but the world seems to declare us simply incapable of rising from narrowness and specialism to take broad view of any facts whatsoever.

561. "Myopy" and "presbyopy": inability to focus objects too far away; corresponding inability for objects too near. I suppose we scientific specialists, technical sharps, connoisseurs, travelers, scholars, are myopic minds, seeing microscopically, but only things under our several noses. Presbyopic minds, with defective accommodation, would be able to see only what stands open to all men's apprehension: these are fogies, average board-members, men whom one believes to be very wise, but whom one perceives to be very ignorant.

562. Is there a corresponding contrast between objects themselves? Some paintings are not easily made out because done in miniature, requiring narrow examination. Others, large and executed broadly, when looked at closely show only brush marks, the design quite invisible. So, some experiences are inapprehensible because minute and recondite. They are (a) scientific observations, only feasible with special instrumental aids, under special precautions, by virtue of special skill; they are (b) strange adventures, happenings dependent on rare chances fallen to few people, unrepeatable at pleasure. In contrast with these phenomena, remote from everyday life, others (let us hasten to acknowledge) are as hard or harder to see, simply because they surround us on every hand; we are immersed in them and have no background against which to view them. A person's heart stops beating; he perceives it; but let it keep on its regular course, and he knows not he has a heart. People do not hear how their own voices sound, nor feel their own manners. Writers are unaware of peculiar impressions produced by their own styles. What is the most obvious characteristic of the universe we live in puzzles one to answer otherwise than by rote.

563. Curious how little impression experience too familiar makes upon men's minds, how little attention is paid to it. With an oversecure, not to say ridiculous, contempt, I bethink me, are we despising everyday experience, we specialists and half the world besides — except where its lessons are followed irreflectively. Recondite experiences, whether scientific or autobiographic, are cherished as very precious. They are rare; the means for acquiring them have been costly; they distinguish their possessor over other men; they are all that many a man has to show for life's labor. Have we professional men often been found underrating importance of special orders of facts we have spent our lives in acquiring and in learning how to acquire? Has it happened to any of us, I wonder, to detect smiles on circumspicient faces at our contrary tendency? Or has it been generally remarked that persons who have gazed upon the midnight sun, or attended Nijni-Novgorod fair, or seen the effigies in Westminster Abbey, have set less store by these experiences than their untraveled interlocutors would seem inclined to do?

564. Let us ask ourselves whether not only scientific specialists, not only professional men, not only all educated men, but whether the bulk of mankind do not place too much stress on particulars, and regard too little the universal. Two persons casually meeting, with wish to develop mild sympathy, call one another's attention to the fair weather or the foul weather — insignificant details. The deeper ground of common feeling, that it is day-time, nobody is ever asked to remark; still less the good cheer that earth contains fellow creatures, heaven a Father. Commonplaces these? Granted. But what are commonplaces but universal experiences?

Ask a thoughtful company the general question where lies the intellectual superiority of one set of experiences over another, and reply will be made with some concord; facts are important only, first, as they are massed and concentrated upon one or more positions, and, secondly, as these positions are themselves important.

Go on, however, to inquire of relative values of experiences familiar and recondite, and differences will emerge. Respectability will remark that worth of anything is equivalent of trouble requisite to supply it, familiar experiences, like air and water, commanding no price — answer veritably redolent of the frankincense and the myrrh of the temple of Solomon. Science will hold scientific experiences more capable of systematic marshaling to great ends than civilian facts. Young America will call familiar phenomena squeezed lemons, whatever they had to teach already learned, things to be left behind in pressing on to things new; and it will recall dazzling inventions sprung from recondite experiences, gunpowder, mariner's compass, steam engine, electric telegraph, India rubber, anæsthetics, sewing machine, telephone, electric light.

565. But all these voices will not drown those that decry and revile specialism, extolling and magnifying perfections of the all-pervading. These will be heard to say that those things are not most intellectually helpful which most dazzle imagination; that great facts of nature which familiar experiences embody are not of the number of those things which can have their juices sucked out of them and be cast aside; that (returning to the principle upon which alone the question can be properly answered) the very circumstance which renders facts familiar is their being grouped into uniformed hordes, in consequence of which no collection of scientific observations can well be vast enough to withstand their concurrent testimony.

566. These protestants against worship of scientific specialties, deeper-thinking of the spiritualists included, will be averse from admitting that the discovery of phenomena of electricity, establishment of its laws, determination of its constants, and application to the uses of life, rank as the greatest triumph of modern knowledge. That distinction they will rather reserve for the evolution of the principle of conservation of energy, résumé of all that man has ever learned about force, great governing principle of all physics, whose history reaches from Archimedes to our day. That history shows that this great investigation has, from first to last, rested almost exclusively upon familiar experiences.

Its completion was involved in the discovery that heat, instead of being something ingenerable, indestructible, is but mechanical work transformed. Humanity wanted time to master that subtilty, energy being yet only letter in algebraic formula and even vis viva no commanding feature of ordinary conceptions of mechanics. Accordingly, the doctrine having been accepted, a vestige of mental confusion remained in disagreements as to nature of the evidence that had demonstrated it. Tyndall †1 and Clausius, †2 sound logicians, uphold Mayer's †3 proof drawn from facts to be reckoned as familiar; but Tait, †4 patriotic Scot, finds adherents for attribution to more special considerations adduced by countrymen. Others, however, had found it out long before, Rumford, Sadi Carnot, †5 and, if I am rightly informed, Uriah Boyden. †6

567. Be those doubts what they may, there can be none that previous steps used familiar experiences as almost their sole premisses. Archimedes proves property of lever, Stevinus that of inclined plane, Huygens that of moments of inertia, by mathematical reasoning from propositions assumed as self-evident — dictates of common sense. Galileo, demonstrating mechanical parallelogram, merely asks imagination how a body would move upon a vessel itself moving, no outward experiment demanded. Newton, establishing the law of action and reaction, treats his facts as matters of course. Even Galileo arguing substantially first two laws of motion in teeth of supposed established facts, though keen observer, though experimenter, rests almost exclusively on familiar experience, and "il lume naturale," adducing but few simple experiments, after all not needed.

568. Dr. Thomas Young, †1 name to conjure with among physicists, thought, in the first quarter of this century, scientific experimentation had gone far enough and should stop till facts already collected were digested. Every scientist will jeer. My individual notion, doubtless warped by specialism, is this. Reasoning is strictly experimentation. Euclid, having constructed a diagram according to prescription, draws an extra line, whereupon his mind's eye observes new relations not among those prescribed quite as surprising as new metals or new stars. Experimentation is strictly appeal to reason. Chemist sets up retort, introduces ingredients, lights fire, awaits result. Why so confident? Because he trusts that what happens once happens always; nature follows general laws, in other words, has a reason. Successful research — say Faraday's — is conversation with nature; the macrocosmic reason, the equally occult microcosmic law, must act together or alternately, till the mind is in tune with nature. This, the distinctively scientific procedure, linked experimentation and reasoning (suppose we say indagation), essentially involves special, new experience. A scientific man is simply one who has been trained to conduct observations of some special kind, with which his distinctive business begins and ends. Nevertheless, reasoning from familiar experience plays a great rôle in science: it lays the indispensable foundation, is needful in frequent later conjunctures. The part so built is the strongest of the structure, upholding the rest.

569. Such reasoning is sometimes elaborate, self-critical; but at its best it is simple, sleepy. The doctrine of Descartes, †1 that the mind consists solely of that which directly asserts itself in unitary consciousness, modern scientific psychologists altogether reject. Swarming facts positively leave no doubt that vivid consciousness, subject to attention and control, embraces at any one moment a mere scrap of our psychical activity. Without attempting accuracy of statement demanding long explanations, and irrelevant to present purposes, three propositions may be laid down. (1) The obscure part of the mind is the principal part. (2) It acts with far more unerring accuracy than the rest. (3) It is almost infinitely more delicate in its sensibilities. Man's fully-conscious inferences have no quantitative delicacy, except where they repose on arithmetic and measurement, which are mechanical processes; and they are almost as likely as not to be downright blunders. But unconscious or semi-conscious irreflective judgments of mother-wit, like instinctive inferences of brutes, answer questions of "how much" with curious accuracy; and are seldom totally mistaken.

570. Conclusions men reach they know not how are better than those fortified by unscientific logic. By logic Aquinas, if not Calvin, persuaded himself that one of the chief joys of the blest will be to peer over heaven's parapet and watch the damned writhing in torments and rage below: †P1 by instinct, or half-conscious inference, a poor peasant girl will inwardly reject the doctrine, for all revered pastor may say. No moral sentiment more universally violent than reprobation of intermarriage of near relatives. Assassin will shudder at thought of incest. But had a man to depend upon conscious reasoning to instruct conscience in this matter, while he might be led to condemn the act, he would be unlikely to regard it with the extreme horror in which actually all share. Generation after generation has, in almost unconscious mode, taken measure of ordinary experiences about family relationships, has transmitted its impression to the next, partly by tradition, partly, one guesses, by congenital bequest, this next has made its observations and discussions, has modified in some insensible degree the sentiment it derived from its fathers, and so at last our strong feeling has been developed. That races tolerating occasional incest have died out and that so horror of it has been bred, there is scant room to believe.

571. This transmission from father to son of dictates of good judgment makes the growth of common sense. Based on large, ordinary experience, far more valuable reservoir of truth than the aggregate of man's special experiences (scientific and extraordinary), worked up in that part of the mind that functions the most delicately and unerringly, reconsidered and revised by countless generations, such conclusion, if unequivocal and pertaining to matter plainly within the competency of good sense, who shall dare to dispute?

572. Let not conscious reason look down upon it as inadequate to problems high, intellectual, intricate. From data of sensations proper to hundreds of nerve-terminals in the optic retina, combined with certain muscular sensations — premisses more tangled and confused than tongue can tell or brain can think — common sense has extricated the marvelously clear and beautiful conception, Space. †1 What simple theory, reducing to order what infinitely complicated facts! Can whole history of science show any discovery whatever half so practically important, half so intrinsically difficult, half so intellectually interesting? It is conceivable that future science should find some principles of geometry to be measurably erroneous. Such discovery would be the most remarkable ever made by science. Yet what insignificant detail compared with that which common sense has taught us of space!

573. Common sense corrects itself, improves its conclusions. The history of the science of dynamics is that of gradual correction by inference from familiar experience (essentially an operation of good sense) of primitive conceptions of "force" and "matter." There, however, the reasoning was of the self-conscious kind. But we see social, political, religious common sense modifying itself insensibly in course of generations, ideas of rights of man acquiring new meaning, thaumaturgic elements of Christianity sinking, spiritual rising in religious consciousness.

574. Common sense improves; it does not, then, attain infallibility. Then, its decisions are subject to review. But in case there be evidence that such a conclusion is definitive, not a mere stage in a changing estimate; if it appears to have been formed under guidance of general experience and to be of the kind such experience can warrant; finally, if its substance is in harmony with individual good judgment from general experience, then the authority of common sense as to the practical truth of the conclusion (subject to minute modification) is so weighty that special experience can hardly attain sufficient strength to overthrow it.

575. How will this rule work in practice? Dr. Zöllner, eminent astronomer and mathematical physicist, man of true genius, keen and subtle, has Mr. Slade, celebrated medium, as visitor in his house. †1 One night he ties the ends of a string together, putting seal upon the knot. Next day, he hands this string to Slade, who thereupon before his eyes makes (or seems to make) a knot in the single string (in contradistinction, I mean, to the double string), and hands it back for examination. The ends of the string not being free, this was impossible according to common sense. But had space a fourth dimension, additional to its three of length, breadth, and thickness, there would be no such impossibility. Hence Dr. Zöllner concludes that space really has four dimensions. Now, it must be admitted that no experiences, familiar or otherwise, are absolutely inconsistent with space having four dimensions. For example, this refutation might be proposed: steam can be subjected to great pressure in a boiler; now if space were open in a fourth dimension, there would be ways round from inside to outside of the boiler, and why should not the steam escape? It might, however, be replied that the molecules having no component velocities in that direction, and there being no component pressure in that direction, there would be no tendency to motion in that direction; indeed various other loop-holes in the argument are discoverable. Only suppose, then, that space really has fourth dimension, and suppose that one single muscle-cell of Slade's had somehow got displaced so as to project in that direction, and force is thus supplied in that direction which, in total absence of resistance in that direction, would suffice to carry Slade's fingers and with them the string round by that path so as to tie the knot; and here we have explanation, simple and beautiful, of the phenomenon; a gentlemanly explanation, too, not unnecessarily offensive to Mr. Slade's honour. Should it be urged that all experience is against space having fourth dimension, because on that hypothesis phenomena similar to that tying of knot ought to be more common, ready reply comes: If space has fourth dimension there is no determining a priori how often it would happen that something would project into it; experience seems to show it happens so rarely that Mr. Slade furnishes the first conclusive instance of it. Now, it is certainly true that no experience whatever can furnish the slightest reason for thinking that an event of any conceivable kind will absolutely never happen. Take a thousand people at random among the inhabitants of the United States, and upon inquiry it may probably be found that not one of them will ever have read a line of Martin Farquhar Tupper. It will be fair to conclude that not one in a thousand of all the people in the country ever read line of this poet; but not to conclude he has no readers in the country, since it might be not one in a thousand were readers of his works, while still those poems were devoured by sixty thousand people. Upon same principle, all accumulable experience will never furnish any smallest reason for thinking that no one, or no million for that matter, of all the bodies in the universe juts out into fourth dimension. Nay, presumption rather holds that this does somewhere occur, since every rule has exceptions; for how could an absolutely universal law ever come about? But the whole of our personal experience, itself an amazing flood, together with the experience of all history as embodied in common sense, compels us to hold such jutting to be so excessively infrequent that the probability of its occurrence in any particular case, as in the person of Mr. Slade, is beyond all compare smaller than the probability of trick, even were we at a loss to conceive how trick could be.

576. Of course, popular belief has often fallen into gross errors. Primitive man peopled woods, streams, earth, air, clouds, stars, with spirits. If intercourse with these beings could be shown to have been believed customary, happening every day, it would be an inference of a kind legitimately to be drawn from familiar experience, and we should have to inquire seriously into its truth. But I fancy intercourse with spirits was never considered matter of course. Belief in it was not formed under guidance of experience, but was hot, extravagant fancy, classable with those superstitions that have inspired or terrified mankind — fountain of perpetual youth, philosopher's stone, fairies, ogres, ghosts, magic, personal devil, jinns sealed up by Solomon, archei, oracles of Apollo, Eleusinian mysteries, metempsychosis, and all other romances about substantial spirits.

577. Faith in these things is fading out; where people are enlightened mere traces of it remain. The essence of these rapidly-decadent beliefs is the doctrine that soul (such as we can know) is able to feel and act independently of its animal body. State the proposition in the abstract, and most men will subscribe to it. Find a practical case, and willingness to risk great interests upon the truth of the principle will commonly be deemed symptomatic of aberration of mind.

578. Common sense is coming to reject the doctrine, good sense does reject it. All ordinary phenomena of life, which crowd upon us every minute, together with such familiar matters as sleep, faintings, bodily illness, insanity, death, show as plainly, as conclusively, dependence of mind upon body, as familiar facts of lifeless things show first law of motion. That law which Galileo †1 substantially first told the world is that a moving body left to itself will move on with no diminution, no increase of speed, in one straight line forever. They say the first thing that made him think so was seeing a lamp hung by chain from roof of the beautiful cathedral at Pisa, just before the choir, swinging backward and forward, through a small arc, once in about four seconds, and continuing so to move all through high Mass, without any perceptible decrement of the amplitude of its oscillations. I can well believe this true. Performance of good judgment is a sluggish movement, a mental peristalsis, slow, obscure, that is favored by beautiful and peaceful surroundings, even by luxurious tedium, which, in most satisfying of cathedrals, ceremonies performed with an elegance in manner, a refinement in spirit, caught it might seem from the architecture, would well produce in mind of boy attending them too often. I remember myself giving that same lamp, as no doubt it was, a small impulse shortly before a function more than ordinarily prolonged — obsequies of prince of the church — and to have watched its grave, impressive, though soft, assertion of the first law of motion, all through service, wondering whether the obvious lesson of mortality which that corpse, whole scene, was bearing in upon me could be less true, less infallible than that.

579. Completely satisfactory discussion of the question of Spiritualism would involve satisfactory theory of connection of soul and body, which is not perhaps forthcoming.

580. The obsolete Cartesian dualism, that soul and body are two substances, distinct, independent, untenable as positing double absolute, rendering connection of soul and body absolutely inexplicable either on mechanical or on psychological principles, had a single element of philosophical strength, its recognition of real reaction between ego and non-ego. Development of this naturally leads to thinking that minds can communicate only through bodies — doctrine unfavorable to Spiritualism.

581. Philosophy tries to understand. In so doing, it is committed to the assumption that things are intelligible, that the process of nature and the process of reason are one. Its explanation must be derivation. Explanation, derivation, involve suggestion of a starting-point — starting-point in its own nature not requiring explanation nor admitting of derivation. Also, there is suggestion of goal or stopping-point, where the process of reason and nature is perfected. A principle of movement must be assumed to be universal. It cannot be supposed that things ever actually reached the stopping-point, for there movement would stop and the principle of movement would not be universal; and similarly with the starting-point. Starting-point and stopping-point can only be ideal, like the two points where the hyperbola leaves one asymptote and where it joins the other.

582. †1 In regard to the principle of movement, three philosophies are possible.

1. Elliptic philosophy. Starting-point and stopping-point are not even ideal. Movement of nature recedes from no point, advances towards no point, has no definite tendency, but only flits from position to position.

2. Parabolic philosophy. Reason or nature develops itself according to one universal formula; but the point toward which that development tends is the very same nothingness from which it advances.

3. Hyperbolic philosophy. Reason marches from premisses to conclusion; nature has ideal end different from its origin.

583. The choice of elliptic philosophy, which refuses to acknowledge the ideal, supposes more interest in nature than in reason. The philosophy which sees nothing in nature but the washing of waves on a beach cannot consistently regard mind as primordial, must rather take mind to be a specialization of matter. Bent on outward studies, it will find the statement that nerve-matter feels, just as carmine is red, a convenient disposition of a troublesome question. Elliptic philosophy is irreconcilable with Spiritualism.

584. He who feels himself and his neighbors under the constraints of overwhelming power, from which they long to take refuge in annihilation — situation less common in this country and age than in other places and times — viewing this little life as rounded with a sleep, readily accepts the idea that the world, too, sprang out of the womb of nothingness to evolve its destiny, and into nothingness back to return. Such life as this philosophy recognizes — a fatal struggle, a mere death-throe — it should extend throughout nature. Soul should be a mere aspect of the body, not tied to it, therefore, but identical with it. Nothing can be more hostile to Spiritualism than this Parabolic philosophy.

585. †2 Hyperbolic philosophy has to assume for starting-point something free, as neither requiring explanation nor admitting derivation. The free is living; the immediately living is feeling. Feeling, then, is assumed as starting-point; but feeling uncoördinated, having its manifoldness implicit. For principle of progress or growth, something must be taken not in the starting-point, but which from infinitesimal beginning will strengthen itself continually. This can only be a principle of growth of principles, a tendency to generalization. Assume, then, that feeling tends to be associated with and assimilated to feeling, action under general formula or habit tending to replace the living freedom and inward intensity of feeling. This tendency to take habits will itself increase by habit. Habit tends to coordinate feelings, which are thus brought into the order of Time, into the order of Space. Feelings coordinated in a certain way, to a certain degree, constitute a person; on their being dissociated (as habits do sometimes get broken up), the personality disappears. Feelings over whose relations to their neighbors habit has acquired such an empire that we detect no trace of spontaneity in their actions, are known as dead matter. The hypothesis here sketched, whose consequences, traceable with precision to considerable detail in various directions, appear to accord with observation, to an extent of which I can here give no idea, affords a rational account of the connection of body and soul. This theory, so far as I have been able as yet to trace its consequences, gives little or no countenance to Spiritualism. Still, it is evidently less unfavorable than any other reasonable philosophy.

586. The myriad strange stories prove nothing. Tell me a marvel; I cannot explain it. Does that teach you or me anything? True, you offer explanation, the spiritualistic one; but that is in conflict with good sense, while we know so little of the mind, at present, that it is not surprising that many things are yet inexplicable. Taking these stories in the gross, the only profitable way, we can roughly compare the phenomena with the general facts at our command for their explanation. These facts are four. First, the fact that all men are liars. Secondly, the fact of deranged imagination, hypnotism, hysteria. Thirdly, the fact that we may receive and act upon indications of which we are quite unconscious, and which, owing to the low sensibility of the conscious part of the mind, seem impossible. Fourthly, the fact that a certain number of coincidences will occur by chance. The result of such rough comparison is that, notwithstanding these four considerations, there are some stories truly surprising. If you have already admitted the general proposition of Spiritualism, you will naturally be inclined to use it to explain some of these stories. If, on the other hand, your judgment is that general experience is emphatically opposed to that proposition, these stories will assuredly not shake that judgment.

587. Meantime, those who are engaged in psychical research should receive every encouragement. They may have reached little or no result, so far; perhaps will not till they dismiss the phantom of telepathy from their minds. But scientific men, working in something like scientific ways, must ultimately reach scientific results. Psychology is destined to be the most important experimental research of the twentieth century; fifty years hence its wonders may be expected to occupy popular imagination as wonders of electricity do now.
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The Collected Papers of Charles Sanders Peirce. Electronic edition.
Volume 6: Scientific Metaphysics
Endmatter
Appendix A: Reply to the Necessitarians; Rejoinder to Dr. Carus
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Appendix A: Reply to the Necessitarians; Rejoinder to Dr. Carus †1

588. In The Monist for January, 1891, and in the number for April, 1892, I attacked the doctrine that every event is precisely determined by law. †2 Like everybody else, I admit that there is regularity: I go further; I maintain the existence of law as something real and general. But I hold there is no reason to think that there are general formulæ to which the phenomena of nature always conform, or to which they precisely conform. At the end of my second paper, the partisans of the doctrine of necessity were courteously challenged and besought to attempt to answer my arguments. This, so far as I can learn, Dr. Carus alone, in The Monist of July and October, 1892, has publicly vouchsafed to do. For this I owe him my particular thanks and a careful rejoinder.

589. I number the paragraphs of his papers consecutively. The following index shows the pages [of The Monist] on which those paragraphs commence, and the numbered sections of this rejoinder in which they are noticed.

Dr. Carus Rejoinder Dr. Carus Rejoinder
Volume II Volume II
Page Par. Secs.Page Par. Secs.
560 1 564 15 595 ter, 603
560 2 615 565 16 608
560 3 616 565 17 590
561 4 610-614 565 18 590
561 5 608 565 19 600n
561 6 605 566 20 601
561 7 605 566 21 600, 601
562 8 605 bis 566 22 590, 599, 609
562 9 608 566 23 599
562 10 566 24 590, 600, 601
563 11 599, 608, 609 567 25 595
563 12 606 567 26 595
563 13 606 567 27 595, 609
564 14 590, 599 bis, 609 567 28 607, 609
Dr. Carus Rejoinder Dr. Carus Rejoinder
Volume II Volume III
Page Par. Secs.Page Par. Secs.
567 29 599 68 84 592
568 30 609 68 85 614
568 31 609bis 68 86
568 32 609 69 87 599
569 33 609 69 88 592, 602bis
569 34 609 69 89
569 35 595 69 90
569 36 616 69 91 592
569 37 69 92 592
570 38 70 93 592
570 39 70 94 592
570 40 70 95 590
571 41 70 96 591, 598
571 42 71 97
571 43 71 98
572 44 610 71 99
572 45 71 100
572 46 592, 610 72 101
573 47 72 102 598
573 48 594 72 103 593
573 49 594 72 104
573 50 594 72 105
574 51 594, 612 73 106 598
574 52 73 107 593
574 53 612 73 108 593
574 54 73 109 593
574 55 612 73 110 593
575 56 604 73 111 593
575 57 604 bis 74 112 593
575 58 604, 612 74 113 593
575 59 604 74 114 593
575 60 604 74 115 593
576 61 594, 604, 612bis 75 116 593, 594
576 62 604, 608 75 117 593
576 63 604 76 118
577 64 604 bis 76 119 596
577 65 613 76 120 593
577 66 612 bis 76 121 601
577 67 612 bis 76 122 598
578 68 593, 594 77 123 590
578 69 604 77 124 597
579 70 593 77 125 594
579 71 590 78 126 595
580 72 590 78 127 616
580 73 590 78 128
580 74 590 79 129
580 75 590 79 130
581 76 590 79 131
581 77 590, 598 79 132
581 78 79 133 614
581 79 608 79 134
582 80 80 135
582 81 616 80 136
582 82 616 80 137 602
582 83 616 80 138 602
Dr. Carus Rejoinder Dr. Carus Rejoinder
Volume III Volume III
Page Par. Secs.Page Par. Secs.
80 139 592, 602 88 174
81 140 602 89 175 614
81 141 602 89 176 614 bis
81 142 602, 612 89 177 614
81 143 602, 612 89 178 614
81 144 602 bis 89 179
81 145 602 bis 89 180 617
81 146 602 bis 89 181
81 147 602 ter 89 182
82 148 602 90 183 617
82 149 599, 602 90 184
82 150 602 bis, 612 90 185 614
83 151 602, 611 90 186 614
83 152 602, 611 91 187 614
83 153 602, 611 91 188
83 154 602, 611 91 189
83 155 602, 611 91 190
84 156 602 bis 92 191 591
84 157 602 92 192 614 bis
84 158 602, 611 92 193 607, 614 bis
85 159 602, 611 93 194
85 160 602, 611 93 195 595
86 161 602 bis 93 196 595
86 162 602 94 197
86 163 592, 601 94 198 593
86 164 601 94 199 617
87 165 591, 601 94 200
87 166 601 94 201
87 167 601 95 202
87 168 614 95 203 607, 616
87 169 614 95 204 616
88 170 614 96 205 607
88 171 614 96 206
88 172 614 96 207
88 173

590. Dr. Carus' philosophy is hard to understand. Some phrases which he frequently uses lead the reader to imagine that he is listening to an old-fashioned Königsberg Kantian. What, then, is our surprise when we find (¶ 14) that he sneers at the Kantian, Sir William Hamilton (whom he calls Mr Hamilton) as having "no adequate conception of the a priori." In his Ursache, Grund und Zweck (1883), an admirably clear and systematic exposition of much of his thought, he takes a Schleiermacherian view of the a priori. He admits it to be founded in the universal conditions of cognition; but he thinks it is among the objective rather than the subjective conditions. This is an opinion to which Hamilton is also at times inclined. It is a weak conception, unless the whole distinction between the inward and the outward world be reformed in the light of agapastic and synechistic ontology. For to deny that the a priori is subjective is to remove its essential character; and to make it both subjective and objective (otherwise than in the sense in which Kant himself makes it objective) is uncalled for, and is cut off by Ockham's razor. But when synechism has united the two worlds, this view gains new life.

Another thing which has astonished me is Dr. Carus's extravagant laudation (¶ 17) of Venn's highly enlightened and remarkably bright-thinking, yet blundering little book, The Logic of Chance. †P1 This is the way he speaks of it: "This admirable work, we will make bold to say, marks a new epoch in the study of logic." He adds that it "paves the way which Mr. Peirce has actually followed." But the question of the nature of probability had long before that publication engaged the attention of some of the most powerful intellects in England; and my opinion concerning it was fully made up before I saw the book. †1 I do not think I learned anything from that except a classification of the philosophies of probability. However, after all his eulogy, Dr. Carus only uses the book to quote from it Mill's rewording of Kant's definition of causation, †2 which he would better have quoted direct.

Let me say, not to Dr. Carus, but to the younger generation of readers, that if they imagine that Hamilton, because he is antiquated, is not worth reading, they are much mistaken. The Scotistic elements of his philosophy, and his method in the notes on Reid, are especially worthy of attention. As for Mill, though his philosophy was not profound, it is, at least in his Examination of Hamilton, admirably set forth. Whoever wishes to appeal to the American philosophical mind needs to be quite familiar with the writings of these two men.

Dr. Carus himself accepts all that I hold for erroneous in Kant's definition of causation as universal and necessary sequence. †1 Mill merely substitutes the exacter words invariable for "universal," and unconditional for "necessary." †P1 In giving his form of the definition, Mill shows †2 why it is not applicable to the sequence of day and night, namely, that that is not necessary. Yet Dr. Carus writes (¶ 18) of this very same sequence as if it came under Mill's definition. †P2

Again, why should he make it "the immortal merit of the great Scotchman" (¶ 22), that is, of Hume, that he admitted the truth of Leibnitz's principle?

The famed puzzle of causation is peculiarly understood by Dr. Carus. The difficulties which the perusal of Hume suggested to the mind of Kant, †P3 were such as belonged to all categories, or general conceptions of the understanding. The pre-critical Kant inherited a very decided nominalism from Leibnitz and Wolf; and the puzzle for him was simply the usual difficulty that plagues nominalism when it finds itself confronted with a reality which has an element of generality. Necessity is, I need hardly say, but a particular variety of universality. But Dr. Carus (¶ 24) passes over this, to dwell upon an entirely different objection to causation, namely, that it seems to be a creation out of nothing, and a miracle.

I find myself equally at cross-purposes with him, when in ¶¶71-77, he speaks of the prevalent views of logicians concerning comprehension. This word, in logic, measures the amount of predicates or marks attached to a conception; †3 but Dr. Carus's criticisms seem to be based upon the idea that by comprehension is meant logical breadth, or the amount of subjects to which the conception is applicable.

I am simply gravelled by his remarks (¶ 95) concerning sundry English words.

No more do I know what to make of his praise (¶ 123) of the German translation of a French phrase used in the theory of functions, meaning univocally determined.

591. One habit which goes far to obscure Dr. Carus's meaning is that whenever he finds his opinion at variance with a familiar saying, instead of rejecting that formula, he retains it and changes the meaning. This is calculated to throw the whole discussion into confusion. Thus, nothing is more certain than that the so-called "law of identity," or A is A, was intended to express the fact that every term is predicable of itself. †1 But Dr. Carus, simply because he finds that "meaningless and useless" (¶ 96), thinks himself authorized to confuse the terminology of logic by making this formula, A = A, under the same old name, mean that things to which the same name is applicable are for some purpose equivalent.

In like manner, he changes the meaning of the word freedom (¶ 165), so that the distinction between those who maintain and those who oppose the freedom of the will may, in words, disappear. It seems scarcely defensible for a thoroughgoing necessitarian, such as he is, to fly the flag of Free Will.

He also changes the meaning of spontaneity so far that, according to him, "masses gravitate spontaneously" (¶ 191), and so pretends that his doctrine does not suppress the spontaneity of nature!

592. There are other questions of terminology in which I am unable to agree with Dr. Carus. Thus, when I define †2 necessitarianism as "the theory that the will is subject to the general mechanical law of cause and effect," Dr. Carus (¶ 139) wishes to delete "mechanical." But the result would be to define a doctrine to which the advocates of free will would generally subscribe, as readily as their opponents. In order properly to limit the definition, it is quite requisite to exclude "free causation." By "mechanical" causation, I mean a causation entirely determinative, like that of dynamics, but not necessarily operating upon matter.

Dr. Carus mentions (¶ 84) that there are several different ideas to which the term necessity is applied. It seems to me that what lies at the bottom of all of them is the experience of reaction against one's will. In the simplest form, this gives the sense of reality. †1 Dr. Carus himself admits (¶ 46) that reality involves the idea of inevitable fate. Yet philosophical necessity is a special case of universality. But the universality, or better, the generality, of a pure form involves no necessity. It is only when the form is materialized that the distinction between necessity and freedom makes itself plain. These ideas are, therefore, as it seems to me, of a mixed nature. Dr. Carus (¶¶ 91-94) insists that by the necessary, he wishes to be understood to mean in all cases the inevitable. This is the idea of fate, †2 and is not the conception which determinists usually attach to the term necessity. Yet he does not appear to be quite consistent. At one time (¶ 88), he carefully distinguishes necessity from fate. At another time (¶ 163), every element of compulsion is to be excluded from the conception of necessity.

593. One important key to Dr. Carus's opinions is the recognition of the fact that, like many other philosophers, he is a nominalist tinctured with realistic opinions.

He says (¶ 103) that "there is no need of discussing the truism that, properly speaking, there is no absolute sameness." Now, upon the nominalistic theory, there is not only no absolute or numerical identity, but there are not even any real agreements or likenesses between individuals; for likeness consists merely in the calling of several individuals by one name, or (in some systems) in their exciting one idea. On the other hand, upon the realistic theory, the fact that identity is a relation of reason does not in the least prevent it from being real. On that theory, it is real unless it is false that anything is itself. Thus, upon either theory, identity is just as real as similarity. But Dr. Carus, being a nominalist leaning toward realism, is inclined to make dynamical relations real, and second-intentional ones unreal. This opinion, I think, is a transitional one.

The declaration (¶ 198) that "natural laws are simply a description of nature as nature is," and that "the facts of nature express the character of nature," are nominalistic. But in another place (¶¶ 107-116) he says distinctly that uniformities are real.

He says (¶ 70), "Mr. Peirce attempts to explain natural laws as if they were concrete and single facts." This is eminently nominalistic. The nominalist alone makes this sharp distinction between the abstract and the concrete, †P1 which must not be confounded with Hegel's distinction for which the same words are used. The nominalist alone falls into the absurdity of talking of "single facts," or individual generals. Yet Dr. Carus says (¶ 68) that natural laws describe the facts of nature sub specie aeternitatis. Now I understand Spinoza to be a realist. In ¶ 117 he considers it "settled" "that there are samenesses." This is realistic. But in ¶ 120, he holds "the whole business of science to be to systematize the samenesses of experience," which is nominalistic.

594. Dr. Carus seems to be in some doubt as to how far evolutionism ought to be carried. In ¶¶ 48-51, he seems to side with my contention that it should be thoroughgoing. In ¶ 116, he makes intellect an evolution from feeling. Yet he is sometimes (¶125) "inclined" to say the world never was a chaos; he sometimes (¶ 61) thinks it weak to suppose that real chance begets order; and he sometimes (¶ 68) goes so far as to pronounce eternity to be the conditio sine qua non of natural law.

595. Every reader of The Monist knows that our good editor's great word is "formal law." The clearest statement he has ever made of this doctrine I find in the following two sentences (¶ 127):

"The a priori systems of thought are . . . constructions raised out of the recognition of the formal, i.e. relational samenesses that appear in experience. All possibilities of a certain class of relations can be exhausted and formulated in theorems." †P2

This is perspicuous. For example, of pairs, we can easily show that there are but two forms A:A and A:B. This proposition—theorem if you will — exhausts the possibilities. If we make believe there is no danger of falling into error in mathematical reasoning — and one danger, though not, perhaps, a very serious one, is eliminated — then this proposition is absolutely certain. But I will say, at once, that such a proposition is not, in a proper sense, synthetic. It is a mere corollary from the definition of a pair. Moreover, its application to experience, or to possible experience, opens the door to probability, and shuts out absolute necessity and certainty, in toto.

Concerning points like this, Dr. Carus, in company with the general body of thinkers, is labouring under a great disadvantage from not understanding the logic of relatives. It is a subject I have been studying for a great many years, and I feel and know that I have an important report that I ought to make upon it. †1 This branch of logic is, however, so abstruse, that I have never been able to find the leisure to translate my conclusions into a form in which their significance would be manifest even to a powerful thinker whose thoughts had not long been turned in that direction. I shall succeed in doing so, whenever I can find myself in a situation where I need think of nothing else for months, and not before. That may not be for thirty years; but I believe it is the intention of providence that it should be. Meantime, I will testify, and the reader can take my testimony for what he thinks it is worth, that all deductive reasoning, except that kind which is so childishly simple that acute minds have doubted whether there was any reasoning there — I mean non-relative syllogism — requires an act of choice; because from a given premiss, several conclusions — in some cases an infinite number — can be drawn. Hence, Dr. Carus is altogether too hasty in his confidence (¶¶ 195, 196) that general thinking machines "are not impossibilities." An act of original and arbitrary determination would be required; and it seems almost evident that no machine could perform such an act except within narrow limits, thought out beforehand and embodied in its construction. †2 Moreover, positive observation is called for in all inference, even the simplest — though in deduction it is only observation of an object of imagination. Moreover, a peculiar act which may properly be called abstraction †P1 is usually required, consisting in seizing evanescent elements of thought and holding them before the mind as "substantive" objects, to borrow a phrase from William James. At the same time, the process I am describing, that is, relative deduction, is perfectly general and demonstrative, and depends upon the truth of the assumed premisses, and not, like inductive reasoning, upon the manner in which those premisses present themselves.

But the application of the logic of relatives shows that the propositions of arithmetic, which Dr. Carus usually adduces as examples of formal law (¶ 15), are, in fact, only corollaries from definitions. They are certain only as applied to ideal constructions and, in such application, they are merely analytical.

The truth is our ideas about the distinction between analytical and synthetical judgments is much modified by the logic of relatives, and by the logic of probable inference. An analytical proposition is a definition or a proposition deducible from definitions; a synthetical proposition is a proposition not analytical. †1 Deduction, or analytical reasoning, is, as I have shown in my "Theory of Probable Reasoning," †2 a reasoning in which the conclusion follows (necessarily, or probably) from the state of things expressed in the premisses, in contradistinction to scientific or synthetical, reasoning, which is a reasoning in which the conclusion follows probably and approximately from the premisses, owing to the conditions under which the latter have been observed, or otherwise ascertained. The two classes of reasoning present, besides, some other contrasts that need not be insisted upon in this place. They also present some significant resemblances. Deduction is really a matter of perception and of experimentation, just as induction and hypothetic inference are; only, the perception and experimentation are concerned with imaginary objects instead of with real ones. The operations of perception and of experimentation are subject to error, and therefore it is only in a Pickwickian sense that mathematical reasoning can be said to be perfectly certain. It is so only under the condition that no error creeps into it; yet, after all, it is susceptible of attaining a practical certainty. So, for that matter, is scientific reasoning; but not so readily. Again, mathematics brings to light results as truly occult †P1 and unexpected as those of chemistry; only they are results dependent upon the action of reason in the depths of our own consciousness, instead of being dependent, like those of chemistry, upon the action of Cosmical Reason, or Law. Or, stating the matter under another aspect, analytical reasoning depends upon associations of similarity, synthetical reasoning upon associations of contiguity. †1 The logic of relatives, which justifies these assertions, shows accordingly that deductive reasoning is really quite different from what it was supposed by Kant to be; and this explains how it is that he and others have taken various mathematical propositions to be synthetical which in their ideal sense, as propositions of pure mathematics, are in truth only analytical.

Descending from things I can demonstrate to things of which various facts, in the light of those demonstrations, fully persuade me, I will say that in my opinion there are many synthetical propositions which, if not a priori in Dr. Carus's sense, are, at least, innate (notwithstanding his frequent denials of this, as in ¶ 15), though he is quite right in saying that their abstract and distinct formulation comes very late. (¶ 126.) †2 But turn the facts as I will, I cannot see that they afford the slightest reason for thinking that such propositions are ever absolutely universal, exact, or necessary in their truth. On the contrary, the principles of probable inference show this to be impossible.

Dr. Carus adduces the instance of a geometrical proposition, namely, "that two congruent regular tetrahedrons, when put together, will form a hexahedron." (¶ 25.) This, he says, seems to be "a very wonderful thing"; for why should not a larger tetrahedron be formed, just as two heaps of flour make a large heap of flour? Yet, he continues, the probability that the two tetrahedrons do always make a hexahedron is 1, "which means certainty." (¶ 27.) But as it happens, the proposition, in the form stated, is quite erroneous. What is true is this. If two tetrahedra are so placed that one face of each is coincident with one face of the other, while all the other faces are inclined to one another, and if of the 8 faces, the 2 that are coincident are not counted, there remain to be counted 8 - 2 = 6 faces. But there is nothing more wonderful about this than that 8 - 2 = 6, which is an easy corollary from definitions. Very few propositions in mathematics that appear "marvellous" will hold water; and those few excite our astonishment only because the real complexity of the conditions are masked in an intuitional presentation of them.

Dr. Carus holds (¶ 15) that formal knowledge is absolutely universal, exact, and necessary. In some cases, as where he says that, given the number of dimensions of space, the entire geometry could be deduced (¶ 35), the boasted infallibility will prove on examination to be downright error. In all other cases, the propositions only relate to ideal constructions, and their applicability to the real world is at the best doubtful and, as I think, false; while in their ideal purity they are not synthetical.

Thus, my good friend and antagonist holds that the combination of oxygen and hydrogen to produce water is not "different in principle" from that of the tetrahedra to produce a hexahedron. (¶ 26.) There is all the difference between the ideal and the real; which to my Scotistic mind is very important. But this is not the only passage in which he speaks as if form were the principle of individuation.

596. Dr. Carus's position is even weaker than that of Kant, who makes space, for example, a necessary form of thought (in a broad sense of that term). But Dr. Carus appears to consider space as an absolute reality. For he says (¶ 119) that "every single point of space has its special and individual qualities." Here again form is made the principle of individuation; whence the queer phrase "individual qualities."

597. Dr. Carus argues that whatever is unequivocally determinate is necessary. (¶ 124.) Were the determination spoken of real dynamic determination, this would be a mere truism. But the expression used, eindeutig bestimmt, merely expresses a mathematical determination, and therefore no real necessity ensues. The equation

x2 - 23x + 132 1/4 = 0

determines x to be either 11.477 or 11.523. In this sense, x has necessarily one value or the other. The equation

x2 - 12x + 6 = 0

determines x to be either 11.477 or 0.523. Together, the two equations uniquely determine x to be 11.477. This shows how much that argument amounts to.

598. By "sameness," Dr. Carus means equivalence for a given purpose. (¶¶ 102, 106.) By the "idea of sameness," he means (¶¶ 77, 96) the principle that things having a common character are for some purpose equivalent. This, he says, "has a solid basis in the facts of experience." By a "world of sameness" (¶ 113), he seems to mean one in which any two given concrete things are in some respect equivalent. He argues (¶ 122) that a "world of sameness is a world in which necessity rules." I do not see this. It seems to me so bald a non sequitur that I cannot but suppose the thought escapes my apprehension. If there were anything in the argument, it would seem to be a marvellously expeditious way of settling the whole dispute; and therefore it would have been worth the trouble of stating, so as to bring it within the purview of minds like mine.

599. My candid opponent sometimes endorses emphatically the Leibnitzian principle. "Necessitarianism must be founded on something other than observation. Observation is a posteriori; it has reference to single facts, to particulars; yet the doctrine of necessity . . . is of universal application. The doctrine of necessity . . . is of an a priori nature." (¶ 11.) "Millions of single experiences . . . cannot establish a solid belief in necessity." (¶ 14.) "No amount of experience is sufficient to constitute causation by a mere synthesis of sequences." (¶ 22.) "Millions of millions of cases" constitute "no proof" that a proposition "is always so." (¶ 29.)

Nevertheless, he holds that the law of "the conservation of matter and energy" so conclusively proves necessary causation that the obstinacy of Hume, himself, could not have withstood the argument. (¶ 23.) One wonders, then, what is supposed to prove this "law of the conservation of matter and energy," if no amount of experience can prove it.

But the a priori itself can "be based on the firm ground of experience." (¶ 14.) In that case, it is not prior to experience, after all! "The idea of necessity is based upon the conception of sameness, and . . . the existence of sameness is a fact of experience." (¶ 87.) If absolute necessity can be irrefragably demonstrated from the fact that two things are alike, it is a pity Dr. Carus should not state this demonstration in a form that I, and men like me, can understand. That would be more to the purpose than merely saying it can be proved. Absolute chance is rejected as "involving a violation of laws well established by positive evidence." (¶ 149.)

All these denials that absolute necessity can be established and absolute chance refuted by experiential evidence, mixed with as clear assertions of the same things, when taken together, have the appearance of an attempt, as the politicians say, to "straddle" the question.

600. †1 But the ingenious Doctor seeks to bolster up necessity by introducing the confused notion of "causation."

I do not know where the idea originated that a cause is an instantaneous state of things, perfectly determinative of every subsequent state. It seems to be at the bottom of Kant's discourse on the subject; yet it accords neither with the original conception of a cause, nor with the principles of mechanics. The original idea of an efficient cause is that of an agent, more or less like a man. It is prior to the effect, in the sense of having come into being before the latter; but it is not transformed into the effect. In this sense, it may happen that an event is a cause of a subsequent event; seldom, however, is it the principal cause. Far less are events the only causes. The modern mechanical conception, on the other hand, is that the relative positions of particles determine their accelerations at the instants when they occupy those positions. In other words, if the positions of all the particles are given at two instants (together with the law of force), then the positions at all other instants may be deduced. †P1 This doctrine conflicts with Kant's second analogy of experience, as interpreted by him, in no less than four essential particulars. In the first place, far from involving any principle that could properly be termed generation, or Erzeugung, which is Kant's word for the sequence of effect from cause, the modern mechanical doctrine is a doctrine of persistence, and, as I have repeatedly explained, positively prohibits any real growth. In the second place, one state of things (i.e. one configuration of the system) is not sufficient to determine a second; it is two that determine a third. To whomsoever may think that this is an inconsiderable divergence of opinions, let me say, study the logic of relatives, and you will think so no longer. In the third place, the two determining configurations, according to mechanics, may be taken at almost any two instants, and the determined configuration be taken at any third instant we like. There is no mechanical truth in saying that the past determines the future, rather than the future the past. We habitually follow tradition in continuing to use that form of expression, but every mathematician knows that it is nothing but a form of expression. We continue, for convenience, to talk of mechanical phenomena as if they were regulated, in the same manner in which our intentions regulate our actions (which is essentially a determination of the future by the past), although we are quite aware that it is not really so. Remark how Kant reasons: †1

"If it is a necessary law of our sensibility, and consequently a formal condition of all perceptions, that the preceding time determines the following (since I can only come to the following through the preceding), then is it also an indispensable law of the empirical representation of the time-series that the appearances of the preceding time determine every occurrence in the following."

What this leads to is a causality like that of mental phenomena, where it is the past which determines the future, and not (in the same sense) the reverse; but the doctrine of the conservation of energy consists precisely in the denial that anything like this occurs in the domain of physics. Had Kant studied the psychological phenomena more attentively and generalized them more broadly, he would have seen that in the mind causation is not absolute, but follows such a curve as is traced in my essay towards "The Law of Mind." †1 Does our judicious editor deem it ungracious to find fault with Kant for not doing so much more than he did, considering what that hero-like achievement was? We must seem to carp, as long as thinkers can hold that achievement for sufficient. In the fourth place, Kant's "Analogy" ignores that continuity which is the life blood of mathematical thought. He deals with those awkward chunks of phenomenon called "events." He represents one such "event" as determined by certain others, definitely, while the rest have nothing to do with it. It is impossible to cement such thought as this into hermetic continuity with the refined conceptions of modern dynamics. The statement that every instantaneous state of things determines precisely all subsequent states, and not at all any previous states, could, I rather think, be shown to involve a contradiction.

The notion which Dr. Carus holds of a cause seems to be that it is a state, embracing all the positions and velocities of all the masses at one instant, the effect being a similar state for any subsequent instant. (¶¶ 21, 24.) This breaks at once with common parlance, with dynamics, and with philosophical logic. In common parlance, we do not say that the position and upward velocity of a missile is the cause of its being at a subsequent instant lower down and moving with a greater downward velocity. †P1 In dynamics, it is the fixed force, gravitation, or whatever else, together with those relative positions of the bodies that determine the intensity and direction of the forces, that is regarded as the cause. But these causes are not previous to, but simultaneous with, their effects, which are the instantaneous accelerations. Finally, logic opposes our calling one of two states which equally determine one another (as any two states of a system do, if the velocities are taken to be included in these states) the determinator, or cause, simply because of the circumstance that it precedes the other in time —a circumstance that is upon the principles of dynamics plainly insignificant and irrelevant.

Everybody will make slips in the use of words that have been on his lips from before the time when he learned to think; but the practice which I endeavor to follow in regard to the word cause is to use it in the Aristotelian sense of an efficient cause, in all its crudeness. In short, I refuse to use it at all as a philosophical word. When my conception is of a dynamical character, I endeavour to employ the accepted terminology of dynamics; †P1 and when my idea is a more general and logical one, I prefer to speak of the explanation.

601. Dr. Carus thinks the element of necessity in causation can be demonstrated by considering the process as a transformation. "It is a sequence of two states which belong together as an initial and final aspect of one and the same event." (¶ 21. Compare ¶¶ 20, 24.) He neglects to explain how he brings under this formula the inward causation of the will and character, as set forth by him in ¶¶ 163-167.

It is unnecessary for me to reply, at length, to an argument so manifestly inconclusive. On the one hand, it conflicts with the principle that absolute necessity cannot be proved from experience; and, on the other hand, it leaves room for an imperfect necessity.

Professor Tait †1 has done an ill office to thought in countenancing the idea that the conservation of energy is of the same nature as the "conservation," or rather perduration, of matter. Dr. Carus says (¶ 121) that

"The law of the conservation of matter and energy rests upon the experience (corroborated by experiments) that causation is transformation. It states that the total amount of matter and the total amount of energy remain constant. There is no creation out of nothing and no conversion of something into nothing."

The historical part of this statement contains only a small grain of truth; but that I will not stop to criticize. The point I wish to make is that the law of the conservation of energy is here represented under a false aspect. The true substance of the law is that the accelerations, or rates of change, of the motions of the particles at any instant depend solely on their relative positions at those instants. The equation which expresses the law under this form is a differential equation of the second order; that is, it involves the rates of change of the rates of change of positions, together with the positions themselves. Now, because of the purely analytic proposition of the differential calculus that

Dt2s = 1/2 Ds(Dts)2,

the first integral of the differential equation of the second order, that is, the differential equation of the first order which expresses the same state of things, equates half the sum of the masses, each multiplied by the square of its velocity, to a function of the relative positions of the particles plus an arbitrary constant. †P1 In order to fix our ideas, let us take a very simple example, that of a single particle accelerated towards an infinite plane, at a rate proportional to the nth power of its distance from the plane. In this case, if s be the distance, the second differential equation will be

Dt2s = -a sn

and the first integral of it will be

(Dts)2 = -(2a/n+1)s(n+1) + C.

By the first law of motion, and the Pythagorean proposition, the part of the velocity-square depending on the horizontal component is also constant.

The arbitrary constant, C, plainly has its genesis in the fact that forces do not determine velocities, but only accelerations. Its value will be fixed as soon as the velocity at any instant is known. This quantity would exist, just the same, and be independent of the time, and would therefore be "conserved" whether the forces were "conservative," that is, simply positional, or not. Now, this constant is the energy; or rather, the energy is composed of this constant increased by another which is absolutely indeterminable, being merely supposed large enough to make the sum positive.

Thus, the law of energy does not prescribe that the total amount of energy shall remain constant; for this would be so in any case by virtue of the second law of motion; but what it prescribes is that the total energy diminished by the living force shall give a remainder which depends upon the relative positions of the particles and not upon the time or the velocities. It is also to be noticed that the energy has no particular magnitude, or quantity. Furthermore, in transformations of kinetical energy into positional energy, and the reverse, the different portions of energy do not retain their identity, any more than, in bookkeeping, the identity of the amounts of different items is preserved. In short, the conservation of energy (I do not mean the law of conservation) is a mere result of algebra. Very different is it with the "conservation" of matter. For, in the first place, the total mass is a perfectly definite quantity; and, in the second place, in all its transformations not only is the total amount constant, but all the different parts preserve their identity. To speak, therefore, of "the conservation of matter and energy" is to assimilate facts of essentially contrary natures; and to say that the law of the conservation of energy makes the total amount of energy constant is to attribute to this law a phenomenon really due to another law, and to overlook what this law really does determine, namely, that the total energy less the kinetic energy gives a remainder which is exclusively positional.

602. Dr. Carus does not make it clear what he means by chance. He does, indeed, say (¶¶ 145, 146):

"What is chance?

Chance is any event not especially intended, either not calculated, or, with a given and limited stock of knowledge, incalculable."

This defines what he means by a chance event, in the concrete; what he understands by probability we are left to conjecture. But from what he says in ¶ 147, I infer that he regards it as dependent upon the state of our ignorance, and therefore nothing real.

I am, therefore, much puzzled when I find him expressing a conviction (¶¶ 88, 156) that chance plays an important part in the real world. He explains very distinctly that "when we call a throw of the dice pure chance, we mean that the incidents which condition the turning up of these or those special faces of the dice have not been, or cannot be, calculated." (¶ 147.) This is the commonest, because the shallowest, philosophy of chance. Even Venn might teach him better than that. However, according to that view, when he writes of "the important part that chance plays in the world — not absolute chance . . . but that same chance of which the throw of the die is a typical instance" (¶ 88), he can be understood to mean no more than that many things happen which we are not in condition to calculate or predict. This is not playing a part in the world, one would say — at least, not in the natural world; it is only playing a part in our ignorance.

Dr. Carus frequently uses phrases which make us suspect he penetrates deeper. Thus, he says, "We do not believe in absolute chance, but we believe in chance" (¶ 144); and again, "Every man is the architect of his own fortune — but not entirely. There are sometimes coincidences determining the fates of men." (¶ 161.) But when we remark the consecution of ¶¶ 137-162, we feel pretty sure he really sees no further. To do so would have been to perceive that indefinitely varied specificalness is chance.

For a long time, I myself strove to make chance that diversity in the universe which laws leave room for, instead of a violation of law, or lawlessness. That was truly believing in chance that was not absolute chance. It was recognizing that chance does play a part in the real world, apart from what we may know or be ignorant of. But it was a transitional belief which I have passed through, while Dr. Carus seems not to have reached it.

As for absolute chance, Dr. Carus makes the momentous admission that it is "not unimaginable." (¶ 150.) If so, its negation, or absolute necessity, cannot be a formal principle.

603. But it is time for me to leave the consideration of Dr. Carus's system and to take up his strictures upon mine. His philosophy is one eminently enlightened by modern ideas, which it synthetizes to an unusual extent. It is distinguished for its freedom from the vice of one-sidedness, and displays every facet of the gem of philosophical inquiry, except the one on which it rests, the question of absolute law. Its prominent faults, which I feel sure must have struck every competent reader, are that it shows little trace of meditation upon the thoughts of the great idealists, and that there is a certain want of congruity between different elements of it. How strangely it sounds, for instance, to find an apriorian, and one who is dinging "formal laws" so perpetually into our ears, one who holds that "in order to weave the woof of the a posteriori elements into coherent cloth we want the warp of the a priori" (¶ 15), to find this man declaring for a positivism "which accepts no doctrine, theory, or law, unless it be a formulation of facts," and proclaiming that "the whole business of science is to systematize the samenesses of experience, and to present them in convenient formulas." (¶ 120.) Now there is just one way of bringing such warring elements into harmony, and curing the greatest defect of the system — and it is a way which would also bring the whole into far better concordance with natural science. It is to lop off the heads of all absolute propositions whose subject is not the Absolute, and reduce them to the level of probable and approximate statements. †1 Were that defalcation performed, Dr. Carus's philosophy would, in its general features, offer no violent opposition to my opinions. Moreover, the Doctor has at heart the conciliation of religion and science. I confess such serious concern makes me smile; for I think the atonement he desires is a thing which will come to pass of itself when time is ripe, and that our efforts to hasten it have just that slight effect that our efforts to hasten the ripening of apples on a tree may have. Besides, natural ripening is the best. Let science and religion each have stout faith in itself, and refuse to compromise with alien and secondary purposes, but push the development of its own thought on its own line; and then, when reconcilement comes — as come it surely will — it will have a positive value, and be an unmixed good. But since our accomplished editor thinks himself called upon to assist in this birth of time, let me ask him whether of all the conditions of such peace the first is not that religious thought should abandon that extravagant absoluteness of assertion which is proper to the state of intellectual infancy, but which it has so long been too timid to let go? This pragmatical and unneeded absoluteness it is which is most deeply contrary to the method, the results, and the whole spirit of science; and no error can be greater than to fancy that science, or scientific men, rest upon it or readily tolerate it.

604. Dr. Carus (¶¶ 56-64) condemns my method of investigation as contrary to that by which science has been advanced; and holds that a radically different, and thoroughly positivistic method is requisite — a method so intensely positivistic as to exclude all originality. I suppose he will not object to my forming an opinion concerning the methods of science. I was brought up in an atmosphere of scientific inquiry, and have all my life chiefly lived among scientific men. For the last thirty years, the study which has constantly been before my mind has been upon the nature, strength, and history of methods of scientific thought. I have no space here to argue the question. In its logical aspect, I have partly considered it in various publications; †1 and in its historical aspect I have long been engaged upon a treatise about it. †2 My critic says (¶ 57) that I am "very positivistic in my logic of science." This is a singular misapprehension. Few of the great scientific minds with whom I have come into personal contact, and from whom I endeavoured to learn, were disposed to contemn originality or the ideal part of the mind's work in investigation; and those few, it was easy to see, really breathed an atmosphere of ideas which were so incessantly present that they were unconscious of them. Were I to name those of my teachers who were most positivistic in theory a smile would be excited. My own historical studies, which have been somewhat minutely critical, have, on the whole, confirmed the views of Whewell, the only man of philosophical power conjoined with scientific training who had made a comprehensive survey of the whole course of science, that progress in science depends upon the observation of the right facts by minds furnished with appropriate ideas. †3 Finally, my long investigation of the logical process of scientific reasoning led me many years ago to the conclusion that science is nothing but a development of our natural instincts. So much for my theory of scientific logic. It is as totally opposed as anything can be to Dr. Carus's theory (¶ 69, note; and Ursache, Grund und Zweck, p. 2) that originality is out of place in science.

But in my practice of scientific reasoning, Dr. Carus accuses me of being what he calls a "constructionist"; that is, a theorizer unguided by indications from observation or accepted facts. To a mind upon whom that celebrated and splendid chapter of Kant upon the architectonical method failed to make a deep impression I may appear so; but travesty is in truth hardly too strong a word to describe the account of my method by Dr. Carus.

Perhaps exaggeration is not without its value. If so, let me sum up the method Dr. Carus recommends. Eschew originality is its pious formula; do not think for yourself, nor countenance results obtained by original minds. Distrust them; they are not safe men. Leave originality to mathematicians and their breed, to poets, and to all those who seek the sad notoriety of having unsettled belief. †P1 Flee all philosophies which smack of this aberrant nineteenth century. †P2 This theory of Dr. Carus condemns itself; for it is highly original, and soars into the free ether untrammelled by historic facts.

Kepler comes very close to realizing my ideal of the scientific method; and he is one of the few thinkers who have taken their readers fully into their confidence as to what their method really has been. †P3 I should not feel justified in inflicting upon mine an autobiographical account of my own course of thought; but some things Dr. Carus's accusation forces me to mention. My method of attacking all problems has ever been to begin with an historical and rational inquiry into the special method adapted to the special problem. This is the essence of my architectonical proceeding upon which Dr. Carus has commented very severely. To look an inch before one's nose involves originality: therefore, it is wrong to have a conscious method. But further, in regard to philosophy, not only the methods, but the elementary ideas which are to enter into those methods, should be subjected to careful preliminary examination. This, especially, Dr. Carus finds very unscientific. (¶ 64, and elsewhere.) It is, undoubtedly, the most characteristic feature of my procedure. Certainly it was not a notion hastily or irreflectively caught up; but is the maturest fruit of a lifetime of reflection upon the methods of science, including those of philosophy; and if it shall be found that one contribution to thought on my part has proved of permanent service, that, I expect, will be the one. This method in nowise teaches that the method and materials for thought are not to be modified in the course of the study of the subject-matter. But instead of taking ideas at haphazard, or being satisfied with those that have been handed down from the good old times, as a mind keenly alive to the dangers of originality would have done, I have undertaken to make a systematic survey of human knowledge (a very slight sketch of which composed the substance of my paper on the "Architecture of Theories") †1 in order to find what ideas have, as a fact, proved most fruitful, and to observe the special utilities they have severally fulfilled. A subsidiary object of this survey was to note what the great obstacles are today in the way of the further advance of the different branches of science. In my "Architecture of Theories," I never professed to do more than make a slight sketch of a small portion of my preliminary studies, devoting thirteen lines to some hints as to the nature of the results. †2 In the four following papers I have given a selection of a few of these results. Among those which remain to be reported are some of much more immediate importance than any of those hitherto set forth. If anybody has been surprised to find my subsequent papers developing thoughts which they were unable to foresee from my first, it is only what I warned people from the outset that they would find to happen. Nor have the greatest of these surprises yet been reached. †P1

The next series of facts reviewed was that of the history of philosophy. I waded right into this fearful slough of "originality," in order to gather what seemed to throw a light upon the subject. Finally, I reviewed the general facts of the universe.

I now found myself forced by a great many different indications to the conclusion that an evolutionary philosophy of some kind must be accepted — including among such philosophies systems like those of Aristotle and of Hegel. From this point the reasoning was more rapid. Evolution had been a prominent study for half a generation; and much light had been thrown upon the conditions for a fruitful evolutionary philosophy. The first question was, how far shall this evolution go back? What shall we suppose not to be a product of growth? I fancy it is this cautious reflectiveness of my procedure which especially displeases Dr. Carus. It is not positivistic: it is architectonic. But the answer to the question was not far to seek. If an evolutionary explanation is to be adopted, philosophy, logic, and the economy of research all dictate that in the first essay, at least, that style of explanation be carried as far back as explanation is called for. What elements of the universe require no explanation? This was a simple question, capable of being decided by logic with as much facility and certainty as a suitable problem is solved by differential calculus. Being, and the uniformity in which being consists, require to be explained. The only thing that does not require it is non-existent spontaneity. This was soon seen to mean absolute chance. The conclusion so reached was clinched by a careful reëxamination of the office of chance in science generally, and especially in the doctrines of evolution. Arrived at this point, the next question was, what is the principle by which the development is to proceed? It was a difficult inquiry, and involved researches from different points of view.

But I will not trouble the reader with further autobiographical details. I have given enough to show that my method has neither been in theory purely empirical, nor in practice mere brain-spinning; and that, in short, my friend Dr. Carus's account of it has been as incorrect as can be.

605. The learned doctor (¶¶ 6, 7, 8) pronounces me to be an imitator of David Hume, or, at least, classes my opinions as closely allied to his. Yet be it known that never, during the thirty years in which I have been writing on philosophical questions, have I failed in my allegiance to realistic opinions and to certain Scotistic ideas; while all that Hume has to say is said at the instance and in the interest of the extremest nominalism. Moreover, instead of being a purely negative critic, like Hume, seeking to annul a fundamental conception generally admitted, I am a positive critic, pleading for the admission to a place in our scheme of the universe for an idea generally rejected. In the first paper of this series, in which I gave a preliminary sketch of such of my ideas as could be so presented, I carefully recorded my opposition to all philosophies which deny the reality of the Absolute, and asserted that "the one intelligible theory of the universe is that of objective idealism, that matter is effete mind." †1 This is as much as to say that I am a Schellingian, of some stripe; so that, on the whole, I do not think Dr. Carus has made a very happy hit in likening me to Hume, to whose whole method and style of philosophizing I have always been perhaps too intensely averse. Yet, notwithstanding my present disclaimer, I have little doubt apriorians will continue to describe me as belonging to the sceptical school. They have their wonderful ways of arriving at truth, without stooping to confront their conclusions with facts; and it is amusing to see how sincerely they are convinced that nobody can have science at heart, without denying all they uphold. †P1

My opponent has a habit of throwing out surprising opinions without the least attempt to illuminate them with the effulgence of reason. Thus he says (¶ 8): "If Kant's answer to Hume had been satisfactory, Mr. Peirce would probably not have renewed the attack." What attack? All that Hume attacked I defend, namely, law as a reality. How could a defense of that which I defend as essential to my position, cause me to surrender that position, namely, that real regularity is imperfect? In any sense in which Hume could have admitted the possibility of law, it must be precisely followed; since its existence could consist only in the conformity of facts unto it. But perhaps Dr. Carus means that if one question had been completely settled, I should probably have confined myself to talking about that, instead of broaching a new one.

606. Another misunderstanding of my position on the part of Dr. Carus (¶¶ 12, 13) is simply due to "boldly" having been twice printed where the reading should have been "baldly," in my paper on "The Doctrine of Necessity." (The Monist, vol. II, p. 336, lines 20 and 25 [63].) I wish printers would learn that I never use the word bold. I have so little of the quality, that I don't know what it means. As I read the "revise," as usual, it was presumably my fault that the erratum occurred. At any rate, had my meaning been clearly expressed, the proofreader would not have been misled by my defective chirography. What I was trying to say was, in substance, this: Absolute chance is a hypothesis; and, like every hypothesis, can only be defended as explaining certain phenomena. †P1 Yet to suppose that an event is brought about by absolute chance is utterly illogical, since as a hypothesis it could only be admitted on the ground of its explaining observed facts; now from mere non-law nothing necessarily follows, and therefore nothing can be explained; for to explain a fact is to show that it is a necessary or, at least, a probable result from another fact, known or supposed. Why is not this a complete refutation of the theory of absolute chance? Answer: because the existence of absolute chance, as well as many of its characters, are not themselves absolute chances, or sporadic events, unsubject to general law. On the contrary, these things are general laws. Everybody is familiar with the fact that chance has laws, and that statistical results follow therefrom. Very well: I do not propose to explain anything as due to the action of chance, that is, as being lawless. I do not countenance the idea that Bible stories, for instance, show that nature's laws were violated; though they may help to show that nature's laws are not so mechanical as we are accustomed to think. But I only propose to explain the regularities of nature as consequences of the only uniformity, or general fact, there was in the chaos, namely, the general absence of any determinate law. †P1 In fact, after the first step is taken, I only use chance to give room for the development of law by means of the law of habits.

607. In ¶ 28, I read: "Mr. Peirce does not object to necessity in certain cases; he objects to necessity being a universal feature of the world." This is correctly stated, and so it is in ¶ 203. I object to necessity being universal, as well as to its ever being exact. In short, I object to absolute universality, absolute exactitude, absolute necessity, being attributed to any proposition that does not deal with the {A} and the {Ö}, in the which I do not include any object of ordinary knowledge. But it is careless to write (¶ 193) that I "describe the domain of mind as the absence of law." Is not one of my papers entitled "The Law of Mind"? It is true that I make the law of mind essentially different in its mode of action from the law of mechanics, inasmuch as it requires its own violation; but it is law, not chance uncontrolled. That it is not "an undetermined and indeterminable sporting" should have been obvious from my expressly stating that its ultimate result must be the entire elimination of chance from the universe. That directly negatives the adjective "indeterminable," and hence also the adjective "undetermined." Still more unwarranted is the statement (¶ 205) that I deny "that there are samenesses in this world." If the slightest excuse for such an accusation can be found in all my writings I shall be mightily surprised.

608. Dr. Carus fully admits (¶ 9) the justice of my first reply to the argument that necessity is postulated in all scientific reasoning, which reply is that to postulate necessity does not make it true. As this reply, if correct, is complete, Dr. Carus was bound after that admission to drop the postulate-argument in favor of necessity. †P1 But he takes no notice, at all, of my four-page argument to show that scientific reasoning does not postulate absolute universality, exactitude, or necessity (The Monist, vol. II, pp. 324-327 [39-43]); but calmly asserts, four or five times over (¶¶ 5, 11, 16, 62, 79), without one scintilla of argumentation, that that postulate is made, and uses this as an argument in favor of necessity.

609. He also fully admits (¶¶ 11, 14, 22) the justice of my argument that the absoluteness of universality, exactitude, and necessity, cannot be proved, nor rendered probable, by arguments from observation. That argument consisted in assuming that all arguments from observation are probable arguments, and in showing that probable inferences are always affected with probable errors.

Had I deemed it requisite, I might easily have fortified that argument by a more profound analysis of scientific reasoning. Such an analysis I had formerly given in my "Theory of Probable Inference" [vol. 2, bk. III, ch. 8] (in Studies in Logic, Boston, Little and Brown).

But, notwithstanding his admissions, Dr. Carus sets up his ipse dixit against my argumentation. "We deny most positively," says the editorial Elohim, "that the calculus of probabilities is applicable to the order of the world, as to whether it may or may not be universal." (¶¶ 27, 31.)

To support this, he cites (¶¶ 31-34) four passages from articles written by me sixteen years ago. I hope my mind has not been stationary during all these years; yet there is little in those old articles which I now think positively erroneous, and nothing in the passages cited. My present views had, at that time, already begun to urge themselves on my mind; but they were not ripe for public avowal. In the first of the passages cited, I express the opinion, which I first uttered in my earlier lectures before the Lowell Institute, in 1866, afterwards in the Popular Science Monthly in 1877 †1 [1878], in still fuller elaboration in my "Theory of Probable Inference" in 1882, †2 and maintain now as strongly as ever, that no definite probability can be assigned to any general arrangement of nature. To speak of an antecedent probability would imply that there was a statistical science of different universes; and a deduced probability requires an antecedent probability for one of its data. †P1 This consideration only goes to fortify my present position, that we cannot conclude from observed facts with any degree of probability, and therefore a fortiori not with certainty, that any proposition is absolutely universal, exact, or necessary. In the absence of any weight of probability in favor of any particular exact statement, the formal presumption is altogether against any one out of innumerable possible statements of that kind.

The second passage cited is one in which I argue that the universe is not a chaos, or chance-medley. Now Dr. Carus admits (¶ 28) that I do not today maintain that it is a chance-medley.

The third passage cited is this: "A contradiction is involved in the very idea of a chance-world." This is in entire harmony with my present position that "a chaos . . . being without connection or regularity would properly be without existence." ("Architecture of Theories," The Monist, vol. I, p. 176 [33].)

The fourth passage is to the effect that "the interest which the uniformities of nature have for an animal measures his place in the scale of intelligence." This I still believe.

So much for my supposed contradictions. If I am not mistaken, our amiable editor, whose admirable editorship springs so largely out of his amiability, in copying out these passages was really not half so much intent on showing me to be wrong at present, as on showing me to have been right formerly. However hard he hits, he contrives to honey his sockdolagers, and sincerely cares more to make the reader admire his antagonist when he is right than to condemn him when he is wrong. There is a touch of art in this that proclaims the born editor, and which I can hardly hope to imitate.

Though Dr. Carus admits over and over again that necessity cannot be based on observation, he often slips back to the idea that it can be so based. He says (¶ 30) that "form is a quality of this world, not of some samples of it, but throughout, so far as we know of existence in even the most superficial way." But does he not see that all we do know, and all we shall tomorrow, or at any date know, is nothing but a sample of our possible experience — nay, is but a sample of what we are in the future to have already experienced? I have characterized inductive inference as reasoning from samples; but the most usual way of sampling a class is by examining all the instances of it that have come under our observation, or which we can at once collect.

610. Dr. Carus (¶¶ 44, 46) holds that from my social theory of reality, namely, that the real is the idea in which the community ultimately settles down, the existence of something inevitable is to be inferred. I confess I never anticipated that anybody would urge that. I thought just the reverse might be objected, namely, that all absoluteness was removed from reality by that theory; and it was many years ago that, in my "Theory of Probable Inference," †1 I admitted the obvious justice, as it seemed to me, of that objection. We cannot be quite sure that the community ever will settle down to an unalterable conclusion upon any given question. Even if they do so for the most part, we have no reason to think the unanimity will be quite complete, nor can we rationally presume any overwhelming consensus of opinion will be reached upon every question. All that we are entitled to assume is in the form of a hope that such conclusion may be substantially reached concerning the particular questions with which our inquiries are busied.

Such, at least, are the results to which the consideration of the doctrine of probability brings my mind irresistibly. So that the social theory of reality, far from being incompatible with tychism, inevitably leads up to that form of philosophy. Socialistic, or as I prefer to term it, agapastic ontology seems to me likely to find favour with many minds at an early day, because it is a natural path by which the nominalist may be led into the realistic ways of thought, ways toward which many facts and inward forces impel him. It is well, therefore, to call attention to the circumstances that the realism to which it leads is a doctrine which declares general truths to be real — independent of the opinions of any particular collection of minds — but not to be destined, in a strictly universal, exact, and sure acceptation, to be so settled, and established. Now to assert that general truths are objectively real, but to deny that they are strictly universal, exact, and certain, is to embrace the doctrine of absolute chance. Thus it is that the agapastic ontologist who endeavours to escape tychism will find himself "led into" that "inextricable confusion" which Dr. Carus (¶ 4) has taken a contract to show that I am led into.

611. Conservatism is wholesome and necessary; the most convinced radical must admit the wisdom of it, in the abstract; and a conservative will be in no haste to espouse the doctrine of absolute chance. I, myself, pondered over it for long years before doing so. But I am persuaded, at length, that mankind will before very long take up with it; and I do not believe philosophers will be found tagging on to the tail of the general procession.

My little dialogue between the tychist and the necessitarian (The Monist, vol. II, pp. 331-333 [53-57]) seems to have represented pretty fairly the views of the latter; for Dr. Carus, in ¶¶ 151-155, does little more than reiterate them, without much, if at all, reinforcing them. His ¶¶ 158-160 merely work out, in a form perhaps not quite clear, what is manifest from the elementary principles of dynamics, and was considered in my dialogue.

His arguments in this connection, apart from those already noticed, are that absolute chance is something which if it existed would require explanation, that the manifold specificalness of nature is explained by law without any aid from chance, and that absolute chance if it existed, in the sense in which it is supposed to exist in my chaos, could not possibly breed law as supposed by me. To the consideration of these arguments I proceed to apply myself.

612. One of the architectonic—and, therefore, I suppose, by Dr. Carus considered as highly reprehensible—features of my theory, is that, instead of saying off-hand what elements strike me as requiring explanation and what as not doing so, which seems to be his way, I have devoted a long time to the study of the whole logical doctrine of explanation, and of the history of explanations, and have based upon the general principles so ascertained my conclusions as to what things do and what do not require to be explained.

Dr. Carus (¶ 67) defines explanation as a description of a special process of nature in such a way that the process is recognized as a transformation. This I cannot quite grant. First, I cannot admit that "special processes of nature" are the only things to be explained. For instance, if I were to meet a gentleman who seemed to conform scrupulously to all the usages of good society, except that he wore to an evening party an emerald satin vest, that would be a fact calling for explanation, although it would not be a "special process of nature." Second, I cannot admit that an explanation is a description of the fact explained. It is true that in the setting forth of some explanations, it is convenient to restate the fact explained, so as to set it under another aspect; but, even in these cases, the statement of other facts is essential. In all cases, it is other facts, usually hypothetical, which constitute the explanation; and the process of explaining is a process by which from those other facts the fact to be explained is shown to follow as a consequence, by virtue of a general principle, or otherwise. Thus, a "special process of nature" calling for explanation is the circumstance that the planet Mars, while moving in a general way from west to east among the fixed stars, yet retrogrades a part of the time, so as to describe loops in the heavens. The explanation is that Mars revolves in one approximate circle and we in another. Again, it has been stated that a warm spring in Europe is usually followed by a cool autumn, and the explanation has been offered that so many more icebergs than usual are liberated during a warm spring, that they subsequently lower sensibly the temperature of Europe. I care little whether the fact and the explanation are correct or no. The case illustrates, at any rate, my point that an explanation is a special fact, supposed or known, from which the fact to be explained follows as a consequence. Third, I cannot admit that every description which recognizes the fact described as a transformation is an explanation; far less that "it is complete and exhaustive." (¶ 67.) A magician transforms a watch into a dove. Recognize it as a transformation and the trick is explained, is it? This is delightfully facile. Describe the change from a caterpillar to a butterfly as a transformation, and does that explain it? Fourth, I cannot admit that every explanation recognizes the fact explained as a transformation. The explanation of the loops in the motion of Mars is not of that nature. But I willingly recognize in Dr. Carus's definition an attempt — more or less successful — to formulate one of the great offices of scientific inquiry, that of bridging over the gap between the familiar and the unfamiliar.

Explanation, however, properly speaking, is the replacement of a complex predicate, or one which seems improbable or extraordinary, by a simple predicate from which the complex predicate follows on known principles. †1 In like manner, a reason, in one sense, is the replacement of a multiple subject of an observational proposition by a general subject, which by the very conditions of the special experience is predicable of the multiple subject. †P1 Such a reason may be called an explanation in a loose sense.

Accordingly, that which alone requires an explanation is a coincidence.

Hence, I say that a uniformity, or law, is par excellence, the thing that requires explanation. And Dr. Carus (¶ 51) admits that this "is perfectly true."

But I cannot imagine anything further from the truth than his statement (¶ 66) that "the only thing in the world of which we cannot and need not give account is the existence of facts itself." I should say, on the contrary, that the existence of facts is the only thing of which we need give account. Forms may indulge in whatever eccentricities they please in the world of dreams, without responsibility; but when they attempt that kind of thing in the world of real existence, they must expect to have their conduct inquired into. But should Dr. Carus reply that I mistake his meaning, that it is only "being in general" (¶ 66) that he holds unaccountable, I reply that this is simply expressing scepticism as to the possibility and need of philosophy. In a certain sense, my theory of reality, namely that reality is the dynamical reaction of certain forms upon the mind of the community, is a proposed explanation of being in general; and be it remarked that the mind of the community, itself, is the thing the nature of whose being this explanation first of all puts upon an idealistic footing.

Chance, according to me, or irregularity—that is, the absence of any coincidence—calls for no explanation. If law calls for a particular explanation, as Dr. Carus admits it does, surely the mere absence of law calls for no further explanation than is afforded by the mere absence of any particular circumstance necessitating the result. An explanation is the conception of a fact as a necessary result, thereby accounting for the coincidence it presents. It would be highly absurd to say that the absence of any definite character must be accounted for, as if it were a peculiar phenomenon, simply because the imperfection of language leads us so to talk of it. Quite unfounded, therefore, is Dr. Carus's opinion that "chance needs exactly as much explanation as anything else" (¶ 53) — an opinion which, so far as I can see, rests on no defensible principle.

Equally hasty is his oft-repeated objection (¶¶ 55, 58, 61) that my absolute chance is something ultimate and inexplicable. I go back to a chaos so irregular that in strictness the word existence is not applicable to its merely germinal state of being; and here I reach a region in which the objection to ultimate causes loses its force. But I do not stop there. Even this nothingness, though it antecedes the infinitely distant absolute beginning of time, is traced back to a nothingness more rudimentary still, in which there is no variety, but only an indefinite specificability, which is nothing but a tendency to the diversification of the nothing, while leaving it as nothing as it was before. †1 What objectionable ultimacy is here? The objection to an ultimate consists in its raising a barrier across the path of inquiry, in its specifying a phenomenon at which questions must stop, contrary to the postulate, or hope, of logic. But what question to which any meaning can be attached am I forbidding by my absolute chance? If what is demanded is a theological backing, or rational antecedent, to the chaos, that my theory fully supplies. The chaos is a state of intensest feeling, although, memory and habit being totally absent, it is sheer nothing still. Feeling has existence only so far as it is welded into feeling. Now the welding of this feeling to the great whole of feeling is accomplished only by the reflection of a later date. In itself, therefore, it is nothing; but in its relation to the end it is everything.

More unreasonable yet is Dr. Carus's pretension that the manifold specificalness, which is what I mean by chance, is capable of explanation (¶¶ 142, 143) by his own philosophic method. He may explain one particularity by another, of course; but to explain specificalness itself would be to show that a specific predicate is a necessary consequence of a generic one, or that a whole is without ambiguity a part of its part. Remark, reader, at this point, that chance, whether it be absolute or not, is not the mere creature of our ignorance. It is that diversity and variety of things and events which law does not prevent. Such is that real chance upon which the kinetical theory of gases, and the doctrines of political economy, depend. To say that it is not absolute is to say that it — this diversity, this specificalness — can be explained as a consequence of law. But this, as we have seen, is logically absurd.

Dr. Carus admits that absolute chance is "not unimaginable." (¶ 150.) Chance itself pours in at every avenue of sense: it is of all things the most obtrusive. That it is absolute is the most manifest of all intellectual perceptions. That it is a being, living and conscious, is what all the dullness that belongs to ratiocination's self can scarce muster hardihood to deny.

Almost as unthinking is the objection (¶ 61) that absolute chance could never beget order. I have noticed elsewhere the historic obliviscence of this objection. †1 Must I once again repeat that the tendency to take habits, being itself a habit, has eo ipso a tendency to grow; so that only a slightest germ is needed? A realist, such as I am, can find no difficulty in the production of that first infinitesimal germ of habit-taking by chance, provided he thinks chance could act at all. This seems, at first blush, to be explaining something as a chance-result. But exact analysis will show it is not so.

In like manner, when the eminent thinker who does me the honor to notice my speculation objects that I do not, after all, escape making law absolute, since the tendency to take habits which I propose to make universal is itself a law, I confess I can find only words without ideas in the objection. Law is a word found convenient, I grant, in describing that tendency; but is there no difference between a law the essence of which is to be inviolable (which is the nominalistic conception of mechanical law, whose being, they say, lies in its action) and that mental law the violation of which is so included in its essence that unless it were violated it would cease to exist? In my essay "The Law of Mind" I have so described that law. [See 148.] In so describing it, I make it a law, but not an absolute law; and thus I clearly escape the contradiction attributed to me. †1

613. In my attack on "The Doctrine of Necessity" I offered four positive arguments for believing in real chance. They were as follows:

1. The general prevalence of growth, which seems to be opposed to the conservation of energy.

2. The variety of the universe, which is chance, and is manifestly inexplicable.

3. Law, which requires to be explained, and like everything which is to be explained must be explained by something else, that is, by non-law or real chance.

4. Feeling, for which room cannot be found if the conservation of energy is maintained.

In a brief conversation I had with him, my friend remarked (and if it was an inconsiderate concession, I certainly do not wish to hold him to it) that, while the theory of tychism had some attractive features, its weakness consisted in the absence of any positive reasons in its favor. I infer from this that I did not properly state the above four arguments. I therefore desire once more to call attention to them, especially in their relations to one another.

Mathematicians are familiar with the theorem that if a system of particles is subject only to positional forces, it is such that if at any instant the velocities were all suddenly reversed, without being altered in quantity, the whole previous history of the system would be repeated in inverse succession. Hence, when physicists find themselves confronted with a phenomenon which takes place only in one order of succession and never in the reverse order — of which no better illustration could be found than the phenomena of growth, for nobody ever heard of an animal growing back into an egg — they always take refuge in the laws of probability as preventive of the velocities ever getting so reversed. To understand my argument number 1, it is necessary to make this method of escape from apparent violations of the law of energy quite familiar to oneself. For example, according to the law of energy, it seems to follow (and by the aid of the accepted theory of light it does follow) that if a prism, or a grating, disperses white light into a spectrum, then the colors of the spectrum falling upon the prism or grating at the same angles, and in the same proportions, will be recombined into white light; and everybody knows that this does in fact happen. Nevertheless, the usual and prevalent effect of prisms and gratings is to produce colored spectra. Why? Evidently, because, by the principles of probability, it will rarely happen that colored lights converging from different directions will fall at just the right angles and in just the right proportions to be recombined into white light. So, when physicists meet with the phenomena of frictional and viscous resistance to a body in motion, although, according to their doctrine, if the molecules were to move with the same velocities in opposite directions the moving body would be accelerated, yet they say that the laws of probability, applied to the trillions of molecules concerned, render this practically certain not to occur. I do no more, then, than follow the usual method of the physicists, in calling in chance to explain the apparent violation of the law of energy which is presented by the phenomena of growth: only instead of chance, as they understand it, I call in absolute chance. For many months I endeavoured to satisfy the data of the case with ordinary quasi chance; but it would not do. I believe that in a broad view of the universe a simulation of a given elementary mode of action can hardly be explained except by supposing the genuine mode of action somewhere has place. If it is improbable that colored lights should fall together in just such a way as to give a white ray, is it not an equally extraordinary thing that they should all be generated in such a way as to produce a white ray? If it is incredible that trillions of molecules in a fluid should strike a solid body moving through it so as to accelerate it, is it not marvellous that trillions of trillions of molecules all alike should ever have got so segregated as to create a state of things in which they should be practically certain to retard the body? It is far from easy to understand how mere positional forces could ever have brought about those vast congregations of similar atoms which we suppose to exist in every mass of gas, and by which we account for the apparent violations of the law of energy in the phenomena of the viscosity of the gas. There is no difficulty in seeing how sulphuric acid acting on marble may produce an aggregation of molecules of carbonic anhydride, because there are similar aggregations in the acid and in the marble; but how were such aggregations brought about in the first place? I will not go so far as to say that such a result is manifestly impossible with positional forces alone; but I do say that we cannot help suspecting that the simulated violation of the law of energy has a real violation of the same law as its ultimate explanation. Now, growth appears to violate the law of energy. To explain it, we must, at least, suppose a simulated, or quasi, chance, such as Darwin calls in to produce his fortuitous variations from strict heredity. It may be there is no real violation of the law, and no real chance; but even if there be nothing of the sort in the immediate phenomenon can the conditions upon which the phenomenon depends have been brought about except by real chance? It is conceivable, again, that the law of the conservation of forces is not strictly accurate, and that, nevertheless, there is no absolute chance. But I think so much has been done to put the law of the conservation of forces upon the level of the other mechanical laws that when one is led to entertain a serious doubt of the exactitude of that, one will be inclined to question the others.

Besides, few psychologists will deny the very intimate connection which seems to subsist between the law, or quasi-law, of growth and the law of habit, which is the principal, if not (as I hold it to be) the sole, law of mental action. Now, this law of habit seems to be quite radically different in its general form from mechanical law, inasmuch as it would at once cease to operate if it were rigidily obeyed: since in that case all habits would at once become so fixed as to give room for no further formation of habits. In this point of view, then, growth seems to indicate a positive violation of law.

Let us now consider argument number 3: and remark how it fortifies number 1. Physical laws that appear to be radically different yet present some striking analogies. Electrical force appears to be polar. Its polarity is explained away by Franklin's one-fluid theory, but in that view the force is a repulsion. Now, gravitation is an attraction, and is, therefore, essentially different from electricity. Yet both vary inversely as the square of their distance. Radiation likewise follows the same formula. In this last case, the formula, in one aspect of it, follows from the conservation of energy. In another aspect of it, it results from the principle of probability, and does not hold good, in a certain sense, when the light is concentrated by a lens free from spherical aberration. But neither the conservation of energy nor the principle of probability seems to afford any possible explanation of the application of this theory to gravitation nor to electricity. How, then, are such analogies to be explained? The law of the conservation of energy and that of the perduration of matter present so striking an analogy that it has blinded some powerful intellects to their radically different nature. The law of action and reaction, again, has often been stated as the law of the conservation of momentum. Yet it is not only an independent law, but is even of a contrary nature, inasmuch as it is only the algebraical sum of opposite momenta that is "conserved." †P1 How is this striking analogy between three fundamental laws to be explained? Consider the still more obvious analogy between space and time. Newton †1 argues that the laws of mechanics prove space and time to be absolute entities. Leibnitz, †2 on the other hand, takes them as laws of nature. Either view calls for an explanation of the analogy between them, which no such reflection as the impossibility of motion without that analogy can supply. Kant's †3 theory seems to hint at the possibility of an explanation from both being derived from the nature of the same mind. Any three orthogonal directions †P1 in space are exactly alike, yet are dynamically independent.

These things call for explanation; yet no explanation of them can be given, if the laws are fundamentally original and absolute.

Moreover, law itself calls for explanation. But how is it to be explained if it is as fundamentally original and absolute as it is commonly supposed to be? Yet if it is not so absolute, there is such a phenomenon as absolute chance.

Thus, the chance which growth calls for is now seen to be absolute, not quasi chance.

Now consider argument number 2. The variety of the universe so far as it consists of unlikenesses between things calls for no explanation. But so far as it is a general character it ought to be explained. The manifold diversity or specificalness, in general, which we see whenever and wherever we open our eyes, constitutes its liveliness, or vivacity. The perception of it is a direct, though darkling, perception of God. †1 Further explanation in that direction is uncalled for. But the question is whether this manifold specificalness was put into the universe at the outset, whether God created the universe in the infinitely distant past and has left it to its own machinery ever since, or whether there is an incessant influx of specificalness. Some of us are evolutionists; that is, we are so impressed with the pervasiveness of growth, whose course seems only here and there to be interrupted, that it seems to us that the universe as a whole, so far as anything can possibly be conceived or logically opined of the whole, should be conceived as growing. But others say, though parts of the universe simulate growth at intervals, yet there really is no growth on the whole — no passage from a simpler to a more complex state of things, no increasing diversity.

Now, my argument is that, according to the principles of logic, we never have a right to conclude that anything is absolutely inexplicable or unaccountable. For such a conclusion goes beyond what can be directly observed, and we have no right to conclude what goes beyond what we observe, except so far as it explains or accounts for what we observe. But it is no explanation or account of a fact to pronounce it inexplicable or unaccountable, or to pronounce any other fact so. Now, to say no process of diversification takes place in nature leaves the infinite diversity of nature unaccounted for; while to say the diversity is the result of a general tendency to diversification is a perfectly logical probable inference. Suppose there be a general tendency to diversification; what would be the consequence? Evidently, a high degree of diversity. But this is just what we find in nature. It does not answer the purpose to say there is diversity because God made it so, for we cannot tell what God would do, nor penetrate his counsels. We see what He does do, and nothing more. For the same reason one cannot logically infer the existence of God; one can only know Him by direct perception.

It is to be noted that a general tendency to diversification does not explain diversity in its specific characters; nor is this called for. Neither can such a tendency explain any specific fact. Any attempt to make use of the principle in that manner would be utterly illogical. But it can be used to explain universal facts, just as quasi chance is used to explain statistical facts. Now, the diversity of nature is a universal fact.

To explain diversity is to go behind the chaos, to the original undiversified nothing. Diversificacity was the first germ.

Argument number 4 was, upon its negative side, sufficiently well presented in my "Doctrine of Necessity Examined." Mechanical causation, if absolute, leaves nothing for consciousness to do in the world of matter; and if the world of mind is merely a transcript of that of matter, there is nothing for consciousness to do even in the mental realm. The account of matters would be better if it could be left out of account. But the positive part of the argument, showing what can be done to reinstate consciousness as a factor of the universe when once tychism is admitted is reinforced in the later papers. This ought to commend itself to Dr. Carus, who shows himself fully alive to the importance of that part of the task of science which consists in bridging gaps. But consciousness, for the reason just stated, is not to be so reinstated without tychism; nor can the work be accomplished by assigning to the mind an occult power, as in two theories to be considered in the section following this. As might be anticipated (and a presumption of this kind is rarely falsified in metaphysics), to bridge the gap synechism is required. Supposing matter to be but mind under the slavery of inveterate habit, the law of mind still applies to it. According to that law, consciousness subsides as habit becomes established, and is excited again at the breaking up of habit. But the highest quality of mind involves a great readiness to take habits, and a great readiness to lose them; and this implies a degree of feeling neither very intense nor very feeble.

I have noticed above (594) Dr. Carus's dubious attitude toward the first argument. I considered in the last section his attempted reply to the second. To the third argument, he replies (¶ 165) that law ought to be accounted for by the principle of sufficient reason. But, of course, that principle cannot recommend itself to me, a realist; for it is nothing but the lame attempt of a nominalist to wriggle out of his difficulties. Reasons explain nothing, except upon some theistic hypothesis which may be pardoned to the yearning heart of man, but which must appear doubtful in the eyes of philosophy, since it comes to this, that Tom, Dick, and Harry are competent to pry into the counsels of the Most High, and can invite in their cousins and sweethearts and sweethearts' cousins to look over the original designs of the Ancient of Days.

614. My fourth argument it is which seems to have made most impression upon Dr. Carus's mind (¶ 85), and his reply is rather elaborate.

While embracing unequivocally the necessitarian dogma, equally for mind and for matter (¶ 193), Dr. Carus wishes utterly to repudiate materialism and the mechanical philosophy (¶ 133). To facilitate his thus walking the slack-rope, he makes (¶ 168) a division of events into "(1) mechanical, (2) physical, (3) chemical, (4) physiological, and (5) psychical events." The first three (¶¶ 169-171) are merely distinguished by the magnitude of the moving masses, so that, for philosophical purposes, they do not differ at all. As for physiological events, though he devotes a paragraph (¶ 172) to their definition, he utterly fails to distinguish them from the mechanical (including the physical and chemical) on the one hand, or from the psychical on the other. Dr. Carus seems to think (¶ 176) that by this division he has separated himself entirely from the materialists; but this is an illusion, for nobody denies the existence of feelings.

The truth is, he distinctly enrolls himself in the mechanical army when he asserts that mental laws are of the same necessitarian character as mechanical laws (¶ 193). The only question that remains as to his position is whether he is a materialist or not. He instances (¶ 185) the case of a general receiving a written dispatch and being stimulated into great activity by its perusal, and causing great motions to be made and missiles to be sped in consequence. Now, the dilemma is this. Will Dr. Carus, on the one hand, say that the motion of those missiles was determined by mechanical laws alone, in which case, it would only be necessary to state all the positions and velocities of particles concerned, a hundred years before, to determine just how those bullets would move and, consequently, whether the guns were to be fired or not, and this would constitute him a materialist, or will he say that the laws of motion do not suffice to determine motions of matter, in which case, since they formally certainly do so suffice, they must be violated, and he will be giving to mind a direct dynamical power which is open to every objection that can be urged against tychism?

Now admire the decision with which he cuts the Gordian knot!

"THERE ARE NO PURELY MECHANICAL PHENOMENA." (¶ 175.)

That is,

"The laws of motion ARE applicable to and will explain all motions." (¶ 177.)

But hold!

"The mechanical philosopher . . . feels warranted in the hope that . . . the actions of man . . . can be explained by the laws of motion. . . . We may anticipate that this conclusion will prove ERRONEOUS. And so it is." (¶ 176.)

At the same time,

"No OBJECTION CAN BE MADE to the possibility of explaining the delicate motions in the nervous substance of the brain by the laws of molar or molecular mechanics." (¶ 178.)

Yet, "The simplest psychical reflexes, including those physiological reflexes which we must suppose to have originated by conscious adaptation, . . . CANNOT be explained from mechanical or physical laws alone." (¶ 186.) However,

"We do NOT say that there are motions . . . in the brain . . . which form exceptions to the laws of mechanics." (¶ 187.)

Nevertheless, "The brain-atoms are possessed of the same spontaneity as the atoms of a gravitating stone. Yet there is present an additional feature; there are present states of awareness. . . . Neither states of awareness nor their meanings can be weighed on any scales, be they ever so delicate, nor are they determinable in footpounds." (¶ 192.)

Clearness is the first merit of a philosopher; and what ¶ 192 comes to is crystal-clear. Dr. Carus wants to have the three laws of motion always obeyed; but he wishes the forces between the molecules to be varied according to the momentary states of awareness. All right: he is entitled to suppose whatever he likes, so long as the supposition is self-consistent, as this supposition is. It conflicts with the law of energy, it is true; for that law is that the forces depend on the situations of the particles alone, and not on the time. It is liable to give rise to perpetual motion. It was intended, no doubt, to be an improvement on my molecular theory of protoplasm, †1 earlier in the same number. It escapes materialism. It supposes a direct dynamical action between mind and matter, such as has not been supposed by any eminent philosopher that I know of for centuries. I am sorry to say that it shows a dangerous leaning toward originality. The argument for thus rejecting the law of the conservation of energy I leave to others to be weighed. It seems to suppose a much larger falsification of that law than my doctrine; but it is a pretty clever attempt to escape my conclusions. It rejects what has to be rejected, the law of the conservation of energy; and is far more intelligent than the theory of those (like Oliver and Lodge) †2 who wish to give to mind a power of deflecting atoms, which would satisfy the conservation of energy while violating the law of action and reaction. If it can have due consideration, I doubt not it will accelerate the acceptance of my views. Meantime, I do not see where that "inextricable confusion" into which I was to be led is to come in. (¶ 4.)

615. Little more requires to be noticed in Dr. Carus's articles. He admits (¶ 2) that indeterminism is the more natural belief, which is no slight argument in its favor.

616. The remarks upon the theological bearings of the theories, if they are found somewhat wide of the mark, are explained by the haste of the editor to show just what all the affiliations of my views were, before I had had time to explain what those views are. The remarks to which I refer will be found in ¶¶ 3, 36, 81, 82, 83, 128, 203, 204. They are worth putting together.

617. The doctrine of symbolism, to which Dr. Carus has recourse, seems to be similar to that of my essay "Some Consequences of Four Incapacities" (Journal of Speculative Philosophy, vol. II). †1 (¶¶ 180, 183, 199.) On this head, I can only approve of his ideas.

618. It is true that I wrote many definitions for one of the "encyclopedic lexicons." But they were necessarily rather vaguely expressed, in order to include the popular use of terms, and in some cases were modified by proofreaders or editors; and, for reasons not needful here to explain, they are hardly such as I should give in a Philosophical Dictionary proper.

Appendix B: Nominalism versus Realism †1

[We print below some strictures upon the position assumed in our last number with reference to M. Janet's version of Hegel's doctrine of the "Becoming." We hope that these acute statements which have been written, for the most part, in the form of queries, will receive a careful reading, especially by those who have differed from our own views hitherto expressed. They seem to us the most profound and compendious statement of the anti-speculative standpoint as related to the Science of Pure Thought (Prima Philosophia), that we have seen. But for this very reason we are fain to believe that the defects of the formalism relied upon are all the more visible. We have endeavoured to answer these queries with the same spirit of candour that animates their author. — Editor.]

Mr. Editor of the Journal of Speculative Philosophy:

619. I should like to make some inquiries in regard to your meaning in the paragraph beginning "Being is the pure Simple," vol. I, p. 255.

I will begin by stating how much of it I already understand, as I believe. I understand that "Being" and "Nothing," as used by you, are two abstract, and not two general terms. That Being is the abstraction belonging in common and exclusively to the objects of the concrete term, whose extension is unlimited or all-embracing, and whose comprehension is null. I understand that you use Nothing, also, as an abstract term = nothingness; for otherwise to say that Being is Nothing is like saying that humanity is non-man, and does not imply at all that Being is in any opposition with itself, since it would only say "Das Sein ist nicht Seiendes," not "Sein ist nicht Sein." By Nothing, then, I understand the abstract term corresponding to a (possible) concrete term, which is the logical contradictory of the concrete term corresponding to "Being." And since the logical contradictory of any term has no extension in common with that term, the concrete nothing is the term which has no extension. I understand, that, when you say "Being has no content," and "Being is wholly undetermined," you mean, simply, that its corresponding concrete has no logical comprehension, or, at least, that what you mean follows from this, and this, conversely, from what you mean.

I come now to what I do not understand, and I have some questions to ask, which I have endeavoured so to state that all can see that the Hegelian is bound to answer them, for they simply ask what you mean, whether this or that; they simply ask you to be explicit upon points upon which you have used ambiguous expressions. They are not put forward as arguments, however, but only as inquiries.

620. Abstract terms, according to the doctrine of modern times, are only a device for expressing in another way the meaning of concrete terms. To say that whiteness inheres in an object is the same as to say that an object is white. To say that whiteness is a color is the same as to say that the white is colored, and that this is implied in the very meanings of the words.

But, you will undoubtedly admit that there is a difference between a hundred dollars in my pocket Being or not Being, and so in any other particular case. You, therefore, admit that there is nothing which is, which is also not. Therefore, it follows that what is, and what is not, are mutually exclusive and not coëxtensive.

Since, then, you nevertheless say that the corresponding abstractions, Being and Nothingness, are absolutely the same (although you at the same time hold that it is not so, at all), it is plain that you find some other meaning in abstract terms than that which other logicians find. I would, therefore, ask what you mean by an abstraction, and how you propose to find out what is true of abstractions. †1

621. You say, in effect,

Being has no determination;

Ergo, It is nothing.

Now, it certainly appears that the contrary conclusion follows from this premiss, namely: that it is not nothingness. I suppose that you have suppressed one of your premisses, and that you mean to argue thus:

Indetermination in respect to any character is the negation of that character;

Being is indeterminate in respect to every character;

Ergo, Being is negative of every character.

In short, you seem to imply that to abstract from a character is to deny it. Is this the manner in which your argument is to be completed, or how else?

622. This suggests another question. You say that nothing has no determination. It is plain that it would not follow from this that Being is nothing, but only that Nothing is being, or rather that Any non-being is a being, thus reducing non-being (nicht-seiende) to an absurdity. This would be nothing new (for Albertus Magnus quotes Avicenna to this effect) and in my opinion would be perfectly true. Non-ens, or "the not being," is a self-contradictory expression. Still, though I thus see no monstrous consequences of saying that nothing has no determination, I see no proof at all that it is so. It might be said, indeed, that the things which are not have no characters in common, and that therefore what is not has no logical comprehension and Being — not no determination. I would ask, then, have you proved that nothing has no determination? Do not suppose that I am endeavouring to drive you into contradiction; for I understand Hegelians profess to be self-contradictory. I only wish to ascertain whether they have an equal disregard for those logical maxims which relate to ambiguities.

623. You say, in effect,

Difference is determination,

Being has no determination;

Ergo, Being has no difference from nothing;

Ergo, Being is nothing.

It is incontestable that difference from anything is determination in respect to being or not being that thing. A monkey, in differing from a man, is determined (negatively) in respect to humanity. Difference, then, in any respect, is determination in that respect. This, I take it, is what you mean. Now let us parallel the above argument:

Difference in any respect is determination in that respect;

Animality, in general, is not determined in respect to humanity;

Ergo, Animality, in general, has no difference from humanity;

Ergo, Animality, in general, is humanity.

This is plainly sophistical. For to say that an abstraction, in general, is undetermined, has two different senses; one resulting from a strict analysis of the language, and the other reposing upon the ordinary use of language. Strictly, to say that an abstraction is undetermined would mean that it may be this or may be that abstraction; that is, that the abstract word by which it is expressed may have any one of a variety of meanings. What is ordinarily meant by the phrase, however, is that the object of the corresponding concrete term is undetermined, so that neither of a certain pair of mutually contradictory predicates are universally true of that concrete. Now, it is true to say that animality is undetermined in respect to humanity, or that being is not determined at all, only in the latter of these senses, to wit: that not every animal is a man, and not every animal is not a man, and (in the other case) that there is no predicate which can be truly affirmed or denied of all beings. For in the other sense we should imply that the abstractions themselves were vague, and that being, for example, has no precise meaning. In the only true sense, therefore, the premiss is, in the one case, that "Animal, simply, is undetermined," and, in the other, that "Ens (seiende) is undetermined"; and what follows is, in the one case, that "not every animal differs from a man," and, in the other, that "not every being differs from any nothing." This latter amounts merely to saying that there is nothing from which every being differs, or that a nothing is an absurdity. These correct conclusions do not in the least imply that animality is humanity, or that being is nothingness. To reach the latter conclusions, it would be necessary (in the first place) to use the premisses in the other and false sense; but even then all that would be legitimately inferable would be that "humanity, in some sense, is animality," and that "being, in some sense, is nothing." Only by a second fallacy could it be concluded that animality, in the sense intended, is humanity, or that being, in the sense intended, is humanity, or that being, in the sense intended, is nothing. Now, I would inquire whether you inadvertently fell into these ambiguities, or, if not, wherein the force of your argumentation lies?

624. Finally, I would inquire whether, in your opinion, the maxims of (ordinary) logic relating to contradictions lack even a prima facie presumption in their favor? Whether the burden of proof is or is not upon the Hegelians to show that the assumption of their falsity is a more tenable position than the assumption of their truth? For in the present state of the question, it seems to me more probable that subtle fallacies lurk in the Hegelian reasoning than that such fallacies lurk in all other reasoning whatsoever.

Appendix C: What is Meant by "Determined"? †1

To the Editor of the Journal of Speculative Philosophy:

625. Your remarks upon my inquiries concerning Being and Nothing are very kind and courteous. Considered as replies, they are less satisfactory than they might have been had I succeeded better in making my difficulties understood.

I suspect that there must be some misunderstanding between us of the meaning of the various terms cognate with "determined." Perhaps, therefore, I shall do well to state more fully than I did before, the manner in which I understand Hegel (in common with all other logicians) to use them. Possibly, the original signification of bestimmt was "settled by vote"; or it may have been "pitched to a key." Thus its origin was quite different from that of "determined"; yet I believe that as philosophical terms their equivalence is exact. In general, they mean "fixed to be this (or thus), in contradistinction to being this, that, or the other (or in some way or other)." When it is a concept or term, such as is expressed by a concrete noun or adjective which is said to be more determinate than another, the sense sometimes is that the logical extension of the former concept or term is a part and only a part of that of the latter; but more usually the sense is that the logical comprehension of the latter is a part and only a part of that of the former.

626. In my former letter (623) I sufficiently expressed my own understanding of "determined" as applied to a concept or term such as is expressed by an abstract noun. Determinate is also used either in express application or with implicit reference to a second intention or term of second denomination. In such an acceptation, we may speak either of a singular as indeterminate, or of a conception of Being, in general, as determinate. Every singular is in one sense perfectly determinate, since there is no pair of contradictory characters of which it does not possess one. Yet if the extension of the term be limited, not by additions to its comprehension, but by a reflection upon the term itself — namely, that it shall denote but one — it is called an indeterminate singular. In this sense, "some one horse" is an indeterminate individual, while "Dexter" is a determinate individual. In a somewhat similar way, every universal conception of Being is quite indeterminate in the sense of not signifying any particular character. Yet, if the reflection is explicitly made (gesetzt) that every thing to which it applies has its particular characters, it is called by Hegel determinate being. Hegel teaches that the whole series of categories or universal conceptions can be evolved from one — that is, from Seyn — by a certain process, the effect of which is to make actually thought that which was virtually latent in the thought. So that this reflection which constitutes Daseyn lies implicitly even in Seyn, and it is by explicitly evolving it from Seyn that Daseyn is evolved from Seyn. (Hegel's Werke, Bd. 3, S. 107.) The term "What is" has reference to pure Seyn only; the term "What is somehow" has reference to Daseyn. This is my understanding of the term "determinate." It must differ from yours, or you would not say that animality, in general, is determined in respect to humanity: so when you say that were animality and humanity, in general, undetermined with respect to each other they would be identical, I take the example of "highness of pitch in general" and "loudness of sound in general," and I conclude again that we are taking the word "determine" in different senses. May I ask you to reperuse my fourth question? (623.)

627. You have apparently understood me as applying the term "abstract" to any concept the result of abstraction. But, as I intimated (620), I adopt that acceptation in which "whiteness" is said to be abstract and "white" concrete. For this use of the terms, I refer to the following authorities: Andrews and Stoddard's Latin Grammar, §26, 5; Scotus, Super Prædicamenta, qu. 8; Durandus à Sancto Porciano, In Sentent., lib. 1, dist. 34, qu. 1; Ockham, Summa Logices, pars 1, cap. 5; Chauvin, Lexicon Rationale, sub. V. Abstractum; Mill, Logic, bk. 1, cap. 2, §4; Trendelenburg, Elementa Logices Arist., 6th ed., p. 117, note; Uberweg, Logik, §51 (where Wolff, also, is cited); Hoppe, Logik, §§256, 257. This misapprehension affects the relevancy of most of your remarks.

628. I think that I have not, as you suppose, greatly mistaken the sense in which Hegelians use the term Pure Being.

At least, my definition seems to be in accord with the explanations of almost all, if not all, the commentators and expositors of Hegel. I would submit respectfully, that your own remarks upon p. 117 of vol. 1, of this Journal contradict, almost in terms, what you say (vol. II, p. 57) in reply to me.

629. Once or twice you use such expressions as "We do not profess to speak for Hegelians," "Hegelians may understand this as they please," etc. Have I been wrong, then, in supposing that the passage to which my queries related was a professed defense of Hegelian doctrine?

630. I am sorry to learn that I have done you injustice in saying that you profess to be self-contradictory. Yet I do not see in what sense you object to the remark. To say that a man is self-contradictory is, of course, but a way of saying that what he believes is self-contradictory. You believe that "finite things contradict themselves"; that is, as I understand it, that contradictions exist. Therefore, what you believe in appears to be self-contradictory. Nor can I see how a person "escapes self-contradiction by not attempting to set up non-contradiction as the first principle of things"; that is, by not professing to be otherwise than self-contradictory.

I do not see that you notice query 3.

Endnotes

1

†1 From "The Logic of Events", 1898, the last of a proposed set of eight lectures. See 212n. Cf. also ch. 7, which appears to be an alternative draft.

1

†2 See 1.244ff.

2

†1 Cf. 216ff., 1.619ff.

4

†1 The Creeds of Christendom, by Philip Schaff, 2d edition, 1878.

4

†2 See 5.589.

5

†1 See 1.186.

5

†2 See vol. 2, bk. III, b for a detailed discussion of the nature of induction and hypothesis (or abduction).

5

†3 For the rest of this manuscript, see 214ff.

5

†4 From an unidentified fragment, c. 1903.

5

†5 See 1.241n, 1.242n for definitions of these terms.

5

†5 See 1.241n, 1.242n for definitions of these terms.

6

†1 See 185f, 364ff, 3.527, 4.65ff, 4.172, 4.514, 5.447f, 5.453ff.

6

†2 See 185ff, 4.61, 5.447f.

6

†3 See 1.433f, 3.93, 3.216, 4.172, 5.299ff, 5.429, 5.448n.

6

†4 See 1.321, 3.527f, 5.45, 5.474, 5.487, 5.493, 5.539.

6

†5 See 132f, 1.305f, 1.412f, 1.549.

6

†6 See 132f, 197, 211, 1.311.

6

†7 See 1.422.

6

†8 See 87, 96, 127f, 506, 1.489ff.

6

†9 See 82f, 1.501ff, 3.134n.

6

†10 See 1.492f, 1.495f.

6

†11 See 82, 86, 127ff, 133ff, 1.170, 1.499, 5.530.

6

†12 See 211, 4.222ff.

6

†13 See 28, 82, 210, 419f, 1.274ff, 4.223.

6

†14 See 24f, 264ff.

7

†1 See 268f.

7

†2 See 350f, 5.142, 5.549ff.

7

†3 See 27, 91, 189f, 311ff, 582.

11

†1 The Monist, vol. 1, pp. 161-176 (1891); the first of a series of five articles. The second appears as ch. 2, the third as ch. 5, the fourth as ch. 9, and the fifth as ch. 11 of this book.

13

†1 Cf. 1.118, 5.47, 5.586, 5.591, 5.603.

14

†1 Cf. 575.

15

†1 Cf. 296ff, 1.103f, 1.173f.

15

†2 See 553f, for Peirce's earliest statement of this view.

15

†3 See his First Principles, part 2, ch. 18.

16

†1 See Lamarck, Philosophie Zoologique, vol. 1, ch. VII, Paris (1873).

16

†P1 The neo-Darwinian, Weismann, has shown that mortality would almost necessarily result from the action of the Darwinian principle. [See his Essays upon Heredity, I, "The Duration of Life" (1889).]

17

†1 See his Catastrophism and the Evolution of Environment, 1877.

17

†2 These categories are discussed in detail in vol. 1, bk. III.

18

†P1 A feeling may certainly be compound, but only in virtue of a perception which is not that feeling nor any feeling at all.

19

†1 Cf. 246ff, 280, 1.385ff.

20

†1 Cf. 264ff, 4.551.

21

†1 Cf. 82f.

22

†1 Cf. 1.275f, 4.142ff.

22

†2 See 4.145ff.

23

†1 See 189f, 582, 1.362.

23

†2 Cf. 4.143.

24

†1 But see 82f.

24

†2 242?

24

†3 According to the Yale Observatory, the above figures "are affected by errors nearly one hundred times as great as good modern determinations."

24

†4 Cf. 1.130ff, 1.401f.

25

†1 Cf. vol. I, bk. 3.

26

†1 Cf. 214ff.

26

†2 Cf. 1.374ff.

26

†3 Cf. 1.395ff.

26

†4 Cf. 1.409.

27

†1 See chs. 7 and 8.

28

†1 The Monist, vol. 2, pp. 321-337 (1892); the second paper of a series of five. See note to ch. 1.

28

†2 Ch. 1.

28

†3 See H. Diels, Die Fragmente der Vorsokratiker, c. 55, A66.

28

†4 See Aetius, Placita, I, 12, 15.

29

†1 See Aristotle, De Interpretatione, 18b, 31: 19a, 7. Ethica Nicomachea, 1112a, 7-10.

29

†2 Epicurus, Epistle, III, 133-134.

29

†3 See Cleanthes, in Epictetus, Manual, ch. 53; Seneca, De Providentia, V, 8.

30

†1 Peirce gives a list of various uses of the term "necessity" in the Century Dictionary (1889) and in Baldwin's Dictionary of Philosophy and Psychology, vol. 2 (1901).

31

†1 The published paper has "compromised".

31

†2 See 2.508-513.

33

†1 Cf. 2.761ff.

34

†1 Cf. 2.683f.

34

†2 See 2.725ff.

35

†P1 Continuous is not exactly the right word, but I let it go to avoid a long and irrelevant discussion.

37

†1 See his Examination of Sir William Hamilton's Philosophy, ch. 16.

38

†1 Cf. 5.445; 5.508f.

38

†2 See page 3042, edition of 1889, for Peirce's definitions.

38

†3 Cf. 322.

39

†1 See 242n for a definition of this term.

43

†1 Cf. ch. 10; 4.611.

43

†2 The editors have been unable to discover any manuscript whose contents clearly answer to the foregoing description.

43

†3 See 606.

44

†1 See chs. 7 and 8.

45

†1 See Appendix A for Peirce's published reply to Dr. Paul Carus's criticisms of this paper.

46

†1 Lecture No. 4 on "Detached Ideas on Vitally Important Topics," 1898. See vol. 1, bk. IV, ch. 5; vol. 4, Preface; vol. 5, bk. III, ch. 6, §1 for the first three lectures.

46

†2 Metaphysica, 983b, 6-8.

46

†3 Ibid., 983a, 24-34.

46

†4 "Retroductive" is an alternative expression for "abductive," for which see vol. 2, passim.

47

†1 See his System of Logic, bk. III, ch. 5, §3.

47

†2 Cf. 1.427ff.

49

†1 (t2-2t1+t0) should be (t2-t0).

54

†1 See 4.188ff.

54

†2 Cf. 3.21, 3.33.

55

†1 See his Pure Logic, and Other Minor Works, London (1890), p. 189.

55

†2 Peirce has here a marginal note — "Repeat with 'follows next after' [substituted] for F."

56

†1 See 3.546ff.

57

†1 Traité du calcul des probabilités, Paris, 1873.

59

†1 Cf. 53f.

60

†1 Four manuscript pages are missing here.

60

†2 Cf. 1.501f.

61

†1 See P. R. J. Boscovich, Theoria philosophiae naturalis, §7, 81, Vienna (1758).

61

†2 See 86f.

63

†1 Cf. 4.145.

66

†1 See 1.652ff.

66

†2 Cf. 1.489ff.

67

†1 From the sixth Lowell Lecture of 1903.

67

†2 Cf. 101.

70

†1 De Trinitate, bk. III, ch. 10.

70

†2 Boëthius, De Consolatione Philosophiae, Liber v, 1, cites Aristotle's Physica, II, 5, 196b.

70

†3 Consolations of Boëthius, translated by H. R. James, pp. 229-230, London (1897).

71

†1 Cf. 67.

71

†2 See 1.549n and 2.428 for a definition of this term.

71

†3 See his Die Philosophie der Griechen, 2te Auf., pp. 252-55.

71

†4 Elements of Philosophy, Pt. II, ch. 10.

71

†5 See the 2me Appendice to his Théodicée, §5.

73

†1 Cf. 108.

73

†2 Cf. 5.340.

74

†1 De Interpretatione, 18a, 28-19b, 4.

74

†2 See Historische Beiträge zur Philosophie, 2te Bd., S. 168, Berlin (1855).

75

†1 Baldwin's Dictionary, vol. 2, pp. 727-731, The Macmillan Co., New York (1902).

76

†1 See Theodor Gomperz, Herculanische Studien, Pt. I (1865). Cf. 2.741, 2.761.

76

†2 System of Logic, bk. III, ch. 4, §2.

76

†3 Cf. 2.761f.

77

†1 Op. cit., bk. III, ch. 3, §3.

77

†2 Ibid., bk. III, ch. 4, §2.

77

†3 Ibid., bk. III, ch. 4, §1.

78

†1 Op. cit., bk. III, ch. 3, §1.

83

†1 See De rerum natura, bk. II, 11. 284-293.

86

†1 The Monist, vol. II, pp. 533-559 (1892); the third paper of a series.

86

†2 See ch. 1.

86

†3 See ch. 2.

87

†1 See 31.

87

†2 See 5.263, 5.311ff.

88

†1 See 1.383, 5.7, 5.288f, 5.307.

88

†2 Cf. 182.

89

†1 Cf. 95.

91

†1 See 4.118, 4.125.

91

†2 See 3.565ff.

91

†3 Gesammelte Abhandlungen, S. 139-140.

91

†4 See 3.286f.

91

†5 See his Formal Logic (1847), pp. 165ff.

92

†1 Cf. 4.113ff.

93

†1 See 3.258f.

93

†2 See Fermat, Opera Omnia (Leipzig, 1911), vol. 1, §§340-351.

94

†P1 This proposition is substantially the same as a theorem of Cantor [Gesammelte Abhandlungen, S. 115ff], though it is enunciated in a much more general form.

94

†1 Gesammelte Abhandlungen, S. 278.

95

†1 See 4.639.

95

†2 Op. cit., S. 289 (13) and (14).

96

†1 See 174ff., 4.121, 4.642.

96

†2 Kritik der Reinen Vernunft, A 169, B 211; cf. 168.

96

†3 Gesammelte Abhandlungen, S. 194.

97

†1 See his Physica, 227a, 10; Metaphysica, 1069a, 5f.

98

†1 Cf. 4.121f.

98

†2 See 3.568, 4.674.

99

†1 See 3.563f, 4.113ff, 4.118n.

99

†2 See his Leçons sur les applications du calcul infinitésimal a la géométrie, Paris (1826).

99

†3 See his Eléments de calcul infinitésimal, Paris (1856).

99

†4 See 4.125ff for a discussion of this concept.

100

†1 See 135ff.

101

†1 Cf. 197.

101

†2 See 1.170, 4.172.

101

†3 Cf. 197, 1.312.

101

†4 Cf. 264.

102

†1 See his Principles of Psychology, vol. 2, ch. 20 (1890).

106

†1 Cf. 2.643, 2.711f, 3.154ff, 5.223.

106

†2 See 2.514f, 2.632.

108

†1 See 275, 1.390.

111

†1 See 553, 613f, 5.536.

112

†1 See 559.

114

†1 164 is from the Century Dictionary (1889). 165-167 is a marginal note dated September 18, 1903, in Peirce's personal copy of the Dictionary, now in the Treasure Room at the Widener Library, Cambridge, Mass.

114

†2 See 120f and 166.

114

†3 See 121.

115

†1 See 120-124.

115

†2 Kritik der Reinen Vernunft, A 169; B 211.

115

†3 See 1.434, 3.612, 5.448, 5.505.

116

†1 See 4.213ff, 4.639, 4.654.

117

†1 Baldwin's Dictionary of Philosophy and Psychology, vol. 2, p. 657, The Macmillan Co., New York (1902).

117

†2 See 103.

117

†3 See 5.3.

118

†1 From "The Bedrock beneath Pragmaticism," 1906; continuing 4.561n.

118

†2 See 120f.

120

†1 Paradoxien des Unendlichen, §22, Leipzig (1851). Cf. 651.

120

†2 See 3.537.

122

†1 From "A Sketch of Logical Critic," c. 1911.

128

†1 In the Pragmatism Lectures of 1903? See 5.181, 5.202.

128

†2 See 4.229ff.

128

†3 See 168.

129

†1 A 169, B 211.

129

†2 See ch. 5.

130

†1 Cf. 1.36ff.

132

†1 The last of a proposed set of eight lectures, 1898. See 212n. Cf. also Preface and ch. 8.

133

†1 A symmetrical dyadic relation, for Peirce, does not enable one to distinguish the individuals related.

141

†1 See 1.274ff.

141

†2 Usually called chorisis by Peirce. See 4.222.

141

†3 Called periphraxis in Listing's Census Raümlicher Complexe (Göttingen, 1862), where it is described as "Eigenschaft einer Fläche oder eines Raumes, wenn sie allseitig zusammenhängen u. einen Complex oder Complextheil rings umhüllen" (p. 182). See also Peirce's definition of Periphractic in the Century Dictionary (1889). Peirce's terminology, which is largely that of Listing, has not been preserved in the development of topology. See Veblen, Analysis Situs, New York (1931); or Seifert and Threlfalls, Lehrbuch der Topologie, Teubner (1934).

142

†1 Called cyclosis by Listing (op. cit., Art. 9, p. 181), and paraphrased by him as "ringmässiger Zuzammnenhang, Anastomose." In modern terms, the connectivity minus one. See 4.225.

144

†1 Apparently not delivered; the series of lectures on "Detached Ideas on Vitally Important Topics" (see ch. 3) apparently having been given by request instead of the proposed eight lectures of which the present chapter and that on the continuity of space are parts.

147

†1 From "The Logic of Events," 1898, continuing 5.

148

†1 Cf. 5.79.

150

†1 "Notes for Eight Lectures," which Peirce specifically says are to follow the preceding.

150

†2 Cf. 1.308f.

151

†1 Cf. 376f.

155

†1 The Monist, vol. 3, pp. 1-22 (1892). The fourth paper of a series of five.

155

†2 Chapter 1.

155

†P1 I am rejoiced to find, since my last paper was printed, that a philosopher as subtle and profound as Dr. Edmund Montgomery ["The Dependence of Quality on Specific Energies," Mind, O. S., vol. 5, pp. 1-29] has long been arguing for the same element in the universe. Other world-renowned thinkers, as M. Renouvier [see Essais de Critique Générale, appendice ix] and M. Delboeuf [see "Déterminisme et Liberté," Revue Philosophique, vol. 13, pp. 453- 480, 608-638; vol. 14, pp. 158-189 (1882)], appear to share this opinion.

155

†3 Chapter 2.

155

†4 Chapter 5.

155

†5 See Chapter 11.

155

†6 See "The Size of Atoms," Popular Lectures and Addresses, p. 218, London (1889).

156

†1 The Concepts and Theories of Modern Physics, Chapter 7, New York (1882).

156

†2 Ueber die Physikalische und Philosophische Atomenlehre, Leipzig (1864).

156

†3 See Complete Works, vol. 1, pp. 471-493ff; vol. 2, pp. 1-22, 166-187, 208-221.

156

†4 See Scientific Papers, pp. 149ff, London (1884).

156

†5 See Transactions of the Royal Society of Edinburgh, vol. 20, p. 192.

156

†6 See Daniel Bernoulli, Hydrodynamica, Section X.

156

†7 See Philosophical Transactions of the Royal Society, vol. 165, p. 519 (1875).

156

†P1 SOLID — A body which throughout its mass (and not merely at its surface) resists for an indefinite time a sufficiently small force that tends to alter its equilibrium figure, always springing back into shape after the force is removed; a body possessing elasticity of figure. Every such body has limits of elasticity and if subjected to a strain exceeding these limits, it takes a set and does not return to its original shape on being let go. This property is called plasticity. The minimum energy required to give a set to a body of definite form and size measures its resilience. When the resilience of a body is small and masks its springiness the body is called soft. Even fluids transmit shearing forces if time be allowed and many substances will yield indefinitely to very small (but not indefinitely small) forces applied for great lengths of time. So solids that have received a small set will sometimes partially recover their figures after a long time. This property in fluids is called viscosity, in solids after-effect (German nachwirkung). The phenomenon is connected with a regrouping of the molecules, and indicates the essential difference between a solid and a liquid. In fluids diffusion is continually active, and in gases it produces phenomena of viscosity. In liquids it is not rapid enough to give rise to sensible viscosity, but the free motion of the molecules makes the body fluid, while the tendency of sets of molecules to continue for a while associated makes the fluidity imperfect. In solids, on the other hand (at least when not under strain), there is no diffusion, and the molecules are consequently in stationary motion or describing quasi-orbits. They thus become grouped in the mode in which they have least positional energy consistent with their kinetic energy. When this grouping is slightly disturbed it tends to restore itself; but when the disturbance is greater, some of the molecules will tend to return to their old places and others to move on to new situations, and this may give rise to a new permanent grouping, and exhibit the phenomenon of plasticity. But if not quite sufficient for this, disturbances of the molecular motions somewhat similar to the secular perturbations of the planets will result, from which there will be no restoration for a very long time. Solid bodies are very strongly cohesive, showing that the molecules attract one another on the whole; and they are generally capable of crystallization, showing that the attractions of the molecules are different in different directions. — Century Dictionary, p. 5759, edition of 1889.

157

†P1 By a vera causa, in the logic of science, is meant a state of things known to exist in some cases and supposed to exist in other cases, because it would account for observed phenomena.

158

†1 See Theoria Philosophicae Naturalis, Sections 8ff, 81ff, 132ff.

158

†P1 Wiedemann, Annalen, 1887-89. [Vol. 30, p. 190; 31, pp. 141, 544; 32, p. 526; 34, p. 981; 35, pp. 76, 370; 36, p. 743; 38, p. 573.]

158

†P2 See Maxwell on Spherical Harmonics, in his Electricity and Magnetism. [Vol. 2, pt. I, ch. 9, p. 179.]

158

†2 This does not seem to have been done.

159

†P1 The word system has three peculiar meanings in mathematics. (A) It means an orderly exposition of the truths of astronomy, and hence a theory of the motions of the stars, as the Ptolemaic system, the Copernican system. This is much like the sense in which we speak of the Calvinistic system of theology, the Kantian system of philosophy, etc. (B) It means the aggregate of the planets considered as all moving in somewhat the same way, as the solar system, and hence any aggregate of particles moving under mutual forces. (C) It means a number of forces acting simultaneously upon a number of particles.

160

†1 "Over de continuitet van den gas en vloeistof-toestand," Academisch Proefschrift, Leiden (1873).

160

†P1 But, in fact, an inspection of these curves is sufficient to show that they are of a higher degree than the third. For they have the line V=0, or some line V a constant for an asymptote, while for small values of P, the values of d2P/(dV)2 are positive.

162

†1 See "Mémoire sur la compressibilité des gaz à des pressions élevées," Annales de Chémie et de Physique, vol. 19, pp. 345-385 (1880).

163

†1 "Ueber die Dissociation der in Wasser gelösten Stoffe," Zeitschrift für Physikalische Chemie, Bd. 1, pp. 631-648 (1887).

163

†P1 Anticipated by Clausius ["Ueber die Elektricitätsleitung in Elektrolyten," Poggendorff's Annalen, Bd. 101, pp. 338-360], as long ago as 1857; and by Williamson ["Ueber die Theorie der Aetherbildung," Annalen der Chemie und Pharmacie, Bd. 77, pp. 37-49] in 1851.

164

†1 Cf. 1.351, 1.386ff.

165

†1 "On the Theory of the Analytical Forms called Trees," American Journal of Mathematics, vol. 4, pp. 266-268 (1881).

165

†2 See 278n.

166

†1 See 149, 275.

166

†2 Lectures and Essays, vol. 2, pp. 311-316 (1879).

169

†1 Cf. 23, 280f, 1.390.

171

†1 Principles of Psychology, vol. 1, p. 105 (1890).

171

†2 See 241n.

172

†1 Cf. 24f.

173

†P1 "Physiologically, . . . accommodation means the breaking up of a habit. . . . Psychologically, it means reviving consciousness." Baldwin, Psychology, Part III, ch. 1, §5.

174

†1 Cf. 5.311.

174

†2 Cf. 215ff, 613.

175

†1 Cf. 135ff, 155ff.

176

†1 See 5.313-14.

177

†1 Cf. 559, 587.

178

†1 c. 1893.

180

†1 See System of Positive Polity, vol. 1, pp. 421-422, Paris (1851).

181

†1 Cf. 68ff.

184

†1 Cf. 133ff.

185

†1 From ch. 3 (Div. II), of the Grand Logic (1893). Cf. 3.154ff.

185

†P1 The theory that there is but one protoplasm shall be considered in our chapter on fallacies. [That chapter is not being published.]

185

†2 See 246f, 1.386ff.

185

†3 Cf. 259f, 1.386f.

187

†P1 I assume for the percentage composition of albumen the following:

Oxygen 21.5 = 1.34 times at. wt.
Hydrogen 7 = 7. times at. wt.
Nitrogen 16.5 = 1.18 times at. wt.
Carbon 54 = 4.5 times at. wt.
Sulphur 1 = 0.03 times at. wt.
100 14.05
I assume the solution having an osmotic pressure of 1/2 at. to be of 12.5 p. c. I assume the Sp. Gr. Albumen to be 1.25. Then by the laws of osmotic pressure, there would be 980 atoms to a molecule.
188

†1 Cf. 5.479.

189

†1 Proverbs, 4.23.

189

†2 Cf. 2.711.

190

†1 The Monist, vol. 3, pp. 176-200 (1893); the last paper of a series of five. See note to ch. 1.

190

†2 See H. Diels, Fragmente der Vorsokratiker, vol. 1, 21B.

191

†1 p. 442.

192

†1 See 270.

192

†2 See ch. 5.

193

†1 Simon Newcomb, Principles of Political Economy, New York (1886).

193

†2 Ibid., p. 534.

194

†P1 How can a writer have any respect for science, as such, who is capable of confounding with the scientific propositions of political economy, which have nothing to say concerning what is "beneficent," such brummagem generalizations as this?

196

†1 See especially Remark G.

197

†1 Cf. 13ff.

197

†2 See "Mr. Charles S. Peirce's Onslaught on the Doctrine of Necessity," The Monist, vol. 2, p. 576.

197

†3 Bruxelles, 1846. Translation by O. G. Downes. London, 1849.

198

†1 "Quetelet on Probabilities," Edinburgh Review, vol. 42, pp. 1-57 (1850).

198

†2 "Ueber die Art der Bewegung welche wir Wärme nennen," Poggendorff's Annalen, Bd. 100, S. 365 (1857).

198

†3 "Grundzüge einer Theorie der Gase," Poggendorff's Annalen, Bd. 99, S. 315 (1856).

198

†4 "Illustrations of the Dynamical Theory of Gases," Philos. Magazine IV, p. 22 (1860). Reprinted in Collected Papers, vol. 1, p. 377.

198

†5 See 71.

198

†6 Ueber die Erhaltung der Kraft. Introduction to a series of lectures delivered at Karlsruhe 1862-63. Translated in Popular Scientific Lectures, vol. 1, pp. 316-362, New York, (1885).

198

†7 "Ueber die bewegende Kraft der Wärme," Poggendorff's Annalen, Bd. 79, S. 368.

198

†8 Transactions of the Royal Society of Edinburgh, vol. 20, p. 192.

199

†1 Cf. 5.64.

200

†1 In his Mechanisch-physiologische Theorie der Abstammungslehre. Einleitung, S. 14ff. München and Leipzig (1884).

200

†2 Entwicklungsgeschichte des Menschen und der Höheren Thiere, Einleitung §1, Leipzig (1879).

200

†3 See Essays on Heredity, vol. 1, essay 2.

200

†P1 I am happy to find that Dr. Carus ["The Soul of Man," Open Court, 1891, p. 215], too, ranks Weismann among the opponents of Darwin, notwithstanding his flying that flag.

200

†4 Philosophie Zoologique, Pt. I, ch. 7, Paris (1873).

201

†1 See 261ff.

202

†1 See 250ff.

204

†1 An engine "invented" in 1874 by J. E. W. Keely, supposed to produce power by responding to the intermolecular vibrations of the ether.

208

†1 See Mark 3, 29.

208

†2 See Mark 9, 48.

208

†3 See Isaiah 66, 24.

209

†1 Ecclesiastical History, vol. 8, p. 2.

209

†2 See "Of the False Wisdom of Philosophers." The Divine Institutes, Bk. III.

209

†P1 See Draper's History of Intellectual Development, ch. 10.

209

†3 See John of Salisbury, Policraticus, ii, 26; viii, 19.

210

†1 Geschichte der Logik in Abendlande, Leipzig (1867), Dritter Band, 17 Abschn., S. 2.

211

†1 See 3.396ff, 3.506ff, 3.641.

213

†1 "Recherches sur les mouvements de la planète Herschel, dite Uranus." Connaissances des temps, 1849.

213

†2 See Nautical Almanac, 1851, p. 3.

213

†3 Transactions of the Royal Society of Edinburgh, vol. 20, p. 192.

213

†4 "Ueber die bewegende Kraft der Wärme," Poggendorff's Annalen, Bd. 79, S. 368.

214

†P1 Thomson, himself, in his article Heat in the Encyclopedia Britannica [edition of 1875-89] never once mentions the name of Clausius.

214

†1 Daniel Bernoulli, Hydrodynamica, Section X (1738).

214

†2 Mendeléeff, Lothar Meyer, and J. A. R. Newlands.

214

†3 W. T. G. Morton, C. T. Jackson, J. C. Warren.

216

†1 §§1-6 are from "Some Amazing Mazes, Fourth Curiosity" (c. 1909). See 4.647.

216

†2 See 3.466f, 3.571.

216

†3 See 3.573f.

217

†1 See 2.357.

218

†1 Cf. 2.590f, 4.355.

218

†2 Anal. priora I, 24b, 28.

219

†1 Cf. 3.575 (6), 3.595.

219

†2 Cf. 3.575 (8), 3.597.

219

†3 Kritik der Reinen Vernunft, A 303, B 360.

219

†4 Cf. 2.496.

219

†5 I.e., ΣwΠc cAw ⤙ Πc Σw cAw.

220

†1 See 3.63, 3.144, 3.421, 3.483f.

221

†1 See OEuvres de Pasteur, vol. 1, pp. 83ff, Paris (1922).

221

†2 See 68.

221

†3 Cf. 1.473, 2.274.

221

†4 Peirce died in 1914, about five years after he wrote this paper, the last detailed study he seems to have made.

225

†1 Cf. 364f, 3.527.

225

†P1 I know no question of metaphysics so pressing as this of whether or not there be a maximum multitude capable of linear arrangement. There appears to be a proof that there is none; but owing to the extreme liability to fallacy of reasoning concerning this question, I have some doubt of its validity. I found what appeared to be a proof to the same effect. After careful and repeated scrutiny, I discovered no fallacy in it; and there was no great intricacy in the proof. I submitted it to two persons, each of whom had devoted so much study to the general subject that I had a right to presume that not a dozen persons living were as competent in the premisses as he. Neither could discover any fallacy. Yet, I subsequently found, myself, that my proof was fallacious. Such an experience naturally renders me very cautious. [Cf. 3.549n. 4.218, 4.652.]

226

†1 Cf. 5.405f, 5.430f.

229

†1 See vol. 2, bk. II, ch. 1.

230

†1 Cf. 2.269, 2.756f.

231

†1 Cf. 1.471ff, 1.536ff.

232

†1 Analytica Posteriora, II, 100a, 18.

232

†2 Categoriæ, 2b, 5.

233

†1 Analytica Posteriora, II, 91b, 34; Categoriae, 1b, 6.

233

†P1 But I am here expressing myself upon points which I have not reexamined for a great many years. I might hold different opinions, if I were to revise my judgments.

233

†2 See 2.247, 2.274ff.

233

†2 See 2.247, 2.274ff.

233

†2 See 2.247, 2.274ff.

234

†1 Principles of Human Knowledge, §3.

234

†2 B 274-279.

234

†3 Anal. Post., I, 31, 87b, 27-32; II, 19, 100a, 14-64.

234

†4 Cf. 4.539.

234

†5 Categoriæ, 1b, 3.

235

†1 Cf. 5.310ff.

235

†2 See 2.251, 2.310.

237

†1 See 2.230, 2.274.

237

†2 §§7 and 8 form a digression in ch. 4 of the Minute Logic (1902-3). The Velian is the stranger of Plato's Sophist, a dialogue which Peirce characterizes in the preceding, unpublished portion of the manuscript (see 1.584n) as being "purely a logical dialogue" with "all Hegel's faults and more than a glimmer of Hegel's merit." The present section is part of an attempt to give the Velian stranger "a little dose of his own cathartic."

238

†1 "Cathode Rays," Philosophical Magazine, October 1897, pp. 293-310; "On Bodies Smaller than Atoms," Popular Science Monthly, August 1901, pp. 323-337.

241

†1 See 2.536.

241

†2 Cf. 2.487n1, 2.550, 2.596f.

243

†1 See 2.412.

245

†1 Cf. 5.505.

246

†1 From Baldwin's Dictionary of Philosophy and Psychology, The Macmillan Co., New York, vol. 2, pp. 50-55 (1902).

246

†2 See Metaphysica, A3, 983b, 7.

247

†1 Metaphysica, Θ, 8, 1050a, 15.

247

†2 De Anima, 415a, 25.

248

†1 Metaphysica, H, 1, 1042a31.

249

†1 Summa Theologica, I, II, 55, 4, c.

249

†2 Summa Theologica, I, 75, 4, c.

250

†1 Ibid., I, II, 50, 2, c.

250

†2 Metaphysica, Δ, 10, 1018b 5. K., 3, 1061a 23.

251

†1 Metaphysica, E, 1, 1025b 30, 1026a 27.

251

†2 Novum Organum, II, 5.

252

†1 Summa Theologica, I, 54, 3, ad. 2.

253

†1 Ibid., I, 61, 1.

257

†1 Baldwin's Dictionary of Philosophy and Psychology, vol. 2, pp. 313-315. Cf. 3.527, 4.65ff.

258

†1 Analytica Priora, I, 13, 32a, 18.

258

†2 Metaphysica, Δ 12, 1019a, 32.

258

†3 Monadology, 33.

258

†4 Kritik der Reinen Vernunft, A151, B191.

261

†1 Baldwin's Dictionary of Philosophy and Psychology, vol. 2, pp. 763-764.

262

†1 Ibid., vol. 2, pp. 734-736.

263

†1 Kritik der Reinen Vernunft, A118, B131.

266

†1 Baldwin's Dictionary of Philosophy and Psychology, vol. 2, pp. 814-815.

266

†2 This paragraph is signed by Peirce, J. M. Baldwin, and G. F. Stout.

267

†1 Cf. 3.537n.

268

†1 Lectures on Metaphysics, XXXVII, vol. 2, p. 340, Edinburgh (1858).

269

†1 Baldwin's Dictionary of Philosophy and Psychology, vol. 1, p. 600 (1901).

270

†1 See 2.407ff.

271

†1 Ibid., vol. 2, pp. 281-282.

271

†2 187A.

271

†3 Metaphysica, Δ, c. XVIII; 1022a 14-36.

273

†1 Baldwin's Dictionary of Philosophy and Psychology, vol. 2, pp. 342-343.

274

†1 Anal. Post., I, 2, 72a 1.

274

†2 Metaphysica, Δ, 11, 1018b 21.

274

†3 Metaphysica A, 8, 989a 16; Categoriae, 12, 14b 3.

275

†1 Baldwin's Dictionary of Philosophy and Psychology, vol 2, pp. 281-282.

276

†1 Ibid., vol. 2, pp. 616-617.

283

†1 Popular Science Monthly, vol. 13, pp. 203-217 (1878); the fifth of a series of six articles called "Illustrations of the Logic of Science." For the first and second articles see vol. 5, bk. II, chs. 4 and 5; for the third, fourth, and sixth see vol. 2, bk. III, chs. 6, 7, and 5.

284

†1 Cf. La Religion (1869), bk. II, ch. 5.

285

†1 Works, vol. 1, p. 346, London (1820).

286

†P1 For the present purpose, the negative of a character is to be considered as much a character as the positive, for a uniformity may either be affirmative or negative. I do not say that no distinction can be drawn between positive and negative uniformities.

286

†P2 There being 5 simple characters, with their negatives, they could be compounded in various ways so as to make 241 characters in all, without counting the characters existence and non-existence, which make up 243 or 35.

287

†1 Op. cit., p. 347.

287

†P1 This principle was, I believe, first stated by Mr. De Morgan. [See his "On the Syllogism, no. V, etc." Transactions of the Cambridge Philosophical Society, vol. 10, pp. 456, 467 (1864); Formal Logic, p. 39, London (1847).]

290

†1 See vol. 2, bk. III, ch. 7.

291

†1 A System of Logic, bk. III, ch. 3, §1.

291

†2 Cf. 2.766f.

292

†1 Ibid., bk. III, ch. 3, §3.

294

†1 A New Theory of Vision, Sections 2 and 3.

294

†2 Cf. 5.223.

295

†1 Cf. 491, 1.118, 5.47, 5.586, 5.591.

296

†1 5.405ff.

302

†1 The Open Court, vol. 7, pp. 3559-60 (1893).

305

†1 The Open Court, vol. 7, pp. 3743-45 (1893).

306

†P1 Edited with translation and notes by Roswell D. Hitchcock and Francis Brown, New York, Scribners (1884). Also, by Philip Schaff, 3d edition, New York, Funk and Wagnalls (1890).

308

†1 Cf. 511ff, 522ff.

309

†1 From "Religion and Politics," c. 1895; apparently a proposed letter to a newspaper.

311

†1 Hibbert Journal, vol. 7, pp. 90-112 (1908).

311

†2 See his Thought and Things, p. 261, London (1906).

312

†1 Cf. 4.545ff.

312

†2 Cf. 2.266ff, 3.160.

315

†1 "It appears to me that this mystery is considered insoluble for the very reason which should cause it to be regarded as easy of solution. I mean the outré character of its features."

316

†1 Cf. 1.333.

319

†1 See 177ff.

319

†2 See 5.397ff.

320

†1 Cf. 2.622ff.

321

†1 Or Abduction. See 2.708ff, 2.755 and vol. 5, bk. I, ch. 7.

322

†1 Cf. 2.267.

322

†2 Cf. 2.756ff.

323

†1 Cf. 2.758f.

323

†2 Kritik der Reinen Vernunft, A154-158; B193-197.

323

†3 See 2.93.

324

†1 Jacques Babinet (1794-1872), a popular writer on hydrodynamics and many other scientific subjects.

325

†1 See "Dialogues Concerning the Two Great Systems of the World," in Mathematical Collections and Translations of Thomas Salisbury, vol. 1, p. 301, London (1661).

326

†1 In a letter to William James, November 17, 1908, Peirce says, "I had never contemplated the possibility of the last section's being published."

328

†1 Cf. 3.457, 5.388ff.

328

†2 See 5.12f.

329

†1 See note to vol. 5, bk. II, Paper No. IV.

329

†2 See The Will to Believe and Other Essays in Popular Philosophy (1897).

329

†3 See "What Pragmatism is Like," Popular Science Monthly, vol. 71, p. 351 (1907).

329

†4 See 5.414.

329

†5 See 5.1f.

329

†6 See 1.106n, 5.13n.

329

†7 See 486.

331

†1 See 5.375.

331

†2 See 5.365ff.

331

†3 See 5.552, 5.555f.

332

†1 F. C. S. Schiller, Humanism, p. 314, note, London (1903); Studies in Humanism, p. 295, London (1907).

332

†2 William James, Pragmatism, p. 59ff, New York (1908).

332

†3 William James, The Will to Believe, p. 11, New York (1899).

332

†4 c. 1910; 491 is from an alternative draft.

335

†1 See 482 and p. v of the Preface to vol. 5.

335

†2 "Philosophical Conceptions and Practical Results," The University of California Chronicle, pp. 24ff (1898); reprinted in Collected Essays and Reviews, pp. 406-437 (1920).

335

†3 "What Pragmatism is Like," Popular Science Monthly, p. 351, vol. 71 (1907).

335

†4 See 5.414.

338

†1 See 418.

338

†2 From an unpaginated fragment, c. 1896.

338

†3 See 5.255f.

340

†1 c. 1906.

340

†2 See Part IV ad init.

340

†3 See e.g. 336, 5.503.

341

†1 Physicorum Liber, I, 1, I.

341

†2 See Sententiarum Libri, III, Distinctio 34.

341

†3 See 1.549n.

341

†4 See 5.448.

342

†1 De civitate Dei, XI, 26.

343

†1 See e.g. 5.265, 5.416ff, 5.438ff.

343

†2 See 17, 33, 296ff, 1.104.

345

†1 Cf. 418, 491.

347

†1 A. Caldecott, The Philosophy of Religion in England and America, p. 9, Macmillan, New York (1901).

347

†2 See chs. 1, 2, 5, 9, 11, in bk. I of the present volume.

347

†3 See La Nouvelle Monadologie, Art. CXXX, p. 163, Paris (1899).

348

†1 Cf. 189ff.

348

†2 See 287.

349

†1 Cf. 4.67, 4.583.

349

†2 Contra Faustum, bk. XXVI, ch. 3.

349

†3 Summa Theologica, I, 105, 6.

350

†1 The Analogy, pt. I, ch. 7.

350

†2 See 47ff, 264, 302.

350

†3 Essais de critique générale, appendice IX (1854-64).

350

†4 La Liberté et le déterminisme, Paris (1872).

350

†5 "Déterminisme et liberté," Revue Philosophique, vol. 13, pp. 433-480, 608-638; vol. 14, pp. 158-189 (1882).

350

†6 Inquiry, Section X.

350

†7 See the next chapter for a detailed consideration of this question.

350

†8 See the long discussion of historical evidence in vol. 8.

350

†9 See e.g. 1.617.

350

†10 Discourses on the Miracles of Our Savior, etc., London (1727-29).

351

†1 Commentaries on the Gospels of Matthew and John. See e.g. on John IV, 46; also in Exod. Hom. v. 7.

351

†2 See Researches in the Phenomena of Spiritualism, London (1874).

351

†3 For Rayleigh's attitude see A. C. Doyle, History of Spiritualism, vol. 1, p. 181, London (1926).

351

†4 "A Further Record of Observations of Certain Phenomena of Trance," Proceedings of the S. P. R., vol. 13, pp. 285-582 (1897-98).

352

†1 "The Prayer for the Sick, Hints Towards a Serious Attempt to Estimate Its Value," Contemporary Review, vol. 20 (1872).

352

†2 I Kings XVIII.

353

†1 Principles of Political Economy, New York (1886).

353

†2 See 290ff.

353

†3 See Peirce's review of Pearson's Grammar of Science in Popular Science Monthly, vol. 58, pp. 296-306 (1901); to be reprinted in vol. 9.

354

†1 Cf. chapter 6.

354

†2 The dots, indicating omissions, occur in the manuscript.

355

†1 The manuscript ends at this point.

356

†1 c. 1901

356

†2 Cf. 2.186ff.

358

†1 Cf. 2.708ff, 2.786, 5.171.

359

†1 Cf. 2.735ff.

359

†2 Cf. 2.759, 2.772.

361

†1 Cf. 1.122ff, 5.600ff.

362

†1 See 418, 491.

362

†2 Cf. 2.740.

363

†1 See 2.101, 2.662f, 2.777.

364

†1 See vol. 8.

364

†2 See 513.

364

†3 Inquiry, Section X.

364

†4 Summa Theol., I, qu. 110, art. 4, ad. 2.

365

†1 Inquiry, X, I, 90.

366

†1 Fragment, 169 (151); see Plato's Gorgias, 484 B, 488 B; Laws, 690 B, 715 A.

366

†2 Gorgias, 483 E.

366

†3 See De rerum natura, I, 148.

366

†4 See Meditation III.

366

†5 See Works, vol. 5, p. 52, London (1672).

367

†1 See his Discourses on the Miracles of Our Savior, etc., London (1727-29).

368

†1 See A Collection of the Tracts of a Certain Free Inquirer, etc., London (1739).

369

†1 1733.

369

†2 Analogy, Part II, bk. IV (1736). Hume's Treatise was published in 1739-40.

370

†1 First published in a Symposium in the Christian Register, Boston, April 7, 1887. Reprinted from Science and Immortality, The Christian Register Symposium, Revised and Enlarged, edited by S. J. Barrows; Geo. H. Ellis, Boston (1887).

372

†1 Cf. 58ff.

372

†2 First Principles, bk. II, ch. 18.

373

†1 Cours de philosophie positive, 19e leçon. vol. 2, p. 8, Paris (1835).

375

†1 Exactly as written and corrected by Peirce. Intended for The Forum, c. 1905.

379

†1 See his Heat Considered as a Mode of Motion, Lecture V (1862).

379

†2 "Ueber einen Grundsatz der Mechanischen Wärmetheorie," Annalen der Physik u. Chemie, Bd. CXX, pp. 426-452 (1863).

379

†3 See "Remarks on the Mechanical Equivalent of Heat," Philosophical Magazine, Series IV, vol. 25, p. 493 (1863).

379

†4 Sketch of Thermodynamics, §§30-39 (1868 and 1877).

379

†5 Réflexions sur la puissance motrice du feu, 1824.

379

†6 An American inventor and scientist (1804-79) who does not seem to have published his theoretic results.

380

†1 "On the Theory of Light and Colours," Philosophical Transactions, 1802, p. 12.

381

†1 Meditation II. Principles, Part I, 9.

381

†P1 Thus in the Scriptum in quartum librum sententiarum Magistri Petri Lombardi (Distinctio 50, questio 3, articulus 4), he says: Dicendum . . . quod . . . ut beatitudo sanctorum eis magis complaceat et de ea uberiores gratias Deo agant, dantur eis ut poenam impiorum perfecte intueantur. In his 8th Quodlibet, question 7, article 16, he says: Dicendum quod videre miseriam damnatorum omnino erit sanctis ad gloriam, gaudebunt enim de justicia Dei et de sua evasione. And in another place: laetantur de justa punitione. "A horrible doctrine, I confess," says Calvin [Institutes of the Christian Religion, bk. III, chapter 23, section 7] of election to damnation; but logic forces him to it.

382

†1 See e.g. 5.223.

383

†1 See Zöllner, Transcendental Physics, trans. by W. H. Harrison, London (1880).

385

†1 Dialogues Concerning Two New Sciences, "Fourth Day" ad init. (1638).

387

†1 Cf. 27, 1.362.

387

†2 Cf. 260ff.

390

†1 The Monist, vol. 3, pp. 526-570 (1893).

390

†2 See bk I, chaps. 1 and 2.

393

†P1 J. S. Mill had in the first edition of his Logic decisively taken an objective conception of chance and probability; but in his second edition he had become puzzled and had retracted [see bk. III, ch. 18], leaving that chapter, and with it his whole logic, a melancholy wreck, over which the qualified reader sighs, "And this once seemed intelligible!" Venn in the first edition of his book set forth the same objective conception with great clearness, and for that he was entitled to high praise, notwithstanding his manifest inadequacy to the problems treated. But in his second edition [see ch. 6] he too has fallen away from his first and correct view, and has adopted a theory which I shall some day show to be untenable. Venn's whole method in logic, as well as his system, is in my opinion of the weakest.

393

†1 See 3.14ff.

393

†2 System of Logic, bk. III, ch. 5, §5.

394

†1 See e.g. Kritik der Reinen Vernunft, A91, B124.

394

†P1 Mill often did good service in substituting precise terms for ambiguous ones; as when in speaking of mathematical conclusions he prefers to say they are legitimate deductions rather than that they are necessary. [System of Logic, bk. II, ch. 5 §1.]

394

†2 In A System of Logic, bk. III, ch. 5, §5.

394

†P2 In his Ursache, Grund und Zweck, Dr. Carus alludes to this passage [Ursache, Grund und Zweck, p. 37, Dresden (1883)]. But he prefers the treatment of the question by Reid, whom he calls Mill's opponent (Gegner).

394

†P3 It is of comparatively little consequence what Hume really meant. The main interest is in what Kant thought he meant.

394

†3 See 2.407ff.

395

†1 Cf. 2.315, 2.594, 3.182.

395

†2 In the Century Dictionary of 1889; see also 38.

396

†1 See 1.322ff.

396

†2 See 4.547n, 5.339, 5.403.

397

†P1 Along with the distinction, I would of course do away with this use of the words abstract and concrete to which no clear idea can be attached, as far as I can see.

397

†P2 I cannot but disapprove of this use of the word "construction" to mean a studied theory, because the word is imperatively required in the theory of cognition to denote a mathematical diagram framed according to a general precept.

398

†1 See Paper No. XVI of vol. 3.

398

†2 Cf. 2.56ff.

399

†P1 I apply this term because it is essentially like the passage from the concrete "virtuous" to the abstract "virtue," or from the concrete "white" (adjective) to the abstract "whiteness," or "white" (substantive). [Cf. 2.428.]

399

†1 Cf. 3.85ff.

399

†2 See 2.694ff.

400

†P1 I can never use this word without thinking of the explanation of it given by Petrus Peregrinus in his Epistole de Magnete. [See vol. 7.] He says that physical properties are occult in the sense that they are only brought out by experimentation, and are not to be deduced from admixtures of hot and cold, moist and dry.

400

†1 Cf. 1.383.

400

†2 See 5.504, 5.591.

403

†1 Cf. 67ff.

404

†P1 It follows as a corollary from this that if the positions of the particles at any one instant, together with the velocities at that instant, and the law of force, are given, the positions at all instants can be calculated. Of course, to give the positions and velocities at one instant is a special case of the giving of the positions at two instants. The two instants may be such that there will be more than one solution of the problem; but this is an insignificant detail.

404

†1 Kritik der Reinen Vernunft, A199, B244.

405

†1 See 139.

405

†P1 It would seem to follow from his notion that in uniform motion each minute's motion is the cause of that of the next. Yet he says (¶ 19) "there is no cause that is equal to its effect."

406

†P1 But, as I have elsewhere said, I should like to persuade mathematicians to speak of "positional energy" as Kinetic potency, the vis viva as Kinetic energy, and the total "energy" as the Kinetic entelechy.

406

†1 Lectures on Some Recent Advances in Physical Science, p. 17 (1876).

407

†P1 The differential equation being an ordinary, not a partial one, this is an absolute constant, determined by initial (or final, or any instantaneous) conditions.

410

†1 Cf. 1.135ff.

411

†1 See vol. 2, bk. III, B.

411

†2 See vol. 1, bk. I, ch. 2.

411

†3 History of the Inductive Sciences, p. 6, third edition, London (1837).

412

†P1 Dr. Carus calls attention to the connection between my doctrine of the fixation of opinion and his anti-originalism.

412

†P2 Dr. Carus passes a sweeping judgment on post-Kantian philosophy as being original.

412

†P3 This was a remark of my father's.

413

†1 See 7ff.

413

†2 See 33.

413

†P1 A person in the last Monist [G. M. McCrie, "The Issues of Synechism," vol. 3, pp. 380-401] breaks in upon my series of articles to foretell what the "issues of synechism" will be. Were he able to do so, it would certainly be the height of ill-manners thus to take the words out of my mouth.

415

†1 See 25.

415

†P1 As I am writing, I am shown a letter, in which the writer says: "Peirce with all his materialistic ideas, yet," etc. I never promulgated a materialistic idea in my life. The writer simply assumes that science is materialistic. As I am correcting the proofs, I notice that Mr. B. C. Burt, in his new History of Modern Philosophy, sets me down as sceptical, though doubtfully. There are a good many inaccuracies in the work. This was inevitable in a first edition. But the ingenious plan of the book admirably adapts it to the wants of just that class of students who cannot understand that no repertory of facts ever can be trusted implicitly.

416

†P1 Its being hypothetical will not prevent its being established with a very high degree of certainty. Thus, all history is of the nature of hypothesis; since its facts cannot be directly observed, but are only supposed to be true to account for the characters of the monuments and other documents.

417

†P1 Somebody may notice that I here admit a proposition as absolutely true. Undoubtedly; because it relates to the Absolute.

418

†P1 Indeed, to admit that reply is all but to admit the non-absolute grade of necessity.

418

†1 See 2.683f.

418

†2 See 2.745f.

419

†P1 I rightly go somewhat further in my Theory of Probable Inference; but that has no bearing on the present discussion.

420

†1 See 2.749.

423

†1 Cf. 2.690, 2.716.

423

†P1 Dr. Carus, in his Ursache, Grund und Zweck, well says that reasons are discovered by induction, in the strict sense. It is often admitted that causes can only be inferred by hypothetic reasoning.

424

†1 See 214ff.

425

†1 See 297.

426

†1 Dr. Carus says of this: "Mr. Peirce's escape is like the disappearance of a medium from a room without doors. He must have got out through the fourth dimension. The argument is so subtle that I cannot see it." (The Monist, vol. 3, p. 599.)

429

†P1 The conservation of a vortex, which consists of the preservation of a certain character of motion by the same particles, though derived from the coöperation of other laws, is, in form, quite different.

429

†1 Principia, I, 9ff.

429

†2 3me Lettre à Clarke 4. Gerhardt, vol. 7, p. 363, Berlin (1890).

429

†3 See Kritik der Reinen Vernunft, A33, B50.

430

†P1 In speaking of directions, we assume the Euclidean hypothesis that the angles of a triangle are equal to two right angles.

430

†1 Cf. 553.

434

†1 See 239-263.

434

†2 Sir Oliver Lodge. See his "Force and determinism," Nature, vol. 43, p. 491; Vol. 44, pp. 198, 272; (1890-91).

435

†1 See vol. 5, bk. II, no. II.

436

†1 A letter in The Journal of Speculative Philosophy, vol. 2, pp. 57-61 (1868) which, to judge from internal evidence, was written by Peirce.

437

†1 Comments of the editor of the Journal follow here.

441

†1 A letter continuing the discussion begun in Appendix B. From The Journal of Speculative Philosophy, vol. 2, pp. 190-191 (1868).