Volume 7: Science and Philosophy.

Book 1: Experimental Science

Chapter 1: Measurement of the Force of Gravity

§1. A Source of Error in pendulum Measurements †1

1. The fact that the rate of a pendulum might be largely influenced by the elastic yielding of its support was first pointed out by Dr. Thomas Young in his article on Tides in the Encyclopædia Britannica, where he gave a correct mathematical analysis of the problem. Kater made use of the noddy, or inverted pendulum of Hardy, to assure himself that its support was sufficiently steady.

2. Hardy's noddy is a pendulum turning with a reed spring and provided with an adjustable bob. It differs from an ordinary pendulum, first, in being upside down, that is, having its center of mass above its point of support; and second, in having a spring so strong as to act a little more strongly than gravity. The force tending to bring the pendulum to the vertical is then the excess of the force of the spring over the moment of gravity. In this way the noddy is easily adjusted so as to have the same period of oscillation as the pendulum used to determine gravity, while its moment of inertia is very small. In a note at the end of this paper I give the mathematical analysis of this state of things, from which it will be seen that Kater might have constructed his noddy in such a manner as to detect any amount of flexure sufficient to have a serious effect upon the period of his pendulum.

3. Bessel, at the end of §3 of his great memoir on the length of the second's pendulum at Königsberg, states that he also used Hardy's noddy, and that he swung his pendulum again after stiffening the support. He adds that the effect on the period would probably be the same for his long pendulum as for his short one — a very just remark — which made it less necessary for him to attend to the rigidity of the stand.

4. The construction of English pendulum supports, that of Bassevi, for example, shows that in that country this source of error was never overlooked. It is noticed even in brief accounts in English of the process of measuring gravity. Thus, a writer in the Encyclopædia Britannica proposed to make use of two different reversible pendulums of the same form but of different weights, in order to take account of the flexure, an idea lately borrowed by M. Cellerier.

5. When the reversible pendulum came into use the study of the writings of the older observers seems to have been neglected, †2 and the grave errors due to flexure were never suspected until Albrecht found a value of gravity at Berlin differing by nearly 2 millimeters from that of Bessel. So little was the true cause of this discrepancy at first suspected that it was paradoxically attributed to the neglect of a buoyancy correction.

6. In 1875, however, General Baeyer gravely suspected that the period of a pendulum swinging upon a Repsold tripod was affected by the oscillation of the latter, and in a circular addressed to the members of the committee on the pendulum of the International Geodetic Congress, he wrote: "The necessity of suspending the pendulum from a stand is a source of error, since a pendulum swinging on a stand sets the latter into oscillation and so influences the rate of the former. The effect could be diminished by the use of a shorter pendulum and smaller stand; but whether it would be rendered entirely insensible is open to question."

7. It was at this time that I first received the Repsold apparatus from the makers, of whom it had been ordered two years before, on the occasion of my first being charged with the pendulum operations of the Coast Survey. Becoming acquainted with General Baeyer's doubts, I determined to settle the question by measuring the flexibility of the Repsold tripod at the earliest opportunity. This I did at Geneva, where, though I only made a rough measurement, I found that the flexure was fully sufficient to account for the discrepancy between the determinations of Bessel and of Albrecht.

8. On September 25 of the same year I communicated my result to the standing committee of the Geodetical Congress. †3 At the same sitting the reports of the different members of the pendulum committee were read. Dr. Bruhns said: "The question whether the stand is set into oscillation, and whether the rate of the pendulum is influenced thereby is, in my opinion, well worth investigation. But I should suppose that the stand could be made so stiff as to eliminate this source of error for a pendulum used only as a relative instrument." The views of M. Hirsch, who is so much occupied with the going of timekeepers, are interesting. He said: "The fear that the tripod of suspension may also enter into oscillation, unless it be a fact established by direct observations, seems to me unfounded. Indeed, it cannot be supposed that there are any true oscillations of a body of such a form resting on three points. Besides, the movement of the pendulum whose mechanical moment (moment mécanique) is slight on account of its small velocity, could only be communicated to the tripod by the friction of the knife on the supporting plane. Now, this friction is insignificant, as the slowness of the decrement of the amplitude shows, this being almost entirely due to the resistance of the air." It may be observed that the rolling friction of the knife edge is, in truth, very slight, but the amount of the sliding friction is sufficient to hold the knife in place on the supporting plane. Dr. von Oppolzer, the designer of the Repsold tripod in its definitive form, said that the construction of the stand rendered any serious flexure a priori improbable; but he did not support this opinion by any calculations.

9. During the spring of 1876, having already measured the flexibility of the tripod in Paris, I remeasured it in Berlin, where my experiments were witnessed by General Baeyer and a party of gentlemen attached to the Prussian Survey.

10. In October, 1876, at the meeting of the standing committee of the International Geodetical Union at Brussels, the result of my experiments was announced by General Baeyer. †4 M. Hirsch described certain experimental researches undertaken by him to ascertain whether there was any such flexure in the case of the Swiss tripod. He had, in the first place, employed an extremely sensitive level, which had not entered into oscillation while the pendulum was swinging upon it. It is not clear why M. Hirsch employed a very sensitive level, the natural time of oscillation of which would differ much more from the period of the pendulum than that of a less sensitive level would do. He also used an artificial horizon in the same way. M. Hirsch's conclusion is that "there remains no doubt that the Swiss stand is free from every trace of such oscillations." Dr. von Oppolzer entirely agreed with the views of M. Hirsch.

11. In the following summer I addressed to M. Plantamour a paper upon the subject, to be submitted to the next meeting of the Geodetical Congress. †5 In this note, which is reprinted at the end of the present report, I first give a mathematical analysis of the problem. I next show experimentally that the motion of the knife-edge support is not a translation, but is a rotation, so that different parts of the head of the tripod, only a few centimeters distant from one another, move through very different distances. Consequently, measures of the flexure made anywhere except at the center of the knife-edge plane require an important correction before they can be used to correct the periods. This is confirmed by experiments with a mirror while the pendulum is in motion. I next give a brief résumé of my statical measures of the flexure. I then give measures of the actual flexure under the oscillation of the pendulum, and show that the statical and dynamical flexibilities are approximately equal. Finally, I swing the same pendulum upon the Repsold support and upon another having seven times the rigidity of that one, and I show that the difference of the periods of oscillation agrees with the theory.

12. Immediately upon the reception of my manuscript, MM. Hirsch and Plantamour commenced new researches, designed to form an "étude approfondie de ce phénomène." These were embodied in a paper by M. Plantamour, which was read to the Geodetical Congress, and which has since been expanded into a memoir entitled "Recherches expérimentales sur le mouvement simultané d'un pendule et de ses supports." †6 M. Plantamour finds fault with me, first, for having measured the flexure with a force five or ten times that of the deflecting force of the pendulum; and second, for measuring the elasticity statically instead of dynamically. The reply to the first objection is that the properties of metals are known to a great extent, that elasticity is not "une force capricieuse," and that no fact is better established than that an elastic strain is proportional to the stress up to near the limit of elasticity, which limit was not approached in the author's experiments. As to the second objection, I had shown by experiment that the statical and dynamical flexures are nearly equal; and I am willing to leave it to time to show whether this will not be assumed in future measures of the flexure of future pendulum supports. M. Plantamour caused a fine point fixed into the head of the tripod to press against a little mirror, mounted on an axis; and then observed the reflection of a scale in a telescope. The length of the path of light from the scale to the telescope divided by the distance of the bearing point from the axis of the mirror he calls the grossissement; so that had he used a fixed star in place of his scale, the grossissement would have been virtually infinite. From the given length of the lever it would appear that a movement of 0{u}.03 in the point would turn the mirror 4''. The aperture of the mirror is not stated, but it cannot be supposed that the error of observation would be less than this. It does not seem to me that the use of this mode of measurement, which magnifies the motion but little more than my method, is conducive to accuracy, especially in investigating the difference between statical and dynamical flexure. A certain finite force presses together the point and the lever. Dividing this force by the minute area of pressure, we find the pressure upon the metal is very great, approaching the crushing pressure. Now, the behavior of metals under great pressure is greatly influenced by the time. But my objection is not merely theoretical; I have myself made experiments upon this method, and, making them as skillfully as I could, I still found great uncertainty in the results.

§2. Six Reasons for the Prosecution of Pendulum Experiments †7

13. [Reason 1.] The first scientific object of a geodetical survey is unquestionably the determination of the earth's figure. Now, it appears probable that pendulum experiments afford the best method of determining the amount of oblateness of the spheroid of the earth; for the calculated probable error in the determination of the quantity in question from the pendulum work already executed does not exceed that of the best determination from triangulation and latitude observations, and the former determination will shortly be considerably improved. Besides, the measurements of astronomical arcs upon the surface of the earth cover only limited districts, and the oblateness deduced from them is necessarily largely affected, as Mr. Schott has remarked, by the old arc of Peru, the real error of which no doubt greatly exceeds that which the calculation attributes to it, so that we cannot really hold it probable that the error of this method is so small as it is calculated by least squares to be. On the other hand, the pendulum determinations are subject to no great errors of a kind which least squares cannot ascertain; they are widely scattered over the surface of the earth; they are very numerous; they are combined to obtain the ellipticity by a simple arithmetical process; and, all things considered, the calculated probable error of the oblateness deduced from them is worthy of unusual confidence. In this connection it is very significant, as pointed out by Colonel Clarke (Geodesy, p. vi), that while the value derived from pendulum work has for a long time remained nearly constant, that derived from measurements of arcs has altered as more data have been accumulated, and the change has continually been in the direction of accord with the other method. It is needless to say that the comparison of the expense of the two methods of obtaining this important quantity is immensely in favor of pendulum work.

14. [Reason 2.] Recent investigations also lead us to attach increased importance to experiments with the pendulum in their connection with metrology. The plan of preserving and transmitting to posterity an exact knowledge of the length of the yard after the metallic bar itself should have undergone such changes as the vicissitudes of time bring to all material objects, was at one time adopted by the British Government. It was afterwards abandoned because pendulum operations had fallen into desuetude, and because doubts had been thrown upon the accuracy of Kater's original measure of the length of the second's pendulum. Yet I do not hesitate to say that this plan should now be revived, for the following reasons.

15. First, because measurements of the length of the second's pendulum, although formerly subject to grave uncertainties, are now secure against all but very small errors. Indeed, we now know that the determinations by Kater and his contemporaries, after receiving certain necessary corrections, are by no means so inaccurate as they were formerly suspected to be. Secondly, metallic bars have now been proved, by the investigations of Professor Hilgard †8 and others, to undergo unexpected spontaneous alterations of their length, so that some check upon these must be resorted to. To this end the late Henri Ste. Claire Deville and Mascart constructed for the International Geodetical Association a metre ruled upon a sort of bottle of platin-iridium, with the idea that the cubic contents of this bottle should be determined from time to time, so as to ascertain whether its dimensions had undergone any change. I am myself charged with, and have nearly completed, a very exact comparison of the length of a metre bar with that of a wave of light, for the same purpose. †9 Neither of these two methods is infallible, however, for the platin-iridium bottle may change its three dimensions unequally, and the solar system may move into a region of space in which the luminiferous ether may have a slightly different density (or elasticity), so that the wave length of the ray of light used would be different. These two methods should therefore be supplemented by the comparatively simple and easy one of accurately comparing the length of the second's pendulum with the metre or yard bar. Thirdly, I do not think it can be gainsaid by any one who examines the facts that the measurements of the length of the second's pendulum by Borda and by Biot in Paris and by Bessel in Berlin do, as a matter of fact, afford us a better and more secure knowledge of the length of their standard bars than we can attain in any other way. So also I have more confidence in the value of the ratio of the yard to the metre obtained by the comparison of the measurements of the length of the second's pendulum at the Kew observatory by Heaviside in terms of the yard and by myself in terms of the metre than I have in all the elaborate and laborious comparisons of bars which have been directed to the same end. I will even go so far as to say that a physicist in any remote station could ascertain the length of the metre accurately to a one hundred thousandth part more safely and easily by experiments with an invariable reversible pendulum than by the transportation of an ordinary metallic bar.

16. A new application of the pendulum to metrology is now being put into practice by me. Namely, I am to oscillate simultaneously a yard reversible pendulum and a metre reversible pendulum. I shall thus ascertain with great precision the ratio of their lengths without any of those multiform comparisons which would be necessary if this were done by the usual method. These two pendulums will be swung, the yard one in the office of the Survey, at a temperature above 62°F., which is the standard temperature of the yard, the other nearly at 0°C., which is the standard temperature of the metre; and thus we shall have two bars compared at widely different temperatures, which, according to ordinary processes, is a matter of great difficulty. The knife-edges of the pendulums will be interchanged and the experiments repeated. Finally, the yard pendulum will be compared with a yard bar and the metre pendulum with a metre bar, and last of all the yard pendulum with its yard bar will be sent to England, the metre pendulum with its metre bar to France, for comparison with the primary standards; and thus it is believed the ratio of yard to metre will be ascertained with the highest present attainable exactitude.

17. [Reason 3.] Geologists affirm that from the values of gravity at different points useful inferences can be drawn in regard to the geological constitution of the underlying strata. For instance, it has been found that when the gravity upon high lands and mountains is corrected for difference of centrifugal force and distance from the earth's centre, it is very little greater than at the sea-level. Consequently it cannot be that there is an amount of extra matter under these elevated stations equal to the amount of rock which projects above the sea-level; and the inference is that the elevations have been mainly produced by vertical and not by horizontal displacements of material. On the other hand, Mendenhall has found that gravity on Fujisan, the well-known volcanic cone of Japan, which is about 12,000 feet high, and which is said to have been upheaved in a single night, about 300 B.C., is as much less than that in Tokio as if the mountain had been wholly produced by horizontal transfer. This conclusion, if correct, must plainly have a decisive bearing upon certain theories of volcanic action. Again, it has long been known that gravity is in excess upon islands, and I have shown that this excess is fully equal to the attraction of the sea-water. This shows that the interior of the earth is not so liquid and incompressible that the weight of the sea has pressed away to the sides the underlying matter. But in certain seas gravity is even more in excess than can be due to the attraction of the ocean, as if they had been receptacles of additional matter washed down from the land. It is evident that only the paucity of existing data prevents inferences like these from being carried much further. On the two sides of the great fault in the Rocky Mountains gravity must be very different, and if we knew how great this difference was we should learn something more about the geology of this region; and many such examples might be cited.

18. [Reason 4.] Gravity is extensively employed as a unit in the measurement of forces. Thus, the pressure of the atmosphere is, in the barometer, balanced against the weight of a measured column of mercury; the mechanical equivalent of heat is measured in foot-pounds, etc. All such measurements refer to a standard which is different in different localities, and it becomes more and more important to determine the amounts of these differences as the exactitude of measurement is improved.

19. [Reason 5.] It may be hoped that as our knowledge of the constitution of the earth's crust becomes, by the aid of the pendulum investigations, more perfected, we shall be able to establish methods by which we can securely infer from the vertical attractions of mountains, etc., what their horizontal attractions and the resulting deflections of the plumb-line must be.

20. [Reason 6.] Although in laying out the plan of a geodetical survey the relative utility of the knowledge of different quantities ought to be taken into account, and such account must be favorable to pendulum work, yet it is also true that nothing appertaining to such a survey ought to be neglected, and that too great stress ought not to be put upon the demands of the practically useful. The knowledge of the force of gravity is not a mere matter of utility alone, it is also one of the fundamental kinds of quantity which it is the business of a geodetical survey to measure. Astronomical latitudes and longitudes are determinations of the direction of gravity; pendulum experiments determine its amount. The force of gravity is related in the same way to the latitude and longitude as the intensity of magnetic force is related to magnetical declination and inclination; and as a magnetical survey would be held to be imperfect in which measurements of intensity were omitted, to the same extent must a geodetical survey be held to be imperfect in which the determinations of gravity had been omitted; and such would be the universal judgment of the scientific world.

Chapter 2: Small Differences of Sensation

§1. Original Paper †1

21. The physiological psychologists assume that two nerve excitations alike in quality will only produce distinguishable sensations provided they differ in intensity by an amount greater than a fixed ratio. The least perceptible difference of the excitations divided by half their sum is what they call the Unterschiedsschwelle. Fechner †2 gives an experiment to prove the fact assumed, namely: He finds that two very dim lights placed nearly in line with the edge of an opaque body show but one shadow of the edge. It will be found, however, that this phenomenon is not a clearly marked one, unless the lights are nearly in range. If the experiment is performed with lateral shifting of one of the lights, and with a knowledge of the effects of a telescope upon the appearance of terrestrial objects at night, it will be found very far from conclusive.

22. The conception of the psychologists is certainly a difficult one to seize. According to their own doctrine, in which the observed facts seem fully to bear them out, the intensity of the sensation increases continuously with the excitation, so that the least increase of the latter must produce a corresponding increase of the former. And, indeed, the hypothesis that a continuous increase of the excitation would be accompanied by successive discrete increments of the sensation, gratuitous as it would be, would not be sufficient to account for a constant Unterschiedsschwelle. We are therefore forced to conclude that if there be such a phenomenon, it has its origin, not in the faculty of sensation, but in that of comparing sensations. In short, if the phenomenon were established, we should be forced to say that there was a least perceptible difference of sensation — a difference which, though existing in sensation, could not be brought into consciousness by any effort of attention. But the errors of our judgments in comparing our sensations seem sufficiently accounted for by the slow and doubtless complicated process by which the impression is conveyed from the periphery to the brain; for this must be liable to more or less accidental derangement at every step of its progress. Accordingly we find that the frequencies of errors of different magnitudes follow the probability curve, which is the law of an effect brought about by the sum of an infinite number of infinitesimal causes. This theory, however, does not admit of an Unterschiedsschwelle. On the contrary, it leads to the method of least squares, according to which the multiplication of observations will indefinitely reduce the error of their mean, so that if of two excitations one were ever so little the more intense, in the long run it would be judged to be the more intense the majority of times. It is true that the astronomers themselves have not usually supposed that this would be the case, because (apart from constant errors, which have no relevancy to the present question) they have supposed this extreme result to be contrary to common sense. But it has seemed to us that the most satisfactory course would be to subject the question to the test of direct experiment. If there be a least perceptible difference, then when two excitations differing by less than this are presented to us, and we are asked to judge which is the greater, we ought to answer wrong as often as right in the long run. Whereas, if the theory of least squares is correct, we not only ought to answer right oftener than wrong, but we ought to do so in a predictable ratio of cases. †3

23. We have experimented with the pressure sense, observing the proportion of errors among judgments as to which is the greater of two pressures, when it is known that the two are two stated pressures, and the question presented for the decision of the observer is, which is which? From the probability, thus ascertained, of committing an error of a given magnitude, the probable error of a judgment can be calculated according to the mathematical theory of errors. If, now, we find that when the ratio of the two pressures is smaller than a certain ratio, the erroneous judgments number one-half of the whole, while the mathematical theory requires them to be sensibly fewer, then this theory is plainly disproved, and the maximum ratio at which this phenomenon is observed the so-called Unterschiedsschwelle. If, on the other hand, the values obtained for the probable error are the same for errors varying from three times to one-fourth of the probable error (the smallest for which it is easy to collect sufficient observations), then the theory of the method of least squares is shown to hold good within those limits, the presumption will be that it extends still further, and it is possible that it holds for the smallest differences of excitation. But, further, if this law is shown to hold good for difference so slight that the observer is not conscious of being able to discriminate between the sensations at all, all reason for believing in an Unterschiedsschwelle is destroyed. The mathematical theory has the advantage of yielding conceptions of greater definiteness than that of the physiologists, and will thus tend to improve methods of observation. Moreover, it affords a ready method for determining the sensibility or fineness of perception and allows of a comparison of one observer's results with the results of others; for, knowing the number of errors in a certain number of experiments, and accepting the conclusions of this paper, the calculated ratio to the total excitation of that variation of excitation, in judging which we should err one time out of four, measures the sensibility. Incidentally our experiments will afford additional information upon the value of the normal average sensibility for the pressure sense, which they seem to make a finer sense than it has hitherto been believed to be. But in this regard two things have to be noted: (1) Our value relates to the probable error or the value for the point at which an error is committed half the time; (2) in our experiments there were two opportunities for judging, for the initial weight was either first increased and then diminished, or vice versa, the subject having to say which of these two double changes was made. It would seem at first blush that the value thus obtained ought to be multiplied by √2(1.414) to get the error of a single judgment. Yet this would hardly be correct, because the judgment, in point of fact, depended almost exclusively on the sensation of increase of pressure, the decrease being felt very much less. The ratio √2(1.414) would therefore be too great, and 1.2 would perhaps be about correct. The advantage of having two changes in one experiment consists in this: If only one change were employed, then some of the experiments would have an increase of excitation only and the others a decrease only; and since the former would yield a far greater amount of sensation than the latter, the nature of the results would be greatly complicated; but when each experiment embraces a double change this difference in the amount of sensation caused by an increase and decrease of pressure affects every experiment alike, and the liability to error is constant. †4

24. Throughout our observations we noted the degree of confidence with which the observer gave his judgment upon a scale of four degrees, as follows:

0 denoted absence of any preference for one answer over its opposite, so that it seemed nonsensical to answer at all.

1 denoted a distinct leaning to one alternative.

2 denoted some little confidence of being right.

3 denoted as strong a confidence as one would have about such sensations.

We do not mean to say that when zero was the recorded confidence, there was absolutely no sensation of preference for the answer given. We only mean that there was no sensation that the observer noticed when attending to his feelings of this sort as closely as he conveniently could, namely, closely enough to mark them on this scale. The scale of confidence fluctuated considerably. Thus, when Mr. Jastrow passed from experiments upon differences of weight of 60, 30, and 15 on the thousand to differences of 20, 10, and 5 on the thousand, although the accuracy of his judgments was decidedly improved, his confidence fell off very greatly, owing to his no longer having the sensation produced by a difference of 60 present to his memory. The estimations of confidence were also rough, and might be improved in future work. The average marks seem to conform to the formula—

m = c log (p/1-p)

where m denotes the degree of confidence on the scale, p denotes the probability of the answer being right, and c is a constant which may be called the index of confidence.

25. To show that this formula approximates to the truth, we compare it with the average marks assigned to estimates of differences for which more than a hundred experiments were made. Mr. Jastrow's experiments are separated into groups, which will be explained below.

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26. The judgments enunciated with any given degree of confidence were more likely to be right with greater differences than with smaller differences. To show this, we give the frequency of the different marks in Mr. Jastrow's second, third, and fourth groups. †5

27. The apparatus used was an adaptation of a "Fairbanks" post-office scale; upon the end of the beam of which was fixed a square enlargement (about one-half inch square), with a flat top, which served to convey the pressure to the finger in a manner to be presently described. This was tightly covered with an India-rubber cap, to prevent sensations of cold, etc., from contact with the metal. A kilogram placed in the pan of the balance brought a pressure of one-fourth of its weight upon the finger. The differential pressure was produced by lowering upon the pan of the balance a smaller pan into which the proper weights could be firmly fixed; this little pan had its bottom of cork, and was placed upon a piece of flannel which constantly remained in the pan of the balance. It was lifted off and on by means of a fine India-rubber thread, which was so much stretched by the weight as certainly to avoid any noise or jar from the momentum of the descending pan. A sufficient weight could also be hung on the beam of the balance, so as to take off the entire pressure from the finger at the end of each experiment. This weight could be applied or removed by means of a cam acting upon a lever; and its bearings upon the beam were guarded by India-rubber. It was found that the use of this arrangement, which removed all annoying irregularities of sensation connected with the removal and replacement of the greater (initial) pressure, rendered the results more uniform and diminished the probable error. It also shortened the time necessary for performing the experiments, so that a series of 25 experiments was concluded before the effects of fatigue were noticeable. It may be mentioned that certain causes tended to the constant decrease of the probable error as the experiments went on, these mainly being an increased skill on the part of the operator and an education of the sensibility of the subject. The finger was supported in such a way as to be lightly but firmly held in position, all the muscles of the arm being relaxed; and the India-rubber top of the brass enlargement at the end of the beam of the balance was never actually separated from the finger. The projecting arm of a filter-stand (the height of which could be adjusted) with some attachments not necessary to detail, gently prevented the finger from moving upwards under the pressure exerted by the weight in the pan. In the case of Mr. Peirce as subject (it may be noted that Mr. Peirce is left-handed, while Mr. Jastrow is strongly right-handed) the tip of forefinger, and in the case of Mr. Jastrow of the middle finger, of the left hand were used. In addition, a screen served to prevent the subject from having any indications whatever of the movements of the operator. It is hardly necessary to say that we were fully on guard against unconsciously received indications.

28. The observations were conducted in the following manner: At each sitting three differential weights were employed. At first we always began and ended with the heaviest, but at a later period the plan was to begin on alternate days with the lightest and heaviest. When we began with the heaviest 25 observations †6 were made with that; then 25 with the middle one, and then 25 with the lightest; this constituted one-half of the sitting. It was completed by three more sets of 25, the order of the weights being reversed. When we began with the lightest the heaviest was used for the third and fourth sets. In this way 150 experiments on each of us were taken at one sitting of two hours.

29. A pack of 25 cards were taken, 12 red and 13 black, or vice versa, so that in the 50 experiments made at one sitting with a given differential weight, 25 red and 25 black cards should be used. These cards were cut exactly square and their corners were distinguished by holes punched in them so as to indicate the scale of numbers (0, 1, 2, 3) used to designate the degree of confidence of the judgment. The backs of these cards were distinguished from their faces. They were, in fact, made of ordinary playing-cards. At the beginning of a set of 25, the pack was well shuffled, and, the operator and subject having taken their places, the operator was governed by the color of the successive cards in choosing whether he should first diminish the weight and then increase it, or vice versa. If the weight was to be first increased and then diminished the operator brought the pressure exerted by the kilogram alone upon the finger of the subject by means of the lever and cam mentioned above, and when the subject said "change" he gently lowered the differential weight, resting in the small pan, upon the pan of the balance. The subject, having appreciated the sensation, again said "change," whereupon the operator removed the differential weight. If, on the other hand, the color of the card directed the weight to be first diminished and then increased, the operator had the differential weight already on the pan of the balance before the pressure was brought to bear on the finger, and made the reverse changes at the command of the subject. The subject then stated his judgment and also his degree of confidence, whereupon the total pressure was at once removed by the cam, and the card that had been used to direct the change was placed face down or face up according as the answer was right or wrong, and with corner indicating the degree of confidence in a determinate position. By means of these trifling devices the important object of rapidity was secured, and any possible psychological guessing of what change the operator was likely to select was avoided. A slight disadvantage in this mode of proceeding arises from the long runs of one particular kind of change, which would occasionally be produced by chance and would tend to confuse the mind of the subject. But it seems clear that this disadvantage was less than that which would have been occasioned by his knowing that there would be no such long runs if any means had been taken to prevent them. At the end of each set the results were of course entered into a book. †7

30. The following tables show the results of the observations for each day: Ratios of pressures. [Subject: Mr. Peirce.] Date. 1.100 1.080 1.060 1.050 1.040 1.030 1.015 Dec. 10 2 errors 13 errors Dec. 13 4 errors 8 errors 15 errors Dec. 17 11 20 errors Dec. 20 7 16 21 errors Jan. 3 14 20 28 Jan. 15 15 29 17 Jan. 22 12 16 20 Jan. 24 6 15 22 Means 2 4 10.4±1.0 13 15 19.3±1.4 21.6±1.1 Calculated from probable error =0.051 4.6±1.0 7.2±1.6 10.7±0.8 12.7±2.1 14.9±2.2 17.2±0.9 21.0±1.1. Average confidence. Observed 1.9 0.9 0.7 0.8 0.3 0.3 0.2 Calculated 1.3 1.0 0.7 0.6 0.5 0.3 0.2 —————————————————————————————————-

The numbers in the columns show the number of errors in fifty experiments. With the average number of errors in a set of fifty we compare the theoretical value of this average as calculated by the method of least squares. The number .051 thus obtained in this case best satisfies the mean number of errors. The numbers affixed with a sign denote, in the upper row the observed (a posteriori) probable error of the mean value as given, in the lower row the calculated (a priori) probable error. The last two lines give the average confidence observed and calculated with each variation of the ratios of pressure. It will be seen that the correspondence between the real and theoretical numbers is close, and closest when the number of sets is large. The probable errors also closely correspond, the observed being, as is natural, slightly larger than the calculated probable errors.

31. The following is a similar table for Mr. Jastrow as subject:

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32. It would obviously be unfair to compare these numbers with any set of theoretical numbers, since the probable error is on the decrease throughout, owing to effects of practice, etc. For various reasons we can conveniently group these experiments into four groups. The first will include the experiments from December 10 to January 22, inclusive; the second from January 24 to February 24, inclusive; the third from March 4 to March 25, inclusive; the fourth from March 30 to the end of the work.

33. The mean results for the different groups are exhibited in the following tables:

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34. The tables show that the numbers of errors follow, as far as we can conveniently trace them, the numbers assigned by the probability curve, †8 and therefore destroy all presumption in favor of an Unterschiedsschwelle. The introduction and retention of this false notion can only confuse thought, while the conception of the mathematician must exercise a favorable influence on psychological experimentation. †9

35. The quantity which we have called the degree of confidence was probably the secondary sensation of a difference between the primary sensations compared. The evidence of our experiments seems clearly to be that this sensation has no Schwelle, and vanishes only when the difference to which it refers vanishes. At the same time we found the subject often overlooked this element of his field of sensation, although his attention was directed with a certain strength toward it, so that he marked his confidence as zero. This happened in cases where the judgments were so much affected by the difference of pressures as to be correct three times out of five. The general fact has highly important practical bearings, since it gives new reason for believing that we gather what is passing in one another's minds in large measure from sensations so faint that we are not fairly aware of having them, and can give no account of how we reach our conclusions about such matters. †10 The insight of females as well as certain "telepathic" phenomena may be explained in this way. †11 Such faint sensations ought to be fully studied by the psychologist and assiduously cultivated by every man.

§2. Later Reflections †12

36. Our knowledge of any subject never goes beyond collecting observations and forming some half-conscious expectations, until we find ourselves confronted with some experience contrary to those expectations. †13 That at once rouses us to consciousness: we turn over our recollections of observed facts; we endeavour so to rearrange them, to view them in such new perspective that the unexpected experience shall no longer appear surprising. This is what we call explaining it, which always consists in supposing that the surprising facts that we have observed are only one part of a larger system of facts, of which the other part has not come within the field of our experience, which larger system, taken in its entirety, would present a certain character of reasonableness, that inclines us to accept the surmise as true, or likely. For example, let a person entering a large room for the first time, see upon a wall projecting from behind a large map that has been pinned up there, three-quarters of an admirably executed copy in fresco of one of Rafael's most familiar cartoons. In this instance the explanation flashes so naturally upon the mind and is so fully accepted, that the spectator quite forgets how surprising those facts are which alone are presented to his view; namely, that so exquisite a reproduction of one of Rafael's grandest compositions should omit one-quarter of it. He guesses that that quarter is there, though hidden by the map; and six months later he will, maybe, be ready to swear that he saw the whole. This will be a case under a logico-psychical law of great importance, to which we may find occasion to revert soon, that a fully accepted, simple, and interesting inference tends to obliterate all recognition of the uninteresting and complex premisses from which it was derived. The brighter the observer's intelligence (unless some circumstance has raised a doubt), the more confident he will soon be that he saw the entire composition. Yet, in fact, the idea of the whole's being on that wall will be merely evolved from his Ichheit: it will be a surmise, conjecture, or guess.

37. We may be aided by previous knowledge in forming our hypotheses. In that case they will not be pure guesses but will be compounds of deductions from general rules we already know, applied to the facts under observation, for one ingredient, and pure guess for the other ingredient. Thus, suppose the surprising facts which puzzle us are the actions of a certain man on a certain occasion; and our conjecture relates to the state of belief that caused such conduct. If we have no previous knowledge of the man, any one state of belief that would account for his conduct might be as good a guess as any other; but if we know that he is particularly inclined, or particularly disinclined, to extravagant beliefs or to any other special kind of belief, we still have to guess; only we shall select our guess from a smaller number of possible hypotheses.

38. In the evolution of science, guessing plays the same part that variations in reproduction take in the evolution of biological forms, according to the Darwinian theory. †14 For just as, according to that theory, the whole tremendous gulf, or ocean rather, between the moner and man has been spanned by a succession of infinitesimal fortuitous variations at birth, so the whole noble organism of science has been built up out of propositions which were originally simple guesses. For my part I refuse to believe that either the one or the other were fortuitous; and indeed I gravely doubt whether there be any tenable meaning in calling them so. As to the biological variations, I will spare the reader my reasons for not believing them fortuitous. For it would only lead us away from our subject. But as to the first guesses out of which science has been developed, I will say a word or two. It is well within bounds to reckon that there are a billion (i.e., a million million) hypotheses that a fantastic being might guess would account for any given phenomenon. For this phenomenon would certainly be more or less connected in the mind of such a being with a million other phenomena (for he would not be restricted to contemporaneous events) and it might be supposed that the special determination of each was connected with the special determinations of each of the others in order to produce the observed phenomenon. I will not carry out this idea further: it suffices to show that according to the doctrine of chances it would be practically impossible for any being, by pure chance, to guess the cause of any phenomenon.

39. There are, indeed, puzzles, and one might well say mysteries, connected with the mental operation of guessing; — yes; more than one. There can, I think, be no reasonable doubt that man's mind, having been developed under the influence of the laws of nature, for that reason naturally thinks somewhat after nature's pattern. This vague explanation is but a surmise; but there is no room to believe that it was merely by luck that Galileo and other masters of science reached the true theories after so few wrong guesses as they did. This power of divining the truths of physics, — for such it is, although it is somewhat imperfect, — is certainly an aid to the instinct for obtaining food, an instinct whose wonders throughout the animal kingdom are exceeded only by that of producing and rearing offspring.

40. This latter function requires all the higher animals to have some insight into what is passing in the minds of their fellows. Man shows a remarkable faculty for guessing at that. Its full powers are only brought out under critical circumstances. . . . †15

41. All the above, be it understood is sober truth, sedulously freed from all exaggeration and colour. If any reader should incline to deem the narrative apocryphal, it will certainly not be the psycholist, equally versed in the theory of his science and skilled in the application of it; for to him the incidents will present no extraordinary features. I suppose almost everybody has had similar experiences. But however frequently such facts may be encountered, there is certainly something a little mysterious in them; they demand explanation. That explanation must itself be conjectural, and must remain so until exact investigation has tested its sufficiency; and unless some new school of psychology should make its appearance, I do not believe that scientific testing of the theory is likely to be performed in our time.

42. I am going to point out a vera causa — a known agency which tends to produce effects like the facts to be explained. But whether it would, under the circumstances described, be sufficient to produce the somewhat surprising facts, or whether it was aided by some other agency that has not suggested itself to my mind, I will not presume to opine.

43. My surmise is that at the bottom of the little mystery is buried a principle often enough asserted but never, I believe, supported by scientific observation, until Professor Joseph Jastrow and I carried through, at the Johns Hopkins University, a certain series of experiments. †16 These experiments were mainly designed for quite another purpose, namely, in order to test Fechner's hypothesis of the "Differenzschwelle," which in no wise concerns us now. I proceed to describe, in outline, the essentials of the experiments. Of the two persons engaged in them, the one acted as experimenter and recorder, while the other, who could neither see nor hear the former, was the "subject" or victim of the experimentation. The latter said, "Ready." Thereupon an automatic arrangement, namely, by exposing a card from a well shuffled pack, indicated to the experimenter what pressure he was to bring to bear upon the finger of the subject, who carefully observed the degree of his feeling of pressure. When he was satisfied, perhaps after from five to twenty seconds, he said "Change." Thereupon by an exceedingly delicate contrivance (to avoid any sudden change or shock), the experimenter, according to an automatic operation of chance, either increased or diminished the pressure by less than one per cent of itself. The subject observed the new feeling of pressure, and again said "Change," whereupon the first pressure was brought back. These experiments were interspersed (by the automatic chance arrangement which was intended, of course, to exclude, as far as possible, mental action on the part of the experimenter), by others in which the changes of pressure were somewhat more considerable. The subject having observed the three states of feeling of pressure (of which the first and last were equal), first pronounced one or another of the four numerals, Naught, One, Two, Three. "Three" would mean that he was sure, or almost sure, of being able to say whether the middle pressure was greater or less than the other two. "Two" would mean that he was by no means sure, yet inclined to think he could tell. "One" would mean that he did not think he really perceived any difference; yet suspected that he perhaps might. "Naught" would mean that he was sure he could not perceive the slightest variation of pressure. Having thus indicated the degree of his confidence, he was obliged to say whether the middle pressure was greater or less than the others. In case his confidence was zero, this declaration would be (to his own consciousness) a purely random one, though he would avoid any particular regularity in his declarations, or any great preponderance of either "greater" or "lesser." Of course he never received the slightest intimation of whether he was right or wrong.

44. When our course of experiments had been carried on two hours daily (with such precautions against fatigue as the imperfect psychology of twenty-five years ago prescribed), and for about a month it was found that of the answers supposed to be given at random, which were a good half of the whole number and must, I think (I have not before me the record, which is given in Vol. III of the Memoirs of the U. S. National Academy of Sciences), †17 have approached a thousand in number, about three out of every five were correct. That is to say, among all those cases in which the subject, after carefully searching his consciousness, felt quite sure he had experienced no variation of the sense of pressure, though a change and reverse change had really been made; and had accordingly said, quite at random, as he thought, that the middle pressure was greater or less than the first and last, what he so said agreed with the real fact half as often again as it disagreed. A reader inexpert in dealing with probabilities may think that so small a preponderance of true answers might have come about by chance. But in truth it is among the most certain things that we know that this was not so. So much is demonstrated truth, quite unquestionable. But if you go on to ask me upon what principle I would explain the fact that a person who, after the closest scrutiny of his consciousness, had pronounced that there was no trace of perceptible difference between two sensations of pressure, should in the very next breath have correctly said which of them was the greater, in three cases out of every five, my confidence largely evaporates. I can, indeed, mention a cause which undoubtedly exists and which must have acted toward producing that indubitable fact; but I cannot say whether that cause would or would not have been sufficient, by itself, for that result.

45. Everybody knows how self-consciousness makes one awkward and may even quite paralyze the mind. Nobody can have failed to remark that mental performances that are gone through with lightly are apt to be more adroit than those in which every little detail is studied while the action is proceeding, nor how a great effort — say to write a particularly witty letter — or even to recall a word or name that has slipped one's memory may spoil one's success. Perhaps it is because in trying very hard we are thinking about our effort instead of about the problem in hand. At any rate my own experience is that self-consciousness, and especially conscious effort, are apt to carry me to the verge of idiocy and that those things that I have done spontaneously were the best done. Now, in the experiments I have described, the so-called "subject," the victim of the experimentation, would not seldom sit in the darkened and silent room, straining with all his might for two or three minutes, to detect the slightest difference between two pressures. Finding himself unable to do so he would utter his "zero" that this inability might be recorded. Thereupon all straining ceased; for all it then remained for him to do was mention at random which one of the pressures he would mark as the heavier — and here his perfect unconsciousness greatly increased his power of discrimination — a discrimination below the surface of consciousness, and not recognized as a real judgment, yet in very truth a genuine discrimination, as the statistical results showed. The circumstances of my talking with the waiters on the boat were almost identical. While I was going through the row, chatting a little with each, I held myself in as passive and receptive a state as I could. When I had gone through the row I made a great effort to detect in my consciousness some symptoms of the thief, and this effort, I suppose, prevented my success. But then finding I could detect nothing I said to myself, "Well, anyway, I must fasten on someone, though it be but a random choice," and instantly I knew which of the men it was. . . .

46. I could tell many other true tales of successful guessings; but I have mentioned here two principles which I have been led to conjecture furnish at least a partial explanation of the mystery that overhangs this singular guessing instinct. I infer in the first place that man divines something of the secret principles of the universe because his mind has developed as a part of the universe and under the influence of these same secret principles; and secondly, that we often derive from observation strong intimations of truth, without being able to specify what were the circumstances we had observed which conveyed those intimations.

47. It is a chapter of the art of inquiry.

48. Our faculty of guessing corresponds to a bird's musical and aeronautic powers; that is, it is to us, as those are to them, the loftiest of our merely instinctive powers. I suppose that if one were sure of being able to discriminate between the intimations of this instinct and the self-flatteries of personal desire, one would always trust to the former. For I should not rate high either the wisdom or the courage of a fledgling bird, if, when the proper time had come, the little agnostic should hesitate long to take his leap from the nest on account of doubts about the theory of aerodynamics.

Book 2: Scientific Method

Chapter 1: Scientific Method

§1. Science †1

49. What is Science? We cannot define the word with the precision and concision with which we define Circle, or Equation, any more than we can so define Money, Government, Stone, Life. The idea, like these, and more than some of them, is too vastly complex and diversified. It embodies the epitome of man's intellectual development. We can only single out some leading properties of it, and different people will select these differently. To most men, including all who are outside of the world of science, the term means a particular kind of knowledge. Wherein lies the essential peculiarity of this knowledge? Some thinkers agree with the ancient Greeks in making it consist in the Method of knowing, the manner in which the truth is laid hold on. But the majority of modern writers regard the Systematic character of the doctrine itself as more characteristic. Both marks of scientific knowledge are exceedingly important; but the former is deeper cut, and because it is at present less noticed, more needs to be emphasized. Plato is quite right in saying that a true belief is not necessarily knowledge. A man may be willing to stake his life upon the truth of a doctrine which was instilled into his mind before his earliest memories without knowing at all why it is worthy of credence; and while such a faith might just as easily be attached to a gross superstition as to a noble truth, it may, by good luck, happen to be perfectly true. But can he be said to know it? By no means: to render the word knowledge applicable to his belief, he must not only believe it, but must know, — I will not say, with the ancients, the rationale of the real fact, as a reality, — but must know what justifies the belief, and just WHY and HOW the justification is sufficient. I beg that the reader will turn this over in his mind and satisfy himself as to how far what I am saying is true. For it is not a very simple point but is one that I intend to insist upon.

50. Before knowledge of any subject can be put to any extensive use, it is almost indispensable that it should be made as thorough and complete as possible, until every detail and feature of the matter is spread out as in a German handbook. But if I am asked to what the wonderful success of modern science is due, I shall suggest that to gain the secret of that, it is necessary to consider science as living, and therefore not as knowledge already acquired but as the concrete life of the men who are working to find out the truth. Given a body of men devoting the sum of their energies to refuting their present errors, doing away with their present ignorance, and that not so much for themselves as for future generations, and all other requisites for the ascertainment of truth are insured by that one. Strictly speaking, one need not ask for so much as that. Given the oxygen, hydrogen, carbon, nitrogen, sulphur, phosphorus, etc., in sufficient quantities and under proper radiations, and living protoplasm will be produced, will develop, will gain power of self-control, and the scientific passion is sure to be generated. Such is my guess. Science was preordained, perhaps, on the Sunday of the Fiat lux.

51. Coming down to the more immediate and more pertinent causes of the triumph of modern science, the considerable numbers of the workers, and the singleness of heart with which, — (we may forget that there are a few self-seekers who succeed in gaining the power to make themselves more despised than they naturally would be; they are so few,) — they cast their whole being into the service of science lead, of course, to their unreserved discussions with one another, to each being fully informed about the work of his neighbour, and availing himself of that neighbour's results; and thus in storming the stronghold of truth one mounts upon the shoulders of another who has to ordinary apprehension failed, but has in truth succeeded by virtue of the lessons of his failure. This is the veritable essence of science. It is in the memory of these concrete living gests that we gain the speaking portraiture of true science in all her life and beauty.

52. The point of view just explained enables us to perceive that a particular branch of science, such as Physical Chemistry or Mediterranean Archeology, is no mere word, manufactured by the arbitrary definition of some academic pedant, but is a real object, being the very concrete life of a social group constituted by real facts of inter-relation, — as real an object as a human carcase, which is made one by the inter-relations of its millions of cells. Any two of these groups (and with them the sciences, which are their lives,) may be related, as to the matter of the groups in either of the three modes of relationship of material wholes; that is, either by Inclusion, one being a part of another; or by Intersection, when each has one part in common with the other, and another part foreign to the other; or by Exclusion, when the two have no part in common. But of greater importance are the dynamical relations between the different sciences, by which I mean that one often acts upon another, not by bringing forward any reason or principle, but as it were with a compulsive quality of action. Thus one group may stimulate another by demanding the solution of some problem. In this way, the practical sciences incessantly egg on researches into theory. For considerable parts of chemical discovery we have to thank the desire to find a substitute for quinine or to make quinine itself synthetically, to obtain novel and brilliant dye-stuffs, and the like. The mechanical theory of heat grew out of the difficulties of steam navigation. For it was first broached by Rankine while he was studying how best to design marine engines. Then again, one group of scientists sometimes urges some overlooked phenomenon upon the attention of another group. It was a botanist who called van't Hoff's attention to the dependence of the pressure of sap in plants upon the strength of the solution, and thus almost instantaneously gave a tremendous impulse to physical chemistry. In 1820, Kästner, a manufacturer of cream of tartar in Mulhouse, called the attention of chemists to the occasional, though rare, occurrence in the wine casks of a modification of tartaric acid, since named racemic acid; and from the impulse so given has resulted a most important doctrine of chemistry, that of the unsymmetric carbon atom, as well as the chief discoveries of Pasteur, with their far-reaching blessings to the human species.

53. It is now time to explain the classification of this chapter, what it aims to be, by what means that aim has been pursued, and how nearly it seems to have been attained. Two questions have to be answered at the outset: What is here meant by science? And what is meant by a science, one of the unit species out of which the system is built up? The spirit of this book is always to look upon those aspects of things which exhibit whatever of living and active there is in them.

54. The prevalent definition of a science, the definition of Coleridge, which influenced all Europe through the Encyclopaedia Metropolitana, that science is systematized knowledge, is an improvement upon a statement of Kant (Metaphysische Anfangsgründe der Naturwissenschaft: 1786): "Eine jede Lehre, wenn sie ein System, dass ist, ein nach Principien geordnetes Ganzes der Erkenntniss sein soll, heisst Wissenschaft." †2 Yet it is to be noted that knowledge may be systematic or "organized," without being organized by means of general principles. Kant's definition, however, is only a modification of the ancient view that science is the knowledge of a thing through its causes, — the comprehension of it, as we might say, — as being the only perfect knowledge of it. In short, the Coleridgian definition is nothing but the last development of that sort of philosophy that strives to draw knowledge out of the depths of the Ich-heit. If, on the other hand, one opens the works of Francis Bacon, one remarks that, with all the astounding greenness and inexperience of his views of science, in some respects he is really a scientific man himself. He met his death as the consequence of an experiment. True, it was rather a foolish one; but what a monument to the genuineness of his intelligence, that he, a great legal light, should, at the age of sixty-six, have perished from his zeal in performing disagreeable and dangerous laboratory work that he thought might go toward teaching him something of the nature of true science! For him man is nature's interpreter; and in spite of the crudity of some anticipations, the idea of science is, in his mind, inseparably bound up with that of a life devoted to singleminded inquiry. That is also the way in which every scientific man thinks of science. That is the sense in which the word is to be understood in this chapter. Science is to mean for us a mode of life whose single animating purpose is to find out the real truth, which pursues this purpose by a well-considered method, founded on thorough acquaintance with such scientific results already ascertained by others as may be available, and which seeks coöperation in the hope that the truth may be found, if not by any of the actual inquirers, yet ultimately by those who come after them and who shall make use of their results. It makes no difference how imperfect a man's knowledge may be, how mixed with error and prejudice; from the moment that he engages in an inquiry in the spirit described, that which occupies him is science, as the word will here be used.

55. By a specific science will be meant a group of connected inquiries of sufficient scope and affinity fitly to occupy a number of independent inquirers for life, but not capable of being broken up into smaller coexclusive groups of this description. For since we are to consider science in general as a mode of life, it is proper to take as the unit science the scientific mode of life fit for an individual person. But science being essentially a mode of life that seeks coöperation, the unit science must, apparently, be fit to be pursued by a number of inquirers.

56. It seems plain that, with these definitions, the classification cannot be concerned with all possible sciences, but must be confined to actually realized sciences. If, however, this limitation is to be maintained, the question will arise, To what date or stage of scientific development is the classification to relate? According to the general spirit of this book, which values everything in its relation to Life, knowledge which is altogether inapplicable to the future is nugatory. Consequently, our classification ought to have reference to the science of the future, so far as we are now able to foresee what the future of science is to be. It will therefore be upon the soil of the near future of science that we shall endeavor to plant our flag. If it be objected that we cannot know enough of the science of the future to classify it accurately, the reply would be that even if all faults of classification could be eliminated by remaining on the threshold of the future, it would still be necessary to advance further. For all the applicability of any writing, though it be not (like this,) the fruit of near half a century of study, must evidently be subsequent to its composition, and all its significance for that time has reference to a time still later. But when the objector comes to see the various imperfections that will have to be confessed in that part of the classification which concerns the present state of science, he will probably be disposed himself to acknowledge that its standard will not be much lowered by the danger of mistake about what is likely soon to be discovered.

57. Meantime, let it not be understood that the classification is to ignore the scientific discoveries of the past. For the memoirs of that work are not so poor as not to merit being read critically, precisely as we shall read the memoirs of tomorrow. Such reading is, therefore, of the nature of scientific inquiry. True, it is not original research; but there is original research still to be done in the same specific science. For none of the sciences of the past is finished. If it be one of the positive sciences that is in question, there is not a single conclusion belonging to it which has in the past been made sufficiently precise or sufficiently indubitable. If it be a branch of mathematics, its propositions require to be further generalized, as well as to be more accurately limited. For these reasons all the old science that still stands is to be retained in the classification, but in its most modern forms.

58. The only remaining instinct on our list is the Gnostic Instinct, or curiosity. In one sense, the sciences that are practically ministrant to this are the Theoretical Sciences; but this remark leads us to signalize a distinction the neglect of which is the source of several of the most fatal errors into which philosophers have fallen. It is quite true that the Gnostic Instinct is the cause of all purely theoretical inquiry, and that every discovery of science is a gratification of curiosity. But it is not true that pure science is or can be successfully pursued for the sake of gratifying this instinct. Indeed, if it were so pursued, it would not be true that this instinct was the cause of it. Its motive would then be the Gust-Instinct, or love of pleasure. One wish may be that another wish should be gratified; but no wish can be that that very wish should be gratified. For in that case, the wish would not have any object at all, and having no object it would not be a wish. The case is precisely like that of an assertion which should have no other subject than itself. For a wish is a sort of proposition. To long for anything is to judge it to be good and urgently good. No doubt every assertion implies that it is itself true; †3 but it cannot consist of that alone; and so every wish that is reflective wishes itself gratified; but it must wish something else, besides. Hence, the hedonist, who opines that man can wish for nothing but pleasure, has fallen into a damnable error from a mere confusion of thought. We should commit the same error if we supposed the gratification of curiosity were the sole, or the principal, object of theoretical science. Curiosity is their motive; but the gratification of curiosity is not their aim.

§2. Logic and Scientific Method †4

59. It might be supposed that logic taught that much was to be accomplished by mere rumination, though every one knows that experiment, observation, comparison, active scrutiny of facts, are what is wanted, and that mere thinking will accomplish nothing even in mathematics. Logic had certainly been defined as the "art of thinking," and as the "science of the normative laws of thought." But those are not true definitions. "Dyalectica," says the logical text-book of the middle ages, "est ars artium et scientia scientiarum, ad omnium aliarum scientiarum methodorum principia viam habens," †5 and although the logic of our day must naturally be utterly different from that of the Plantagenet epoch, yet this general conception that it is the art of devising methods of research, — the method of methods, — is the true and worthy idea of the science. Logic will not undertake to inform you what kind of experiments you ought to make in order best to determine the acceleration of gravity, or the value of the Ohm; but it will tell you how to proceed to form a plan of experimentation.

60. It is impossible to maintain that the superiority of the science of the moderns over that of the ancients is due to anything but a better logic. No one can think that the Greeks were inferior to any modern people whatever in natural aptitude for science. We may grant that their opportunities for research were less; and it may be said that ancient astronomy could make no progress beyond the Ptolemaic system until sufficient time had elapsed to prove the insufficiency of Ptolemy's tables. The ancients could have no dynamics so long as no important dynamical problem had presented itself; they could have no theory of heat without the steam-engine, etc. Of course, these causes had their influence, and of course they were not the main reason of the defects of the ancient civilization. Ten years' astronomical observations with instruments such as the ancients could have constructed would have sufficed to overthrow the old astronomy. The great mechanical discoveries of Galileo were made with no apparatus to speak of. If, in any direction whatever, the ancients had once commenced research by right methods, opportunities for new advances would have been brought along in the train of those that went before. But read the logical treatise of Philodemus; see how he strenuously argues that inductive reasoning is not utterly without value, and you see where the fault lay. When such an elementary point as that needed serious argumentation it is clear that the conception of scientific method was almost entirely wanting.

61. Modern methods have created modern science; and this century, and especially the last twenty-five years, have done more to create new methods than any former equal period. We live in the very age of methods. Even mathematics and astronomy have put on new faces. Chemistry and physics are on completely new tracks. Linguistics, history, mythology, sociology, biology, are all getting studied in new ways. Jurisprudence and law have begun to feel the impulse, and must in the future be more and more rapidly influenced by it.

62. This is the age of methods; and the university which is to be the exponent of the living condition of the human mind, must be the university of methods.

63. Now I grant you that to say that this is the age of the development of new methods of research is so far from saying that it is the age of the theory of methods, that it is almost to say the reverse. Unfortunately practice generally precedes theory, and it is the usual fate of mankind to get things done in some boggling way first, and find out afterward how they could have been done much more easily and perfectly. And it must be confessed that we students of the science of modern methods are as yet but a voice crying in the wilderness, and saying prepare ye the way for this lord of the sciences which is to come.

64. Yet even now we can do a little more than that. The theory of any act in no wise aids the doing of it, so long as what is to be done is of a narrow description, so that it can be governed by the unconscious part of our organism. For such purposes, rules of thumb or no rules at all are the best. You cannot play billiards by analytical mechanics nor keep shop by political economy. But when new paths have to be struck out, a spinal cord is not enough; a brain is needed, and that brain an organ of mind, and that mind perfected by a liberal education. And a liberal education — so far as its relation to the understanding goes — means logic. That is indispensable to it, and no other one thing is.

65. I do not need to be told that science consists of specialties. I know all that, for I belong to the guild of science, have learned one of its trades and am saturated with its current notions. †6 But in my judgment there are scientific men, all whose training has only served to belittle them, and I do not see that a mere scientific specialist stands intellectually much higher than an artisan. I am quite sure that a young man who spends his time exclusively in the laboratory of physics or chemistry or biology, is in danger of profiting but little more from his work than if he were an apprentice in a machine shop.

66. The scientific specialists — pendulum swingers †7 and the like — are doing a great and useful work; each one very little, but altogether something vast. But the higher places in science in the coming years are for those who succeed in adapting the methods of one science to the investigation of another. That is what the greatest progress of the passing generation has consisted in. Darwin adapted to biology the methods of Malthus and the economists; Maxwell adapted to the theory of gases the methods of the doctrine of chances, and to electricity the methods of hydrodynamics. Wundt adapts to psychology the methods of physiology; †8 Galton adapts to the same study the methods of the theory of errors; Morgan adapted to history a method from biology; Cournot adapted to political economy the calculus of variations. The philologists have adapted to their science the methods of the decipherers of dispatches. The astronomers have learned the methods of chemistry; radiant heat is investigated with an ear trumpet; the mental temperament is read off on a vernier.

67. Now although a man needs not the theory of a method in order to apply it as it has been applied already, yet in order to adapt to his own science the method of another with which he is less familiar, and to properly modify it so as to suit it to its new use, an acquaintance with the principles upon which it depends will be of the greatest benefit. For that sort of work a man needs to be more than a mere specialist; he needs such a general training of his mind, and such knowledge as shall show him how to make his powers most effective in a new direction. That knowledge is logic.

68. In short, if my view is the true one, a young man wants a physical education and an aesthetic education, an education in the ways of the world and a moral education, and with all these logic has nothing in particular to do; but so far as he wants an intellectual education, it is precisely logic that he wants; and whether he be in one lecture-room or another, his ultimate purpose is to improve his logical power and his knowledge of methods. To this great end a young man's attention ought to be directed when he first comes to the university; he ought to keep it steadily in view during the whole period of his studies; and finally, he will do well to review his whole work in the light which an education in logic throws upon it.

69. I should be the very first to insist that logic can never be learned from logic-books or logic lectures. The material of positive science must form its basis and its vehicle. Only relatively little could be done by the lecturer on method even were he master of the whole circle of the sciences. Nevertheless, I do think that I can impart to you something of real utility, and that the theory of method will shed much light on all your other studies.

70. The impression is rife that success in logic requires a mathematical head. But this is not true. The habit of looking at questions in a mathematical way is, I must say, of great advantage, and thus a turn for mathematics is of more or less service in any science, physical or moral. But no brilliant talent for mathematics is at all necessary for the study of logic.

71. The course which I am to give this year begins with some necessary preliminaries upon the theory of cognition. †9 For it is requisite to form a clear idea at the outset of what knowledge consists of, and to consider a little what are the operations of the mind by which it is produced. But I abridge this part of the course as much as possible, partly because it will be treated by other instructors, and partly because I desire to push on to my main subject, the method of science.

72. I next take up syllogism, the lowest and most rudimentary of all forms of reasoning, but very fundamental because it is rudimentary. †10 I treat this after the general style of De Morgan, with references to the old traditional doctrine. Next comes the logical algebra of Boole, a subject in itself extremely easy, but very useful both from a theoretical point of view and also as giving a method of solving certain rather frequently occurring and puzzling problems. From this subject, I am naturally led to the consideration of relative terms. The logic of relatives, so far as it has been investigated, is clear and easy, and at the same time it furnishes the key to many of the difficulties of logic, and has already served as the instrument of some discoveries in mathematics. An easy application of this branch of logic is to the doctrine of breadth and depth or the relations between objects and characters. I next introduce the conception of number, and after showing how to treat certain statistical problems, I take up the doctrine of chances. A very simple and elegant mathematical method of treating equations of finite differences puts the student into possession of a powerful instrument for the solution of all problems of probability that do not import difficulties extraneous to the theory of probability itself.

73. We thus arrive at the study of that kind of probable inference that is really distinctive; that is to say, Induction in its broadest sense — Scientific Reasoning. The general theory of the subject is carefully worked out with the aid of real examples in great variety, and rules for the performance of the operation are given. These rules have not been picked up by hazard, nor are they merely such as experience recommends; they are deduced methodically from the general theory.

74. Finally, it is desirable to illustrate a long concatenation of scientific inferences. For this purpose we take up Kepler's great work, De Motu Stellae Martis, the greatest piece of inductive reasoning ever produced. Owing to the admirable and exceptional manner in which the work is written, it is possible to follow Kepler's whole course of investigation from beginning to end, and to show the application of all the maxims of induction already laid down.

75. In order to illustrate the method of reasoning about a subject of a more metaphysical kind, I shall then take up the scientific theories of the constitution of matter.

76. Last of all, I shall give a few lectures to show what are the lessons that a study of scientific procedure teaches with reference to philosophical questions, such as the conception of causation and the like.

77. I will assume, then, that scientific doubt never gets completely set to rest in regard to any question until, at last, the very truth about that question becomes established. †11 Taking the phenomenon as a whole, then, without considering how it is brought about, science is foredestined to reach the truth of every problem with as unerring an infallibility as the instincts of animals do their work, this latter result like the former being brought about by some process of which we are as yet unable to give any account. It is, we will say, the working of the human instinct. It is not (always considering it in its entirety,) of a rational nature, since, being infallible, it is not open to criticism, while "rational" means essentially self-criticizing, self-controlling and self-controlled, and therefore open to incessant question. But this instinctive infallibility is brought about by the exercize of reason, which is all along subject to blunder and to go wrong. The manner in which this comes about may be, I will not quite say illustrated, but may be rendered intelligible, by the following skeletal example. I call it skeletal because it involves the one character of research which is here to be considered, while attempting no representation of it in other respects. Let us suppose, then, that you have a die which may, for all you know, be loaded; and that you proceed to experiment upon it by throwing it repeatedly, counting as you go the total number of throws and also the number of them which turn up the ace side. For the sake of simplicity, I will suppose that the die is really perfect, although you do not know that it is so. After you have thrown it six times, it will be more likely to give either no ace or more than one ace than to give just one. Namely, there is one chance in three that there will be no ace in the first six throws, there are two chances in five that there will be just one, one chance in five that there will be just two; and there will remain one chance in fifteen that there will be more than two aces. Suppose you go on throwing the die a great many times, and after each throw you divide the number of aces that have turned up by the whole number of throws so far. The quotient will be [the] result for the probability of throwing an ace with this die. You will get a new and amended, though not always a really improved, result after every throw. Now although the throws are purely fortuitous, so that to most questions about them only probable answers can be given, yet one thing will certainly happen. Namely, sooner or later, probably very soon, but it may be only very late, yet certainly at length, a time will come after which all your values for the probability of throwing an ace with this die will be correct in the first figure after the decimal point. A later time there will be after which all the successive determinations will be correct in the first two figures, and so on. You will never be certain that that time has come, but it certainly some time will have come. Thus to the question, What is the first figure of the probability?; to the question, What are the first two figures, etc.; all the answer you will obtain will after a time be free from error. This will be the necessary result. Now that which is necessarily inerrant may in a somewhat indefinite sense be fairly called infallible. Thus, a skillful use of fortuitous events will bring infallibly correct replies to an endless series of questions. This kind of infallibility, which may [be], for aught we know, not to say quite probably is, the infallibility of the instinct of animals, is certainly the only kind of infallibility that can be attributed to the results of science, inasmuch as we can so little know when the very truth is reached that even the second law of motion is at this moment under indictment. Moreover, when we come to subject the processes of science to criticism, we shall find it impossible to deny that a conditional form of this kind of infallibility must be attributed to science.

78. In the light of what has been said, what are we to say to that logical fatalism whose stock in trade is the argument that I have already indicated? I mean the argument that science is predestined to reach the truth, and that it can therefore make no difference whether she observes carefully or carelessly nor what sort of formulae she treats as reasons. The answer to it is that the only kind of predestination of the attainment of truth by science is an eventual predestination, — a predestination aliquando denique. Sooner or later it will attain the truth, nothing more. It means that if you take the most pigheaded and passionate of men who has sworn by all the gods that he never will allow himself to believe the earth is round, and give him time enough, and cram that time with experience in the pertinent sphere, and he will surely come to and rest in the truth about the form of the earth. Such is the infallibility of science. But the secret of the matter is that the man's wilfulness and prejudice will break down before such experience. Such, at least, must be our assumption, if we are to adhere to our faith in the infallibility of science. So far as this assumption goes beyond ordinary everyday experience, it rests on the deeper assumption that that which experience has done for generations of men, who a thousand years ago were substantially in that man's plight, it would do for an individual who were to go through the experiences that those generations have gone through. If one does not believe in this, then the present question does not arise. Our belief in the infallibility of science, which alone prompts the fatalistic suggestion, rests upon our experience of the overwhelming rationalizing power of experience. As long as the man keeps to his determination to exclude from his thoughts whatever might tend to make him assent to the proposition that the earth is round, he certainly will not come to that truth. Granting, therefore, that it is of the nature of experience to develope albuminous matter into rational brain, and to make the mind unceasingly agitate doubt until it finally comes to repose in the true belief, — which is only a more developed way of formulating our belief in the infallibility of science, it is entirely uncertain when the truth will be reached. It will be reached; but only after the investigator has come, first, to a conception of the nature of truth, and to a worship of it as the purest emanation of That which is creating the universe, and then, to an understanding of the right method to absorb it from the universe of experience. It will infallibly be reached sooner or later, if favorable conditions continue; but man having a short life, and even mankind not a very long one, the question is urgent, How soon? And the answer is, as soon as a sane logic has had time to control conclusions. Everything thus depends upon rational methods of inquiry. They will make that result as speedy as possible, which otherwise would have kicked its heels in the anteroom of chance. Let us remember, then, that the precise practical service of sound theory of logic is to abbreviate the time of waiting to know the truth, to expedite the predestined result. But I here use the words 'abbreviate' and 'expedite' in a peculiar sense. Imagine a derelict wreck to be floating about on the ocean; and suppose that it will be driven hither and thither until it chances to be cast upon a shore. Then, a vessel which should go and take that derelict in tow and deliberately strand it upon the nearest shore, would be "abbreviating" or "expediting" the fulfillment of the destiny of that derelict in the same sense in which I hold that logic "abbreviates" inquiry, and "expedites" its result. It changes a fortuitous event which may take weeks or may take many decennia into an operation governed by intelligence, which will be finished within a month. This is the sense in which logic "abbreviates" and "expedites" the attainment of truth.

§3. Scientific Method †12

79. Scientific Method: The general method of successful scientific research. The following are some of its characteristics. Cf. Science. †13

80. (1) The student's first step is to form a perfectly definite and consistent idea of what the problem really is; then he ought to develop the mathematics of the subject in hand as far as possible; and to establish a mathematical method appropriate to the particular problem, if it be one which allows exact treatment. As examples and models of what is meant, may be mentioned Maxwell's researches on colour sensation in the Philos. Trans. for 1860, Flinders Petrie's book Inductive Metrology, the last chapters of Pearson's Grammar of Science. Of course, as the student's understanding of the matter advances, he will return to this first task, and continually improve upon his first essays.

81. The second step will be to consider the logic and methodeutic of the research in hand, unless it is itself a question of pure mathematics, where the logic is inseparable from the mathematics. He will do well to study the manner in which questions somewhat analogous to his own have been successfully resolved in widely different fields; for the greatest advantage has accrued from the extension of methods from one subject to a widely different one, especially from simple to intricate matters.

82. The third step should be to reform his metaphysics, if the question is a broad one. Perhaps he thinks he has no metaphysics, and does not wish to have any. That will be a sure sign that he is badly handicapped with metaphysics of the crudest quality. The only way to disburden himself of it is to direct his attention to it. But he cannot reduce himself to anything like absolute scepticism in metaphysics without arresting his work.

83. The fourth step will be to study the laws of the phenomena dealt with, so far as they can be made out at this stage. The general order of discovery in the nomological sciences is first to pick up the phenomena by excursions in those fields in which they are to be found, with alertness of observation, with those clear ideas that make the new fact instantly recognizable as new, and with the energy that seizes upon the faint trace and follows it up. Witness the manner in which all the new phenomena of radiation have been brought to light during the last generation: cathode rays, X rays, Becquerel rays, etc. After making some acquaintance with the phenomena, the next discovery is of their laws (nomological). In the light of one's metaphysics and general conception of the department of truth dealt with, one considers what different hypotheses have any claims to investigation. The leading considerations here will be those of the 'economics' of research. †14 If, for example, a hypothesis would necessitate an experimental result that can be cheaply refuted if it is not true, or would be greatly at variance with preconceived ideas, that hypothesis has a strong claim to early examination. But one must not give up a hypothesis too readily. Many a discovery has been missed by that fault. Gravitation would have been known a decade earlier if Newton had not hastily thought it refuted, and so set back all the subsequent history of physics by something like that amount of time lost. It is likely that thousands of persons more will die of consumption — as remote as that may seem — than would have died if he had not made that error. The testing of the hypothesis proceeds by deducing from it experimental consequences almost incredible, and finding that they really happen, or that some modification of the theory is required, or else that it must be entirely abandoned. The law of the phenomena once made out, it only remains to measure with precision the values of the coefficients in the equation which expresses it.

84. The problem under investigation may not be of a nomological kind. Not that the phenomena are not conceivably subject to law, so that the subject may ultimately be received into the nomological sciences, — as chemistry, for example, promises some day to mature into a nomological science; but in the present state of knowledge the question, we will suppose, cannot be so studied. Still, a certain amount of nomological study is a necessary preliminary to engaging with the problem itself. Biology calls for aid from physiology. The student who is studying the growth of languages must avail himself of all the knowledge that there is about the physics of speech sounds. In case, then, the question has not yet reached the nomological stage, the sixth step in the work will be of a classificatory nature. Such order, of a more or less imperfect kind, as can be traced in the phenomena must be made out. Students of the classificatory sciences like to call such regularities laws. The tendency is a symptom of health; because it shows that law is their ideal, and that they are striving to bring their sciences to the nomological stage. But such orderlinesses as 'Grimm's Law' (see Gender) and 'Mendeléef's Law' are not laws in the sense in which the association of ideas and the three laws of motion are laws. They are not satisfactory for a minute. They are nothing that can blend with our metaphysics; they are not of a universal kind; and they are not precise. You may imagine that there might be a chain of more and more universal, precise, and reasonable regularities leading from these to those. But there is, in fact, a great gap, which has to be acknowledged. A hypothesis may be made about the cause of the three laws of motion; but we can have no present hopes of satisfactorily proving the truth of such a thing; while we at once set to work with great hopes of making considerable steps towards explaining Mendeléef's Law and Grimm's Law. But the most important distinction between true laws and such regularities lies in the very different way in which we proceed to the discovery of the one and of the other. The whole attitude of mind is so different that it is difficult to believe that the same man would have great success in the two tasks. We have seen in our day the establishment of a grand example of each kind, the Law of the Conservation of Energy (q.v.) and the Periodic Law. The one dealt with a small number of observations. Exactitude was the main thing. The hypothesis itself sprang almost immediately from the natural light of reason. In the other case, it was necessary with a positive effort to put ideas of exactitude aside and to find order in a great tangle of facts.

85. Perhaps the problem in hand relates to one of those sciences basely called descriptive, that is, sciences which study, not classes of facts, but individual facts, such as history, descriptive astronomy, geography. No science is merely descriptive. These sciences are investigations of causes. The historian's facts of observation are not those contained in his text, but those mentioned in the foot-notes — the documents and monuments. †15 It is the supposed causes of these which make the text. Nor is he contented with a mere chronicle of striking public events; he endeavours to show what the hidden causes of them were. So the astronomer's real business is to prove the Nebular Hypothesis (q.v.) or whatever ought to replace it. The geologist does not merely make a geological map, but shows how the existing state of things must have come to pass. To do this the historian has to be a profound psychologist, the geologist a master of physics and dynamics. Just as the classificatory sciences tend to become nomological, so the descriptive, or explanatory, sciences tend to become classificatory. The astronomer finds so many examples of systems in formation, that he can formulate the cycle of events through which they generally pass; as the historian formulates cycles through which communities usually pass, and the geologist formulates cycles through which continents commonly pass. These are analogous to the cyclical laws of the classificatory sciences.

86. But perhaps the problem before the student is not one of theoretical physics or of theoretical psychics, but a practical problem. He wishes to invent. In that case he ought to have a great knowledge both of facts about men's minds and of facts about matter; for he has to adapt the one to the other. He ought to know more than any pure scientist can be expected to know. Of course, as the world goes, he does not.

87. (2) The most vital factors in the method of modern science have not been the following of this or that logical prescription — although these have had their value too — but they have been the moral factors. First of these has been the genuine love of truth and conviction that nothing else could long endure. Given that men strive after the truth, and, in the nature of things, they will get it in a measure. The greatest difference between the scientific state of the modern scientific era from Copernicus and the middle ages, is that now the whole concern of students is to find out the truth; while then it was to put into a rational light the faith of which they were already possessed. The chief obstacle to the advance of science among students of science in the modern era has been that they were teachers, and feared the effect of this or that theory. But the salvation from this danger has been the fact that there was no vast institution which anybody for a moment hoped could withstand the mighty tide of fact. The next most vital factor of the method of modern science is that it has been made social. On the one hand, what a scientific man recognizes as a fact of science must be something open to anybody to observe, provided he fulfils the necessary conditions, external and internal. As long as only one man has been able to see a marking upon the planet Venus, it is not an established fact. Ghost stories and all that cannot become the subject of genuine science until they can in some way be welded to ordinary experience. †16 On the other hand, the method of modern science is social in respect to the solidarity of its efforts. The scientific world is like a colony of insects, in that the individual strives to produce that which he himself cannot hope to enjoy. One generation collects premises in order that a distant generation may discover what they mean. When a problem comes before the scientific world, a hundred men immediately set all their energies to work upon it. One contributes this, another that. Another company, standing upon the shoulders of the first, strike a little higher, until at last the parapet is attained. Still another moral factor of the method of science, perhaps even more vital than the last, is the self-confidence of it. In order to appreciate this, it is to be remembered that the entire fabric of science has to be built up out of surmises at truth. All that experiment can do is to tell us when we have surmised wrong. The right surmise is left for us to produce. The ancient world under these circumstances, with the exception of a few men born out of their time, looked upon physics as something about which only vague surmises could be made, and upon which close study would be thrown away. So, venturing nothing, they naturally could gain nothing. But modern science has never faltered in its confidence that it would ultimately find out the truth concerning any question in which it could apply the check of experiment.

88. These are some of the more vital factors of the method of modern science. For the purely logical elements the reader should consult special topics, e.g. Reasoning, †17 Probable Inference, †18 Psychophysical Methods, Errors of Observation, Empirical Logic, Variation, etc.

89. Verification: It is desirable to understand by a verifiable hypothesis one which presents an abundance of necessary consequences open to experimental tests, and which involves no more than is necessary to furnish a source of those consequences. The verification will not consist in searching the facts in order to find features that accord or disagree with the hypothesis. That is to no purpose whatsoever. The verification, on the contrary, must consist in basing upon the hypothesis predictions as to the results of experiments, especially those of such predictions as appear to be otherwise least likely to be true, and in instituting experiments in order to ascertain whether they will be true or not.

90. These experiments need not be experiments in the narrow and technical sense, involving considerable preparation. That preparation may be as simple as it may. The essential thing is that it shall not be known beforehand, otherwise than through conviction of the truth of the hypothesis, how these experiments will turn out. It does not need any long series of experiments, so long as every feature of the hypothesis is covered, to render it worthy of positive scientific credence. What is of much greater importance is that the experiments should be independent, that is, such that from the results of some, the result of no other should be capable of reasonable surmise, except through the hypothesis. But throughout the process of verification the exigencies of the economy of research should be carefully studied from the point of view of its abstract theory.

91. When, in 1839, Auguste Comte laid down the rule that no hypothesis ought to be entertained which was not capable of verification, it was far from receiving general acceptance. But this was chiefly because Comte did not make it clear, nor did he apparently understand, what verification consisted in. He seemed to think, and it was generally understood, that what was meant was that the hypothesis should contain no facts of a kind not open to direct observation. That position would leave the memory of the past as something not so much as to be entertained as plausible.

§4. Simplicity †19

92. Parsimony (law of): Ockham's razor, i.e. the maxim 'Entia non sunt multiplicanda praeter necessitatem.' The meaning is, that it is bad scientific method to introduce, at once, independent hypotheses to explain the same facts of observation.

93. Though the maxim was first put forward by nominalists, its validity must be admitted on all hands, with one limitation; namely, it may happen that there are two theories which, so far as can be seen, without further investigation, seem to account for a certain order of facts. One of these theories has the merit of superior simplicity. The other, though less simple, is on the whole more likely. But this second one cannot be thoroughly tested by a deeper penetration into the facts without doing almost all the work that would be required to test the former. In that case, although it is good scientific method to adopt the simpler hypothesis to guide systematic observations, yet it may be better judgment, in advance of more thorough knowledge, to suppose the more complex hypothesis to be true. For example, I know that men's motives are generally mixed. If, then, I see a man pursuing a line of conduct which apparently might be explained as thoroughly selfish, and yet might be explained as partly selfish and partly benevolent, then, since absolutely selfish characters are somewhat rare, it will be safer for me in my dealings with the man to assume the more complex hypothesis to be true; although were I to undertake an elaborate examination of the question, I ought to begin by ascertaining whether the hypothesis of pure selfishness would quite account for all he does.

94. The whole aim of science is to find out facts, and to work out a satisfactory theory of them. Still, a theory does not necessarily lose its utility by not being altogether true. . . .

95. No theory in the positive sciences can be supposed to satisfy every feature of the facts. Although we know that the law of gravitation is one of the most perfect of theories, yet still, if bodies were to attract one another inversely as a power of the distance whose exponent were not 2, but 2.000001, the only observable effect would be a very slow rotation of the line of apsides of each planet. Now the lines of apsides all do rotate in consequence of perturbations, which virtually do alter slightly the sun's attraction, and thus such an effect would probably only produce slight discrepancies in the values obtained for the masses of the planets. In very many cases, especially in practical problems, we deliberately go upon theories which we know are not exactly true, but which have the advantage of a simplicity which enables us to deduce their consequences. This is true of almost every theory used by engineers of all kinds. The most extraordinary departure from the known facts occurs when hydrodynamics is applied, where the theory is in striking opposition to facts which obtrude themselves upon every spectator of moving water. Nevertheless, even in this case, the theory is not useless.

96. In all the explanatory sciences theories far more simple than the real facts are of the utmost service in enabling us to analyse the phenomena, and it may truly be said that physics could not possibly deal even with its relatively simple facts without such analytic procedure. Thus, the kinetical theory of gases, when first propounded, was obliged to assume that all the molecules were elastic spheres, which nobody could believe to be true. If this is necessary even in physics, it is far more indispensable in every other science, and most of all in the moral sciences, such as political economy. Here the sane method is to begin by considering persons placed in situations of extreme simplicity, in the utmost contrast to those of all human society, and animated by motives and by reasoning powers equally unlike those of real men. Nevertheless, in this way alone can a base be obtained from which to proceed to the consideration of the effects of different complications. Owing to the necessity of making theories far more simple than the real facts, we are obliged to be cautious in accepting any extreme consequences of them, and to be also upon our guard against apparent refutations of them based upon such extreme consequences.

§5. Kinds of Reasoning †20

97. First of all I must establish, as well as I can, the proposition that all Reasoning is either Deduction, Induction, or Retroduction. †21

98. Unfortunately, I am unable to make this as evident as would be desirable, although I think there is very little room for doubting it, since in the course of a long life of active study of reasonings, during which I have never met with any argument not of a familiar type without carefully analyzing and studying it, I have constantly since 1860, or 50 years, had this question prominently in mind, and if I had ever met with an argument not of one of these three kinds, I must certainly have perceived it. But I never have found any such kind of argument except Analogy, which, as I have shown, is of a nature, — a mixture of the three recognized kinds. Therefore, it may be taken as substantially certain that I have never in 50 years met with a reasoning of any fourth type.

99. Now I have not been the only man whose attention would have been roused by the appearance of any such reasoning; and if anybody in the civilized world had found such an argument, I should have heard of it.

100. Now it is of the nature of a genus of reasoning that it applies to any kind of matter in inexhaustible variety. It is therefore very difficult to believe that there is any kind of reasoning that has not been familiarly employed and known by all the world from time immemorial. On the whole, then, I think my negative experience ought to be pretty convincing, inductively.

101. Though I do not profess to render it strictly speaking, evident that there are but the three types of reasoning, yet it will be interesting to see how nearly I can approach that desideratum.

102. A sound reasoning justifies us in some kind of belief in the truth of a proposition that in the absence of the reasoning we should not have been so much justified in believing.

103. In reasoning, one is obliged to think to oneself. In order to recognize what is needful for doing this it is necessary to recognize, first of all, what "oneself" is. One is not twice in precisely the same mental state. One is virtually (i.e. for pertinent purposes, the same as if one were) a somewhat different person, to whom one's present thought has to be communicated. Consequently, one has to express one's thought so that that virtually other person may understand it. One may, with great advantage, however, employ a language, in thinking to oneself, that is free from much explanation that would be needed in explaining oneself to quite a different person. One can establish conventions with oneself, which enable one to express the essence of what [one] has to communicate free from signs that are not essential. For that reason for example a mathematician has, in thinking of mathematical subjects, an immense advantage. Thus if he has to express to himself a force he will think of D(2/t)S, which, he will remember, or can readily see if he should not remember it, is the same as Ds[1/2(DtS)2]. †22 Or he may express the same thing by means of a geometrical diagram, and that in any one of various forms. In like mathematical fashion Existential Graphs †23 enable me here and there greatly to abridge the labor and increase the exactitude of my thought by putting intricate logical relations in the forms that display to me precisely what they involve.

104. In particular, [the system of] Existential Graphs shows clearly that all logical relations are compounds of the relation of consequence, provided we look upon identity as so composed. But Existential Graphs does not so regard Identity. That is, it does not assert that to say that the Battle of Waterloo was the final downfall of Napoleon is precisely the same as to say, that if the Battle of Waterloo was the final downfall of Napoleon then for Napoleon to lose that battle as completely as he did, necessarily involved his final overthrow, while if he had not so lost that battle, he would not then and there have been finally overthrown.

105. My reason in constructing the system of Existential Graphs for not allowing such an identity was that no single actual event can follow as logically consequent upon any other, since if it [were] otherwise in the smallest particular, it would be a different event. If in the Battle of Waterloo one man's wound were shifted a hundredth of an inch, or if it had occurred a tenth of a second earlier or later, the Battle would not have been that actual event that did take place; and we never can be in a situation to affirm that under specified circumstances that which did take place must have taken place with such absolute precision; and it is the merest moonshine to claim to know that only as any describable circumstances had taken place the Battle of Waterloo or any other actual historical event must have taken place precisely as it did. It is a pretty theory although there are grave objections to its precise truth, but to claim to know it is a pretension that I do not think any sober minded man who sufficiently considers the subject will allow himself to make. It has all the ear-marks of the doctrinaire, the man who is willing to accept theories as absolutely true. All the difficulties into which metaphysicians contrive to snarl themselves up are traceable to just that doctrinaire disposition. Certainly, I will take care that my system of logic is not inoculated with that easily avoidable but fatal infection.

106. Therefore, the System of Graphs is so constructed that nothing can be recognized as an apodictic proof that in any circumstances defined in general terms, an event must have happened precisely as it did.

107. But as long as we have to do with general states of things, Existential Graphs analyzes all logical relations into cases of the one relation of consequence, that is the relation between one general description of event, A, an antecedent, and another general description of event, C, a consequent, the relation consisting in the fact that whenever A is realized, C will be realized. All known laws of dynamics as well as all other truths consist of such relations.

108. I will not, therefore, admit that we know anything whatever with absolute certainty. †24 It is possible that twice two is not four. For a computer might commit an error in the multiplication of 2 by 2; and whatever might happen once might happen again. Now 2 has never been multiplied by 2 but a finite number of times; and consequently all such multiplications may have been wrong in the same way. It is true that it would be difficult to imagine a greater folly than to attach any serious importance to such a doubt. Still foolish as that would be, its folly would not be so great as to assert that there is some number of repetitions of a multiplication that renders their result, if all agree, absolutely certain. For if this be the case there is some number which is the least that is sufficient to produce certainty. Let this number be denoted by N. Then N-1 repetitions of the multiplication do not yield an absolutely certain result, but one more, if it agree with all the others, will have that result. Consequently a single multiplication will be sufficient to give us absolute certainty, that the result is the same, unless some other one of N-1 repetitions should give a different result. Thus, disregarding the particular proposition in question one is driven to maintaining that a single experiment is capable of giving us certain knowledge as to the result of any number of experiments. This is sufficient to show that such an assumption is dangerous in the extreme. It is also absurd from various points of view. The only safety is to say that man is incapable of absolute certainty.

109. But some one will ask me, "Do you, then, really entertain any doubt that twice two is four?" To this I must answer, "No, as well as I can perceive, there is not the slightest real doubt of it in my mind." †25 "But," he will say, "how can that be? You say it is not certain. Ought you not then, to entertain a doubt of it; and if you feel that it ought to be doubted, do you not, ipso facto, actually doubt it?" I reply: "Doubt is a certain kind of feeling. It has not only grades of intensity, but also varieties of quality. Now if I were able to modify my state of mind by a sufficiently slight tincture of the right kind of doubt, I ought to do so. But if I were to attempt really to feel any doubt at all, I should certainly either feel none at all or else millions upon millions of times too much. For I could not in the least recognize a tincture so small nor even one that should be millions of times too great. If I were to devote my whole life to the useless task of trying to make such slight distinctions in my feelings, I could not come near to the requisite delicacy. My feeling of doubt is one of the coarser of my sensations; and there would be no practical use in making it more delicate than it is, for it is already so far more delicate than that of almost all the persons with whom I converse, that I often find an insuperable difficulty in making them comprehend the slighter grades of my feeling, and there is no practical difference in my conduct whether, say, 3/8 or 5/13 be the proper degree of doubt about a matter not measurable. It would be a waste of time to adjust my feeling of doubt more accurately, since it neither would have, nor ought to have, any effect upon my scientific conduct. Instead of wasting effort on my feeling, I devote my energies to learning more about the subjects concerning which I have any considerable doubts, while very small doubts I neglect until I can reduce the amount of my doubt concerning subjects of greater importance."

§6. Kinds of Induction †26

110. Suppose we define Inductive reasoning as that reasoning whose conclusion is justified not by there being any necessity of its being true or approximately true but by its being the result of a method which if steadily persisted in must bring the reasoner to the truth of the matter or must cause his conclusion in its changes to converge to the truth as its limit. Adopting this definition, I find that there are three orders of induction of very different degrees of cogency although they are all three indispensable.

111. The first order of induction, which I will call Rudimentary Induction, or the Pooh-pooh argument, proceeds from the premiss that the reasoner has no evidence of the existence of any fact of a given description and concludes that there never was, is not, and never will be any such thing. The justification of this is that it goes by such light as we have, and that truth is bound eventually to come to light; and therefore if this mode of reasoning temporarily leads us away from the truth, yet steadily pursued, it will lead to the truth at last. This is certainly very weak justification; and were it possible to dispense with this method of reasoning, I would certainly not recommend it. But the strong point of it is that it is indispensable. It goes upon the roughest kind of information, upon merely negative information; but that is the only information we can have concerning the great majority of subjects.

112. I find myself introduced to a man without any previous warning. Now if I knew that he had married his grandmother and had subsequently buried her alive, I might decline his acquaintance; but since I have never heard the slightest suspicion of his doing such a thing, and I have no time to investigate idle surmises, I presume he never did anything of the sort. I know a great many men, however, whose whole stock of reasoning seems to consist in this argument, which they continue to use where there is positive evidence and where this argument consequently loses all force. If you ask such a man whether he believes in the liquefaction of the blood of St. Januarius, he will say no. Why not? Well, nothing of that kind ever came within the range of my experience. But it did come within the range of Sir Humphrey Davy's experience, who was granted every facility for the thorough investigation of it. His careful report simply confirms the usual allegations with more circumstantial details. You are not justified in pooh-poohing such observations; and that the fact is contrary to the apparent ordinary course of nature is no argument whatever. You are bound to believe it, until you can bring some positive reason for disbelieving it.

113. In short this rudimentary kind of induction is justified where there is no other way of reasoning; but it is of all sound arguments the very weakest and must disappear as soon as any positive evidence is forthcoming.

114. The second order of induction consists in the argument from the fulfillment of predictions. After a hypothesis has been suggested to us by the agreement between its consequences and observed fact, there are two different lines that our further studies of it may pursue. In the first place, we may look through the known facts and scrutinize them carefully to see how far they agree with the hypothesis and how far they call for modifications of it. That is a very proper and needful inquiry. But it is Abduction, not Induction, and proves nothing but the ingenuity with which the hypothesis has been adapted to the facts of the case. To take this for Induction, as a great proportion of students do, is one of the greatest errors of reasoning that can be made. It is the post hoc ergo propter hoc fallacy, if so understood. But if understood to be a process antecedent to the application of induction, not intended to test the hypothesis, but intended to aid in perfecting that hypothesis and making it more definite, this proceeding is an essential part of a well-conducted inquiry.

115. The other line which our studies of the relation of the hypothesis to experience may pursue, consists in directing our attention, not primarily to the facts, but primarily to the hypothesis, and in studying out what effect that hypothesis, if embraced, must have in modifying our expectations in regard to future experience. Thereupon we make experiments, or quasi-experiments, †27 in order to find out how far these new conditional expectations are going to be fulfilled. In so far as they greatly modify our former expectations of experience and in so far as we find them, nevertheless, to be fulfilled, we accord to the hypothesis a due weight in determining all our future conduct and thought. It is true that the observed conformity of the facts to the requirements of the hypothesis may have been fortuitous. But if so, we have only to persist in this same method of research and we shall gradually be brought around to the truth. This gradual process of rectification is in great contrast to what takes place with rudimentary induction where the correction comes with a bang. The strength of any argument of the Second Order depends upon how much the confirmation of the prediction runs counter to what our expectation would have been without the hypothesis. It is entirely a question of how much; and yet there is no measurable quantity. For when such measure is possible the argument assumes quite another complexion, and becomes an induction of the Third Order. Inductions of the second order are of two varieties, that are logically quite distinct.

116. The weaker of these is where the predictions that are fulfilled are merely of the continuance in future experience of the same phenomena which originally suggested and recommended the hypothesis, expectations directly involved in holding the hypothesis. Even such confirmation may have considerable weight. This, for example, is the way in which the undulatory theory of light stood before Maxwell. The phenomena of interference suggested undulations, which measures of the velocity of light in different media confirmed; and the phenomena of polarization suggested transverse vibrations. All the direct expectations involved in the hypothesis were confirmed, except that there no phenomena due to longitudinal vibrations were found. But all physicists felt that it was a weakness of the theory that no unexpected predictions occurred. The rotation of the plane of polarization was an outstanding fact not accounted for.

117. The other variety of the argument from the fulfillment of predictions is where truths ascertained subsequently to the provisional adoption of the hypothesis or, at least, not at all seen to have any bearing upon it, lead to new predictions being based upon the hypothesis of an entirely different kind from those originally contemplated and these new predictions are equally found to be verified.

118. Thus Maxwell, noticing that the velocity of light had the same value as a certain fundamental constant relating to electricity, was led to the hypothesis that light was an electromagnetic oscillation. This explained the magnetic rotation of the plane of polarization, and predicted the Hertzian waves. Not only that, but it further led to the prediction of the mechanical pressure of light, which had not at first been contemplated.

119. The second order of induction only infers that a theory is very much like the truth, because we are so far from ever being authorized to conclude that a theory is the very truth itself, that we can never so much as understand what that means. Light is electro-magnetic vibrations; that is to say, it [is] something very like that. In order to say that it is precisely that, we should have to know precisely what we mean by electro-magnetic vibrations. Now we never can know precisely what we mean by any description whatever.

120. The third order of induction, which may be called Statistical Induction, differs entirely from the other two in that it assigns a definite value to a quantity. It draws a sample of a class, finds a numerical expression for a predesignate character of that sample and extends this evaluation, under proper qualification, to the entire class, by the aid of the doctrine of chances. The doctrine of chances is, in itself, purely deductive. It draws necessary conclusions only. The third order of induction takes advantage of the information thus deduced to render induction exact.

121. This family of inductions has three different kinds quite distinct logically. Beginning with the lowest and least certain, we have cases in which a class of individuals recur in endless succession and we do not know in advance whether the occurrences are entirely independent of one another or not. But we have some reason to suppose that they would be independent and perhaps that they have some given ratio of frequency. Then what has to be done is to apply all sorts of consequences of independence and see whether the statistics support the assumption. For instance, the value of the ratio of the circumference of a circle to its diameter, a number usually called π has been calculated in the decimal notation, to over seven hundred figures. Now as there is not the slightest reason to suppose that any law expressible in a finite time connects the value of π with the decimal notation or with any whole number, we may presume that the recurrences of any figure say 5 in that succession are independent of one another and that there is simply a probability of 1/10 that any figure will be a 5.

122. In order to illustrate this mode of induction, I have made a few observations on the calculated number. There ought to be, in 350 successive figures, about 35 fives. The odds are about 2 to 1 that there will be 30-39 [and] 3 to 1 that there will be 29-41. Now I find in the first 350 figures 33 fives, and in the second 350, 28 fives, which is not particularly unlikely under the supposition of a chance distribution. During the process of counting these 5's, it occurred to me that as the expression of a rational fraction in decimals takes the form of a circulating decimal in which the figures recur with perfect regularity, so in the expression of a quantity like π, it was naturally to be expected that the 5's, or any other figure, should recur with some approach to regularity. In order to find out whether anything of this kind was discernible I counted the fives in 70 successive sets of 10 successive figures each. Now were there no regularity at all in the recurrence of the 5's, there ought among these 70 sets of ten numbers each to be 27 that contained just one five each; and the odds against there being more than 32 of the seventy sets that contain just one five each is about 5 to 1. Now it turns out upon examination that there are 33 of the sets of ten figures which contain just one 5. It thus seems as if my surmise were right that the figures will be a little more regularly distributed than they would be if they were entirely independent of one another. But there is not much certainty about it. This will serve to illustrate what this kind of induction is like, in which the question to be decided is how far a given succession of occurrences are independent of one another and if they are not independent what the nature of the law of their succession is.

123. In the second variety of statistical induction, we are supposed to know whether the occurrences are independent or not, and if not, exactly how they are connected, and the inquiry is limited to ascertaining what the ratio of frequency is, after the effects of the law of succession have been eliminated. As a very simple example, I will take the following. The dice that are sold in the toy shops as apparatus for games . . . are usually excessively irregular. It is no great fault, but rather enhances the Christmas gaiety. Suppose, however, that some old frump with an insatiable appetite for statistics [were to] get hold of a die of that sort, and he will spend his Christmas in throwing it and recording the throws in order to find out the relative frequency with which the different faces turn up. He assumes that the different throws are independent of one another and that the ten thousand or so which he makes will give the same relative frequencies of the different faces as would be found among any similar large number of throws until the die gets worn down. At least he can safely assume that this will be the case as long as the die is thrown out of the same box by the same person in the same fashion.

124. This second variety is the usual and typical case of statistical induction. But it occasionally happens that we can sample a finite collection of objects by such a method that in the long run any one object of the collection would be taken as often as every other and any one succession as often as any other. This may [be] termed a random selection. It is obviously possible only in the case of an enumerable collection. When this sort of induction is possible it far surpasses every other in certainty and may closely approach that of demonstration itself.

125. I have now passed in review all the modes of pure induction with which I am acquainted. Induction may, of course, be strengthened or weakened by the addition of other modes of argument leading to the same conclusion or to a contrary conclusion. It may also be strengthened or weakened by arguments which do not directly affect the conclusion of the induction but which increase or diminish the strength of its procedure. There are in particular four kinds of uniformities which may greatly affect an induction.

126. In the first place the members of a class may present a greater or less general resemblance as regards certain kinds of characters. Birds for example are, generally speaking, much more alike than are fishes or mammals; and that will strengthen any induction about birds. Orchids, on the other hand, are extraordinarily various.

127. In the second place a character may have a greater or less tendency to be present or absent throughout the whole of certain kinds of groups. Thus, coloration often differs within one species, while the number of the principal bones of the skeleton, and almost all characters which are developed early in individual life and which persist to maturity are common to all the members of large classes.

128. In the third place, a certain set of characters may be more or less intimately connected, so as probably to be present or absent together in certain kinds of objects. Thus, we generally associate insistency upon minute forms with narrowness of mind, cleanliness with godliness, and so on.

129. In the fourth place, an object may have more or less tendency to possess the whole of certain sets of characters when it possesses any of them. Thus, one meets one man whose views whatever they may be are extreme, while the opinions of another form a strange mosaic.

130. From the knowledge of a uniformity of any one of these four classes or from the knowledge of the lack of such uniformity it may be deductively inferred that a given induction is either stronger or weaker than it otherwise would be.

§7. Uniformity of Nature †28

131. There is still another sense in which we might speak of the uniformity of nature. If we select a good many objects on the principle that they shall belong to a certain class and then find that they all have some common character, pretty much the whole class will generally be found to have that character. Or if we take a good many of the characters of a thing at random, and afterwards find a thing which has all these characters, we shall generally find that the second thing is pretty near the same as the first.

132. It seems to me that it is this pair of facts rather than any others which are properly expressed by saying that nature is uniform. We shall see that it is they which are the leading principles of scientific inference.

Let us ask, then, whether these facts are statements of a particular constitution of the world so as to be properly speaking matters of fact or whether they are purely formal propositions, laws of logic, having no more application to one state of things than they would have to any other.

133. In the first place, I would call your attention to the quantitative indeterminateness of both propositions. The first speaks of a good many samples being selected, and of pretty much all the things in the class from which they are taken being like them, and of this occurring almost always. The second speaks of a good many characters of a thing being taken, and of any thing found to have them being pretty near the same thing, and of this happening almost always. We have no means whatsoever of defining the propositions in either of the three respects in which they are thus seen to be so utterly vague.

134. Now you know how a malicious person [who] wishes to say something ill of another, prefers insinuation; that is, he speaks so vaguely that he suggests a great deal while he expressly says nothing at all. In this way he avoids being confronted by fact. It is the same way with these principles of scientific inference. They are so vague that you cannot bring them to any touch-stone of experience. They rather insinuate a uniformity in nature than state it. And as insinuation always expresses the state of feeling of the person who uses it rather than anything concerning its object, so we may suppose these principles express rather the scientific attitude than a scientific result.

135. But what if we were in a world of chance? How would it be with these principles then, or, to simplify the matter, with the first principle? In that case, it would be extremely seldom that, having selected a number of objects as having certain characters, we should find that they had any other common character; and thus there would be very little applicability for this principle. But, we have seen that the proportion of cases where this principle applies is indefinitely small in our present world. Cases might occur, doubtless would in a world of chance and when they did occur the principle doubtless would hold true.

136. It is a mistake to suppose that there would be no laws in a world of chance. At least, so I should think. Suppose we were to throw a die any number of times and set down the numbers thrown in a column. I could show you that there would be some very curious laws in reference to those numbers. They would appear quite surprizing. So that chance is not the abrogation of all laws.

137. But there is a peculiarity about those laws that chance does not abrogate; suppose that in throwing the die other numbers had turned up from those which actually turned up, so that the row of numbers would have been somewhat different; still the laws would have held; they would hold with one set of numbers as well as with another. Whereas if we were to give a whale legs or a woman wings, the laws of the animal kingdom would be interfered with. So that there are two kinds of laws, those which in a different state of things would continue to hold good and those which in a different state of things would not hold good. The former we call formal laws, the latter material laws. The formal laws do not depend on any particular state of things, and hence we say we have not derived them from experience; that is to say, any other experience would have furnished the premisses for them as well as that which we have experienced; while to discover the material laws we require to have known just such facts as we did. But as the laws which we have mentioned, that as is sample so is the whole and that the sameness of a number of characters manifests identity, are laws which would hold so long as there were any laws, though only formal ones, it is plain that no alteration in the constitution of the world would abrogate them, so that they are themselves formal laws, and therefore not laws of nature but of the conditions of knowledge in general.

138. Two classes of thinkers wish to make the difference between formal and material laws merely relative; namely, those who would reduce all formal laws to material laws, and those who would reduce all material laws to formal laws. But neither can deny that there is a great difference between what we must consider formal and what we must consider material laws. Those who would reduce all material laws to formal laws, have indeed shown that what we call material laws are only those which we cannot discover to be formal; and thus that all material laws may be formal; and in so doing they have cut anyone off from saying that there is a peculiar uniformity of nature consisting in its material laws. On the other hand, those who would reduce formal laws to material laws, among whom is Mr. Mill, have shown that laws may be thought to be formal, that is to be such that a violation of them is unimaginable, owing to a want of imaginative power in us arising from a defective experience, and they infer from that that all formal laws may be material. But so long as there are any laws whatsoever, these laws that the whole is as the sample and that identity goes with similarity in respects [not] chosen to make out the similarity, these laws I say must exist. For these are but as much as to say that there is law. That we shall see in future lectures. Now all law may, in one sense, be contingent. But that there should be knowledge without the existence of law, that there should be intelligence without anything intelligible, all admit to be impossible. These laws therefore cannot be abrogated without abrogating knowledge; and thus are the formal conditions of all knowledge.

Chapter 2: Economy of Research

§1. Original Paper †1

139. When a research is of a quantitative nature, the progress of it is marked by the diminution of the probable error. The results of non-quantitative researches also have an inexactitude or indeterminacy which is analogous to the probable error of quantitative determinations. To this inexactitude, although it be not numerically expressed, the term "probable error" may be conveniently extended.

140. The doctrine of economy, in general, treats of the relations between utility and cost. That branch of it which relates to research considers the relations between the utility and the cost of diminishing the probable error of our knowledge. Its main problem is, how, with a given expenditure of money, time, and energy, to obtain the most valuable addition to our knowledge.

141. Let r denote the probable error of any result, and write s = 1/r. Let Ur . dr denote the infinitesimal utility of any infinitesimal diminution, dr, of r. Let Vs . ds denote the infinitesimal cost of any infinitesimal increase, ds, of s. The letters U and V are here used as functional symbols. Let subscript letters be attached to r, s, U, and V, to distinguish the different problems into which investigations are made. Then, the total cost of any series of researches will be

Σi ∫ Visi . dsi;

and their total utility will be

Σi ∫ Uiri . dri;

The problem will be to make the second expression a maximum by varying the inferior limits of its integrations, on the condition that the first expression remains of constant value.

142. The functions U and V will be different for different researches. Let us consider their general and usual properties. And, first, as to the relation between the exactitude of knowledge and its utility. The utility of knowledge consists in its capability of being combined with other knowledge so as to enable us to calculate how we should act. If the knowledge is uncertain, we are obliged to do more than is really necessary, in order to cover this uncertainty. And, thus, the utility of any increase of knowledge is measured by the amount of wasted effort it saves us, multiplied by the specific cost of that species of effort. Now, we know, from the theory of errors, that the uncertainty in the calculated amount of effort necessary to be put forth may be represented by an expression of the form

c√(a+r2)

where a and c are constants. And, therefore, the differential coefficient of this, multiplied by the specific cost of the effort in question, say h/c, gives

Ur = h · (r/√(a+r2))

When a is very small compared with r this becomes nearly constant, and in the reverse case it is nearly proportional to r. An analogous proposition must hold for non-quantitative research.

143. Let us next consider the relation between the exactitude of a result and the cost of attaining it. When we increase our exactitude by multiplying observations, the different observations being independent of one another as to their cost, we know from the theory of errors that ∫Vs . ds is proportional to s2, and that consequently Vs is proportional to s. If the costs of the different observations are not independent (which usually happens), the cost will not increase so fast relatively to the accuracy; but if the errors of the observations are not independent (which also usually happens), the cost will increase faster relatively to the accuracy; and these two perturbing influences may be supposed, in the long run, to balance one another. We may, therefore, take Vs = ks, where k represents the specific cost of the investigation.

144. We thus see that when an investigation is commenced, after the initial expenses are once paid, at little cost we improve our knowledge, and improvement then is especially valuable; but as the investigation goes on, additions to our knowledge cost more and more, and, at the same time, are of less and less worth. Thus, when chemistry sprang into being, Dr. Wollaston, with a few test tubes and phials on a tea-tray, was able to make new discoveries of the greatest moment. In our day, a thousand chemists, with the most elaborate appliances, are not able to reach results which are comparable in interest with those early ones. All the sciences exhibit the same phenomenon, and so does the course of life. At first we learn very easily, and the interest of experience is very great; but it becomes harder and harder, and less and less worth while, until we are glad to sleep in death.

145. Let us now apply the expressions obtained for Ur and Vs to the economic problem of research. The question is, having certain means at our disposal, to which of two studies they should be applied. The general answer is that we should study that problem for which the economic urgency, or the ratio of the utility to the cost

(Ur . dr)/(Vs . ds) = r2(Ur/Vs) = (h/k)(r4/√(a+r2))

is a maximum. When the investigation has been carried to a certain point this fraction will be reduced to the same value which it has for another research, and the two must then be carried on together, until finally, we shall be carrying on, at once, researches into a great number of questions, with such relative energies as to keep the urgency-fraction of equal values for all of them. When new and promising problems arise they should receive our attention to the exclusion of the old ones, until their urgency becomes no greater than that of others. It will be remarked that our ignorance of a question is a consideration which has between three and four times the economic importance of either the specific value of the solution or the specific cost of the investigation in deciding upon its urgency.

146. In order to solve an economical problem, we may use as variables

x = ∫ Vs · ds,

or the total cost of an inquiry, and

y = (Ur · dr)/(Vs · ds),

or the economic urgency. Then, C being the total amount we have to spend in certain researches, our equations will be

C = x1 + x2 + x3 + etc.

y1 = y2 = y3 = etc.

Then, expressing each y in terms of x, we shall have as many equations as unknown quantities.

147. When we have to choose between two researches only, the solution may be represented graphically, as follows:

inline image

148. From any point O1 taken as an origin, draw the axis of abscissas O1 X1, along which x1, the total cost of the first investigation, is to be measured. Draw also the axis of ordinates O1 Y1, along which Y1, the economic urgency of the first investigation, is to be measured. Draw the curve S1 T1 to represent the relations of x1 and y1. Take, on the axis O1 X1, a point O2 such that O1 O2 shall measure the total cost of the two investigations. Let x2, the total cost of the second investigation, be measured on the same axis as x1, but in the opposite direction. From O2 draw the axis of ordinates O2 Y2 parallel to O1 Y1, and measure y2, the economic urgency of the second investigation, along this axis. Draw the curve S2 T2 to represent the relations of x2 and Y2. Then, the two curves S1 T1 and S2 T2 will generally cut one another at one point, and only one, between the axes O1 Y1 and O2 Y2. From this point, say P, draw the ordinate PQ, and the abscissas O1Q and O2Q will measure the amounts which ought to be expended on the two inquiries.

149. According to the usual values of U and V, we shall have

y=(1/4)/(hk/x√(ax2+1/2 kx))

150. In this case, when there are two inquiries, the equation to determine x1 will be a biquadratic. Two of its roots will be imaginary, one will give a negative value of either x1 or x2, and the fourth, which is the significant one, will give positive values of both.

151. Let us now consider the economic relations of different researches to one another. 1st, as alternative methods of reaching the same result, and 2d, as contributing different premises to the same argument.

152. Suppose we have two different methods of determining the same quantity. Each of these methods is supposed to have an accidental probable error and a constant probable error, so that the probable errors, as derived from n observations in the two ways, are:

r1 = √R12+(ρ12/n) and r2 = √R22+(ρ22/n)

The probable error of their weighted mean is

1/√(1/(r12+1/r22))

if their constant probable errors are known. The sole utility of any observation of either is to reduce the error of the weighted mean; hence,

Ur1 = Dr1(r1-2 + r2-2)-1/2 = r1-2 + r2-2)-3/2r1-3.

And as the cost is proportional to the number of observations

inline image

Hence, the urgency is (omitting a factor common to the values for the two methods)

inline image

And, as the urgency of the two methods ought to be the same at the conclusion of the work, we should have

inline image

which equation serves to determine the relative values of n1 and n2. We again perceive that the cost is the smallest consideration. The method which has the smallest accidental probable error is the one which is to be oftenest used in case only a small number of observations are made; but if a large number are taken the method with the larger accidental probable error is to be oftenest used, unless it has so much greater a probable constant error as to countervail this consideration. If one of the two methods has only (1/p)th the accidental probable error of the other, but costs p2 times as much, the rule should be to make the total cost of the two methods inversely proportional to the squares of their constant errors.

153. Let us now consider the case in which two quantities x1 and x2 are observed, the knowledge of which serves only to determine a certain function of them, y. †2 In this case the probable error [dy] of y is

inline image

and [since Ur1 = Dr1(dy)] we shall have

inline image

Vs1 will have the same value as before; but neglecting now the constant error, we may write

Vs1 = 2k1ρ1n11/2

Then the urgency (with omission of the common factor) is

inline image

and, as the two urgencies must be equal, we have

inline image

154. The following is an example of the practical application of the theory of economy in research: Given a certain amount of time, which is to be expended in swinging a reversible pendulum, how much should be devoted to experiments with the heavy end up, and how much to those with the heavy end down? †3

155. Let Td be the period of oscillation with heavy end down, Tu the same with heavy end up. Let hd and hu be the distances of the center of mass from the points of support of the pendulum in the two positions. Then the object of the experiments is to ascertain a quantity proportional to †4

hd Td - hu Tu.

Accordingly, if dTd and dTu are the probable errors of Td and Tu, that of the quantity sought will be

√(hd2 (dTd2 + hu2(dTu2).)

156. We will suppose that it has been ascertained, by experiment, that the whole duration of the swinging being C, and the excess of the duration of the swinging with heavy end down over that with heavy end up being x, the probable errors of the results are

inline image

where a, b, and c are constants. Then, the square of the probable error of the quantity sought will be

inline image

The differential coefficient of this relatively to x is

inline image

Putting this equal to zero and solving, we find for the only significant root,

inline image

when b vanishes, x reduces to zero, and the pendulum should be swung equally long in the two positions. When c vanishes, as it would if the pendulum experiment were made absolutely free from certain disturbing influences, we have

x/C = (hd-hu)/(hd+hu),

so that the duration of an experiment ought to be proportional to the distance of the center of mass from the point of support. This would be effected by beginning and ending the experiments in the two positions with the same amplitudes of oscillation.

157. It is to be remarked that the theory here given rests on the supposition that the object of the investigation is the ascertainment of truth. When an investigation is made for the purpose of attaining personal distinction, the economics of the problem are entirely different. But that seems to be well enough understood by those engaged in that sort of investigation.

§2. Later Reflections †5

158. In all economics the laws are ideal formulae from which there are large deviations, even statistically. In the economics of research the "laws" are mere general tendencies to which exceptions are frequent. The laws being so indefinite, at best, there is little advantage in very accurate definitions of such terms as "amount of knowledge." It is, however, possible to attach a definite conception to one increment of knowledge being greater than another. To work this out will be the first business of the memoir. I also establish a definite meaning for the amount of an increment in diffusion of knowledge. I then consider the relation of each of these to the expenditure of energy and value required to produce them in varying conditions of the advancement or diffusion of knowledge already attained. Comparing knowledge with a material commodity, we know that in the latter case a given small increment in the supply is very expensive, in most cases, when the supply is very small, that as the supply increases, it sinks to a minimum, from which it increases to a very large but finite value of the supply where no further increment would be possible at any finite cost. Putting instead of supply, the amount of knowledge attained, we find that there is a "law," or general tendency, subject to similar large irregularities as in the case of the supply of a material commodity, but here even greater. The final increase of cost of an increment with the increase of attainment already achieved is marked, on the whole, in almost all cases, while in many cases, at least, there is a point of attainment where the cost of an increment is at a minimum. The same general tendency appears in reference to the diffusion of knowledge; but there is this striking difference, that attainments in advance of sciences are very commonly actually on the upward slope where increments are costing more and more, while there are few branches of knowledge whose diffusion is already so great that a given increment of the diffusion will cost more and more, as the diffusion is increased.

159. I shall next pass to a study of the variation of the utility (meaning, generally, the scientific utility) of given small increments of scientific knowledge and of the diffusion of knowledge in varying states of attainment. This is to be compared with the variation of the total amount that will be paid for a commodity for a fixed small increment of the demand, or amount thrown upon the market to fetch what it will, with varying amounts of that demand. Here, the additional total amount that will be paid for the small increment of amount sold will correspond to the utility of the small fixed increase of scientific knowledge or of the diffusion of knowledge; while, the demand being equal to the supply, this demand, or total amount that is sold, will correspond as before to the amount of attainment in scientific knowledge or in the diffusion of knowledge. For a material commodity we know that if it is given away people will only carry home a finite amount. One would have to pay them to carry away more. On the other hand there is probably some maximum price for most things, above which none at all would be sold. It necessarily follows that beyond a certain amount thrown upon the market, a small increment in that amount would actually diminish the total receipts from the sale of it, while for any smaller amount the increment of receipts for a given small increment of amount sent to market would be less and less. With regard to the scientific utility of a small fixed advance of knowledge, the "law" is certainly very different from that. In the first place, there is no degree of knowledge of which a small increase would be worse than useless, and while the general tendency is that the utility of such fixed increase becomes less and less, yet this curve is rather saw shaped, since like Rayleigh's small addition to our knowledge of the density of nitrogen, now and then a small increment will be of great utility and will then immediately sink to its former level. The scientific advantage of the diffusion of knowledge is difficult to determine. It cannot be believed than any increment of diffusion is positively unfavorable to science. It is favorable in two ways; first, by preparing more men to be eminent researchers; and secondly, by increasing general wealth, and therefore the money bestowed on science. I am inclined to think that the general tendency is that a given increment of diffusion is less and less advantageous to science the greater the attained diffusion. But I am not confident that this is so, at any rate without very important deflexions. The general effect, however, is nearly the same for the advancement as for the diffusion of knowledge. Namely, beginning with dense ignorance, the first increments cost more than they come to. That is, knowledge is increased but scientific energy is spent and not at once recovered. But we very soon reach a state of knowledge which is profitable to science, that is, not only is knowledge increased, but the facility of increasing knowledge gives us a return of more available means for research than we had before the necessary scientific energy was spent. This increases to a maximum, diminishes, and finally, there is no further gain. Yet still, in the case of energy expended upon research, if it is persisted in, a fortunate discovery may result in a new means of research. I shall analyze as far as I can the relative advantages, for pure science exclusively, of expending energy (which is of such a kind as to be equally capable of being directed either way) to the direct advancement of knowledge and to the diffusion of knowledge. I find the latter so overwhelmingly more important (although all my personal sympathies are the other way) that it appears to me that, for the present, to give to research, in money, one or two per cent of what is spent upon education is enough. Research must contrive to do business at a profit; by which I mean that it must produce more effective scientific energy than it expends. No doubt, it already does so. But it would do well to become conscious of its economical position and contrive ways of living upon it.

160. Many years ago I published a little paper on the Economy of Research, in which I considered this problem. †6 Somebody furnishes a fund to be expended upon research without restrictions. What sort of researches should it be expended upon? My answer, to which I still adhere, was this. Researches for which men have been trained, instruments procured, and a plant established, should be continued while those conditions subsist. But the new money should mainly go to opening up new fields; because new fields will probably be more profitable, and, at any rate, will be profitable longer.

161. I shall remark in the course of the memoir that economical science is particularly profitable to science; and that of all the branches of economy, the economy of research is perhaps the most profitable; that logical methodeutic and logic in general are specially valuable for science, costing little beyond the energies of the researcher, and helping the economy of every other science. It was in the middle of the 13th century that a man distinguished enough to become pope opened his work on logic with the words, "Dialectica est ars artium et scientia scientiarum, ad omnium methodorum principia viam habens." †7 This memorable sentence, whose gothic ornamentation proves upon scrutiny to involve no meaningless expression nor redundant clause, began a work wherein the idea of this sentence was executed satisfactorily enough for the dominant science of the middle ages. Jevons adopted the sentence as the motto of his most scientific contribution to logic; and it would express the purpose of my memoirs, which is, upon the ground well prepared by Jevons and his teacher De Morgan, and by the other great English researchers, especially Boole, Whewell, Berkeley, Glanvill, Ockham, and Duns Scotus, to lay a solid foundation upon which may be erected a new logic fit for the life of twentieth century science.

Chapter 3: The Logic of Drawing History from Ancient Documents

§1. Abstract †1

162. Mr. C. S. Peirce gave an abstract of a long paper on the logic of the process of drawing history from ancient testimonies. He endeavored to show that the method of balancing the veracity of a witness against the improbability of his narrative, although it may be defended upon the principles of the calculus of probabilities under certain conditions, is nevertheless in the great majority of cases illogical, because there is not the roughest approximation to fulfillment of those conditions. For the testimonies are seldom even approximately independent, and still more seldom independent of the antecedent probability of the narrative; and moreover there is no determinate objective probability that a witness will tell the truth, and often no objective probability that the fact is as stated. Furthermore, we ought not to seek probabilities in such problems, but ought to pursue a method which must ultimately lead to the truth. Nor can such a method pursue the path of mathematical demonstration, which all reasoning that deduces a probability is, at its very best. But the probabilities upon which the critics of history rely are not objective, but are mere expressions of their preconceived notions, than which no guide can be less trustworthy.

163. Mr. Peirce then undertook to develope the principles upon which ancient historical research ought to proceed in order to be scientific. He pointed out that the logic of scientific investigation, in which a conclusion is not established for many years, perhaps not for generations, cannot be assumed to be the same as the proper logical procedure for an individual who seeks a practical basis for present action. Although the latter has to be hastily performed, the accurate theory of it is far more difficult than is the logic of scientific procedure, to which the present paper limited itself. Here the question is, what is the process by which the truth will be attained most speedily. It does not content itself with probabilities, although absolute certainty can never be fully attained; nor has it anything to do with belief, which is a practical concern. This scientific procedure consists, according to Mr. Peirce, in carefully framing a hypothesis, in tracing out the experiential consequences of that hypothesis, and in testing those consequences by comparison with facts not taken into account in the formation of the hypothesis. If the facts refute the hypothesis, it must be abandoned and another substituted; but if the predictions based upon it are verified, it will be entitled to be received as a scientific result until we find deductions from it which are contrary to the facts.

§2. The Theory of Balancing Likelihoods †2

164. Ancient history is drawn partly from documents and partly from monuments. The last generation has afforded so many examples of the refutation by archeology of the conclusions of the critics of documents as to suggest the question whether the whole logical procedure of the latter class of students has not been radically wrong. The purpose of the present paper is to show that this is the case; that the logical theory upon which the critics proceed is as bad as logic can be; to set forth and defend the true logical method of treating ancient historical documents; and to set this new theory in a clear light by applying it to two or three examples, including a case where the testimonies are comparatively strong and another where the testimony is at best very feeble.

165. The theory of the logic of testimony which forms the basis of the procedure of historical critics today is, I suppose, old. But it can only have taken a distinct form when the doctrine of probabilities was developed, in the early years of the eighteenth century. A popular statement of it was, I believe, first given by Hume, in his essay on Miracles, in 1748. Hume's statement is, mathematically considered, excessively crude. It seems evident that he had been reading either De Moivre's Doctrine of Chances (first edition, 1716; second enlarged edition, 1735) or De Montmort's Essai d'Analyse sur les Jeux de Hazard (1708; second edition, 1713). For Jacob Bernoulli's posthumous Ars Conjectandi (1713) would have been beyond him. Whatever work he read he did not understand; yet in a confused and untenable form, he put forth ideas of his own of considerable value. I may restate Hume's doctrine, correcting such errors as are not inseparable from it, as follows. When a reputable witness makes, or witnesses make, an assertion which experience renders highly improbable, or when there are other independent arguments in its favor, each independent argument pro or con produces a certain impression upon the mind of the wise man, dependent for its quantity upon the frequency with which arguments of those kinds lead to the truth, and the algebraical sum of these impressions is the resultant impression that measures the wise man's state of opinion on the whole. For example, if there are a number of independent arguments, pro, such that, in general, such arguments lead to the truth, p1 times, p2 times, p3 times, etc., respectively, for every q1 times, q2 times, q3 times, etc., that they lead to error; and if there are arguments con, which lead to the truth q5 times, q6 times, q7 times, etc., for every p5 times, p6 times, p7 times, etc., that they lead to error, then the probability that the arguments pro all lead to the truth, and the arguments con all lead to error will be

p1/p1+q1 · p2/p2+q2 · p3/p3+q3 · etc. × p5/p5+q5 · p6/p6+q6 · p7/p7+q7 · etc.;

and the probability that all the arguments pro lead to error while all the arguments con lead to truth, will be

q1/p1+q1 · q2/p2+q2 · q3/p3+q3 · etc. × q5/p5+q5 · q6/p6+q6 · q7/p7+q7 · etc.

But one or [the] other of these two alternatives must be the case; so that the odds or ratio of favorable to unfavorable probability on the whole is simply

(p1·p2·p3· etc. p5·p6·p7 etc.)/(q1·q2·q3· etc. q5·q6·q7 etc.).

Now if we suppose that the impression made on the mind of the wise man is proportional to the logarithm of the odds as its exciting cause, then the total impression will be

log.{p1/q1 · p2/q2 · p3/q3 · etc. p5/q5 · p6/q6 · p7/q7 · etc.}=

log. p1/q1 + log. p2/q2 + log. p3/q3 + etc.

+ log. p5/q5 + log. p6/q6 + log. p7/q7 + etc.

166. This is Hume's Theory Improved, by merely being disembarrassed of blunders. If we strip the mathematics from it, we have the simple theory of balancing likelihoods, which is the theory that Hume undertook to elaborate and to render scientific. It really hardly differs from Hume's Theory Improved except in its vagueness. At any rate, it involves the notion that the different arguments have likelihoods, that they are quantities upon an algebraical scale, and that they are to be combined as independent.

167. Now the practice of those modern German critics of ancient history whose works I have read, particularly those who treat of the history of philosophy, and whose methods are generally extolled, is based upon the theory of balancing likelihoods. In so far as their general logical method departs from that of Hume, it is only less refined. The principal difference between Hume and them is that the word 'Proof' is continually in their mouths, a word which Hume scrupulously avoided in speaking of the minor facts of ancient history. He recognized the question as purely one of probabilities. They seem to be discontented with mere probability; and are always in search of an argument that something "must" be. The necessity which enters into the conclusion of such an argument as part of its subject matter is confounded by them with the necessity of a mathematical demonstration, in the conclusion of which the word "must" does not frequently occur. Now since it happens ten times that we can argue that testimony must be false to every once that we can argue that it must be true, it naturally follows and is a fact, that these critics show far greater favor to views which reject all the historical evidence in our possession than they do to views which are based on some part of the evidence. "That, however, is not proved," is their usual comment upon any such hypothesis. Another particular in which they depart from Hume is in applying to history generally the canon of Bentley concerning the criticism of texts, that, in general, the more difficult reading is to be preferred. In like manner, they hold that that narrative which was least likely to be invented, owing to its improbability, is to be preferred. They are thus provided with two defences against historical testimony. If the story told appears to them in any degree unlikely, they reject it without scruple; while if there is no taint of improbability in it, it will fall under the heavier accusation of being too probable; and in this way, they preserve a noble freedom in manufacturing history to suit their subjective impressions.

§3. Criticism of the Theory of Balancing Likelihoods

168. I now propose to show some weighty reasons for holding that the theory of balancing likelihoods, however it may be worked out, and though there are, undoubtedly, special cases where it ought to be followed, is nevertheless, as a general method of treating ancient documents, a bad one. In cases where objective and somewhat definite probabilities can be attributed to all the different arguments on both sides, and where they are, as arguments, independent of one another, it seems to be incontestable that Hume's method improved is sound. In the ordinary text books on the Doctrine of Chances, so much of this theory as is given at all is only given in their chapters on the probability of testimony; and I will mention that Professor F. Y. Edgeworth says that in extending it to all independent arguments that have definite general probabilities I am "confusing" testimonies with arguments. But however obliging his attribution to me of this extension may be, it is mistaken; for the same extension has been made by several writers, among them one whom Professor Edgeworth holds in peculiar respect, Augustus De Morgan, who gave the necessary demonstration as far back as 1846 (Cambridge Phil. Trans. VIII. 393.). . . . But I will now set down the reasons which compel me to acknowledge the justice of Hume's method when improved as above, and applied to all independent arguments to which definite general probabilities can be attributed. But I will first call attention to a confusion of thought which might easily lead a man to infer that the theory in question was not applicable to arguments in general, unless his mind had been brought to an edge worth assiduous care before one presumes to discuss questions of probability. Taking the time-honored urn from which balls are drawn at random and thrown back after each drawing, I will suppose, that every ball is, in fact, a box, and that out of every 7 of them 3 contain gold and 4 lead. I will also suppose that I have two expert witnesses, one of whom judges by the color, and is right 3 times to every time he fails, while the other judges by the weight, and is right 9 times for every 5 failures. Let us suppose the testimony is independent, the color-expert being just as proportionally often right when the material-expert is right as when he is wrong. In order to fix our ideas, let us suppose the numbers are as follows:

Auriferous. Plumbiferous.
Heavy Light Heavy Light
Yellow, aAa 15 pAa 35 aPa 14 pPa 6
Grey, aAp 21 pAp 1 aPp 10 pPp 66

The total number of auriferous balls is A=72: of plumbiferous is P=96.

The total number of heavy auriferous and light plumbiferous, aA+pP= 108: that of the light auriferous and heavy plumbiferous is pA+aP=60.

The total number of yellow auriferous and grey plumbiferous, Aa+Pp= 126: that of the grey auriferous and yellow plumbiferous is Ap+Pa=42.

Now both witnesses report a ball to be auriferous; and according to the rule, I infer that the odds are 9/5 . 3/1=27/5 that it is gold; and that is correct since (aAa+pPp)/(pAp+aPa)= 81/15=27/5. But suppose that the witnesses, instead of testifying to the ball being auriferous, or otherwise, testify, the one that it is heavy, and the other that it is yellow, and leave the inference to me. Then the argument from its being heavy will be true 3 times to every 2 times that it is false, whether the color test succeed or fail; for aAa:aPp=15:10=3:2 and aAp:aPa=21:14=3:2, and in like manner the argument from its being yellow will hold 5 times for every 2 failures; for aAa:pPa= 15:6=5:2 and pAa:aPa=35:14=5:2. But if, following the rule, I were to infer that the odds that the ball was auriferous were 3/2.5/2= 15/4 I should be wrong; for the true odds are aAa:aPa=15:14. If I should take into account the argument that 3/7 of all the balls are auriferous, and say the odds were 3/2.5/2.3/4=45/16, I should still be wrong. From this an unskilled person might suppose that the rule did not hold in case of arguments. But two errors would be involved. In the first place the odds in favor of a sign's signifying a fact are equal to the ratio of the probability of the occurrence of the sign when the fact takes place to the probability of the occurrence of the sign when the fact does not take place; and in the second place the independence of two signs, considered as signifying the same fact, consists in the one occurring with the same proportionate frequency whether the other occurs or not, and when the fact takes place, and further, with the same proportionate frequency whether the other occurs or not, when the fact does not take place. But it is not necessary that the one should occur with the same proportionate frequency whether the other occurs or not, in general, without reference to whether the fact occurs or not. The required independence is not found in the above numbers. It is, however, found in the following:

Auriferous. Plumbiferous.
Heavy Light Heavy Light
Yellow, aAa=21 pAa=3 aPa=10 pPa=2
Grey, aAp=14 pAp=2 aPp=15 pPp=3

The odds in favor of a ball being auriferous:

Antecedently are 40 : 30 = 4:3
As yellow are 24/40 : 12/30 = 3:2
As heavy are 35/40 : 25/30 = 21:20
Hence, on the whole, the odds in favor of a heavy yellow ball being auriferous are 4/3 . 3/2 . 21/20 = 21/10, which is, of course, correct. The demonstration that this is always so, is now extremely simple. Write x for aAp/pAp and y for pAa/pAp. Also ξ for aPp/pPp and η for pPa/pPp. Then the condition of independence is that

aAa/pAp = xy and aPa/pPp = ξη

Then the odds

Antecedently will be

pAp (1 + x)(1 + y):pPp(1 + ξ)(1+ η);

As yellow will be (y(1+η)/(1+y)η);

As heavy will be (x(1+ξ)/(1+x)ξ;)

and the product of the three will be (pAp xy)/(pPp ξη) = aAa/aPa, as it should be.

169. Thus, when the essential conditions are fulfilled, this method is perfectly correct. Nor is it requisite that they should be fulfilled with any exactitude. A rough approximation is sufficient to give the conclusion some value. But the further from fulfilment the conditions are, the further from any scientific value is the conclusion; and with sufficient time and space I would undertake to show that, in reference to ancient history, they are, in a large majority of those cases in which there is any room for two opinions, so far from fulfilment, that it not only becomes utter nonsense to talk of "proof" and "perfect demonstration," — phrases perpetually in the mouths of the critics, — but, were there no better way of investigation, this method, taken as the general and regular method of treating questions of ancient history, must sink it in all its details to the rank of idle surmise. In this paper, however, I shall only give an outline of what this argument would be, because it is here not my principal object to refute the method now prevalent, but to expound a different logical theory, and to show what method of study results from it.

170. Let it be clearly understood, then, that what I attack is the method of deciding questions of fact by weighing, that is by algebraically adding, the feelings of approval produced in the mind by the different testimonies and other arguments pertinent to the case. I acknowledge that this method is supported, under abstract conditions, by the doctrine of chances, and that there are cases in which it is useful. But I maintain that these conditions are not often even roughly fulfilled in questions of ancient history; so that in those investigations it commonly has no value worth consideration.

171. Let us first make sure that we take proper account of everything that can be urged in favor of the method. Now, as far as I am aware, beyond its foundation in the doctrine of chances, the argument which was stated with such consummate skill by Hume, there are only two things to be said in favor of this method.

172. The first is that every science must develop its own method out of the natural reason of man; and that is the very way in which this method has been developed. Balancing reasons pro and con is the natural procedure of every man. No man can avoid doing so continually; and if he could, he would only have trained himself to the observance of rules having no foundation in reason. For reason is nothing but man's natural way of thinking, carefully and consistently observed.

173. The remaining argument in favor of this method is that the only alternatives are that of using this method and that of swallowing uncriticized all the incredible tales with which ancient history abounds.

174. This last argument need not detain us, because I shall in this paper develop a different method, which, instead of being less critical than that of balancing likelihoods, is much more so. But I repeat that I do not maintain that the ordinary method is never to be employed, but that its use should be restricted to exceptional cases, instead of being made the regular and standard procedure.

175. Now as to this method's being natural, I admit that there is some foundation for that. There is no kind of fallacious reasoning to which mankind is liable for which as much as that might not be said. But I appeal to modern psychologists to support me in the assertion, that it is not at all natural for men to employ this method as a usual procedure. On the contrary, the natural thing is to believe anything that one may hear said, until it is found that that assumption leads to difficulties; and when it is found to lead to difficulties, the most natural impulse is to make further inquiries, to cross-examine, etc. The occasions when we naturally balance reasons pro and con mostly relate to what we prefer to do, not to questions of fact. But, in the next place, I demur to the principle that what is natural is necessarily reasonable. It is one of the consequences of German preeminence in science and philosophy, which I hope will not last much longer, that subjective ways of deciding questions are, at this time, far too highly esteemed. Logic itself is made a pure question of feeling by Sigwart, whose treatise is now more in vogue than any other. †3 The Anglo-Saxon mind will never assent to that. I am sorry to say that it has been only too true that, under the German lead, the methods of reasoning in the different branches of science and philosophy have been left to grow up pretty much as they naturally would; and sooner or later, no doubt, natural tendencies do bring them right; but that result would be brought about much more quickly if methods were subjected to a more continual and strict criticism from exact logic; and what I mean by this, I must hope that this very paper may illustrate.

176. Passing now to the objections to the method of balancing likelihoods in the study of ancient history, the most obvious, perhaps, although not the most important, is, that the different testimonies and other arguments, are not commonly even in a rough sense independent, as the only rational basis for the method requires that they should be. Circumstantial evidences are, no doubt, often sufficiently independent; but direct testimony seldom is so. The same circumstances which lead one witness into error are likely to operate to deceive another. Nor does this want of independence always lead them into agreement. It may, frequently, be the cause of disagreement. Conflict of testimony in the vast majority of cases is not principally a mere chance result, as the theory supposes it to be. That concordance of testimony commonly has some other cause than its mere tendency to truth, is too obvious to need saying. The method of balancing likelihoods not only supposes that the testimonies are independent but also that each of them is independent of the antecedent probability of the story; and since it is far more difficult to make allowance for a violation of this requirement than of that of the independence of the testimonies, it becomes a much more serious matter. But how very remote from the real state of things it is to suppose that the narration of an ancient event is independent of the likelihood of the story told! Roughly speaking, it may be said that all detached stories of Greece and Rome, were told chiefly because the writer had something marvellous to recount; so that we may almost say that ancient history is simply the narrative of all the unlikely events that happened during the centuries it covers. It is evident that this circumstance in itself almost destroys the legitimate weight of any argument from the antecedent improbability, unless that improbability is so great as to render the story absolutely incredible. Examples are useful at this point. It is well-known that three ancient authorities give the story that Pythagoras had a golden thigh; and the custom of modern critics is simply to pass it by, hardly mentioned. Now had any historian asserted that the thigh of Pythagoras was a metallic gold to the centre while his lower leg and foot were solid flesh, that would unquestionably have been a case in which the method under consideration might very properly have been employed to reject the testimony. I may mention, however, that one of the authorities affords an illustration of the opposite kind of influence of antecedent probability upon the matter of testimony. For when Diogenes Laertius softens the story as he does, it is in my opinion, in order to avoid extreme improbability. As another example, let us take a story the extreme improbability of which has caused almost, if not quite, every modern critic to over-rule the testimony of a baker's dozen of the greatest authorities that antiquity can boast. This story is that the mathematician Thales once stumbled and fell into a ditch while he was showing an old woman the constellations. Zeller, one of the few modern writers who so much as condescends to show reasons for almost giving Aristotle, Plato, Cicero, and all the rest the lie, says that it is utterly incredible that Thales should have been such an impracticable theorist. Considering that pretty much all we know about the personality of Thales is that the Greeks considered him as the first of the wise men, and that eccentricity was, according to the Greek conception, essential to the character of a philosopher, that reason of Zeller's shows a wonderful depth of psychological insight. Of all the modern mathematicians whom I have known, there have been perhaps not over one in five, of whom I should not hesitate to believe such a thing. But I should like to know how the story ever came to be so generally stated, both by ancient writers, and by all modern writers until the days of modern criticism, if it is not that the whole thing, both Thales stumbling and old woman's and Zeller's contempt for him for doing so, is too richly true to human nature. If it is not historical, it must surely have been its extreme antecedent likelihood which caused so many authorities to assert that it was true. Many more examples are needed in order to show how very far ancient testimony is from being independent of the antecedent probability of its matter. But I leave this point, in order to hasten to another which is more important.

177. The theory of probabilities has been called the logic of the modern exact sciences; †4 and it is known to be the basis of the vast business of insurance; and therefore when a literary man learns that the method which he has been pursuing has the sanction of such a great mathematical doctrine, he begins to feel that he is a very scientific person. I notice that this sense of personal scientificality is far more developed in men who write second-hand commentaries on ancient authors than it is in the Faradays, the Helmholtzes, and the Mendeléefs. It is, therefore, well to point out to such persons that the word probability, taken in the sense in which the insurance business uses it, means a well-founded statistical generalization. Nor are probabilities assumed in the exact sciences without either a statistical basis or else a thoroughly criticized assurance that no serious error can result. But if by "probability" be meant the degree to which a hypothesis in regard to what happened in ancient Greece recommends itself to a professor in a German university town, then there is no mathematical theory of probabilities which will withstand the artillery of modern mathematical criticism. A probability, in that sense, is nothing but the degree to which a hypothesis accords with one's preconceived notions; and its value depends entirely upon how those notions have been formed, and upon how much objectivity they can lay a solid claim to. If a man bring me a collection of sphygmograph-tracings accompanied with notes of the circumstances under which they were taken, and tells me that he thinks they prove that the pulse of a man is affected by the mental state of another man on the other side of a brick wall, I confess that his hypothesis is so contrary to my preconceived notions that I shall not easily be persuaded to interrupt my work to make a study of the case. But those preconceived notions I hold to have a far more solid basis than those which ordinarily influence historical critics to pronounce an ancient narrative improbable. Yet even so, it is only my practical conduct which I allow to be influenced by that improbability. My action has to be decided one way or the other, and without loss of time; and "rough and ready" is unavoidably the character of the majority of practical decisions. But were I once to undertake the study of the sphygmograph-tracings, I would endeavor to get to the bottom of the question, without reference to my preconceived notions. For preconceived notions are only a fit basis for applications of science, not for science itself.

178. Thus everything that is put into one pan of the balance in weighing historical probabilities is utterly uncertain. Yet, if possible, what goes into the other pan is worse still. This consists of the "credibilities" of the testimonies. The inappropriateness of the application of the conception of probability here is striking. In playing a game, say with dice, there is this good reason for the calculation of chances, that any one face turns up as often as any other, quite independently of the result of any other throw, and the cause of the die turning up any particular face at any particular throw is quite beyond our powers of analysis. It is probably due to the combination of many little influences. In like manner, in insurance, though the cause of any one man's death might be ascertained, yet that would have no relation to the purposes of insurance, and why it is that out of a thousand men insured at the age of thirty, just so many will die each year afterward, is a question not to be answered, except that it is due to the coöperation of many causes. It is this which makes the calculation of chances appropriate. So, in making astronomical observations, why it is that out of a thousand observations, just so many will have just such an amount of error, can only be answered by saying that it is due to the summation of many small effects. But now on the other hand, take a question of history. We do not care to know how many times a witness would report a given fact correctly, because he reports that fact but once. If he misstates the matter, there is no coöperation of myriad causes. It is on the contrary, due to some one cause which, if it cannot often be ascertained with certainty, can at any rate be very plausibly guessed in most cases, if the circumstances are closely inquired into; and it is most pertinent to the business of the historical critic to consider how a mistake, if mistake there be, might credibly have arisen. A mere general ratio of true statements to false, would be utterly insufficient for his purpose, even if it really existed. But it does not exist. In the case of the die, we know that one throw in every six will bring up an ace in the future as it has done in the past; and so it is with insurance, and with the errors of observations. However complex the causes, that simple law will be followed, we are sure. But nothing of the kind is true in the case of a witness. His new statements, if he makes any, will necessarily relate to different topics from his old ones which he has exhausted; and his personal relation to them will be different. There is, therefore, no arguing from what his credibility was in one case, to what it will be in another, as there would be if the error were a sum due to the recurrence of myriad small effects. There thus neither is any such quantity as a real, general, and predictive truthfulness of a witness; nor if there were, would it answer the purposes of the historian to deal with it. For he does not want to know merely how many of a witness's statements out of a hundred are wrong; but just which ones of them are wrong.

179. This objection goes vastly deeper and is vastly weightier than that based on the want of independence of the arguments. Yet even this objection is downright insignificant as compared with the principal one, which I now proceed to state, although I have already hinted at it.

180. All mathematical reasoning, even although it relates to probability, is of the nature of necessary reasoning. All necessary reasoning consists of tracing out what is virtually asserted in the assumed premisses. While some of these may be new observations, yet the principal ones relate to states of things not capable of being directly observed. As has often been said, especially since Kant, such reasoning really does not amplify our positive knowledge; although it may render our understanding of our own assumptions more perfect. It is the kind of reasoning proper for any application of science. For example, it is by such reasoning that, assuming the law of gravitation to have been scientifically established, we go on to predict the time and place of an eclipse of the sun. Or, if our desire is to rectify our theory of the moon, we may do so by comparing such predictions, regarded as conditional, with observations. If, in making the correction, we assume that there can be no error discoverable by these observations except in the values of one or two constants employed, the correction is itself made by a mere application of principles assumed to be already scientifically established; and although it will be called a contribution to science, it leaves the frame-work of the theory untouched, and merely consists in incorporating the new observations into the places provided for them in our existing assumptions, so that there really is, in the logician's sense, no enlargement of our knowledge, but merely an arrangement or preservation of the systematization of knowledge already established. In applying observations to the fundamental correction of a theory, as Kepler applied Tycho's observations to the correction of the crude Copernican system, a kind of reasoning comes in which is not purely mathematical demonstration. If I remember rightly, there were only three points in the orbit of Mars, — I am sure there were only about three or four, — where Kepler ascertained the position of Mars in space by positive triangulation. Even those triangulations involved hypothetical elements, such as the assumption that the orbit was the same at every revolution, which might very well not have been true; and even had they been absolutely positive, they were altogether inadequate to determining the form of the orbit. These, therefore, as well as all the other items of his argument, were merely of this nature, that all simpler theories having been proved inadequate, all the predictions which could be based upon the theory of the elliptical orbit were verified by the observations well within the limits of possible, and even of not apparently unlikely, error. This was not mathematical demonstration; and all the subsequent work upon the solar system has merely multiplied and made more precise the same kind of proof, but has not changed its character. It is not now mathematical demonstration any more than it was then. Empirical science can never be enlarged by mathematical demonstration or any other kind of necessary reasoning; although when nomological science has advanced to a certain point, a mathematical theory can be based upon it which will be useful, not only for nomological science itself, but also for the classificatory and descriptive sciences which depend upon it.

181. Now ancient history occupies a place among the psychical sciences somewhat analogous to that of astronomy among the physical sciences. The one is a description of what is distant in the world of mind, as the other is a description of what is distant in the world of matter; and curiously enough, or significantly enough, an ancient alliance exists between the two sciences through chronology. Yet the amount of aid which physical astronomy can derive from mathematics is quite moderate, notwithstanding the mathematical perfection of nomological physics. †5 Anybody can convince himself that the reasoning of physical astronomy is not of a demonstrative kind by simply running over any text-book on the subject. But the science of nomological psychics, †6 — psychology, as we call it, — is still far too backward to afford any distinguished aid to history; and consequently, the demonstrative part of rightly reasoned history, exclusive of mere chronology, must, for a long time, remain very small. History, however, is as much more worthy than astronomy of being studied scientifically as mind is more worthy of our attention than matter. The use we should desire to make of ancient history is to learn from the study of it, and not to carry our preconceived notions into it, until they can be put upon a much more scientific basis than at present they can. Consequently, the staple of our reasoning in ancient history should not be of the demonstrative kind, as it is, as long as it remains, at best, an application of the mathematical doctrine of chances. If somebody replies that in weighing arguments pro and con critics make no use of the mathematical calculus of probabilities, the rejoinder will be that their proceeding only differs from that by its greater vagueness, and that a vague and inexact use of probabilities has no logical advantage over a more critical employment of them. If it is said that, as far as possible, the critics avoid likelihoods, and aim at positive certainty, the answer will be that they endeavor to do this by the employment of apodictic arguments, which only mark a still less exact grade of the same kind of demonstrative reasoning. Fully to appreciate the force of this argument one must have a well-matured comprehension of the logic of science; but when it is fairly apprehended, it cannot but be deemed quite conclusive.

182. Nevertheless, there still remains a further objection to the method of balancing likelihoods in the study of ancient history which is worthy of attention even after what has been said. We all know that as soon as a hypothesis has been settled upon as preferable to others, the next business in order is to commence deducing from it whatever experiential predictions are extremest and most unlikely among those deducible from it, in order to subject them to the test of experiment, and thus either quite to refute the hypothesis or make such corrections of it as may be called for by the experiments; and the hypothesis must ultimately stand or fall by the result of such experiments. Now what is true of any single hypothesis should equally hold good for any method of constructing many hypotheses. It, too, should have its consequences experimentally tested, and must stand or fall by the ultimate result. Now within the last half of the nineteenth century the merits of the procedure of the historical critics have been many times subjected to the test of archeological exploration; and what has been the result? I have not the necessary knowledge myself to sum it up in a magisterial manner; but from what I have casually heard about the relation of Egyptian exploration to the critics' previous opinion of Manetho and even of Herodotus, about the explorations in the Troiad and in Mycenae, and much else, I gather that, on the whole, it has been shown that the critics were found to be more or less fundamentally wrong in nearly every case, and in particular that their fashion of throwing all the positive evidence overboard in favor of their notions of what was likely, stands condemned by those tests. If this be so, it is no slight modification, but a complete revolution, of their logic which is called for; because, considering their great learning and competence, and the absolute confidence which they attached to their conclusions, as perfectly ineluctable, there is no middle course between pronouncing those men to have been a pack of charlatans and concluding that their method was wrong in principle. If it were not so, their pretensions to scientific determinacy of those conclusions would have been simply disgraceful. †7

§4. The Logic of Science

183. Having thus outlined the argument for the timeliness of a new logical theory of the proper method of dealing with ancient testimonies, I proceed to show how the question appears from the point of view of the "Minute Logic" †8 of which I am a defender.

184. I could not present the reason which has the greatest weight to my own mind, so that it should be convincing, unless I were to write a paper more than fifteen times the length of this one. That has to be foregone. Meantime, the secondary considerations that remain will be strong enough to maintain the position successfully.

185. To begin with, let me say that I propose to confine myself exclusively to the consideration of the proper scientific procedure concerning the documents in question. I do not propose to touch upon the question of miracles in so far as it is a practical religious question for an individual man. †9 This is not from timidity or any indisposition to express myself, could I have my whole say; but it is because it would expand this paper beyond all bounds of convenience in all respects. A practical belief is what a man proposes to go upon. A decision is more or less pressing. What ought it to be? That must depend upon what the purpose of his action is. What then, is the purpose of a man? That is the question of pure ethics, a very great question which must be disposed of before the logic of practical belief can be entered upon to any good effect. With science it is entirely different. A problem started today may not reach any scientific solution for generations. The man who begins the inquiry does not expect to learn, in this life, what conclusion it is to which his labors are tending. Strictly speaking, the inquiry never will be completely closed. Even without any logical method at all, the gradual accumulation of knowledge might probably ultimately bring a sufficient solution. Consequently, the object of a logical method is to bring about more speedily and at less expense the result which is destined, in any case, ultimately to be reached, but which, even with the best logic, will not probably come in our day. Really the word belief is out of place in the vocabulary of science. If an engineer or other practical man takes a scientific result, and makes it the basis for action, it is he who converts it into a belief. In pure science, it is merely the formula reached in the existing state of scientific progress. The question of what rules scientific inference ought to follow in order to accelerate the progress of science to the utmost is a comparatively simple one, and may be treated by itself. The question of how a given man, with not much time to give to the subject, had best proceed to form his hasty decision, involves other very serious difficulties, which make it a distinct inquiry. The former question, taken by itself, will be enough for the present communication.

186. I have said that in order to determine what the logic of the individual man should be, it would be necessary to consider what his purpose was. The same remark applies to the logic of science. It is easier to determine the purpose of science. It does not involve opening the question of ethics. Yet it is not a perfectly simple matter, either. Several definitions of the purpose of science that I have met with made it the business of science to ascertain that certain things were so, to reach foregone conclusions. Nothing could be more contrary to the spirit of science. Science seeks to discover whatever there may be that is true. I am inclined to think that even single perceptual facts are of intrinsic value in its eyes, although their value in themselves is so small that one cannot be quite sure that there is any. But every truth which will prevent a future fact of perception from surprising us, which will give the means of predicting it, or the means of conditionally predicting what would be perceived were anybody to be in a situation to perceive it, this it is, beyond doubt, that which science values. Although some will contradict me, I am bound to say that, as I conceive the matter, science will value these truths for themselves, and not merely as useful. Mathematics appears to me to be a science as much as any science, although it may not contain all the ingredients of the complete idea of a science. But it is a science, as far as it goes; the spirit and purpose of the mathematician are acknowledged by other scientific men to be substantially the same as their own. Yet the greater part of the propositions of mathematics do not correspond to any perceptual facts that are regarded as even being possible. The diagonal of the square is incommensurable with its side; but how could perception ever distinguish between the commensurable and the incommensurable? The mathematical interest of the imaginary inflections of plane curves is quite as great as that of the real inflections. Yet we cannot say that the scientific man's interest is in mere ideas, like a poet's or a musician's. Indeed, we may go so far as to say that he cares for nothing which could not conceivably come to have a bearing on some practical question. Whether a magnitude is commensurable or not has a practical bearing on the mathematician's action. On the other hand, it cannot be said that there is any kind of proportion between the scientific interest of a fact and its probability of becoming practically interesting. So far is that from being the case, that, although we are taught in many ways the lesson [of] the Petersburg problem, — so stupidly obscured by the extraneous consideration of moral expectation, — the lesson that we utterly neglect minute probabilities, yet for all that, facts whose probabilities of ever becoming practical are next to nothing are still regarded with keen scientific interest, not only by scientific men, but even by a large public. Here, then, are the facts to be reconciled in order to determine what the purpose of science, what scientific interest, consists in. First, every truth which affords the means of predicting what would be perceived under any conceivable conditions is scientifically interesting; and nothing which has not conceivable bearing upon practice is so, unless it be the perceptual facts themselves. But, second, the scientific interest does not lie in the application of those truths for the sake of such predictions. Nor, thirdly, is it true that the scientific interest is a mere poetical interest in the ideas as images; but solid truth, or reality, is demanded, though not necessarily existential reality. Carefully comparing these three conditions, we find ourselves forced to conclude that scientific interest lies in finding what we roughly call generality or rationality or law to be true, independently of whether you and I and any generations of men think it to be so or not. I might enunciate and prove this with more accuracy and evidence; but since I am not now undertaking to present the subject with the strictest method, I think what I have said will answer my purpose. But however this question be argued, it is one of those concerning which

A man convinced against his will
Is of his own opinion still,

(a current corruption worth dozens of such as its original). The dry light of intelligence is manifestly not sufficient to determine a great purpose: the whole man goes into it. So the fact that logic depends upon such a question is sufficient to account for the endless disputes of which logic is still the theatre.

187. Confining ourselves to science, inference, in the broadest sense, is coextensive with the deliberate adoption, in any measure, of an assertion as true. For deliberation implies that the adoption is voluntary; and consequently, the observation of perceptual facts that are forced upon us in experience is excluded. General principles, on the other hand, if deliberately adopted, must have been subjected to criticism; and any criticism of them that can be called scientific and that results in their acceptance must involve an argument in favor of their truth. My statement was that an inference, in the broadest sense, is a deliberate adoption, in any measure, of an assertion as true. The phrase "in any measure" is not as clear as might be wished. "Measure," here translates modus. The modes of acceptance of an assertion that are traditionally recognized are the necessary, the possible, and the contingent. But we shall learn more accurately, as our inquiry proceeds, how the different measures of acceptance are to be enumerated and defined. Then, as to the word "true," I may be asked what this means. Now the different sciences deal with different kinds of truth; mathematical truth is one thing, ethical truth is another, the actually existing state of the universe is a third; but all those different conceptions have in common something very marked and clear. We all hope that the different scientific inquiries in which we are severally engaged are going ultimately to lead to some definitely established conclusion, which conclusion we endeavor to anticipate in some measure. Agreement with that ultimate proposition that we look forward to, — agreement with that, whatever it may turn out to be, is the scientific truth.

188. Perhaps there will here be no harm in indulging in a little diagrammatic psychology after the manner of the old writers' discussions concerning the primum cognitum; for however worthless it may be as psychology, it is not a bad way to get orientated in our logic. No man can recall the time when he had not yet begun a theory of the universe, when any particular course of things was so little expected that nothing could surprise him, even though it startled him. The first surprise would naturally be the first thing that would offer sufficient handle for memory to draw it forth from the general background. It was something new. Of course, nothing can appear as definitely new without being contrasted with a background of the old. At this, the infantile scientific impulse, — what becomes developed later into various kinds of intelligence, but we will call it the scientific impulse because it is science that we are now endeavoring to get a general notion of, — this infantile scientific impulse must strive to reconcile the new to the old. The first new feature of this first surprise is, for example, that it is a surprise; and the only way of accounting for that is that there had been before an expectation. Thus it is that all knowledge begins by the discovery that there has been an erroneous expectation of which we had before hardly been conscious. Each branch of science begins with a new phenomenon which violates a sort of negative subconscious expectation, like the frog's legs of Signore Galvani.

§5. Regularity and Explanation

189. What, then, is that element of a phenomenon that renders it surprising, in the sense that an explanation for it is demanded? Par excellence, it is irregularity, says Dr. Paul Carus, in substance. †10 I cannot but think that there is a faulty analysis here. Nobody is surprised that the trees in a forest do not form a regular pattern, or asks for any explanation of such a fact. So, irregularity does not prompt us to ask for an explanation. Nor can it be said that it is because the explanation is obvious; for there is, on the contrary, no explanation to be given, except that there is no particular reason why there should be a regular pattern, — or rather that there is no sufficient reason, because there must be a tendency for large trees to grow where there is most room, which tendency, if it were strong enough and undisturbed enough, would produce a regular pattern. I mention this to show that, so far is mere irregularity [from being] a motive for demanding an explanation, that, even when there is a slight reason for expecting a regularity and we find irregularity, we do not ask for an explanation; whereas if it were an equally unexpected regularity that we had met with, we certainly should have asked for an explanation. I am, for reasons similar to this, as well as for others, confident that mere irregularity, where no definite regularity is expected, creates no surprise nor excites any curiosity. Why should it, when irregularity is the overwhelmingly preponderant rule of experience, and regularity only the strange exception? In what a state of amazement should I pass my life, if I were to wonder why there was no regularity connecting days upon which I receive an even number of letters by mail and nights on which I notice an even number of shooting stars! But who would seek explanations for irregularities like that?

190. Let me not, however, be understood to make the strength of an emotion of surprise the measure of a logical need for explanation. The emotion is merely the instinctive indication of the logical situation. It is evolution ({physis}) that has provided us with the emotion. The situation is what we have to study.

191. Before dismissing irregularity, I may note, as aiding to clear the matter up, that a breach of an existing regularity always stimulates a demand for an explanation; but where, having expected regularity, we only find irregularity without any breach of regularity, we are only induced to revise our reasons for expecting anything. Irregularity, be it noted, cannot be expected, as such. For an expectation is, in every case, founded upon some regularity. For the same reason, merely not finding regularity where no particular regularity was expected, occasions no surprise.

192. In order to define the circumstances under which a scientific explanation is really needed, the best way is to ask in what way explanation subserves the purpose of science. We shall then see what the evil situation is which it remedies, or what the need is which it may be expected to supply. Now what an explanation of a phenomenon does is to supply a proposition which, if it had been known to be true before the phenomenon presented itself, would have rendered that phenomenon predictable, if not with certainty, at least as something very likely to occur. It thus renders that phenomenon rational, — that is, makes it a logical consequence, necessary or probable. Consequently, if without any particular explanation, a phenomenon is such as must have occurred, there is no room at all for explanation. If the phenomenon is such as need not have occurred on the special occasion, but must occur on occasions differing in no discoverable and exactly assignable pertinent respect from the special occasion on which the phenomenon in question actually occurs, still there is nothing for explanation to do, until it is ascertained in what respects, if any, the individual occasion differs from those other occasions. For example, I throw a die, and it turns up ace. Now I know already that this die will turn up ace once in six times; and I am persuaded that it would be hopeless to attempt, at present, to find any pertinent conditions fulfilled on this occasion which are not fulfilled every time the die is thrown. Hence, no proposed explanation of the die's turning up an ace can be in order, unless we can discover some peculiar and pertinent feature about the present occasion. Why should my lottery-ticket have drawn a blank, and somebody else's a prize? No explanation is called for. The question is silly.

193. Let us now pass to the case of a phenomenon in which, apart from a particular explanation, there was antecedently no reason for expecting it, and as little for expecting it not to happen. Suppose, for example, that on the day of the Lisbon earthquake the brightest new star had appeared in the heavens. There might possibly have been some explanation for this; but there would have been no motive for searching for one. To have done so would, indeed, have been a foolish proceeding, for reasons we need not now consider.

194. Thus, the only case in which this method of investigation, namely, by the study of how an explanation can further the purpose of science, leads to the conclusion that an explanation is positively called for, is the case in which a phenomenon presents itself which, without some special explanation, there would be reason to expect would not present itself; and the logical demand for an explanation is the greater, the stronger the reason for expecting it not to occur was.

195. Since it is never prudent to rely upon reasoning that is largely deductive, without a check upon its accuracy, especially where the conclusion is disputed, as this is, I will select a few examples calculated to refute it, if it is to be refuted; and examine its application to them. First, suppose the phenomenon observed consists simply in irregularity; then, if there were no ground for anticipating any particular regularity, there is simply nothing to explain (irregularity being the prevailing character of experience generally). This agrees with our natural judgment. But if we anticipate a regularity, and find simple irregularity, but no breach of regularity, — as for example if we were to expect that an attentive observation of a forest would show something like a pattern, then there is nothing to explain except the singular fact that we should have anticipated something that has not been realized. Here, by our theory, there is need of an explanation, not of an objective, but of a subjective phenomenon (pardon the jargon, — slang jargon, at that). This again agrees with our natural judgment; for in such a case we straightway commence reviewing our logic to find how our error is to be explained.

196. Street cars are famous ateliers for speculative modelling. Detained there, with no business to occupy him, one sets to scrutinizing the people opposite, and to working up biographies to fit them. I see a woman of forty. Her countenance is so sinister as scarcely to be matched among a thousand, almost to the border of insanity, yet with a grimace of amiability that few even of her sex are sufficiently trained to command: — along with it, those two ugly lines, right and left of the compressed lips, chronicling years of severe discipline. An expression of servility and hypocrisy there is, too abject for a domestic; while a certain low, yet not quite vulgar, kind of education that is evinced, together with a taste in dress neither gross nor meretricious, but still by no means elevated, bespeak companionship with something superior, beyond any mere contact as of a maid with her mistress. The whole combination, although not striking at first glance, is seen upon close inspection to be a very unusual one. Here our theory declares an explanation is called for; and I should not be long in guessing that the woman was an ex-nun.

197. In this last case, the emotion of surprise is not felt, because the cognitive part of the mind must be uppermost in order to recognize the rarity of the phenomenon. There are cases in which the most familiar of facts seem to call for explanation. I am myself, for example, fond of urging that no theory of space can be satisfactory which does not explain why it should have three dimensions. Perhaps all will not agree with me on this point. They will say, it must have some number of dimensions; why not three as well as any number? Or I may be asked what number of dimensions I should expect space to have. My reply is, that if I did not know what number of dimensions space really had, and was obliged to investigate the question as we usually investigate scientific questions, by trying successive hypotheses until I found one that experiment would not refute, I should soon see that one dimension would not be sufficient; and I should try two as giving, not only the simplest, but by far the most comprehensible, of continua. I should guess that it was similar to the field of imaginary quantity. When that was refuted, I should pass to the next most comprehensible continuum, that of the field of real quaternions, quadridimensional space. Although the reasons for those numbers are not at all apodictic, yet I should, I am sure, be much surprised to learn that its dimensionality was three, which is so much more difficult to conceive than four. No doubt, it may be said that rationality has nothing to do with the question; and I have to confess that the fact that space has three dimensions has the air, at least, of proving that rationality has, in fact, nothing to do with it. But if it has not, still it seems to me that three is a number one would decidedly not expect. For triads mostly have some connection with Rationality; while things that are not governed by Rational considerations very seldom have three elements. I say all this, because it seems to me that this is almost a crucial instance for my theory of what it is that demands explanation. For, to the majority of minds, who would not definitely expect one number of dimensions rather than another, the fact that space has three dimensions does not seem to call for any particular explanation. That this is the fact seems to be proved by the circumstance that, of all the philosophers who have elaborated theories of space, hardly one has paid the smallest attention to the number of its dimensions, or regarded it as at all significant. But in me we have an instance of a mind to which it does seem that this feature of space calls for some definite explanation; and this same mind we find differs from the others in that it would decidedly have expected antecedently some other number. Certainly, my theory of what it is that demands explanation appears to be remarkably verified in this instance.

198. It is singular that there are not many logicians who attempt to define the circumstances which render an explanation of a phenomenon desirable or urgent. The majority of them seem tacitly to assume that any one fact calls for explanation as much as any other. Mr. Venn, however, in his Empirical Logic, †11 states, without much discussion, that it is the isolation of a fact that creates the need of an explanation. This approaches pretty close to my opinion, since the work of reason consists in finding connections between facts. Still, the distinctions between the two doctrines are manifold, too. All facts are more or less connected and more or less separated; so that Mr. Venn ought to say, and probably would say, that all facts call for explanation more or less. According to me, however, the demand for explanation is a more definite demand. All conceivable facts are divisible into those which, upon examination, would be found to call for explanation and those which would not. For if any fact would call for explanation, then if that which was ascertained in the consequent investigation was no more nor less than the falsity of that supposed fact, this latter would not call for explanation. Although I have not bestowed upon Mr. Venn's whole volume the minute study which it merits, so that I may be mistaken, I think I can account for this discrepancy. Mr. Venn belongs to a school which considers the logical process as starting at the percepts, if not at impressions of sense. Mr. Venn is himself so candid and so acute that he may perhaps have seen the error of this. But supposing that he has followed his school, the discrepancy between him and me would easily be accounted for, because there can be no doubt that every percept does involve elements that call for explanation. But I maintain that logical criticism cannot go behind perceptual facts, which are the first judgments which we make concerning percepts. A perceptual fact is therefore an abstract affair. Each such fact covers only certain features of the percept. I look at an object and think that it seems white. That is my judgment of the object perceived, or my judgment concerning the percept, but not the percept itself; and it is idle to attempt to criticize by any logic that part of the performance of the intellect which draws that judgment from the percept, for the excellent reason that it is involuntary and cannot be prevented or corrected. Such a fact which represents the percept in a very meagre way, although it is, in itself, a relatively isolated fact, — as isolated as any fact can be, — nevertheless does not, in itself, call for any explanation. On the contrary, it can only do that when it has been connected with other facts which taken by themselves would justify an expectation of the contrary of this fact. For example, if we should find that this object which seemed white, in the first place was white, and then that it was a crow, and finally that all the crows known were black, then the fact of this seeming and really being white would require explanation. It might be an albino, or it might be some new species or variety of crow. But perhaps it will be insisted that this thing's appearing white does call for an explanation; — that we want to know the cause of its being white. To this I reply that it has always been agreed that the tendency of the understanding was merely toward synthesis, or unification. Now no fact could possibly be more unified and simple than the fact that this is white, taken in itself. It would seem, therefore, that, if we consider this fact isolated from all others, it completely accomplishes the tendency of reason. To find a cause for the whiteness would only be to complicate our conception of the matter; and I never heard it suggested that intelligence per se demands complexity and multiplicity. But I suspect that when Mr. Venn speaks of isolation, he is thinking of there being other facts from which the given fact is separated; and that it is not isolation that he means, but separation. Now separation is itself a kind of connection; so that if that be his meaning, the state of things which calls for explanation is a connection which is not satisfactory to the mind. In that case, it is incumbent on Mr. Venn to explain himself more precisely, and to say in what respect it is unsatisfactory. If he were to say, "unsatisfactory in being contrary to what ought to be expected," he would come to my position, precisely.

199. Further light on the question may be obtained by considering the different types of explanation, of which Mr. Venn admits three after Mill, although he says of the third that it is to be received with reserve. I so far agree with him in this, that I think if the second type is accurately defined, it will be seen to include the third as a special and not important variety. The others I fully accept, though with my own definitions of them. I will take the examples of each which Mr. Venn has himself proposed. In illustration of the first type, he says: "We notice a plant that is flagging on a hot summer day: next morning it stands up again fresh and green. 'Why has it revived in the morning?' — 'Oh they always do."' One may smile at the naïveté of this; and certainly, it is not an explanation in the proper sense of the word. Still, its general function is the same as that of explanation; namely, it renders the fact a conclusion, necessary or probable, from what is already well known. It might be called a regularization, explanation and regularization being the two types of rationalization. The regularization, stated in full, would be,

Plants of a certain class usually revive in the morning;

This plant belongs to that class;

∴ This plant might be expected to revive in the morning.

Now it is true that the effect of the regularization is that the fact observed is less isolated than before; but the purpose of the regularization is, I think, much more accurately said to be to show that it might have been expected, had the facts been fully known. That the demand for regularization is due to the contrary being expected is shown by the fact that when that contrary expectation is very strong indeed, a regularization which even leaves the event quite improbable will in great measure satisfy the mind. When my father, Benjamin Peirce, stated (as Leverrier himself also did, at first) that the planet discovered by Galle was not that predicted by Leverrier, †12 people generally, who imagined that, in the absence of any prediction, the entire sphere of the heavens might have had to be swept to find the planet, asked, "How, then, was it that Galle found it in the very telescopic field in which Leverrier located his planet?" This was a challenge for a regularization; to which the response was that Galle's planet was about 50 minutes of longitude distant from Leverrier's place, and that this would occur by pure chance once in two hundred times. It was, therefore, about as extraordinary as that a given man of 75 should live to be a hundred. But the popular notion was that its probability was as one square degree is to the surface of the sphere, or as one to 41254. It is plain that the partial satisfaction which such a regularization affords is due to the great diminution of the unexpectedness.

200. The other type of demand for explanation is exemplified by Mr. Venn by the question, "Why is it so difficult to walk on ice?" He gives several supposed attempts at explanation; but the one he pronounces satisfactory is, 'Because, owing to the absence of friction, there is no horizontal reaction to the impulse of the feet,' which except for the misuse of the word impulse is correct, but I fear not very perspicuous to anybody who really needed the explanation! If we endeavor to place ourselves into the shoes of such a person, we must imagine ourselves noticing how easy it looks to skate upon ice, and to have remarked some such fact as that if a wagon receives a push from the land to the ice, it moves with the utmost ease on the ice. All these hazy ideas about the ice-surface, jostle one another in the mind in a perplexing way. It is, therefore, not the simple fact that ice is hard to walk on which creates the demand for an explanation: it is, on the contrary, a puzzling complexus of facts. Tell a man who never saw ice that frozen water is very hard to walk on, and he may ask whether the feet stick to it, or put other questions in order to figure to himself what you mean; but as long as the fact is apprehended by him as a simple one, he will no more ask why it should be so than a common man asks why lead should be heavy. The fact is entirely sufficient as long as it is simple and isolated. It is when the difficulty of walking on ice is compared with the extraordinary distance that a ball can be bowled upon it, or with such other facts as would naturally lead one to expect that ice would be particularly easy to walk on, that a scientific explanation is sought. This is shown by the rarity of the inquiry why it is tiresome to walk on sand. Everybody knows that it is hard to make a vehicle go over sand; and so it seems, to minds in the state of ignorance supposed, to be quite natural that walking on sand should be tiresome; and thus no explanation is asked for, although, in other respects, the question is so similar to that about ice. An isolated fact is precisely what a demand for an explanation proper never refers to; it always applies to some fact connected with other facts which seem to render it improbable.

201. I think I have now said enough to show that my theory — that that which makes the need, in science, of an explanation, or in general of any rationalization of any fact, is that without such rationalization the contrary of the fact would be anticipated, so that reason and experience would be at variance, contrary to the purpose of science — [that this theory] is correct, or as nearly so as we can make any theory of the matter at present. I will add, however, one more argument. Mr. Venn has felt the need of accounting for that desire of getting rid of isolated facts, to which he attributes the demand for an explanation; and he does so by remarking that isolated facts are dangerous. Now how, I should be glad to know, are isolated facts dangerous? The only way in which they would appear to be so, and it is the only way which Mr. Venn points out, is that in their presence we do not know what to expect. But if this is so, getting rid of the isolation of facts is not, after all, the ultimate motive of seeking an explanation; but on the contrary, an ulterior purpose has reference to expectation. And what is this condition described as being full of risk, of not knowing what to expect? It is not a mere negation of all expectation, — the state of mind in which a man takes his Sunday afternoon's stroll. It is a state in which a man seems to have ground for expecting certain things, and yet has evidence that those expectations may be falsified. Now this precisely describes the conditions under which according to my theory rationalization is called for. It may, however, be objected that if we are to go back to the ultimate motive for explanation, I should have asked what the danger is to which error would expose us. I reply that were I investigating the practical logic of the individual man, then, as I have already remarked, the question of pure ethics would have to be taken up, namely, the question 'What can a man deliberately accept as his ultimate purpose?' But restricting myself, as I do, to scientific reasoning, I need not go behind the recognized purpose of science, which stops at knowledge.

§6. Abduction, Induction, and Deduction †13

202. Accepting the conclusion that an explanation is needed when facts contrary to what we should expect emerge, it follows that the explanation must be such a proposition as would lead to the prediction of the observed facts, either as necessary consequences or at least as very probable under the circumstances. A hypothesis then, has to be adopted, which is likely in itself, and renders the facts likely. This step of adopting a hypothesis as being suggested by the facts, is what I call abduction. I reckon it as a form of inference, however problematical the hypothesis may be held. What are to be the logical rules to which we are to conform in taking this step? There would be no logic in imposing rules, and saying that they ought to be followed, until it is made out that the purpose of hypothesis requires them. Accordingly, it appears that the early scientists, Thales, Anaximander, and their brethren, seemed to think the work of science was done when a likely hypothesis was suggested. I applaud their sound logical instinct for that. Even Plato, in the Timaeus and elsewhere, does not hesitate roundly to assert the truth of anything, if it seems to render the world reasonable; and this same procedure, in a more refined modification, is the essence of modern historical criticism. It is all right as long as it is not found to interfere with the usefulness of the hypothesis. Aristotle departs a little from that method. His physical hypotheses are equally unfounded; but he always adds a 'perhaps.' That, I take it, was because Aristotle had been a great reader of other philosophers, and it had struck him that there are various inconsistent ways of explaining the same facts. Ultimately, the circumstance that a hypothesis, although it may lead us to expect some facts to be as they are, may in the future lead us to erroneous expectations about other facts, — this circumstance, which anybody must have admitted as soon as it was brought home to him, was brought home to scientific men so forcibly, first in astronomy, and then in other sciences, that it became axiomatical that a hypothesis adopted by abduction could only be adopted on probation, and must be tested.

203. When this is duly recognized, the first thing that will be done, as soon as a hypothesis has been adopted, will be to trace out its necessary and probable experiential consequences. This step is deduction. Here I may notice a rule of abduction much insisted upon by Auguste Comte, to the effect that metaphysical hypotheses should be excluded; and by a metaphysical hypothesis he means, as he tells us, a hypothesis which has no experiential consequences. I suppose a partially metaphysical hypothesis would be one that had, among its consequences, some not relating to possible experience; and that from those Comte would wish us to tear away the metaphysical part. I have no particular objection to Comte's rule. Indeed, I think it would obviously be fully justified by a consideration of the purposes of hypothesis. Only I beg to remark that its positive utility is limited by the circumstance that such [a] thing as a hypothesis which is either wholly or partially metaphysical cannot be constructed. I may be asked what I should say to the proposition that

The warranted genuine Snark has a taste
Which is meagre and hollow, but crisp;
Like a coat that is rather too tight in the waist,
With a flavor of Will-o-the-wisp.

I reply that it is not a metaphysical proposition, because it is no proposition at all, but only an imitation proposition. For a proposition is a sign separately indicating what it is a sign of; and analysis shows that this amounts to saying that it represents that an image is similar to something to which actual experience forces the attention. Consequently a proposition cannot predicate a character not capable of sensuous presentation; nor can it refer to anything with which experience does not connect us. A metaphysical proposition in Comte's sense would, therefore, be a grammatical arrangement of words simulating a proposition, but in fact, not a proposition, because destitute of meaning. Comte's use of the word metaphysical, in a sense which makes it synonymous with nonsense, simply marks the nominalistic tendency of Comte's time, from which he was unable to free himself, although the general tendency of his philosophy is rather opposed to it. However, be that as it may, the entire meaning of a hypothesis lies in its conditional experiential predictions: if all its predictions are true, the hypothesis is wholly true.

204. This appears to be in harmony with Kant's view of deduction, namely, that it merely explicates what is implicitly asserted in the premisses. This is what is called a half-truth. Deductions are of two kinds, which I call corollarial and theorematic. The corollarial are those reasonings by which all corollaries and the majority of what are called theorems are deduced; the theorematic are those by which the major theorems are deduced. If you take the thesis of a corollary, — i.e. the proposition to be proved, and carefully analyze its meaning, by substituting for each term its definition, you will find that its truth follows, in a straightforward manner, from previous propositions similarly analyzed. But when it comes to proving a major theorem, you will very often find you have need of a lemma, which is a demonstrable proposition about something outside the subject of inquiry; and even if a lemma does not have to be demonstrated, it is necessary to introduce the definition of something which the thesis of the theorem does not contemplate. In the most remarkable cases, this is some abstraction; that is to say, a subject whose existence consists in some fact about other things. Such, for example, are operations considered as in themselves subject to operation; lines, which are nothing but descriptions of the motion of a particle, considered as being themselves movable; collections; numbers; and the like. When the reform of mathematical reasoning now going on is complete, it will be seen that every such supposition ought to be supported by a proper postulate. At any rate Kant himself ought to admit, and would admit if he were alive today, that the conclusion of reasoning of this kind, although it is strictly deductive, does not flow from definitions alone, but that postulates are requisite for it.

205. Deduction, of course, relates exclusively to an ideal state of things. A hypothesis presents such an ideal state of things, and asserts that it is the icon, or analogue of an experience.

206. Having, then, by means of deduction, drawn from a hypothesis predictions as to what the results of experiment will be, we proceed to test the hypothesis by making the experiments and comparing those predictions with the actual results of the experiment. Experiment is very expensive business, in money, in time, and in thought; so that it will be a saving of expense, to begin with that positive prediction from the hypothesis which seems least likely to be verified. For a single experiment may absolutely refute the most valuable of hypotheses, while a hypothesis must be a trifling one indeed if a single experiment could establish it. †14 When, however, we find that prediction after prediction, notwithstanding a preference for putting the most unlikely ones to the test, is verified by experiment, whether without modification or with a merely quantitative modification, we begin to accord to the hypothesis a standing among scientific results. This sort of inference it is, from experiments testing predictions based on a hypothesis, that is alone properly entitled to be called induction.

207. I may as well say that arguments which I cannot now stop to set forth ought to remove all doubt that, accepting the term induction in this sense, the critical distinction, that is, the distinction in respect to the nature of their validity between deduction and induction consists in this, — namely, deduction professes to show that certain admitted facts could not exist, even in an ideal world constructed for the purpose, either without the existence of the very fact concluded, or without the occurrence of this fact in the long run in that proportion of cases of the fulfilment of certain objective conditions in which it is concluded that it will occur, or in other words, without its having the concluded objective probability. In either case, deductive reasoning is necessary reasoning, although, in the latter case, its subject matter is probability. Induction, on the other hand, is not justified by any relation between the facts stated in the premisses and the fact stated in the conclusion; and it does not infer that the latter fact is either necessary or objectively probable. But the justification of its conclusion is that that conclusion is reached by a method which, steadily persisted in, must lead to true knowledge in the long run of cases of its application, whether to the existing world or to any imaginable world whatsoever. Deduction cannot make any such claim as this; since it does not lead to any positive knowledge at all, but only traces out the ideal consequences of hypotheses.

§7. Three Kinds of Induction †15

208. It is desirable to consider a large range of inductions, with a view to distinguishing accurately between induction and abduction, which have generally been much confounded. I will, therefore, mention that, in the present state of my studies, I think I recognize three distinct genera of induction. I somewhat hesitate to publish this division; but it might take more years than I have to live to render it as satisfactory as I could wish. It is not that there seems to be any very serious want of clearness in it, or that the reasons for maintaining it are wanting in conclusiveness, or that I have any particular reason to doubt, either the conclusion or the correctness of the reasoning; but it is simply that the factor of safety is too small. I have not so thoroughly considered the subject as to be quite secure against possible oversights of one kind or another; nor have I collected a sufficient surplus of proofs so that they will hold even although oversights there be. Consequently, I am not yet willing to incorporate this division with the body of results of this investigation. But with this warning, I now state the division.

209. The first genus of induction is where we judge what approximate proportion of the members of a collection have a predesignate character by a sample drawn under one or other of the following three conditions, forming three species of this genus. First, the sample be a random one, an expression to which I attach a peculiar meaning. Namely, I mean by a random sample, a sample drawn from the whole class by a method which if it were applied over and over again would in the long run draw any one possible collection of the members of the whole collection sampled as often as any other collection of the same size, and would produce them in any one order as often as in any other. In this peculiar sense of the term random sample, it is only from a finite collection that a random sample can be drawn. And here it will be well to call to mind the exact meaning of a few terms relating to multitudes. †16 . . . The multitude of every collection is either enumerable or finite, denumeral or indefinite, abnumerable or transfinite. The scientific definitions of these terms were, I believe, first given by me in 1881; †17 but Dedekind gave, perhaps independently, in 1888, substantially the same definition of a finite multitude. An enumerable multitude is the multitude of a collection, — say the A's, — if and only if, no matter what relation ρ may be, either it is not true that every A is in the relation, ρ, to some A to which no other A stands in the relation, ρ, or else to every A some one A, and no other, stands in the relation ρ. This is as much as to say that the A's form a non-enumerable or infinite collection, if and only if there be some relation, ρ, such that every A stands in the relation ρ to an A to which no other A stands in the relation ρ, although there is an A of which it is not true that any A stands in the relation ρ, while no other A does so. Now according to our definition of the relation of being as small as, this is the same as to say, that a collection, say the A's, is non-enumerable or infinite, if and only if, the entire collection of A's is as small as a collection of A's from which some A is excluded; and this again is obviously identical with Dedekind's definition of an infinite collection which is that a collection is infinite if and only if the whole of it is as small as some part of it not the whole. But a more readily intelligible definition, coming to the same thing, is to say that an enumerable multitude is a multitude less than that of all the finite whole numbers. The denumeral multitude, for there is but one, is the multitude of a collection, say the A's, if and only if, there is a relation, say {s}, and an A, say A0, such that every A stands in the relation {s} to some A to which no other A stands in this relation, and no A stands in the relation {s} to A0, and taking any predicate, P, whatever, either every A has this character, P, or A0 does not possess the character P, or there is an A having the character P which is not in the relation {s} to any A that has the character, P. This comes to the same thing as saying that the denumeral multitude is the multitude of the finite whole numbers. Every denumeral collection is numerable; that is to every member of it a separate ordinal number may be assigned; and this may be done in such a way as to exhaust the entire collection of finite whole numbers. Every denumeral collection, therefore, either has an order or may receive an order. . . . To show that the whole is no more numerous than a part, or all the numbers than the even numbers, it suffices to write down

1 2 3 4 5 6 7 8 9, etc.

2 4 6 8 10 12 14 16 18, etc.

Of course, there is no number without a double, and each double is an even number. An abnumerable multitude is one of a denumeral succession of multitudes greater than the denumeral multitude; each of these being the multitude of the different possible collections of members of a collection of the next lower abnumerable multitude. I have proved that there is no multitude greater than every abnumerable multitude; and it seems to follow from a theorem of Cantor's about ordinal numbers that there is no multitude intermediate between two abnumerable multitudes. It will, therefore, suffice to define an abnumerable multitude as a multitude greater than that of all the finite whole numbers. If there is room on a line for any multitude of points, however great, a genuine continuity implies, then, that the aggregate of points on a line is too great to form a collection: the points lose their identity; or rather, they never had any numerical identity, for the reason that they are only possibilities, and therefore are essentially general. They only become individual when they are separately marked on the line; and however many be separately marked, there is room to mark more in any multitude.

210. Returning to the first genus of induction, it now becomes plain that a random sample, in the exact sense defined, can only be drawn from a finite collection. For the definition contains the phrase "the long run." Now what is meant by "the long run?" The phrase is only used in saying that the ratio of frequency of an event has such and such a value in the long run. The meaning is that if the occasion referred to upon which the event might happen were to recur indefinitely, and if tallies were to be kept of the occurrences and the non-occurrences, then [the] ratio of the one number to the other, as the occasions went on, would indefinitely converge toward a definite limit. The word 'converge' is here used in a different sense from that which is usual in mathematics. The common definition is that a series of values, x[1], x[2], x[3], etc., converges toward a limiting value x, provided, after any discrepancy {e} has been named it is possible to find one of the members of the series x{n} such that, for every value of n greater than {n}, (x[n]-x)2 < {e}2. This ought to be called definite convergence. No such member x[n] can, in the indefinite convergence with which we have to do, be fixed in advance of the experiment. Nevertheless, there will be some such value.

211. Such being the nature of a long run, we see that the idea of a random sample supposes that in a denumeral series of trials all possible samples of the class sampled are to be capable of being drawn, and that in every possible order inter se. But all possible orders in which all possible samples, however small, could be drawn from a denumeral collection, would be abnumerable, and therefore not to be completed in a long run. It follows that it is only a finite or enumerable class from which a random sample in the sense of the definition can be drawn. It is, indeed, evident that one cannot take even a single whole number at random; for a whole number taken at random would be infinitely more likely to be larger than any predesignate number than not.

212. Let us now consider another species of the first genus of induction. It had better be mentioned, by the way, that no multitude not enumerable is increased by being multiplied by itself; so that a denumeral collection of denumeral collections makes up a denumeral collection of the members of the latter collections. Let us now suppose that we are about to sample a denumeral collection in order to ascertain the proportionate frequency with which its members have a certain character designated in advance of the examination. Usually, there is no sense in speaking of a definite finite proportion of a denumeral collection; but I am going to suppose that this collection has an order which gives it a sense. The sample is to be drawn under the guidance of a precept under which we can enlarge any sample drawn indefinitely and can also draw an indefinite number of samples. Now I shall suppose that in some way, no matter how, we become assured that a relation exists between four correlates, to wit, the predesignate character, the precept of sampling, the collection sampled, and the future course of experience, this relation being such that, in the long run, the distribution of the predesignate character in samples drawn under the precept will be the same as if they had been drawn strictly at random from an indefinitely large finite collection composing all our future experience of members of the same collection. Then, as before, we can infer inductively the proportional frequency of that character in future experiences of members of the same collection; and the induction must approximate indefinitely, though irregularly, to the true proportion. As an example, take a certain die. All the falls of it shall form the denumeral collection. In future experience this die will probably be thrown a very large but finite number of times. Let me sample the throws in order to find out (since it may be loaded or badly made) with what relative frequency it will turn up an ace. My precept shall be to throw it from the dicebox after shaking, replace it, and go on in the same way. I will not stop to inquire how I know that my sample throws will, as far as the distribution of aces is concerned, be determined as if they had been drawn strictly at random among all future throws, because this question has, at this stage, no relevancy, and would only divert our minds from our point. And besides, the elements of the difficulty will find their solution in questions we have presently to take up.

213. Perhaps we may reckon, as a third species under the first genus of induction, those cases in which we find a denumeral series in an objective order of succession, and wish to know what the law of occurrence of a certain character among its members is, without at the outset so much as knowing whether it has any definite frequency in the long run or not. As an example, I will make a very slight examination of the occurrence of the figure 5 in the endless decimal that would express the value of π. Since the enormous labor has been performed of calculating this number to over seven hundred places, it seems a pity that no use whatever should be made of it. An instructor having a class in probabilities might very well give out as an exercise the examination of the calculated figures with a view to drawing such inferences as might be drawn by the doctrine of chances. I shall confine myself to illustrating this sort of induction by beginning an inquiry whether the figure 5 occurs in a purely chance way. I do not know why I chose this particular figure: I did so before I looked at the value of π. Taking the first 700 places, I separate them into the first 350 and the second 350. If these are quasirandom samples of the whole and all the figures occur equally often, there ought not to be far from 35 fives in each set. The odds that the number will fall in the thirties are about 2 to 1. The odds that it will fall between 28 and 42 exclusive is just 3 to 1. We find, in fact, that there are 33 fives in the first 350, and 28 in the second 350. Since the odds against this are only about 2 to 1, we conclude that the fives, and presumably the other figures, either occur by chance or very nearly so. It would, however, perhaps not be surprising if they were to occur with a little more approach to regularity than if they were purely fortuitous. Therefore, as a further illustration of this kind of induction, I have counted the number of 5's in each of the seventy sets of ten successive figures. In these seventy sets, the normal number of those having one 5 should be 27 1/8. But we suspect there will be more owing to the fives coming a little more regularly than merely by chance. We will ask then what is the probability that there will be no more than 32 tens containing just one 5. It is about 5/6; but the actual number of such tens is 33. There is, therefore, a doubtful indication of such regularity.

214. These are all the species I can mention of the first type of induction, in which we ascertain the value of a ratio and are morally certain to approximate to it indefinitely in the long run for each problem. By "morally certain," I mean that the probability of that event is 1. Of course, there is a difference between probability 1 and absolute certainty. In like manner, "bare possibility" should mean the possibility of that whose probability is zero. It is barely possible that a well made pair of dice should turn up doublets every time they were thrown: it is a conceivable chance, though morally certain not to happen. But that a pair of dice will not turn up sevens is absolutely certain; it is not possible.

215. The second genus of induction comprises those cases in which the inductive method if persisted in will certainly in time correct any error that it may have led us into; but it will not do so gradually, inasmuch as it is not quantitative; — not but that it may relate to quantity, but it is not a quantitative induction. It does not discover a ratio of frequency. The first species under this genus is where the collection to be sampled is an objective series of which some members have been experienced, while the rest remain to be experienced, and we simply conclude that future experience will be like the past. We may take Quetelet's well-known example of the ancient Greek who, never having heard of the flux and reflux of the ocean, should have wandered to the shores of the Bay of Biscay and should have there seen the tide rise for m successive half-days. I need hardly say that I utterly reject the doctrine that there is any consequent definite probability that the event will happen during the next half-day. That doctrine has been absolutely disproved. If the Greek's conclusion is that the tide rises about once every half-day, it is an induction of the first genus, second species. He may say that the indication is that the frequency is somewhere between m-1/2/m and m+1/2/m although this is only a rough approximation. He may, thence, deduce the conclusion that a tide will not be wanting in the following m half-days, although he ought not to risk much upon it. Beyond that it cannot be said that the quantitative induction warrants such a prediction. But if the Greek had seen the tide rise just often enough to suggest to him that it would rise every half-day forever, and had proposed then to make observations to test this hypothesis, had done so, and finding the predictions successful, had provisionally accepted the theory that the tide would never cease to rise every half-day, there would be just this justification for this conclusion, that it was the result of a method which, if it be persisted in, must correct its result if it were wrong. For if the tide was going to skip a half-day, he must discover it, if he continued his observations long enough. This degree of justification and no more he would have whether he made a dozen trials, or half a dozen, or three, or two, or one only, or even none at all. The argument would have precisely the same justification in either case. The method would infallibly correct itself, provided he continued this series of experiments; but not if he dropped it and subsequently commenced another series, as would be the case with quantitative induction. For this induction not being quantitative, does not conclude that the probability of the tides rising is 1; but that it raises every half-day without exception. It has nothing to do with probabilities or improbabilities; and if the series of observations skips a single day, that day may be the very day of the exceptional fact. This kind of induction further differs from quantitative induction, inasmuch as there is no probable indication in advance, if its conclusion is to break down; so that, as long as it does not break down, there is nothing to be said but that no reason appears as yet for giving up the hypothesis. It gives, therefore, but a very slight and merely negative support to the hypothesis. It is a proper answer enough to gratuitous hypotheses. It is impossible to avoid making some use of it for that purpose. But it must be set down as the weakest possible of inductive arguments. I have confined myself to cases in which the series of occasions considered is objective. But I am unable to perceive that there is any intrinsic logical distinction between these cases and those in which the series results from our own subdivision of a continuum. It might, for example, be suggested that the action of gravitation may be intermittent, either with a very short period, or without any definite period. In that case, a body moving for a considerable time would show merely the average acceleration; but two molecules might, during the interval of their encounter, either undergo no acceleration, so that it would be as if there were no encounter, or they might undergo acceleration many times that of average gravitation; and this might account for there seeming to be greater attraction at small distances than the law of average gravitation would account for. Moreover, greater masses moving slower than smaller ones, a periodic relation between atomic weights and attractions of atoms might be expected. Now, as a test of that hypothesis, it might be proposed to shorten the period of a pendulum more and more, and try to observe some irregularities of its amplitudes. If we found that, as far as we could go, say with pendulums oscillating 50 times a second, there were no observable irregularities of amplitude, and were to infer that there was no intermittency of gravitation, I am unable to see that the argument would differ from the argument that the tide will rise on every half-day forever, because it has been seen to do so on several successive half-days. It is true that this latter argument is weakened by the consideration that states of things not universal usually come to an end; while the other is strengthened by the consideration that, time being continuous, it is reasonable to suppose that, in sufficiently short intervals, there will be no further variation of any given phenomenon. But both of these are extraneous considerations. As far as the mere argument that what has not been found need not be expected is concerned, there seems to be no logical distinction between them. Let us consider one more example. By means of a well-constructed color-box, two adjacent rectangles are illuminated, each with nearly homogeneous violet light, of the same apparent luminosity; the one of a wave-length of about 404 micromicrons, the other 402 micromicrons, and the observer who knows only what he sees, is asked which is the redder. He says he sees no difference. But the operator insists upon his deciding for one or the other; and with reluctance he names one, as it seems to him quite at random. However, the experiment having been repeated several hundred times, it is found that in each set of a hundred answers, a decided majority makes the more refrangible the redder. Now then, what do we proceed to infer from this, — that there is no such thing as a Differenz-Schwelle, but that no matter how small the difference of excitations a sufficient number of answers would betray a difference of sensation? The only justification for this would be that it is the result of a method that persisted in must eventually correct any error that it leads us into. I may mention, that the argument that there is no Differenz-Schwelle is, in reality, stronger than this. But a negative induction of this sort, a refusal to expect what is contrary to experience, will rightly be resorted to when gratuitous objections are raised to any induction.

216. I seem to recognize a third genus of inductions where we draw a sample of an aggregate which can not be considered as a collection, since it does not consist of units capable of being either counted or measured, however roughly; and where probability therefore cannot enter; but where we can draw the distinction of much and little, so that we can conceive of measurement being established; and where we may expect that any error into which the sampling will lead us, though it may not be corrected by a mere enlargement of the sample, or even by drawing other similar samples, yet must be brought to light, and that gradually, by persistence in the same general method. This kind of reasoning may be described in slightly different terms by saying that it tests a hypothesis by sampling the possible predictions that may be based upon it. Predictions are not units; for they may be more or less detailed. One can say roughly that one is more significant than another; but no approach to actual weighing of their significance can, in most cases, be made. Consequently, we cannot say that a collection of predictions drawn from a hypothesis constitutes a strictly random sample of all that can be drawn. Sometimes we can say that it appears to constitute a very fair, or even a severe, sample of the possible predictions; while in other cases, we cannot even say that, but only that it comprises all the predictions which we can as yet draw and put to the test. Those two classes of cases may be taken as constituting two species under this genus. We cannot ordinarily hope that our hypothesis will pass through the fire of induction, absolutely unmodified. Consequently, we ought not to conclude that it is absolutely correct, but only that it very much resembles the truth. In so far as further induction will modify it, as it must be expected that it will do, if it is not to meet with downright refutation, it can hardly fail that the modification should come about gradually. We shall first find facts, reconcilable yet unexpected. These will be discovered in greater volume, until they show that a modification of the theory is necessary. The familiar history of the kinetical theory of gases well illustrates this. It began with a number of spheres almost infinitesimally small occasionally colliding. It was afterward so far modified that the forces between the spheres, instead of merely separating them, were mainly attractive, that the molecules were not spheres, but systems, and that the part of space within which their motions are free is appreciably less than the entire volume of the gas. There was no new hypothetical element in these modifications. They were partly merely quantitative, and partly such as to make the formal hypothesis represent better what was really supposed to be the case, but which had been simplified for mathematical simplicity. There was, besides, an important modification which was imposed by mathematical necessity. So far as these modifications were introduced in order to bring the hypothesis into better accord with the facts, they were indicated and suspected long before the need of them became quite apparent; so that this genus of induction shares with the first the advantage that where the inductive conclusion errs, it will be but slightly, and the discovery, instead of being shot like a bolt out of the blue, creeps upon us as a dawning day.

217. The reasonings of science are for the most part complex. Their parts are so put together as to increase their strength. Our attention has been confined to the elements out of which scientific argumentations are built up. We have now passed in review all the logically distinct forms of pure induction. It has been seen that one and all are mere processes for testing hypotheses already in hand. The induction adds nothing. At the very most it corrects the value of a ratio or slightly modifies a hypothesis in a way which had already been contemplated as possible.

§8. Abduction

218. Abduction, on the other hand, is merely preparatory. It is the first step of scientific reasoning, as induction is the concluding step. Nothing has so much contributed to present chaotic or erroneous ideas of the logic of science as failure to distinguish the essentially different characters of different elements of scientific reasoning; and one of the worst of these confusions, as well as one of the commonest, consists in regarding abduction and induction taken together (often mixed also with deduction) as a simple argument. Abduction and induction have, to be sure, this common feature, that both lead to the acceptance of a hypothesis because observed facts are such as would necessarily or probably result as consequences of that hypothesis. But for all that, they are the opposite poles of reason, the one the most ineffective, the other the most effective of arguments. The method of either is the very reverse of the other's. Abduction makes its start from the facts, without, at the outset, having any particular theory in view, though it is motived by the feeling that a theory is needed to explain the surprising facts. Induction makes its start from a hypothesis which seems to recommend itself, without at the outset having any particular facts in view, though it feels the need of facts to support the theory. Abduction seeks a theory. Induction seeks for facts. In abduction the consideration of the facts suggests the hypothesis. In induction the study of the hypothesis suggests the experiments which bring to light the very facts to which the hypothesis had pointed. The mode of suggestion by which, in abduction, the facts suggest the hypothesis is by resemblance, — the resemblance of the facts to the consequences of the hypothesis. The mode of suggestion by which in induction the hypothesis suggests the facts is by contiguity, — familiar knowledge that the conditions of the hypothesis can be realized in certain experimental ways.

219. I now proceed to consider what principles should guide us in abduction, or the process of choosing a hypothesis. Underlying all such principles there is a fundamental and primary abduction, a hypothesis which we must embrace at the outset, however destitute of evidentiary support it may be. That hypothesis is that the facts in hand admit of rationalization, and of rationalization by us. That we must hope they do, for the same reason that a general who has to capture a position or see his country ruined, must go on the hypothesis that there is some way in which he can and shall capture it. We must be animated by that hope concerning the problem we have in hand, whether we extend it to a general postulate covering all facts, or not. Now, that the matter of no new truth can come from induction or from deduction, we have seen. It can only come from abduction; and abduction is, after all, nothing but guessing. We are therefore bound to hope that, although the possible explanations of our facts may be strictly innumerable, yet our mind will be able, in some finite number of guesses, to guess the sole true explanation of them. That we are bound to assume, independently of any evidence that it is true. Animated by that hope, we are to proceed to the construction of a hypothesis.

220. Now the only way to discover the principles upon which anything ought to be constructed is to consider what is to be done with the constructed thing after it is constructed. That which is to be done with the hypothesis is to trace out its consequences by deduction, to compare them with results of experiment by induction, and to discard the hypothesis, and try another, as soon as the first has been refuted; as it presumably will be. How long it will be before we light upon the hypothesis which shall resist all tests we cannot tell; but we hope we shall do so, at last. In view of this prospect, it is plain that three considerations should determine our choice of a hypothesis. In the first place, it must be capable of being subjected to experimental testing. It must consist of experiential consequences with only so much logical cement as is needed to render them rational. In the second place, the hypothesis must be such that it will explain the surprising facts we have before us which it is the whole motive of our inquiry to rationalize. This explanation may consist in making the observed facts natural chance results, as the kinetical theory of gases explains facts; or it may render the facts necessary, and in the latter case as implicitly asserting them or as the ground for a mathematical demonstration of their truth. In the third place, quite as necessary a consideration as either of those I have mentioned, in view of the fact that the true hypothesis is only one out of innumerable possible false ones, in view, too, of the enormous expensiveness of experimentation in money, time, energy, and thought, is the consideration of economy. †18 Now economy, in general, depends upon three kinds of factors: cost; the value of the thing proposed, in itself; and its effect upon other projects. Under the head of cost, if a hypothesis can be put to the test of experiment with very little expense of any kind, that should be regarded as a recommendation for giving it precedence in the inductive procedure. For even if it be barely admissible for other reasons, still it may clear the ground to have disposed of it. In the beginning of the wonderful reasonings by which the cuneiform inscriptions were made legible, one or two hypotheses which were never considered likely were taken up and soon refuted with great advantage. Under the head of value, we must place those considerations which tend toward an expectation that a given hypothesis may be true. These are of two kinds, the purely instinctive and the reasoned. In regard to instinctive considerations, I have already pointed out that it is a primary hypothesis underlying all abduction that the human mind is akin to the truth in the sense that in a finite number of guesses it will light upon the correct hypothesis. Now inductive experience supports that hypothesis in a remarkable measure. For if there were no tendency of that kind, if when a surprising phenomenon presented itself in our laboratory, we had to make random shots at the determining conditions, trying such hypotheses as that the aspect of the planets had something to do with it, or what the dowager empress had been doing just five hours previously, if such hypotheses had as good a chance of being true as those which seem marked by good sense, then we never could have made any progress in science at all. But that we have made solid gains in knowledge is indisputable; and moreover, the history of science proves that when the phenomena were properly analyzed, upon fundamental points, at least, it has seldom been necessary to try more than two or three hypotheses made by clear genius before the right one was found. I have heard it said that Kepler tried nineteen orbits for Mars before he hit upon the right one; but in the first place, I cannot admit that that is a fair description of his elaborate series of inductions, and in the second place the subject of the hypothesis was not of the fundamental class. We cannot go so far as to say that high human intelligence is more often right than wrong in its guesses; but we can say that, after due analysis, and unswerved by prepossessions, it has been, and no doubt will be, not very many times more likely to be wrong than right. As we advance further and further into science, the aid that we can derive from the natural light of reason becomes, no doubt, less and less; but still science will cease to progress if ever we shall reach the point where there is no longer an infinite saving of expense in experimentation to be effected by care that our hypotheses are such as naturally recommend themselves to the mind, and make upon us the impression of simplicity, — which here means facility of comprehension by the human mind, — of aptness, of reasonableness, of good sense. For the existence of a natural instinct for truth is, after all, the sheet-anchor of science. From the instinctive, we pass to reasoned, marks of truth in the hypothesis. Of course, if we know any positive facts which render a given hypothesis objectively probable, they recommend it for inductive testing. When this is not the case, but the hypothesis seems to us likely, or unlikely, this likelihood is an indication that the hypothesis accords or discords with our preconceived ideas; and since those ideas are presumably based upon some experience, it follows that, other things being equal, there will be, in the long run, some economy in giving the hypothesis a place in the order of precedence in accordance with this indication. But experience must be our chart in economical navigation; and experience shows that likelihoods are treacherous guides. Nothing has caused so much waste of time and means, in all sorts of researches, as inquirers' becoming so wedded to certain likelihoods as to forget all the other factors of the economy of research; so that, unless it be very solidly grounded, likelihood is far better disregarded, or nearly so; and even when it seems solidly grounded, it should be proceeded upon with a cautious tread, with an eye to other considerations, and a recollection of the disasters it has caused. The third category of factors of economy, those arising from the relation of what is proposed to other projects, is especially important in abduction, because very rarely can we positively expect a given hypothesis to prove entirely satisfactory; and we must always consider what will happen when the hypothesis proposed breaks down. The qualities which these considerations induce us to value in a hypothesis are three, which I may entitle Caution, Breadth, and Incomplexity. In respect to caution, the game of twenty questions is instructive. In this game, one party thinks of some individual object, real or fictitious, which is well-known to all educated people. The other party is entitled to answers to any twenty interrogatories they propound which can be answered by Yes or No, and are then to guess what was thought of, if they can. If the questioning is skillful, the object will invariably be guessed; but if the questioners allow themselves to be led astray by the will-o-the-wisp of any prepossession, they will almost as infallibly come to grief. The uniform success of good questioners is based upon the circumstance that the entire collection of individual objects well-known to all the world does not amount to a million. If, therefore, each question could exactly bisect the possibilities, so that yes and no were equally probable, the right object would be identified among a collection numbering 220. Now the logarithm of 2 being 0.30103, that of its twentieth power is 6.0206, which is the logarithm of about 1,000,000 (1+.02x2.3) (1+.0006x2.3) or over one million and forty-seven thousand, or more than the entire number of objects from which the selection has been made. Thus, twenty skillful hypotheses will ascertain what two hundred thousand stupid ones might fail to do. The secret of the business lies in the caution which breaks a hypothesis up into its smallest logical components, and only risks one of them at a time. What a world of futile controversy and of confused experimentation might have been saved if this principle had guided investigations into the theory of light! The ancient and medieval notion was that sight starts from the eye, is shot to the object from which it is reflected, and returned to the eye. This idea had, no doubt, been entirely given up before Römer showed that it took light a quarter of an hour to traverse the earth's orbit, a discovery which would have refuted it by the experiment of opening the closed eyes and looking at the stars. The next point in order was to ascertain of what the ray of light consisted. But this not being answerable by yes or no, the first question should have been 'Is the ray homogeneous along its length?' Diffraction showed that it was not so. That being established, the next question should have been 'Is the ray homogeneous on all sides?' Had that question been put to experiment, polarization must have been speedily discovered; and the same sort of procedure would have developed the whole theory with a gain of half a century.

221. Correlative to the quality of caution is that of breadth. For when we break the hypothesis into elementary parts, we may, and should, inquire how far the same explanation accounts for the same phenomenon when it appears in other subjects. For example, the kinetical theory of gases, although it was originally proposed with a view merely to explaining the law of Boyle, never attracted much attention, nor was there any good reason why it should, until the conservation of energy was brought to light, and it was found that the kinetical theory would account, in a remarkably satisfactory way, for non-conservative phenomena. It accounts for those phenomena, so far as it does account for them, by representing that they are results of chance; or, if you please, of the law of high numbers; for it is remarkable that chance operates in one way and not in the opposite way. Under those circumstances, the economical consideration which we now have in view, would recommend that we at once inquire into non-conservative phenomena, generally, in order to see whether the same sort of explanation is equally admissible in all cases, or whether we are thus led to some broad category of conditions under which non-conservative phenomena appear, or whether there are several distinct ways in which they are brought about. For great economy must result in whichever way this question is answered, provided it can be answered at not too great an expense. Thus, if we find that there are several explanations of non-conservative phenomena, we have only to trace out their several consequences, and we shall have criteria for distinguishing them; while if we find there is but one cause, we at once reach a wide generalization which will save repetitious work. It is, therefore, good economy, other things being equal, to make our hypotheses as broad as possible. But, of course, one consideration has to be balanced against another. There still remains one more economic consideration in reference to a hypothesis; namely, that it may give a good "leave," as the billiard-players say. If it does not suit the facts, still the comparison with the facts may be instructive with reference to the next hypothesis. For example, I might be inclined to surmise that an observable quantity y was such a function of a quantity x, determined by the conditions of experiments, as to be expressible in the form y = a + bx2. Still, as I am not sure of this, perhaps it would be wise first to try how well the experiments could be satisfied by y = cx; because the residuals will be more readily interpretable in the latter case. As a provisional hypothesis, it will, for this reason, other considerations apart, be better to assume something very simple, even although we imagine that by complicating the hypothesis it could be brought nearer the truth. Let us suppose, for example, that I wished to find some mathematical relation between the Atomic weights and the succession of chemical elements according to Mendeléef's system. In point of fact, I hardly think that the time has yet come when it is worth while to take up that question for its own sake. The discoveries of Gallium, Germanium, and Scandium have proved that there is some truth in one part of Mendeléef's theory; but the non-discovery of hecamagnesium inclines me, I must say, to think that Chromium and Magnesium are exceptional elements; and it seems to me that the groups, unless it be the extreme ones, are founded on pretty superficial characters. And if we are to separate all elements into what Mendeléef calls groups, it seems to me that the rare earths seem to afford symptoms that an additional group must be admitted, say perhaps between the group of Zinc and the group of Gallium. However, if we are to retain Mendeléef's system, let us suppose, as a first rough approximation to the truth, that, in the absence of disturbing conditions of which we know nothing, the atomic weights of the elements would increase from K = 39 by 2 1/2 units at each step. Even if it is of little service as chemistry, it will, at least, serve as a tolerable illustration of the point of logic we have under consideration to compare the numbers required by this hypothesis with the numbers found. The latter depend upon the purity of the materials, of which the sole and insufficient guarantee is that atomic weights of material from different sources and subjected to different chemical operations agree. The table [next page] shows the comparison.

222. There are 16 consecutive elements undiscovered, according to Mendeléef's theory. Those that we know of the same groups, that is those in the table just above and just below the vacant spaces, may very well be contaminated with the unknown elements. The 24 first, not open to this suspicion, mostly differ from our calculation by not more than 1. Those just above the missing elements have on the average atomic weights 2 units too great, those just below are on the average about 1/2 a unit too small. Thus, this very incomplex and even rough hypothesis has done for us what a more elaborate one would almost surely have failed to do, namely, it has brought to light an indication that all the elements from Ruthenium up are probably largely contaminated with undiscovered elements, which contaminations have mostly atomic weights between 146 and 182, but are partly of large atomic weights, say from 211 up. Since this perturbation is largest in tellurium and barium, we should naturally look in these elements, especially, for admixtures of substances of higher atomic weight. In tellurium they have been sought, in vain; yet one cannot say that the negative has been rendered altogether improbable. In barium, on the other hand, there are indications of something of the sort, though whether it is sufficient to account for the large atomic weight, it is impossible to decide at present. I will not say that the hypothesis merits much attention, for the reason that it rests upon the acceptance of Mendeléef's arrangement, and that arrangement is itself in considerable doubt.

§9. The Logic of History

223. Having now passed in review all the elements of merit of an hypothesis, I ought, in regular procedure, to consider the general principles of synthesis of these elements. But I think that that would delay us to no advantage; for once it is granted that the elements I have enumerated are the points to consider, the mode in which they are to be combined in the case of ancient history is too obvious for dispute. The elements are as follows: Experiential character of the hypothesis. {as natural concomitants. Its explaining all the facts{ {as deductions {Corrollarial. {Theorematic. {Cheapness. { {Intrinsic Value {Naturalness. { {Likelihood. Economical considerations { { {Relation of {Caution {Hypotheses {Breadth { {Incomplexity. Element K Ca Sc Ti V Cr Mn Calc 39 41 1/2 44 46 1/2 49 51 1/2 54 Obs 39.1 40.0 44 48.2 51.4 52.1 55.0 O-C +0 -1 1/2 0 +1 1/2 +2 1/2 +1/2 +1 Element Fe Co Ni Cu Zn Ga Ge Calc 56 1/2 59 61 1/2 64 66 1/2 69 71 1/2 Obs 55.9 59.0 58.7 63.6 65.4 70.0 72.5 O-C -1/2 0 -3 -1/2 -1 +1 +1 Element As Se Br Kr Rb Sr Y Calc 74 76 1/2 79 81 1/2 84 86 1/2 89 Obs 75.0 79.2 80.0 81.6 85.4 87.7 89.0 O-C +1 +2 1/2 +1 +0 +1 1/2 +1 0 Element Zr Cb Mo Ru Rh Pd Calc 91 1/2 94 96 1/2 99 101 1/2 104 106 1/2 Obs 90.6 94 96.0 .. 101.7 103.0 106.5 O-C -1 0 -1/2 .. +0 -1 0 Element Ag Cd In Sn Sb Te I Calc 109 111 1/2 114 116 1/2 119 121 1/2 124 Obs 107.9 112.3 114 119.0 120.0 127.5 126.8 O-C -1 +1 0 +2 1/2 +1 +6 +3 Element X Cs Ba La Ce Pr Nd Calc 126 1/2 129 131 1/2 134 136 1/2 139 141 1/2 Obs 128.0 132.9 137.4 138.5 140 140.5 143.6 O-C +4 +6 +4 1/2 +3 1/2 +1 1/2 +2 Element Calc 144 146 1/2 149 151 1/2 154 156 1/2 159 Obs .. .. .. .. .. .. .. O-C .. .. .. .. .. .. .. Element Calc 161 1/2 164 166 1/2 169 171 1/2 174 176 1/2 Obs .. .. .. .. .. .. .. O-C .. .. .. .. .. .. .. Element Ta W Os Ir Calc 179 181 1/2 184 186 1/2 189 191 1/2 194 Obs .. .. 183 184 .. 190.8 193.0 O-C .. .. -1 -2 1/2 .. - 1/2 -1 Element Pt Au Hg Tl Pb Bi Calc 196 1/2 199 201 1/2 204 206 1/2 209 211 1/2 Obs 195.2 197.3 200.0 204.2 206.9 208 .. O-C -1 -1 1/2 -1 1/2 0 + 1/2 -1 .. Element Calc 214 216 1/2 Obs .. .. O-C .. ..

224. In the case of ancient history, the facts to be explained are, in part, of the nature of monuments, among which are to be reckoned the manuscripts; but the facts in greater part are documentary; that is, they are assertions and virtual assertions which we read either in the manuscripts or upon inscriptions. This latter class of facts is so much in excess, that ancient history may be said to consist in the interpretation of testimonies, occasionally supported or refuted by the indirect evidence of the monuments.

225. Now the first rule which we should set up is that our hypothesis ought to explain all the related facts. It is not sufficient to say that testimony is not true, it is our business to explain how it came to be such as it is.

226. The second rule is that our first hypothesis should be that the principal testimonies are true; and this hypothesis should not be abandoned until it is conclusively refuted. No practice is more wasteful than that of abandoning a hypothesis once taken up, until it becomes evident that it is quite untenable. An excellent method in the great majority of those cases in which it is applicable and in which it leads to any unequivocal results is to give precedence to that hypothesis which reposes upon a deep and primary instinct, such as is the instinct to believe testimony, without which human society could not exist. There is no surer mark of inexperience in dealing with witnesses than a tendency to believe that they are falsifying, without any definite, objective, and strong reason for the suspicion. But especially in ancient history, where the only facts we have are, in most cases, testimonies, the extremely bad economy of supposing those testimonies false, before we have first thoroughly tried the hypothesis that they are true, and have found it quite inadmissible, is so obvious, that it is difficult to repress a certain contempt for the reasoning powers of those critics who are given to this procedure.

227. The third rule will be that probabilities that are strictly objective and at the same time very great, although they can never be absolutely conclusive, ought nevertheless to influence our preference for one hypothesis over another; but slight probabilities, even if objective, are not worth consideration; and merely subjective likelihoods should be disregarded altogether. For they are merely expressions of our preconceived notions. Now one of the main purposes of studying history ought to be to free us from the tyranny of our preconceived notions.

228. The fourth rule will be that we should split up a hypothesis into its items as much as possible, so as to test each one singly.

229. The fifth rule will be that when we are in doubt which of two hypotheses ought to have precedence, we should try whether, by enlarging the field of facts which they are to explain, a good reason will not appear for giving one of them a decided preference over the other.

230. The sixth rule will be that if the work of testing a particular hypothesis will have substantially or largely to be done in any case, in the process of testing another hypothesis, that circumstance should, other things being equal, give this hypothesis which thus involves little or no extra expense, a preference over another which would require special work of no value except for testing it.

231. A hypothesis having been adopted on probation, the process of testing it will consist, not in examining the facts, in order to see how well they accord with the hypothesis, but on the contrary in examining such of the probable consequences of the hypothesis as would be capable of direct verification, especially those consequences which would be very unlikely or surprising in case the hypothesis were not true. It is not easy to enumerate the different kinds of consequences; but among them may be, that the hypothesis would render the present existence of a monument probable, or would result in giving a known monument a certain character; that if it were true, certain ancient documents ought to contain some allusion to it; that if it is misstated by some authority not considered in the selection of the hypothesis, that misstatement would be likely to be of a certain kind; that if the hypothesis is true, and an assertion or allusion found in an ancient work is to be explained by the author's knowing it to be true, he must have had certain other knowledge, etc. When the hypothesis has sustained a testing as severe as the present state of our knowledge of the particular branch of history to which it belongs renders imperative, it will be admitted provisionally into the list of our present historical results, subject of course to reconsideration along with all those other results, when we are in a condition to insist upon a higher grade of security. In order to make the difference between this method and that usually pursued quite clear, I propose to give three illustrative examples. I shall draw them from the history of philosophy, with which I am better acquainted than I am with political history. I shall endeavor to make the examples illustrative of different kinds of questions, and in departments of history where various grades of probability can be insisted upon. I shall, in each case, first show how the question would be treated in accordance with the method of this paper; and then I shall show how some one or more of the best critics actually have treated it. I shall not notice the theories of those who carry higher criticism to its last extravagances, but shall confine myself to those who are most esteemed for their sobriety and thoroughness. It will be necessary to confine our illustrations to some minor points, because these are the only ones which can be discussed within moderate limits.

232. If the necessity of this rule is not at once apparent, it will soon become so; for I am going to begin by breaking it in taking up the question of the authenticity of the writings of Aristotle, — a question which has formed the subject of several laborious books, and which I can here consider only in the most insufficient manner.

§10. Application of the Method

233. The facts to be explained may be outlined as follows. The works in our edition of Aristotle are forty-six in number, containing a million words, equal, if translated, to perhaps ten volumes of Herbert Spencer. In addition, a hundred ancient authors give some six hundred fragments from some sixty other works. Diogenes Laertius gives a catalogue of the writings of Aristotle, probably made in Alexandria, (but the date of it is a matter for conjecture,) which contains 146 titles, which Diogenes says had 445,270 lines, which would be more than three times the size of our edition. Yet this catalogue does not seem to refer to any large part of the substance of the works that we possess. Moreover, down to the time of Cicero, Aristotle, whose reputation was more Roman than Greek, was chiefly known by works which we do not possess. The style of those works, as it is described, and as we see it in the fragments, was highly artistic; while that of the general mass of the works we possess is harsh and excessively condensed. They seem like notes for books rather than finished books. We find, however, in them a few long passages in the same polished style as the fragments, as if Jeremy Bentham had allowed Ruskin to write a few pages for him. The works we possess are also extremely repetitious. More than once, a whole book, or even a whole work, is substantially written again. And of the lost works, some, we are told by those who had seen them, agreed in substance with some of those in our possession. Shorter passages, and especially definitions, are often repeated almost verbatim. Our Aristotle abounds in references to his own works, sometimes to lost works, but mostly apparently to the works we know under other titles, but the nomenclature of the titles in the references presents no fixity; the same work will receive from Aristotle himself various names, — unless he means to refer to some works that we do not know. Two different works will refer reciprocally to one another, and a work will contain a reference to a part further on in the same work. In one case, at least, it seems pretty clear that the reference involves a misunderstanding of the passage referred to; but I do not know why a voluminous author may not fall into a misunderstanding of a passage of his own writing. The surprising circumstances will in part be explained if we trust to a narrative given by Strabo in the XIIIth book of his Geography, of which we know that the IVth book, or a passage of it, was composed A.D. 19, — and Strabo is supposed, on tolerably good grounds, to have been born 66 B.C. This narrative is confirmed by Strabo's younger contemporary Plutarch in his life of Sulla, and in great part by Athenaeus in the IIIrd century of our era, and in part by Porphyry, also of the IIIrd century. The story is as follows.

234. Alexander died in June 323 B.C., Aristotle's school having been running in Athens for twelve years, and in the later years Aristotle was supposed to be almost the secret boss of Athens, was enormously rich, and was decidedly unpopular. Athens and Macedonia were instantly at war, and Aristotle retired to Chalcis in Euboea where there was a Macedonian garrison, leaving Theophrastus in charge of his school. Athens was subdued in September 322 B.C.; but just about that time Aristotle died. His will does not mention his precious library nor his personal papers; but it seems they passed into the possession of Theophrastus. Theophrastus lived until 287 B.C., and at his death bequeathed his books to a friend, Neleus, who lived at Scepsis in Aeolis, Asia Minor. Strabo is of opinion that this loss of Aristotle's writings was a severe blow to the peripatetic school; for many of the writings, it would seem, had not been published. At any rate, it seems to be a fact that the school became rather colorless. Meantime, about 250 B.C., the kings of Pergamus, to whom Scepsis belonged, began to collect a vast library, by the simple method of seizing books wherever they could lay hands upon them. The consequence was that the heirs of Neleus hid the books in a cellar. The cellar was damp; but there the books remained until, in 133 B.C., the last of that dynasty of kings bequeathed his kingdom to the Roman people. Soon after this, it would seem that the peripatetic school had been somewhat drawn into politics, although this is an obscure point. However, it is certain that a peripatetic, Aristion, or Athenion, became tyrant of Athens; and a peripatetic friend of his, Apellicon, who was so fond of books that he would steal them from the archives of Greek cities, and who had become rich by plunder, as an agent of Aristion, — this Apellicon, purchased the library of Neleus and brought it back to Athens. The papers of Aristotle had suffered grievously, during their century and a half of incarceration, from damp and insects, and were in places illegible; but Apellicon, in the intervals of his raids, occupied himself with copying and editing them. But in 87 B.C., Apellicon having died shortly before, Sulla took Athens, executed Aristion, and carried away the library to Rome. Without this accident, Aristotle would probably be to us today a name like Democritus; for the Greeks never regarded him as a supremely great philosopher. In mind and in breeding he was not exactly a Greek, but, like Democritus, was a Thracian. At any rate, Sulla took the library to Rome, and handed it over to the learned peripatetic Tyrannion, whose library finally amounted, according to Suidas, to 30,000 volumes. Tyrannion found that the editing of Apellicon was excessively bad. Ultimately, the peripatetic scholiarch Andronicus of Rhodes undertook the arrangement of the papers, the correction of the text, and the publication of a new edition.

235. The hypothesis that this story is true is so natural, and it ought to be so easily refuted if it is not true, that I am strongly inclined, in spite of the jeers of all the great German critics, to admit it on probation. †19 When I ask what, then, would be the source of information of Strabo, I find that he was the personal scholar of Tyrannion, and that the labors of Andronicus, which would have made considerable noise in the world of letters, were probably performed in his life-time. Still, before admitting the hypothesis to probation, we must ask whether it would explain all the principal facts. It explains the two styles. The one was for the outer public, the other for use in the school, whether as notes for lectures only, or for general reference, we have not sufficient positive evidence concerning the methods of instruction there to say, or not. The question has been put, as an unanswerable one, how it could be, according to this hypothesis, that some of the works of our collection were known previously to Andronicus. But this seems to mark a great eagerness to raise difficulties. Even if Strabo had said that none of these works had been published before, and on the contrary, he implies that some of them had been published, we should still be inclined to think that this could not be true in every sense. For how could the notes of students upon Aristotle's lectures have been prevented from circulating? We shall undoubtedly naturally conclude that the publication of Andronicus would be of Opera Inedita, including all works of which a decidedly new recension was found; but naturally of Aristotle's polished and finished productions no such text would be found. Strabo, it is true, surmises that the decadence of the peripatetic school was due to their want of Aristotle's writings; but that, from the nature of things, could only be Strabo's surmise. We are at liberty, on our side, if we think it best to do so, to suppose that it was because Aristotelianism was a little outside the general current of Greek thought. Nevertheless, if in place of imperfect notes by students, the school had had the works of Aristotle which we have, we too may surmise, if we find reason for it, that the school would have been somewhat better able to stem the current of thought, and not have been so swept into it as it seems to have been.

236. We are also asked how, upon this hypothesis can the cross-references have been inserted? But to make a difficulty of this does seem a little childish. The manuscripts had been upon the average six years in the school at Aristotle's death, and remained there for 35 years longer. Was not this time enough to insert any cross-references which had not been inserted in the first writing?

237. A more difficult question is how, upon the hypothesis, we are to explain the insertion of some spurious works; and how we are to explain the fact that Andronicus is said to have himself believed that the book of the categories was spurious. It seems, certainly, to be probable that there had originally been autographs of all the writings, except perhaps some of the most polished ones, which do not concern us, and perhaps some of the memoranda of facts. But those which touched upon subjects often gone through by classes would naturally be revised and copied; especially since papyrus, judging by what was made in Sicily in 1870, is not nearly so durable as modern paper. Thus, a considerable part of the works, and those of evident authenticity, would not be autographs. Consequently, if a book were marked as being by Aristotle, which might accidentally have happened by error, it could not be excluded. Other manuscripts were perhaps neither autographs nor distinctly attributed to Aristotle; and in such case, Andronicus would have been guided by such information as he could obtain. [It is certain that chirography could not have been, at that time, so characteristic of the individual as now.] †20

238. Another apparent difficulty is that Athenaeus, in one passage, says that Ptolemy Philadelphus purchased the books of Aristotle from Theophrastus; while, in another passage, he says the same king purchased the same books from Neleus. But Athenaeus must not be supposed to be acquainted with all the details of a transaction that happened five centuries before his time, especially since he seems not even to know that Theophrastus died before Ptolemy Philadelphus acceded to the throne. It is also to be noted that it was for the interest of the heirs of Neleus to say that Ptolemy Philadelphus had bought all the books, since it was about the end of his reign that they secreted the books lest Eumenes, King of Pergamus, should grab them. It is further to be noted that the reputation of Aristotle as a philosopher was not, at that time, very high; and such reputation as he had was chiefly that of a rhetorician. If there was a purchase it would probably be of copies. At any rate, copies would be returned to the seller, according to practice in other cases. What the agents of the libraries would want of the writings of the rhetorician Aristotle would be finished works. They would not care for lecture notes nor for memoranda.

239. Having thus reviewed all the supposed difficulties of this hypothesis and having found that they are not serious, we may admit it upon probation, and proceed to trace out its consequences. In the first place, then, supposing it to be true, the works of Aristotle which we possess should be expected to belong to the following classes: first, unfinished works intended for publication; second, lecture notes, or memoirs of investigations; third, brief outlines of theories to be studied further; fourth, memoranda of facts concerning subjects upon which Aristotle had not completed any theory nor written any book; fifth, jottings of ideas. In the third of these classes, that of briefs, almost every writer has a tendency to write nearly to the end of his last sheet, often crowding a little at the end; or, if his sheets are large, he may cut the last into halves and use but one half. In order to ascertain whether or not Aristotle had this habit, I have counted the number of lines in the Berlin edition in nineteen of the shortest books. I have added ten to each number to allow for the heading; and comparing the numbers so increased I find that in the majority of cases, namely in 11 out of the 19, they differ from the nearest multiples of 68 by less than 1/8 of 68, which, of course, ought by chance to happen only once in 4 times. The probability of its occurring 11 times out of 19, is less than 1/500. But in addition to that these eleven cases embrace all but one of the books whose length is short enough to afford decided indications, say less than 6 times 68 lines. Moreover, of the remaining 8 cases all but two are equally near to being multiples of half 68. Finally, the only two real exceptions are both spurious works. The following table gives the numbers. I think we may conclude with reasonable certainty that Aristotle generally wrote about 70 Berlin lines on a sheet. I put it at 70, because I think the method would naturally tend to give too small a number. The amount would be determined by the average size of a sheet of papyrus and the average size of Aristotle's writing, both of which would vary considerably. Lines + 10 De Ventorum situs et appell. . . . 60 + 8 = 1 X 68 De Divinatione per somnum . . . . 134 + 2 = 2 X 68 De longi. et brevitate vitae . . . 198 + 6 = 3 X 68 De juventute et senectute . . . . . 206 - 2 = 3 X 68 De memoria et reminisentia . . . . 266 + 6 = 4 X 68 De insomniis . . . . . . . . . 277 - 5 = 4 X 68 De somno et vigiliis . . . . . . 341 - 1 = 5 X 68 De insecalibus lineis . . . . . . 324 + 16 = 5 X 68 De audibilibus . . . . . . . . 408 = 6 X 68 De Xenoph. Lenone et Gorgia . . . 489 - 13 = 7 X 68 De respiratione . . . . . . . . 676 + 4 = 10 X 68 De animalium incessu . . . . . . 686 - 6 = 10 X 68 Physiognomica . . . . . . . . 679 + 1 = 10 X 68 De spiritu . . . . . . . . . 444 - 2 = 6 1/2 X 68 De animalium motione . . . . . . 434 + 8 = 6 1/2 X 68 De coloribus . . . . . . . . . 576 + 2 = 8 1/2 X 68 De plantio I . . . . . . . . . 577 + 1 = 8 1/2 X 68 De plantio II . . . . . . . . . 656 - 8 = 9 1/2 X 68 De Mundo . . . . . . . . . . 643 + 3 = 9 1/2 X 68

240. I may add that a cursory examination leads me to think that Aristotle liked to fill a sheet with the whole of a chapter; for a large part of the chapters are of about that length.

241. Now let us consider what would be done with the sheets. When the work was finished, they would be pasted together, rolled up, and sent to the copyist. They would not be pasted together before the work was quite written, since that might prove inconvenient; for insertions might be desirable, or even rearrangement. Now our collection probably does not contain any finished works. For although it does contain a few which were published during Aristotle's life-time, yet the quoted fragments of them indicate that what we now possess come from MSS. in more or less unfinished states. At any rate the great bulk of what we have are either short essays, lecture notes or notes of researches, memoranda of facts, or memoranda of ideas. It is unlikely that the sheets were pasted together. They must have been rolled up; because the method of keeping papers flat is so superior, that had it once come into use, rolls would have been almost given up, as they are today. Before being rolled up, they would have been arranged in order, with the end at the back; and they would be rolled up face inwards, and most likely put into leather cases. The manuscripts were in very bad condition, and it would be the outside of the roll which would be most exposed to injuries, which would often penetrate several sheets, so that bad places would occur at intervals of about seventy Berlin lines. Cocoons would also be deposited on the insides of the rolls, unless they were wound tight about their sticks; so that, in some cases, the beginnings of books would be injured.

242. For the sake of brevity, I pass over my reasons for thinking that the heirs of Neleus disposed of all the works that appeared to be finished, and that neither Neleus nor anybody else meddled much with the MSS. of those that have come down to us, until they passed into the hands of that Apellicon who corrected them so stupidly. We need to take account of the character of Apellicon. He was a peripatetic and a great book-collector. He stole a number of books from the archives of different cities; and having been detected, was obliged to abscond. He joined himself to another peripatetic scoundrel, Aristion, or Athenion, by whom he was sent to loot the sacred treasury of Delos. This he succeeded in doing, and both conspirators were made enormously rich, although by the extreme recklessness and carelessness of Apellicon his army was destroyed. Apellicon then bought the library of Neleus, while Aristion at once made himself tyrant of Athens, where he distinguished himself by his frightful cruelty, in which Apellicon was his right hand man. It was during the brief tyranny of Aristion at Athens that Apellicon's work upon the MSS. of Aristotle was done. It must have been marked by extreme carelessness and utter want of conscience, though we are told that its stupidity was its most striking characteristic.

243. Owing to the subsequent editing by Andronicus, the traces of Apellicon's work would naturally be obliterated in great measure. But we cannot doubt that such a character as we see him to have been would not hesitate to write over the bad places, so as to make what he judged to be sense; and in some cases, Andronicus must have been forced to accept what Apellicon had written, although, by close attention, we may be led to very strong suspicion that the text is not what Aristotle wrote. If Apellicon had any pet doctrine of philosophy, nothing but want of ingenuity would stand in the way of his altering the text of Aristotle, so as to get that philosopher's apparent support for his own views.

244. At any rate, some of the phenomena to which our hypothesis points as probable are as follows:

1st, strange stupidities, or commonplaces, where what went before led us to think that a remarkable idea was to be developed.

2nd, stupidities, commonplaces, and puzzling places occurring toward the ends of books at intervals of about 70 Berlin lines or multiples thereof; at least when Aristotle's autographs and not copies were there.

3rd, the appearance of transpositions of passages of about 70 Berlin lines, under the same limiting condition.

4th, omissions of matter which it was in the line of Aristotle's highly systematic thought to insert, and which he would probably have treated in about 70 Berlin lines or a multiple.

245. Now I have noted the first of these four phenomena, as I suppose every reader has done. But I have not had time to make any search for the others. It is, perhaps, just as well that I have not; because their predictive character is thus made manifest. Only since drawing up this list of predictions, I have had the curiosity to make a hasty examination of one book in order to see whether any of the phenomena would present themselves. I have chosen the second book of the Prior Analytics, in which my attention had already been directed to a circumstance which has influenced me to give the name of abduction to the process of selecting a hypothesis to be tested.

246. In the beginning of this book, I find nothing suspicious unless it be the word method ({methodon}) in the fifth line, for a syllogistic figure. As the test stands, Aristotle is made to say that he has already done precisely what it is his intention in the present book to do. The first four chapters are devoted to considering how true conclusions may happen to be drawn from false premisses. Then follow three chapters, of about twice 70, or exactly 146 lines, concerning demonstration in a circle. These appear to me to be out of place, for the reason that Aristotle has not yet concluded his purely formal investigation which these interrupt; and for the further reason that as soon as these inquiries are brought to a close, with the 15th chapter, Aristotle has a chapter on the Petitio Principii, which is almost exactly the same thing as circular demonstration; and I do not think that so systematic a thinker would have separated them. The next three chapters, VIII, IX, X, relate to the apagogical contraposition of syllogisms, which come in here very well, but a subsequent chapter, the XXIInd, of 63 lines, on almost exactly the same subject should have followed them immediately. Next follow four chapters on the Reductio ad absurdum; and after these is placed a chapter, which, being of purely formal interest, ought to have preceded them. This chapter relates to syllogisms from two premisses which contradict one another, like this: No A is B Some A is B ∴ Some A is not A. I am all but certain that Aristotle, with his mind directed, as it was, to contrapositions of syllogisms, which is the main subject of this book, would not have treated syllogisms which conclude [to] logical absurdities, without also considering syllogisms which take truisms as premisses, such as: No A is B All A is A All B is B Some A is B ∴ No B is A ∴ Some B is A. I therefore suspect that this matter was originally there. If we suppose that Aristotle would have treated these in 50 lines, which I estimate to be correct from a minute study, the chapter would have been brought up from its present length of 87 lines to 137, or two sheets of papyrus, which I am inclined to suspect originally preceded those on the Reductio ad absurdum. After a chapter on reasonings that conclude that such and such circumstance explains the non-occurrence of an expected event, there are a series of chapters on false reasonings and disputations. Then comes the XXIInd chapter which, as just observed, seems to be misplaced; and the rest of the book is devoted to Induction in a broad sense, except one chapter on Objections, which is perhaps not out of place. This chapter on Objections ends with the remark "We have to consider objections adduced from what is contrary, what is like, and what is according to opinion; and further whether a particular objection can be urged in the first or second figure." Evidently the intention was to take up these subjects, at once. But nothing further is said about objection, although some things in the following chapter, which is the last of the book, may be understood as virtually fulfilling the promise. But we cannot believe that Aristotle intended this XXVIth chapter to end as it does. We thus find abundant reason for suspecting omissions, and also transpositions of sheets.

247. Let us now look for corrupt passages. The last chapter but one being apparently incomplete, we must suppose that the last chapter began a sheet. It is 72 lines long, and therefore would just fill the sheet. The unfinished penultimate chapter XXVI was probably written on a sheet, being only 43 lines long. Chapters XXIII, XXIV, XXV, which are intimately connected, fill just 70 Berlin lines, and, no doubt, just filled a sheet, which would be the third from the end. There is some doubt what it was which originally preceded them.

248. In chapters XXIII, XXIV, XXV, I strongly suspect two blunders. As an example of an induction, Aristotle supposes that by a simple induction we prove that all animals without gall are long-lived. Using the letters A, B, {G}, he says that he is to prove that the predicate A belongs [to] B, by an induction from {G}. Then the text now reads: "Let A be long-lived, B without gall, {G} the single long-lived animals, as man, horse, mule. Then to the whole of {G} belongs A, because everything without gall is long-lived." It is perfectly evident to anybody but another Apellicon, that {G} is the single animals without gall. That is, he has put {makrobion} where he ought to read {acholon}, unless Aristotle or a copyist made the blunder.

249. The other blunder requires much more careful study to assure oneself of it. It is to be observed that Aristotle's theory of induction, in the narrow sense, is that it is the inference of the major premiss of a syllogism in Barbara or Celarent, from the minor premiss and conclusion, as data, or premisses. I may add that this is, as far as it goes, the correct theory. Only it is not from any syllogism in Barbara or Celarent, but from a statistical deduction in which the distinctions between Barbara, Celarent, Darii, and Ferio, disappear. Having treated of induction proper, Aristotle goes on to {Paradeigma}, or Analogy, which he regards as a modification of induction proper. Now, Aristotle is throughout the Prior Analytics, especially, so unfailingly thorough in examining every case which is formally analogous to other cases treated by him, that we cannot doubt for an instant that, having remarked that induction, {Epagögé} is the inference of the major premiss of a syllogism in Barbara or Celarent from its other two propositions as data, [he] would have asked himself whether the minor premiss of such a syllogism is not sometimes inferred from its other two propositions as data. Certainly, he would not be Aristotle, to have overlooked that question; and it would no sooner be asked than he would perceive that such inferences are very common. Accordingly, when he opens the next chapter with the word {Apagögé} a word evidently chosen to form a pendant to {Epagögé} we feel sure that this is what he is coming to. In the excessively abridged and obscure style of the Analytics, he begins as follows: "Abduction, {apagögé} is when it is well-known that the major term is true of the middle, and that the middle is true of the last is not known, but yet is antecedently more credible than is the conclusion." He should have added, "which conclusion we find to be a fact," but he overlooks that, in his wish to add the clause, "and if moreover the middles between the middle and the minor term be few; for thus it will be decidedly nearer to a thorough comprehension of the matter, {epistémé}."

250. To translate this into our ordinary conceptions, as nearly as possible, it means that it will be better if the minor premiss which is not known to be true but is so easy to believe, is such that it seems as if little were needed to render it evident; and the object of the proceeding is to approach the thorough comprehension of things. In order to make sure of his meaning, we need examples; and it is to be observed that Aristotle's examples are almost always arguments well-known at his time to have been actually employed. He immediately proceeds to give the needed examples. The first is this: "Let {A} be capable of being taught, {didakton}; {B}, science or comprehension, {epistémé}; {G}, righteousness, {dikaiosyné}. Now that comprehension is capable of being taught is plain; but that virtue is comprehension is not known. If, however, this is as antecedently likely or more so, than that virtue should be capable of being taught [which, it seems needless to say, everybody knows to be the fact], †21 then there is ground for the abduction; since we are brought by the hypothesis, '{to proeiléphenai}' nearer to a comprehension of virtue being capable of being taught, than we were before." This seems very clear. He is giving as his illustration the incessant argument of Socrates that virtue must be comprehension, since how otherwise could one explain the patent fact that it can be taught. I have translated {epistémé}, comprehension, because this is what Aristotle meant by it; and the ordinary translation science conveys an utterly wrong idea to the modern mind. It must be admitted, however, that before Aristotle wrote this men had paradoxically doubted righteousness being taught. Consequently, this example is neutral, favoring neither the old interpretation nor mine more than the other. He now gives another example to illustrate the case in which the hypothesis brings us nearer to comprehension because, to use his phrase, "the middles are few"; that is, it seems near to first principles. It is here that the text seems to me corrupt. It reads as follows:

"Let {D} be capable of being squared; {E}, rectilinear; {Z}, the circle. If there is only one middle to {EZ}, that the circle is equal to a rectilinear figure, then the circles being equal by lunes to a rectilinear figure, is near to being known."

251. Let us endeavor to make sense out of that. The reference plainly is to the discovery of Hippocrates of Chios that certain lunes, or figures bounded by two arcs of circles, were equal to rectilinear figures and capable of being squared; and Aristotle plainly meant that this fact justified the hope, which we know was entertained on this ground, that the circle could be squared. There was "only one middle," or remove from knowledge, concerning the circle's being equal to a constructible rectilinear figure, since it is evidently equal to some square. Mathematics was not Aristotle's strong point, and possibly he did not clearly understand that it was only two or three special lunes that Hippocrates had squared. It is likely, however, that he understood the argument to be the inference of the minor premiss of the following syllogism from its other two propositions: Whatever is equal to a constructible rectilinear figure is equal to a sum of lunes; The circle is equal to a constructible rectilinear figure; ∴ The circle is equal to a sum of lunes. To make this out, we have to change just one word of the text. In place of saying that the major term is {tetralönizesthai} we have to put {ison méniskois}. This change of a single word of the text, not only renders the whole chapter intelligible; but gives it the very meaning which it ought to have in the development of Aristotle's doctrine. Such a singular corruption of the text as I suppose could hardly have taken place without an Apellicon; but with him, it was easy enough. †22 If we do not suppose this corruption to have taken place, we are reduced to accepting the text as it stands; and if we accept the text as it stands we must accept the usual interpretation of it. This interpretation is that abduction is nothing but an ordinary syllogism of the first figure, when we are not sure of the minor premiss, but still are more inclined to admit it than we should be to admit the conclusion if the latter were not a necessary consequence of the former. The abstract description at the beginning of the chapter will bear this construction perfectly well; only it makes the chapter an impertinent obtruder at this point, and not in the style of Aristotle's thought. But when we come to the examples, the ordinary interpretation reduces the latter, at least, to nonsense. The first becomes, Comprehension can be taught, Virtue is comprehension; ∴ Virtue can be taught. In the first place, this is a petitio principii, or very near to one since there is no way of proving that virtue is comprehension, except by its being taught. In the next place, few in Aristotle's time had used this absurd argument; it had scarcely been seriously doubted, what all experience shows, that virtue can be taught. A very few ethical writers of modern times have denied it; but it had hardly been denied then, except as a temporary shift in debate. A philosopher who, like Socrates, maintained that it was better to do wrong, knowing it was wrong, than not knowing this, could not doubt that righteousness could be taught.

252. The other example is still worse. It becomes, Whatever is equal to a rectilinear figure can be squared, Every circle is equal to a rectilinear figure; ∴ Every circle can be squared. We here naturally understand by "equal to a rectilinear figure," equal to a rectilinear figure, constructible or inconstructible. But in that case, the minor premiss, instead of being not known, is the most evident thing in the world; while the major premiss which ought to be manifest, is far from being so; for if a figure cannot be constructed it cannot be squared. Supposing however that by a rectilinear figure is meant one that can be constructed, which must have been the meaning, since Aristotle says that it is almost known through lunes, who ever used such a ridiculous argument? And how can Aristotle say, as he does, that lunes in any way help the matter, or are at all relevant? Whatever bearing lunes were supposed to have upon the quadrature of the circle disappears entirely from this representation. Nothing can be more utterly unlike Aristotle's usual examples, which bring up in vivid aptness actual reasonings well known to his scholars.

253. I think, then, that my interpretation of the passage, considering its being what the current of thought demands, considering how the word {Apagögé} balances {Epagögé} and considering that it renders both the examples their real historic forms, comes within a tolerably close approach to certainty. If we accept it, it affords a remarkable confirmation of the Scepsis story; because of the bold insertion it supposes to have been made in the text.

254. I have looked forward seventy lines from each of the two corruptions I have mentioned; but the measure falls in each case upon a passage so plain, that had it been totally obliterated, not even an Apellicon could fail to restore it correctly. I have said enough to show how I think this hypothesis should be treated.

255. All the best critics of Germany, on the other hand, utterly reject the Scepsis story. Their reasons I have already indicated. They are so weak that I think I am justified in surmising that the real motive of their rejection is a reluctance to accepting any ancient testimony without dressing it up and putting a new face upon it. At any rate, their general principle is that they think the story told by Strabo is less likely than that Strabo should tell a false story; and that principle seems to me to amount to believing whatever they are inclined to believe. †23

Chapter 4: Notes on Science

§1. The Study of Great Men †1

256. Having been asked to write something about the productiveness of the nineteenth century in great men, I ought to begin by frankly confessing just what the facts are that, being known, will lead the reader to attach a certain value, and no more, to my opinions on this subject. In the year 1883, having charge of the instruction in logic in the Johns Hopkins University, I cast about for a subject that might afford valuable training in such inductive investigation [as] the members of my class might need in future life and which they would not be likely to acquire in their other studies. I wished it to be a subject susceptible of mathematical treatment, since an inductive investigation so treated may throw abundant light on the proper logical procedure where mathematics is not available, while the converse can hardly be true. Yet there were several reasons for selecting a subject concerning which no exact observations could be made. Much more logical caution is requisite in such a field; and it was desirable to explode the ordinary notions that mathematical treatment is of no advantage when observations are devoid of precision and that no scientific use can be made of very inexact observations. Besides, very little training is required in the purely observational part of the business of making observations that can be rendered extremely precise; while great training is requisite for the making of the very observations themselves when the observations are of the kind which can never be made precise. In order to make my meaning clear, I will take an example of each kind. The matching of two colors is an observation that can be rendered precise. In order to learn to perform this observation what is chiefly requisite is to appreciate the fact that the two surfaces to be compared have to be put in precisely the same light, and that, unless various precautions are taken, they will not usually receive light of the same intensity and color though they be held quite close together. The mere observation itself of whether they match or not will very soon be made so accurately that all the effort has to be expended, not upon that pure observational part of the work, but on the experimentation. On the other hand, an example of an observation that can never be rendered precise is that of saying which of two different colors, say a red and a blue, is the more luminous. Here, no extraordinary experimental precautions are called for. The thing is to look at the colors and disregarding entirely their extreme difference of hue, as well as the circumstance that red is a very high color while blue is comparatively greyish, to just note the relative impressions of luminousness that they make upon us. A great deal of training is required before a person can do this well enough to give any uniformity to his judgments. It is not an education of the eye or of part of the brain particularly connected with the eye, so much as it is of the mind. A certain person upon hearing a note struck upon the piano was utterly unable to pick out any harmonic by ear. He then went through a course of training with a color-box, involving observations of the general kind I have mentioned, until he acquired a good deal of skill. Upon now returning casually to the observation upon the piano-tone he found to his surprise that he could pick out three or four harmonics without difficulty. Now this pure observational power is of great value in life. It is true that the only thing that is disclosed by such pure observation is one's own feelings. But then different persons' feelings are so closely similar, that that is of the utmost use in a world of men and women. It is this that the word tact ought to denote independent of adroitness in playing upon people. A Sherlock Holmes's habit of making deductions from minor circumstances is all very well, in itself; but if attention to these circumstances is to draw it away from the Lavaterian, artist-like, direct, and pure observation of the suspected person, it will do more harm than good. I should be afraid to tell what I have known this power to accomplish, because it is unpleasant to have one's veracity doubted. Lavater's 'Essays on Physiognomy' is a book very much discredited; and I cannot say that I am a strong believer in such notions, as that a large and prominent nose is associated with push and energy. But matter of that sort makes but a small part of the work, the diligent study of which, in a good edition, will, I can testify, stimulate a young person to train the faculty of which I am speaking. At any rate, ever since I read it, I have been convinced that psychology would assume its legitimate dignity among the sciences from the day on which it should be recognized as based mainly upon the pure observation of which I speak, and not before. The sciences of objective nature do not train this power, because they can make no use of the sort of data it affords. The exact sciences, physics and chemistry, do not teach any observation of any kind, to speak of; but only manipulation and experimentation. The purely observational business is confined to such trifles as bisecting stars, putting crosswires upon spectral lines, reading verniers and the like. Natural history undoubtedly trains a certain kind of observational power, the taking note of circumstances that would escape an untrained attention. But that is not the power I had in view. †2 These are among the reasons that led to my pitching upon the study of great men as affording useful training for my class. I have dwelt upon these reasons at some length, simply because they throw some light upon the matter with which I seek to acquaint the reader, the degree of my qualifications to give an opinion upon a subject upon which any opinion must be largely subjective and rough, even though it should attain a certain degree of validity. . . .

257. The first thing we did was to make what I called an impressionist list of great men, — impressionist, because the admission to it of any name was to depend upon our pure observation of the impression of greatness which we received from the contemplation of his life and labors, while carefully abstaining from any analysis of greatness or of the reason for the impression we felt, since one of the very purposes of the list was to serve as a test of any theory of the nature of greatness and the cause of the impression it makes upon us. A preliminary list of nearly a thousand names was first formed; and these were considered and reconsidered, three or four times with increasing care, until we finally settled upon 288 great men. I was desirous of having this include substantially all the great men of history. Yet I was less concerned that it should omit none whom it ought to contain than that those that it did contain should form a fair sample of what great men were like. Since we were all students, no doubt we had a bias in favor of men of intellect; but against this we were on our guard. There was naturally some moral leaning, and the social atmosphere of Baltimore must have affected our judgments. Moreover, it is humanly impossible in such a selection to do justice to contemporaries, compatriots, and acquaintances, whose greatness we are too close by to discern. I could now improve the list in details, besides doing something toward bringing it down to date. But it was formed with so much care that I would not venture to touch it short of a good six months solid preparatory study.

258. The list having been formed was found to be too large for so small a class to study to advantage, and we therefore restricted ourselves to the consideration of every sixth name. I do not intend to weary the reader with any account of the elaborate inductive inquiries, about seventy in number, which we undertook in regard to those men, and which I have followed out with some diligence all through the seventeen years which have since elapsed. But there is one point which it is important for my present purpose that I should explain. Everybody knows, I suppose, that the ancient astronomers divided the stars visible to the naked eye into six orders of brightness, called "magnitudes," the first magnitude containing the brightest stars, and the sixth those that are barely visible in an ordinary atmosphere on a clear and moonless night. Ptolemy already subdivided each magnitude into thirds, and in our century they were first divided into tenths, and after the introduction of photometrics into hundredths. Now when photometry came into use, it was found that there was a nearly constant ratio of light between the light of average stars of successive magnitudes. Thus, in my book entitled 'Photometric Researches' p. 47, †3 I show that the differences between the light of the faintest stars normally referred by Ptolemy to the first four magnitudes, expressed upon a scale of magnitudes which makes the ratio of light strictly equable, are 0.94, 1.07, 0.99, which are practically equal. This remarkable fact is connected with Fechner's psychophysical law (at which the utter ignorance of German philosophical professors of the mathematical theory of metrics, their fondness for expressing opinions about matters of which they are ignorant, and the awe with which they are copied by Americans, has made it the fashion to sneer) according to which equal ratios of excitation produce equal differences of sensation. The old astronomers assigned successive numbers to stars which gave equal differences of sensation, and these, when the stars are not so faint that another influence, the nature of which is made clear in my book, interferes, correspond to a geometrical progression of intensities of light measured physically, so as to make the intensity of light proportional to the square of the amplitude of vibration. The scale of star-magnitudes, having been found to lend itself perfectly to mathematical treatment, was imitated by us in expressing our impressions of the greatness of the different men. That is to say, we marked the greatest man on our list 1 and the least 6. Some member of the class to whom the duty had been assigned would read an account drawn up by him of one of the men, and each member would then secretly jot down in units and tenths, his evaluation of the impression produced upon him. The ballots giving these numbers would then be handed up to me and the mean would be adopted as the "magnitude" of that man. As this method was no novelty to me, I having often applied it to all sorts of feelings, so that I knew about how well the numbers would agree, I never took the trouble to preserve the individual estimates; so that I can now only put before the reader the results of the ballotings in three cases which occurred at an informal meeting when the whole class was not present, and when I calculated the means upon the margin of a paper which has been preserved for another purpose. These three ballotings thus casually preserved are as follows: Bolivar Julian Swedenborg 4.2 3.6 4.0 4.2 3.8 4.5 4.0 3.8 4.3 3.8 4.8 †4 3.8 3.9 —- —- —- Means 4.0 4.0 4.1

259. I do not think that there was any man for whom the extreme estimates exceeded two magnitudes. Such a discrepancy could only occur in the case of some vaguely known and semi-mythical hero, such as King David. It is obvious, therefore, that if what we mean by a judgment being "objectively valid" is that all the world will agree in it, and after all Kant's discussion that is about what it comes to, then there was a satisfactory degree of "objectivity" in the mean magnitudes we assigned, although they referred, not to the man as he really was, but to the man as he was presented in the account read to the class, and although the marking could not escape a large "subjective" percentage due to our common, but not thoroughly catholic, culture and environment.

260. At the meeting I have just spoken of, we tried estimating, in the same way, the "magnitude" of the average man. This was a matter of difficulty and uncertainty, for two reasons. The value was so far removed from the part of the scale to which we were habituated that slight differences in the value of the unit of "magnitude," as employed by different members of the class would necessarily be exaggerated. This, however, was probably of little account compared with the uncertainty as to what kind of a person the truly "average man," with whom we were none of us accustomed to associate, really was. It is not surprising, therefore, that the ballots, which here follow were pretty wild. Average Man 10.5 13 13 11 ——

Mean 11.9

261. At the same meeting we balloted, with very little preparatory discussion, for the "magnitude" of the leader of the Baltimore bar, with the following results: Leader of the bar 8 8.8 9 8.5 —-

Mean 8.4

262. Just as a young gentleman nine years of age looks upon a lad of eight as a person of little knowledge of the world or experience of life, and as altogether inferior in intellectual grasp, so the nineteenth century has had the habit of looking down upon the eighteenth; and no doubt the judgment is a sound one in both cases. But when we ask whether the nineteenth century had shown any vastly superior productiveness of great personalities, we have a difficult question before us. A pretty careful sampling enables one to say that if we were to enumerate the men whose achievements in art, in practical life, or in science, can never be forgotten by history, we should find upwards of a thousand in the nineteenth century against not more than five hundred in the eighteenth. But there is a vast difference between a man who accomplishes something great, — say, the introduction of the first anaesthetic, ether, — and the man who, upon the whole, impresses us as a great man; and if we confine ourselves to great men, we shall find only about seventy in the nineteenth century against some sixty in the eighteenth, — a very marked falling off, when the increase in the number who can read and write, and in the opportunities for distinction, generally, is considered.

263. It is an observation as true as it is trite that the nineteenth century has been an era of machinery, — not of machinery of steel merely, but of machinery in politics and in business, such as trusts and trade-unions, machinery in all the methods of research, physical, philological, historical, philosophical, mathematical, even of machinery in art and in poetry. Consider Mathematics, as a field where, if anywhere, it might be supposed that machinery would be of little avail. In the early eighteenth century the greatest geometers in Europe were still "stumping" one another with problems, and the discovery of a theorem might raise a man to greatness, — witness Taylor's theorem, published in 1717. Subsequently, it must be a method, no longer a mere theorem, to impress the world so powerfully. Nowadays, methods of the greatest profundity and power are turned out at such an astonishing rate that nobody but professional mathematicians ever hear of them singly, at all. Hermann Schubert's Calculus of Geometry, which enables us, for example, by a brief computation, to determine that the number of cubic curves each of which shall touch any twelve given spheroids, is just 5 billion 819,539 million, 783,680, hardly makes a ripple in the ocean of modern mathematics. In Addison's time, the man who could write graceful English was a prodigy. Now, everybody writes decently well: the leader-writer of the yellowest journal has a better command of his pen than the accomplished Shaftesbury or the learned Toland. An age which in every department has offered a thousand new appliances to enable a puny man to do a giant's work has been an age of machinery, indeed.

264. Whether machinery, organization, and a great development of methods and of the methodus methodorum, †5 with their fruits of incessant new discoveries, inventions, improvements of all kinds, ought a priori to be unfavorable to the production of great personalities is a problem for a more sagacious man than I can pretend to be, to compute with any confidence. One might incline to think not; for, on the one hand, just as we know that plants transferred to new soil are the more apt to sport, so it might be expected that under novel social conditions the proportion of births of extraordinary minds would be increased, while on the other hand, once born, one would suppose they would find in novel situations just the opportunities that were needed to bring their superiority into exercise. History, too, seems to confirm this, in always showing us a wealth of great men at every great social transformation. The list of heroes of our own country shows this. Rigidly exclude every man not unquestionably great, and how few will be left outside the groups that cluster about our two cataclysmic upheavals, the revolution and the rebellion!

265. Yet somehow, the nineteenth century has certainly lacked its due quota of great personalities. When about a fifth of the century was still in the future, I drew up, with the coöperation of a class at the Johns Hopkins University, and with much outside assistance, what I called an Impressionist List of about 300 Great Men. It was one of those matchless classes, — the very salt of the earth, — which it was my privilege to enjoy in Baltimore. Almost every member of it has since signally distinguished himself, and those who have less obtrusively done so are among those whose observations I now, after twenty years, most frequently recall as forcible and just. I called it an impressionist list, not that it was at all hastily drawn up, but because, in the process of sifting out the names from a much larger list, we were to set aside all preconceived ideas of what greatness consists in, and were simply to estimate the impression made upon us by a fair review of each man's life and labors. Being all of us students, no doubt, we had some bias in favor of the philosophers; but against this we endeavored, as much as possible, to be upon our guard. The social atmosphere of Baltimore, too, probably affected us somewhat; and I think we had a human prejudice against monsters of iniquity and against men of greed. Everybody would, I know, find fault with our list. Not a few of its omissions were violently counter to my own personal impressions. Still, it would be very difficult, if not impossible, to draw up a much better list. I may mention that this list formed the basis for much subsequent study; and one of my main purposes was to train the men to the nice observation of their own sensations, to show them that feelings are capable of direct evaluation with sufficient precision to serve a scientific purpose, and to admit of mathematical treatment, and to demonstrate that they do not, for the most part, differ extravagantly among different persons in the same environment. For instance, after an account of a man had been read to the class, we would each estimate the impression of greatness produced upon him, somewhat as astronomers estimate the magnitude of a star, calling Pythagoras, as he is represented in the life of Iamblichus, a first magnitude man, and Cola Rienzi a tenth magnitude man. Each of us would, after hearing the account, secretly mark upon paper his estimate of the man's magnitude. The papers would then be collected and the values copied in a column upon the blackboard. The extreme variation would not ordinarily exceed two magnitudes, so that we all came to feel pretty confident that the averages of our estimates would for the most part be pretty close to those that would be produced in the average man of the same general breeding and culture, by the same biographies. I have, since the list was first made, never allowed it entirely to drop out of mind, but have spent a good deal of time, all told, in the further study of the 288 great men it includes, and recently, with all the aid I could get, in adding such names as seemed to [be] required by the history of [the] last twenty years.

266. This long explanation was necessary in order to show what degree of objectivity might fairly be attributed to my impressions of the productiveness of the century in historic personalities. This objectivity is, like Mercutio's wound, not as wide as a church door, yet 'twill serve. It will not be valid for every normal mind as my matching of a color might be valid for every normal eye; but it tolerably represents how an average student of science sixty years old, not unobservant of human life, and not very narrow in his interests, would be likely to be impressed. †6

§2. The History of Science †7

267. I have now expounded to you as much of the history of science as I found myself able to do in 12 hours. Of course, a great deal remains to be considered; but even the few facts we have collected will do something to answer the questions with which I set out. †8

268. We have found as I suggested at the outset that there are three ways by which Human Thought grows, by the formation of habits, by the violent breaking up of habits, and by the action of innumerable fortuitous variations of ideas combined with differences in the fecundity of different variations.

269. As for the last mode of Development which I have called Darwinian, however important it may be in reference to some of the growths of mind, — and I will say that in my opinion we should find it a considerable factor in individual thinking, — yet in the history of science it has made as far as we have been able to see, no figure at all, except in retrograde movements. In all these cases it betrays itself infallibly by its two symptoms of proceeding by insensible steps and of proceeding in a direction different from that of any strivings. Whether or not it may not be more or less influential in other cases, in which its action is masked, the means of investigation which I have so far been able to bring to bear fail to disclose.

270. The manner in which the great and startling advances in scientific thought have been made appears very clearly. It is by the violent breaking up of certain habits, combined with the action of other habits not broken up. Thus, the highest level of Egyptian thought seems to have been reached at a very early age. So it appears to us, and so it always appeared to the Egyptians, for they always reverence the ideas of antiquity, as superior to those of their own time. Now the great factor in the development of the Egyptian mind was undoubtedly the physical geography of the country which probably produced its effects in a reasonably small number of generations after it was first felt. So with the Greeks. Their thought remained in its primeval condition until the extension of commerce brought them within the sphere of influence of other peoples, the Phoenicians, the Egyptians, and the Babylonians, and then within a few generations they made great strides in thought, to be succeeded by a slower movement of another kind. At first, we have a rather servile copying of the ideas of those countries, a syncretism such as we see in Pythagoras. But soon the foreign ideas begin to react with the ideas and faculties peculiar to the Greeks, and a great original life commences. So it was again, when in the 13th century, the ideas of the Dark Ages were rudely shaken up by contact with the more civilized Saracens; although as far as science was concerned that movement was quickly stifled by the rapid development of theological ideas.

271. The renaissance in Italy was of slower growth, because foreign ideas had been slowly filtering in since the thirteenth century uninterrupted. However, after the fall of Constantinople in 1454, there was a much more rapid movement. That movement was first strongest in the direction of art, which I take to be a mark of rapidly growing minds, of minds receiving nutrition too rapidly to be packed down into the forms of science. But the scientific development came later. Galileo was born the very day of Michelangelo's death.

272. In this early development of science there were two great factors. In the first place, the direct strivings of the astronomers, the European successors of the Arabians, who brought to astronomy more masculine intellects than the Arabians had, had brought out at length a world-shaking idea, the Copernican conception. In the existing state of the church, this was more easily accomplished in Northern Europe, and there it was brought to its perfection by Kepler, and I have traced out the birth of this conception with some minuteness because it is remarkable as being a birth from within, not an influence from without. Although the authors of this, Copernicus, Tycho, and Kepler were all Teutons, the value of their work was better understood and more accurately appreciated in Italy than north of the Alps.

273. The other great factor, which chiefly influenced the development of dynamics, was the study of the works of Archimedes; and a strongly Hellenic color is apparent everywhere in that branch of science down to the time of Newton. It is shown in the great fondness for demonstrations from axioms, in the desire to put all special experimentation out of sight, and to rely on the Light of Nature. It is also shown in the geometrical methods which are preferentially employed.

274. As to the third mode of intellectual development, we should see more of it if we were to trace out the history of science into its later era. Though it is not so startlingly manifest, it is certainly the method of the ordinary successful prosecution of scientific inquiry. We see its action clearly in the history of astronomy at all periods, and especially in Kepler's gigantic work. It is growth by exercise, or by direct efforts in the direction of the growth. If we have seen little of it, it is because I felt it necessary to the understanding of the subject to begin at the beginning and I could not in twelve hours carry you on to the point in which science, except in astronomy and to some extent in the last developments of dynamics, was really settled down to its work. I will mention, however, that in the January number of the Monist, †9 I have endeavored to give an analysis of this kind of evolution, and especially have connected it with the Christian theory of the way in which the world is to be made better and wiser.

275. I have to thank the company very gratefully for the patience and kind indulgence with which my lectures have been listened to. I have done what lay in my power to present as much of the History of Science as I have been able to treat in a lucid manner, and to show that it is governed by Law like other departments of nature. But these laws are not of the nature of mechanical forces, such that the individual and the spirit of man is swallowed up in cosmical movements, but on the contrary it is a law by virtue of which lofty results require for their attainment lofty thinkers of original power and individual value. You cannot silence or stifle or starve a single one of them without a loss of civilization from which it never can wholly recover. It is not more certain that the inches of a man's stature will be affected all his life by an attack of fever as a baby, than that we are now less happy because of the many great geniuses whom untoward circumstances have put down. The country that can first find the means not to provide the million with miscellaneous reading matter, and elementary education, but to utilize its superior intellects for the general good, will experience a wonderful acceleration of civilization from which the benefit of the million, in much more valuable ways, will come about of itself.

276. Although by far the greater part of almost every treatise on psychology is devoted to the department of Cognition, yet it is curious that less is known about thought than about either of the other two modes of consciousness. What I have to say about it is even more inadequate than what I have said of Primisense and Altersense. †10 In order to make out what the main processes of Thought, or varieties of Medisense, are, I naturally turn to Logic, which has been my chief study for the last forty years. In the process of inference, or the self-controlled formation of new belief on the basis of Knowledge already possessed, I remark three chief steps. They are, first, the putting together of facts which it had not occurred to us to consider in their bearings upon one another, second, experimentation, observation, and experimental analysis, which is substantially the same process whether it be performed with physical apparatus such as the chemist uses or with an apparatus of diagrams of our own creation, such as the mathematician employs, and third, the generalization of experimental results, that is, the recognition of the general conditions governing the experiment, and the formation of a habit of thought under the influence of it. If we turn to the history of the physical sciences, as the most perfect example of the successful application of thought to the external world, we find that they have all gone through five stages. First, an interesting phenomenon has attracted attention. Here, inquiry has often come to a stop for a long time. It does not proceed until, Secondly, somebody invents an instrument or a method by means of which the elements of the phenomenon can be subjected to experiment. Third, a process of experimental analysis has been carried out, resulting in the ascertainment of a law, or exact relation between the different elements of the phenomenon. Thus, the lodestone must have been known for a long time, before somebody invented the idea of experimenting upon it with iron rings. This rude instrument led to the discovery that a second ring would be supported by the first, that a third could be hung to that, and so on. Nothing more was discovered until Petrus Peregrinus invented a new method of experimentation. †11 Namely, he shaped the lodestone into a terella or ball, and then applied to it short pieces of iron needles. With this apparatus he at once discovered the poles of the magnet and their properties. Then, discovery stuck fast again; because nothing more could be made out with those instruments; until Gilbert invented a new instrument consisting of an iron needle balanced on a point, and free to turn round. †12 Such has been the history of every science. After a while a Fourth class of studies has commenced, consisting in the exact measurement of the constants concerned. In optics there was, for example, the velocity of light. Finally, Fifthly, has come the construction of mechanical theories by which the causes of the phenomena were probably assigned.

277. Comparing the teachings of the history of science, on the one hand, with those of logic, on the other, we notice a certain agreement between the two. The interesting phenomenon which gives the first impulse to scientific thought corresponds with that interesting colligation of facts, which is the first step of the inferential procedure. Experimental analysis plays a great part in both. Finally, the generalization of the experimental result which completes the inference is represented in physical inquiry by speculation into the mechanical causes of the phenomenon. For as the mechanical explanation of the physicist consists in a reference of the experimental result to the higher principle of dynamics, so the generalization of the reasoner is the reference of the experimental result to the higher principle of mathematical necessity or probability.

278. Perhaps, just as the study of a physical phenomenon must depend upon applying such instruments as we can find, so in our attempt to enumerate the processes of thought, we cannot do better than to begin by laying hold of the suggestions that are offered by these analogies between the process of inference and the history of physical science.

279. Some thirty years ago I made a remark upon the course of physical studies which has been repeated by very competent men, to the effect that there were three stages; first, the observation and miscellaneous research into the phenomena; secondly, the analysis of the phenomena and formulation of their laws, including hypothetical explanations of them; thirdly, the determination of the constants. Nothing intellectual, — no casts of mind, — more diverse than those needed for these three steps can well be imagined within the sphere of physics. These three steps occur in every branch. True, ordinary observation supplies many of the phenomena in optics and acoustics; but not all, by any means. Not circular polarization; not the zones of silence about a fog-horn. In electricity, in galvanism, in X-rays, and other radiations, in fluorescence, the first breaking of ground required a peculiar genius, not to be undervalued, yet not for an instant to be likened to that which analyzes the phenomena, — the work of a Galileo, a Kepler, a Faraday, a Maxwell. Then the painful and technical business of accurately determining the constants is not one of genius or insight but of perfect thoroughness and flawless technique. It is the work of the Regnaults, the Michelsons, the Rowlands, — the accomplished experts.

§3. Measurement †13

280. Definition. A character is a possible fact regarded as concerning a particular thing or things.

Illustration. The moon may come between the sun and the earth so as to cast a shadow upon the latter. That is a possible fact. Now, if we think of this fact as something that concerns, or modifies what we can say of, the sun, we call it an eclipse of the sun; and so considered, it is what we mean by a character of the sun at such an instant.

281. Explanation. I say a possible fact, because if a character is not actually true of a given thing, that is not sufficient to prevent its being a character. Thus, when the sun is not eclipsed, it does not possess that character, but we do not say that there is no such character. If it could be shown that the supposition of the moon coming between the sun and the earth so as to cast a shadow on the latter, could only be carried out in ways which, being examined, would prove all of them to involve contradictions, then we should say this is no real character, but only a phrase, which cannot be realized in any imaginable manner. In short, the character in itself does not pretend to belong to the world of experience; to be a character it only needs to have a place in the realm of ideas. When the character is attributed to any particular thing, that thing is something having its place in experience. It is not needful, for the purposes of mathematics, to inquire particularly what experience is. It may be said, however, that it is something which is forced upon us; so that one element of it is its insistence, whether we like it or not. And it is also something which forces itself not merely momentarily upon me; but upon me and you alike, at various times, so that it has a certain consistency and extension in its forcefulness. Finally, it is something of which our knowledge can never be complete; so that there is always a difference between the experienced thing and our idea of it. But since the character, to be a character, need not really belong to the particular thing, but it is sufficient if we can really ask whether or not it belongs to that thing, it will be seen that we do not need to go very far into a study of its nature.

282. Analysis. Characters may be more or less precisely defined. A general character may be conceived as a multitude of precise characters. Mathematical thought consists in the study of precise relationships between ideal objects. But a possible fact may vary in an indefinite multitude of different ways. The moon coming between the earth and the sun, may not only have a multitude of different positions, but it may have a multitude of different shapes and colors and chemical compositions; and so may the sun and earth. For the purposes of mathematics, it is necessary, in the first place, to abstract from most of those differences, and consider them as insignificant and, for our purposes, nil. Then, those varieties which still, for our purposes, are different, have to be arranged, as far as possible, dimensionally. To do this, we imagine any one precise variety of the character, — precise, I mean, after the proper abstractions have been made, — and conceive that as undergoing a multitude of variations in time, from the infinitely distant past to the infinitely distant future, such that in the course of all time it will be continually changing; and we prefer to take this series so that the character will ultimately return to its initial state, and just barely return to that state. If this series of changes does not include all the variations, we think of the whole multitude of states through which the character passes in all time, as belonging at one instant to an equal multitude of objects; and then we conceive the characters of those objects to undergo in the whole course of time a continuous series of changes of a different kind, so as to be entirely distinct. We call this a second dimension, or series of variations. We can make any number of these dimensions; and as far as possible we thus seek to give some precise arrangement to all the variations of characters. When this method fails us, we can resort to other systems of arrangement, of some of which we shall have examples in geometry.

283. Any one of those dimensions is such that the characters can pass through the whole series of states in the course of time. It is easy to imagine multitudes of variations so related to one another that one precise character could not even in all time pass through them all by insensible gradations. For example, colors differ from one another, not merely in hue, but also in luminosity, and in chroma, or intensity of departure from grey. Now, starting with a color of some precise hue, precise luminosity, and precise chroma, if it is to change its hue gradually, for each precise hue that it takes, it will have just one sole luminosity and one sole chroma; so that, when it has gone through the whole cycle of hues, it will have had for each of them but one single luminosity and but one single chroma. Though it should pass through the cycle of hues times without end, it would still not have begun to exhaust the possible luminosities and chromas for each hue. The student may admit that it might be possible (and, in fact, it might be shown to be possible) that if the color were so to jump from hue to hue, from luminosity to luminosity, and from chroma to chroma, that taking any two instants, no matter how near to one another, if during the interval between them the variations should embrace the whole cycle of hues, the whole range of luminosity, and the whole range of chroma, then the color might in the course of time precisely assume for an instant every special variety of color. But if the variation is to take place gradually, then it is not possible that the color should in the course of time assume every possible variation.

284. The meaning of this seems to be clear. That is, it possesses the first grade of clearness of ideas, that of containing no element which perfect familiarity does not enable us to use with entire confidence. †14 But that grade of clearness is not sufficient for precision of statement, and logical security. For that purpose, we must say what we mean by "gradually." In attempting to state this, it first occurs to us to say that we mean by a gradual change of hue, such a change that in passing from one exact hue to another we pass through all intermediate hues. There are two reflections to be made upon this statement. First, it supposes that the different hues are so related in our minds that we are able to say what ones are, and what ones are not, intermediate between any given pair of hues. That is to say, we must have a precise idea of what it means to say that the hues are mentally arranged in a line. But if that be so, we need not introduce the conception of a change in time; for that was only a device to enable us to describe what we mean by a line of variations of character. In truth, though the introduction of the idea of time gives sensuous clearness to our idea, it contributes not in the least to logical clearness. The second reflection which has to be made upon our attempt to define gradual change of hue is that the hues form a circle, the so-called color-circle; so that it is possible to pass from any one to any other by going either way round the circle; and thus there is no particular hue that we need pass through. To define a linear arrangement, the line being permitted to return into itself, it is necessary to speak of four points on the line.

285. Definition. A state is an exact character, that is, one which, certain understood abstractions being made, admits of no varieties.

286. Definition. A line of variations of states is a continuous multitude of states such that, taking any four of them all different, there are in the nature of the characters two that are adjacent to any one, or else it would be so were two that are extremes made adjacent to one another; and any fifth character of the same line occupies in its nature a definite position between two adjacent characters of the first four.

287. Definition. A circuit of states is a line of variation of states which returns into itself and has no extreme states.

Illustrations. Suppose a light to be increasing in intensity from that of a fire-fly toward that of the planet Venus at such a rate that it would at a certain instant, say Midnight, attain that brightness. Suppose next that it increases at a more and more rapid rate, so that after a while its rate of brightening is such that at that rate it would attain the brightness of Venus at 11 o'clock. Suppose it continues to increase more rapidly, so that after a while, its rate of brightening is such that it would attain the brightness of Venus at 10 o'clock. Finally, suppose that its increase becomes so rapid that at that rate it would become as bright as Venus at 9 o'clock. Thus, there is this order among these characters: such a change of brightness as would make it equal Venus at 12, at 11, at 10, at 9. But when it was increasing at a rate to make it equal Venus at 12, its increase might become slower and slower so that the time at which it would equal Venus would become later and later. If it ceased to increase, the time would be thrown into the indefinite future. If it began slowly to decrease, its change would be as if it had been as bright as Venus a long time before. If it decreased faster, this time might become nearer and nearer, until at some time after 9, it was decreasing as if it had been as bright as Venus at 9 o'clock. At a little after 10, it might be at ten o'clock, at a little after 11, at 11 o'clock, and at a little after 12, at 12 o'clock. Thus the order would be reversed. But there is no imaginable way in which the time could gradually change from 12 o'clock to 10 o'clock without passing through either 11 o'clock or 9 o'clock. This shows that the instants of time form a circuit.

288. Definition. A Quality is that character of a character which consists in its belonging to a particular line of variation of states.

Illustrations. Thus, temperature, probability, wealth, the happening earlier or later than something else are qualities.

289. Scholium. The order of states in a line of variation may be shown by attaching to sensibly different states different numbers. For if the line of variation forms a circuit, its states are related to one another like the real numbers, rational and irrational, positive and negative, including ∞, except that the states may perhaps be so multitudinous that it is impossible to assign distinct numbers to them all. Whether any example can be given of a quality in which there are sensible variations too multitudinous for numbers to discriminate or not, there can be no doubt that such a quality might exist. †15

290. In mathematics, we have to deal with an ideal condition of things. We imagine ourselves to be in possession of a general method of working by which definite states can be assigned, in the first place, to all rational numbers, in their order. That is, the states in their own nature shall have the same order of succession as the values of the rational numbers. We then suppose states for the irrational numbers to be interposed in their orders. States which the particular method of assignment of numbers may leave unnumbered, between the numbered states, are for this method not sensibly different from the irrational numbers that are near them. A new distribution of numbers by a different method might possibly distinguish some of these, and in doing so it might, or might not, leave others undistinguished.

291. The numbers may occur in every assignable part of the circuit, or may be contained between two limits, or a part of the series of numbers may cover the whole circuit. In the last case, we suppose the remaining numbers to be assigned to the circuit taken over and over again in regular arithmetical progression. In the second case, we are at liberty to fill up the vacant part of the circuit with a second series of numbers which will be distinguished by having a quantity not a number added to it. But in doing this, we shall assume that the numbers are so assigned that taking any three states A, B, C, a state, D, can be found whose number diminished by that of C equals the number of B diminished by that of A.

292. Definition. A method of measurement upon a circuit of variation is a general rule according to which, it is possible to assign each rational number to an exact state and to but one; and conversely, given the numbers assigned to any three states, it is possible to ascertain whether any fourth rational number is exactly assignable to a given state or not, and if not in what one of the four intervals between the four numbers, the number that ought to be assigned to the given state falls. [Corollary. This affords the means of vaguely assigning states to the irrational numbers.] †16 Numbers so assigned to states may be called state-numbers. States to which definitely different places in the scale of numbers cannot be assigned are said not to be measurably distinct, according to the particular system of measurement employed. If the whole circuit of numbers does not precisely correspond to the whole circuit of states, it is assumed that either, on the one hand, the same state receives different numbers or, on the other hand, that different states receive the same numbers distinguished by the addition of a non-numerical quantity. But in all such cases the numbers are to be so distributed that if any three states have a, b, c for state-numbers not infinite (in the same system of measurement) then there shall be one state and but one which has for a state-number, a + b - c.

293. Scholium. Were we to say, at once, that there is a state for every syzygy of two state-numbers, we should no longer have a line of variation, in case a non-numerical increment is required for part of the circuit.

294. Scholium. Suppose we have two objects both capable of taking states of the same quality and of changing those states, but only in the inherent order of the circuit of variation. Suppose further that the whole pair has but a single degree of freedom of changes, so that for each state of the one there is one and but one state of the other. Finally, suppose that one member of the pair can always be changed to the state which before the change was that of the other. If, then, we affix numbers to the states in such a way that every change in the state-number of one of the pair shall be equal to that of the other, these numbers will fulfil the necessary conditions. But if there is a region over which the pair cannot be moved, then it will be necessary to have as many such changeable pairs as there are regions. Each pair may conveniently consist of one object in one region and one in another.

295. Another method of measurement would be obtained if we had a multitude of objects so that there was just one for each state of the quality in the whole circuit, and if the whole multitude had but a single degree of freedom of change and two positions of the whole multitude were given.

296. Of course, it would be still more convenient if we had given all states of such a multitude of objects. But in that case, they must conform [to] the condition that, let A, B, C, D, be what different states they may, if a change of one member of the multitude from A to B is synchronous with the change of another member from C to D, then every change of any member from A to B is simultaneous with the change of the member in state C to D.

297. Definition. A standard of measurement upon a circuit of variation is a pair of objects subject to the quality of the circuit, such that either can be changed to the state of the other in respect to that quality, but all its changes must follow the inherent order of the states, and the whole pair has but one degree of freedom of position, so that if one of the pair is in any given state there is but one state in which the other can be; and the method of measurement is such that station-numbers of the states of the two objects change by equal differences simultaneously.

298. Definition. A metron is an object composed of parts in one to one correspondence with all the states of a circuit of variation, such that any two form a standard of measurement, and the whole has steady displacements, that is, if the change of one part from state A to state B is synchronous with the change of the part at first in state C to state D, then the change of any other part from state A to state B is synchronous with the change of the part at first in state C to state D.

299. Definition. The quantity, or modular quantity, of an interval between two states in a line of variation is that which there is in the inherent difference between two states which justifies their receiving state-numbers whose difference has this or that amount. Otherwise, it is that whose measure is the difference of their state-numbers multiplied by a unit expressive of the unit of difference.

300. Division. Measurement is either

A. Parabolic, when the circuit of real numbers corresponds to the circuit of variation of states, or

B. Non-parabolic, when the two circuits are not coincident. Non-parabolic measurement is of two kinds, viz.: — a. Elliptic, when the entire circuit of states coincides with a finite part of the circuit of numbers. b. Hyperbolic, when the entire line of finite numbers occupies but a portion of the circuit of variation, and leaves a portion vacant.

301. Definition. An absolute, or firmamental, state is a state to which or from which no member of the metron can change.

302. Theorem. In parabolic measurement upon one circuit there is just one firmamental state.

Demonstration. In every measurable change of the metron, the station-numbers of all members are changed by the same finite increment. Now, a finite number added to any number gives a different number with one sole exception. Namely, if the number increased is infinite, the sum has the same value. But only one state has a given state-number. Therefore, the state of that member of the metron which has ∞ for its state-number is never changed. Hence, since every change can be reversed, no member is by any measurable change carried to the state whose state-number is infinite.

303. Theorem. In elliptical motion there is no firmamental state, and the modular quantity of the whole circuit is finite, and the measurement proceeds in one annular order.

Demonstration. If the entire circuit of variation is covered by a finite part of the scale of numbers, let the metron receive any measurable change. Then, the state-numbers of all its members will receive the same finite increment. Consequently, those members whose state-numbers were sufficiently great will be made greater than the finite difference of numbers of the whole circuit, and will be made greater than any of the numbers were at first. Since no state-number is infinite no member will have its state unchanged. And every member will have an arithmetical progression of state-numbers, the difference of all these progressions being the same. That difference will be the modular quantity of the circuit.

304. Theorem. In hyperbolic motion there are just two firmamental states, and in both the regions into which they sever the circuit the state-numbers increase toward one of these and away from the other; and the quantity of the whole circuit is not infinite. . . . †17

305. Analysis. Our measures of space are of various descriptions. Some of them, as square measure, cubic measure, etc. are composite. Thus, square measure depends upon long measures of length and breadth. Other kinds of measure are derivative. Thus, the distance of a point from a surface is the distance of the point from the nearest point of the surface. The measures which are neither composite nor derivative are two: long measure between pairs of points and angular measure between pairs of planes.

306. There are many different sorts of standards which might be assumed for long measure. From the point of view of theoretical physics the average distance that a molecule of hydrogen at a standard temperature would move in a day would have something to recommend it. But the primitive and most usual sort of standard, as well as the most convenient for the purposes of geometry, is a rigid body which is carried about from place to place, such as a yard-stick.

307. Let us ask what we mean by a rigid body. If we say that it is a body whose measures remain fixed, somebody may reply that if it is taken as the standard of measure it means nothing to say that its measure relatively to itself remains the measure of itself. Some care is, therefore, required in saying what we mean by a rigid body. If a rigid body were a single body there would be less meaning in the word rigid than there is when it is a kind of body which the working of Nature makes to be a usual kind, or a kind toward the ideal properties of which many objects closely approximate. Our general experience leads us to think that solid bodies come very near to being bodies which at fixed temperature and free from external influences have certain properties which we proceed to consider. First, every particle of such a body, or part of it occupying an indivisible place, always occupies a single indivisible place. It never goes out of existence or out of space; nor does it separate so as to occupy a number of points, nor does it enlarge so as to occupy a line or a surface or a solid space. Second, every flat film of such a body, or part of it occupying a plane, always continues (there being no stress upon the body) to occupy a plane. It neither breaks nor bends. Third, in any straight fibre of such a body, or part of it occupying a ray, (and which must always continue to occupy a ray, since every flat film in which it lies continues to lie in a plane) the order and continuity of the particles remain always the same, and round such straight fibre the order and continuity of the flat films through it remain always the same. These three properties, taken together, may be termed the optical property of the rigid body.

308. In the next place, our general experience leads us to believe that a perfectly rigid body, which ordinary solid bodies sensibly resemble, is such that if a given particle of it be brought to a point [M] and the straight filament through that particle and a second particle be brought into a given ray through [M], then there are just two points to which that second particle can be brought. In like manner, if of three particles two are brought to two points [M] and [N], there are, in each plane through {MN} just two points to which the third particle might be brought. But there is a difference between the two cases. Namely, as long as the straight filament remains in the ray, if at one time one particle is at the point [M] and another at the point [N], then, no matter how the filament is moved in the ray, every time the first particle is brought back to [M] the second particle can be brought to no other point than [N]. But in the plane, though the flat film remain in all its movements in that plane, yet if the first particle is at first at [M] the second at [N] and the third at [P], if the first two particles are carried along {MN} until they have performed an entire circuit, while the third always remains in the plane, it will not return to the same point [P] (supposing it has ever left that point) but will return to a fourth point [Q] and it will not be until a second circuit has been performed that it returns to [P]. We shall demonstrate that this must be so. It is mentioned now for a special purpose. We shall find the difference is owing to the ray having an odd number, and the plane an even number of dimensions. Hence, in three dimensions if of four particles of a rigid body three are restored to their initial positions, there is only one point to which the fourth can be brought, although there is another point which it could perfectly well occupy (as shown by its looking glass image) if there were only any fourth dimension through which it could be carried to that point. On this account, it is convenient in geometry to imagine ourselves to be in possession of a rigid body to be used as a standard of measurement which shall have the purely imaginary property that, while any three of its particles remain fixed, it shall be capable of being perverted, that is, of being suddenly converted into its looking glass image. On account of this property, we will denominate the thing, not a rigid body, but a rigid image.

309. Finally, we are led to believe that if any number of parts of a rigid body occupy at one time certain positions and at another time certain other positions, then any other parts which may at any time occupy the first set of positions may be carried into the second set of positions.

310. There is another property of rigid bodies which makes all long measure to be parabolical and all angular measure to be elliptical; but it is best, at first, to consider the consequences of the other properties, and to reserve the consideration of this until later.

311. Definition. A metrical image is a continuous multitude of particles, straight filaments, and flat films having the following properties:

1st, it has the optical property that whatever part occupies at one instant a point or a plane occupies the same kind of place (whichever it may be) at every instant, and with the same connective relations to straight filaments.

2nd, the fixation of a particle of such image at a point or of a flat film in a plane diminishes by unity the freedom of motion of all other such parts of the same metrical image.

3rd, when the particles and flat films of [a] metrical image are subject to such conditions as just suffice to reduce the freedom of motion to zero, there are just two positions, said to be perverse of one another, in which it can fulfill those conditions.

4th, if one metrical image or part of such image can occupy one place at one instant and another at another instant, then every such image or part of an image which can occupy the former place at one instant can occupy the latter place at another instant.

312. Definition. Two places (whether the same or different) are said to be equal which can be occupied by the same metrical image or by the same part of one metrical image. And the order of the occupied parts makes no difference. †18

Chapter 5: The Logic of 1873 †1

§1. Investigation †2

313. The very first of distinctions which logic supposes is between doubt and belief, a question and a proposition. Doubt and belief are two states of mind which feel different, so that we can distinguish them by immediate sensation. We almost always know without any experiment when we are in doubt and when we are convinced. This is such a difference as there is between red and blue, or pleasure and pain. Were this the whole distinction, it would be almost without significance. But in point of fact the mere sensible distinguishability is attended with an important practical difference. †3 When we believe, there is a proposition which according to some rule determines our actions, so that our belief being known, the way in which we shall behave may be surely deduced, but in the case of doubt we have such a proposition more or less distinctly in our minds but do not act from it. There is something further removed from belief than doubt, that is to say not to conceive the proposition at all. Nor is doubt wholly without effect upon our conduct. It makes us waver. Conviction determines us to act in a particular way while pure unconscious ignorance alone which is the true contrary of belief has no effect at all.

314. Belief and doubt may be conceived to be distinguished only in degree. †4

315. Living doubt is the life of investigation. When doubt is set at rest inquiry must stop. . . . †5

316. From this conception springs the desire to get a settlement of opinion [that] is some conclusion which shall be independent of all individual limitations, independent of caprice, of tyranny, of accidents of situation . . ., — a conclusion to which every man would come who should pursue the same method and push it far enough. The effort to produce such a settlement of opinion is called investigation. Logic is the science which teaches whether such efforts are rightly directed or not.

317. There is an important difference between the settlement of opinion which results from investigation and every other such settlement. It is that investigation will not fix one answer to a question as well as another, but on the contrary it tends to unsettle opinions at first, to change them and to confirm a certain opinion which depends only on the nature of investigation itself. The method of producing fixity of belief by adhering obstinately to one's belief, tends only to fix such opinions as each man already holds. The method of persecution tends only to spread the opinions which happen to be approved by rulers; and except so far as rulers are likely to adopt views of a certain cast does not determine at all what opinions shall become settled. The method of public opinion tends to develop a particular body of doctrine in every community. Some more widely spread and deeply rooted conviction will gradually drive out the opposing opinions, becoming itself in the strife somewhat modified by these. But different communities, removed from mutual influence, will develop very different bodies of doctrine, and in the same community there will be a constant tendency to sporting which may at any time carry the whole public. What we know of growth, in general, shows that this will take place; and history confirms us. The early history of sciences before they begin to be really investigated, especially of psychology, metaphysics, etc., illustrates as well as anything the pure effect of this method of fixing opinions. The numerous well-defined species of doctrines which have existed on such subjects and their progressive historical succession give the science of the history of philosophy considerable resemblance to that of paleontology.

318. Thus no one of these methods can as a matter of fact attain its end of settling opinions. Men's opinions will act upon one another and the method of obstinacy will infallibly be succeeded by the method of persecution and this will yield in time to the method of public opinion and this produces no stable result.

319. Investigation differs entirely from these methods in that the nature of the final conclusion to which it leads is in every case destined from the beginning, without reference to the initial state of belief. Let any two minds investigate any question independently and if they carry the process far enough they will come to an agreement which no further investigation will disturb.

320. But this will not be true for any process which anybody may choose to call investigation, but only for investigation which is made in accordance with appropriate rules. Here, therefore, we find there is a distinction between good and bad investigation. This distinction is the subject of study in logic. Some persons will doubt whether any sort of investigation will settle all questions. I refrain, however, from arguing the matter, because I should thus be led to anticipate what comes later, and because after any demonstration I might give I should still rest on some assumption and it is as easy to see that investigation assumes its own success as that it assumes anything else.

321. Logic is the doctrine of truth, its nature and the manner in which it is to be discovered.

322. The first condition of learning is to know that we are ignorant. A man begins to inquire and to reason with himself as soon as he really questions anything and when he is convinced he reasons no more. Elementary geometry produces formal proofs of propositions which nobody doubts, but that cannot properly be called reasoning which does not carry us from the known to the unknown, and the only value in the first demonstrations of geometry is that they exhibit the dependence of certain theorems on certain axioms, a thing which is not clear without the demonstrations. When two men discuss a question, each first endeavors to raise a doubt in the mind of the other, and that is often half the battle. When the doubt ceases there is no use in further discussion. Thus real inquiry begins when genuine doubt begins and ends when this doubt ends. And the premises of the reasoning are facts not doubted. It is therefore idle to tell a man to begin by doubting familiar beliefs, unless you say something which shall cause him really to doubt them. Again, it is false to say that reasoning must rest either on first principles or on ultimate facts. For we cannot go behind what we are unable to doubt, but it would be unphilosophical to suppose that any particular fact will never be brought into doubt.

323. It is easy to see what truth would be for a mind which could not doubt. That mind could not regard anything as possible except what it believed in. By all existing things it would mean only what it thought existed, and everything else would be what it would mean by nonexistent. It would, therefore, be omniscient in its universe. To say that an omniscient being is necessarily destitute of the faculty of reason, sounds paradoxical; yet if the act of reasoning must be directed to an end, when that end is attained the act naturally becomes impossible.

324. The only justification for reasoning is that it settles doubts, and when doubt finally ceases, no matter how, the end of reasoning is attained. Let a man resolve never to change his existing opinions, let him obstinately shut his eyes to all evidence against them, and if his will is strong enough so that he actually does not waver in his faith, he has no motive for reasoning at all, and it would be absurd for him to do it. That is method number one for attaining the end of reasoning, and it is a method which has been much practised and highly approved, especially by people whose experience has been that reasoning only leads from doubt to doubt. There is no valid objection to this procedure if it only succeeds. It is true, it is utterly irrational; that is to say it is foolish from the point of view of those who do reason. But to assume that point of view is to beg the question. In fact, however, it does not succeed; and the first cause of failure is that different people have different opinions and the man who sees this begins to feel uncertain. It is therefore desirable to produce unanimity of opinion and this gives rise to method number two, which is to force people by fire and sword to adopt one belief, to massacre all who dissent from it and burn their books. This way of bringing about a catholic consent has proved highly successful for centuries in some cases, but it is not practicable in our days. A modification of this is method number three, to cultivate a public opinion by oratory and preaching and by fostering certain sentiments and passions in the minds of the young. This method is the most generally successful in our day. The fourth and last method is that of reasoning. It will never be adopted when any of the others will succeed and it has itself been successful only in certain spheres of thought. Nevertheless those who reason think that it must be successful in the end, and so it would if all men could reason. There is this to be said in favor of it. He who reasons will regard the opinions of the majority of mankind with contemptuous indifference; they will not in the least disturb his opinions. He will also neglect the beliefs of those who are not informed, and among the small residue he may fairly expect some unanimity on many questions.

325. I hope it will now be plain to the reader, that the only rational ground for preferring the method of reasoning to the other methods is that it fixes belief more surely. A man who proposes to adopt the first method may consistently do so simply because he chooses to do so. But if we are to decide in favor of reasoning, we ought to do so on rational grounds. Now if belief is fixed, no matter how, doubt has as a matter of fact ceased, and there is no motive, rational or other, for reasoning any more. Any settlement of opinion, therefore, if it is full and perfect, is entirely satisfactory and nothing could be better. It is the peculiarity of the method of reasoning, that if a man thinks that it will not burn him to put his hand in the fire, reasoning will not confirm that belief but will change it. This is a vast advantage to the mind of a rationalist. But the advocate of any one of the first three methods, will be able to say (if either of these methods will yield a fixed belief) either that he knows by his method that fire will burn, so that reasoning is inferior to his method in that it may permit a man for a moment to doubt this, or else that he knows that fire will not burn, so that reasoning leads all astray. In either case therefore he will conceive that which to the rationalist seems the great advantage of reasoning, to be a great fault. Thus the only ground of a fair decision between the methods must be that one actually succeeds while the others break up and dissolve. Pope expresses the philosophy of the matter perfectly: Truth struck to earth shall rise again The eternal years of God are hers While error . . . writhes in pain And dies amidst her worshippers.

§2. Logic †6

326. It is the business of the logician to study the nature of the fourth method of inquiry and to discover the rules for conducting it with success. The whole subject will in the exposition of it here offered to the reader be divided into three parts. The first shall treat of the essence of investigation in general, by whatever mind it is conducted and to whatever subject it is applied. The second shall treat of those maxims of investigation which become necessary owing to the peculiar constitution of man in his senses, and his mental nature. The third shall give some slight outline of the special methods of research which are applicable in the different branches of science, and which arise from the peculiarities of the matter investigated. In this first part then we have, broadly speaking, nothing to do with the nature of the human mind. Only as there are some faculties which must belong to any mind which can investigate at all, these must come under our consideration. All inquiry, for example, presupposes a passage from a state of doubt to a state of belief; and therefore there must be a succession of time in the thoughts of any mind which is able to inquire. In the fourth method of inquiry a certain predetermined though not pre-known belief is sure to result from the process; no matter what may have been the opinion of the inquirer at the outset. It follows that during the investigation elements of thought must have sprung up in the mind which were not caused by any thought which was present at the time the investigation was commenced. Such new ideas springing up in the mind and not produced by anything in the mind, are called sensations. Every mind capable of investigation must therefore have a capacity for sensations. But were all thoughts of this kind investigation would be almost an involuntary process. We might will to investigate but we could not change the course which investigation should take. There would therefore be no distinction between a right and a wrong method of investigation. Now we have seen in the last chapter, that such a distinction is essential to the fourth method of inquiry and is, in fact, the only thing which distinguishes it from the third. There must be thoughts therefore which are determined by previous thoughts. And such a faculty of producing thoughts from others must belong to every mind which can investigate. Without a succession of ideas in time it is clear that no reasoning is possible. I shall proceed to show that without it and without the determination of one idea by another no thought in any proper sense of the word is possible.

§3. Observation and Reasoning †7

327. Because the only purpose of inquiry is the settlement of opinion, we have seen that everyone who investigates, that is, pursues an inquiry by the fourth method assumes that that process will, if carried far enough, lead him to a certain conclusion, he knows not what beforehand, but which no further investigation will change. No matter what his opinion at the outset may be, it is assumed that he will end in one predestinated belief. Hence it appears that in the process of investigation wholly new ideas and elements of belief must spring up in the mind which were not there before.

328. Some thoughts are produced by previous thoughts according to regular laws of association, †8 so that if the previous thoughts be known, and the rule of association be given, the thought which is so produced may be predicted. This is the elaborative operation of thought, or thinking par excellence. But when an idea comes up in the mind which has no such relation to former ideas, but is something new to us, we say that it is caused by something out of the mind, and we call the process by which such thoughts spring up, sensation. And those parts of investigation which consist chiefly in supplying such materials for thought to work over, combine and analyze, are termed observations. The first thing to be noted then is that since investigation leads us from whatever state of opinion we may happen to have to an opinion which is predetermined, it must be that investigation involves observation as one part of it, and, in fact, the conclusion to which we finally come ultimately depends entirely upon the observations.

329. We may pause here to make a practical application of this principle. No argument can possibly be a correct one which pretends to disclose to us a fact wholly new without being based on evidence which is new. The metaphysicians are given to this kind of reasoning; even those of them who are the most energetic in maintaining that all our knowledge comes from sense. Writers upon the nature of the human mind, especially, have built up a great body of doctrine without the aid of any observations or facts, except such as are familiar to all the world. Such things justly excite our suspicion. When Hobbes, for example, would persuade us that no man can act otherwise than for the sake of pleasure, it is clear that this belief would deeply modify our conceptions of men, and our plans of life; but when on asking what supports this momentous conclusion we learn that it is but the simple fact — if it can be dignified by that name — that every man desires to do what he does do, we are led at once to suspect that there is some sophistry in the process by which so novel a conclusion can be drawn from so familiar a premise. So, when modern necessitarians maintain that every act of the will proceeds from the strongest motive, they lay down a principle which should be expected to give rise to a psychological science as exact as mechanics, and capable of reducing human actions to precise calculation. But when we find that the advocates of this principle have made no experiments to test their law, we are strongly inclined to think that there has been some juggle of reasoning which has enabled them thus to create something out of nothing.

330. An observation, as we have defined it, is merely an idea arising in the mind, and not produced by previous ideas. This is not the complete description of observation as understood by scientific men, and we must be careful that the word does not lead us to conclusions which we are not yet warranted in drawing. For example a dream, a presentiment or some fancied inspiration from on high, might, as far as we have yet seen, involve entirely new elements of thought, and, therefore, be an observation in the sense of our definition, so that we are not yet warranted in saying that such things cannot be the ground of legitimate reasoning. This is a question which we shall have again to examine when we come to consider those maxims of inference which depend upon the peculiar constitution of man.

331. But Observation alone cannot constitute investigation; for if it did the only active part which we should have to play in this method of inquiry would be simply the willing to observe, and there would be no distinction of a wrong method and a right method of investigation. But we have seen that such a distinction is essential to the idea of investigation, and that it is, in fact the only thing which separates this from the third method of inquiry. Accordingly, besides observation it must be that there is also an elaborative process of thought by which the ideas given by observation produce others in the mind. †9 Besides, the observations are most varied and are never exactly repeated or reproduced so that they cannot constitute that settled opinion to which investigation leads. Two men, for example, agree in an opinion, and if you ask upon what their opinions rest they will perhaps allege the same fact. But trace the matter back further; ask them upon what grounds they believe that fact again and you will eventually come to premises that are different. Two minds, for example, may have formed the same judgment of a certain person's character and yet may have based their opinions on observing his behavior on different occasions. The rotation of the earth was at first inferred from the movement of the heavenly bodies; but afterwards the manner in which a long pendulum when allowed to swing would gradually turn around and change its direction of oscillation, afforded an entirely new proof; and there are certain very small movements of the stars, which, if they were capable of sufficiently exact observation, would show another ground for the same conclusion. Indeed, the fact which one man observes, is in no case precisely the same as the fact which another man observes. One astronomer observes that the moon passes over a star so as to hide it at a certain instant at his observatory, another astronomer observes that the same star is occulted at a certain instant at his observatory. These two facts are not the same, because they relate to different stations of observation. What is so plain in regard to astronomical observation, because we are accustomed to precision of thought about this, is equally true in regard to the most familiar facts. You and I both see an ink-stand on the table; but what you observe, is that there is a certain appearance from where you sit, and what I observe, is that there is a certain appearance from where I sit. The fact in which we agree, that there is an ink-stand there, is what we conclude from the different appearances which we each severally observe. We may change places and still we shall fail to get each other's observations; for the difference of time then comes in. I may observe that there is such an appearance now as you describe as having existed a few moments before; but I cannot observe that there was such an appearance before I took your place. It is needless to multiply these examples, because the slightest reflection will supply them in any number; but what have been adduced are sufficient to show that observations are for every man wholly private and peculiar. And not only can no man make another man's observations, or reproduce them; but he cannot even make at one time those observations which he himself made at another time. They belong to the particular situation of the observer, and the particular instant of time.

332. Indeed, if we carefully distinguish that which is first given by sensation, from the conclusion which we immediately draw from it, it is not difficult to see that different observations are not in themselves even so much as alike; for what does the resemblance between the two observations consist in? What does it mean to say that two thoughts are alike? It can only mean that any mind that should compare them together, would pronounce them to be alike. But that comparison would be an act of thought not included in the two observations severally; for the two observations existing at different times, perhaps in different minds, cannot be brought together to be compared directly in themselves, but only by the aid of the memory, or some other process which makes a thought out of previous thoughts, and which is, therefore, not observation. Since, therefore, the likeness of these thoughts consists entirely in the result of comparison, and comparison is not observation, it follows that observations are not alike except so far as there is a possibility of some mental process besides observation.

333. Without however insisting upon this point which may be found too subtile, the fact remains that the observations are not the same in the sense in which the conclusions to which they give rise are the same. All astronomers, for example, will agree that the earth is ninety-two or ninety-three millions of miles from the sun. And yet, one would base his conclusion on observations of the passage of Venus across the sun's disk; another upon observations of the planet Mars; another upon experiments upon light combined with observations of the satellites of Jupiter. And the same thing is equally true in regard to most of the ordinary affairs of life.

334. Now how is it that the springing up into the mind of thoughts so dissimilar should lead us inevitably though sometimes not until after a long time to one fixed conclusion? Disputes undoubtedly occur among those who pursue a proper method of investigation. But these disputes come to an end. At least that is the assumption upon which we go in entering into the discussion at all, for unless investigation is to lead to settled opinion it is of no service to us whatever. We do believe then in regard to every question which we try to investigate that the observations though they may be as varied and as unlike in themselves as possible, yet have some power of bringing about in our minds a predetermined state of belief. This reminds us of the species of necessity which is known as fate. The fairy stories are full of such examples as this: A king shuts his daughter up in a tower because he has been warned that she is destined to suffer some misfortune from falling in love before a certain age and it turns out that the very means which he has employed to prevent it is just what brings the prophecy to fulfillment. Had he pursued a different course, the idea seems to be that that would equally have brought about the destined result. Fate then is that necessity by which a certain result will surely be brought to pass according to the natural course of events however we may vary the particular circumstances which precede the event. In the same manner we seem fated to come to the final conclusion. For whatever be the circumstances under which the observations are made and by which they are modified they will inevitably carry us at last to this belief.

335. The strangeness of this fact disappears entirely when we adopt the conception of external realities. We say that the observations are the result of the action upon the mind of outward things, and that their diversity is due to the diversity of our relations to these things; while the identity of the conclusion to which the mind is led by them is owing to the identity of the things observed, the reasoning process serving to separate from the many different observations that we make of the same thing the constant element which depends upon the thing itself from the differing and variable elements which depend on our varying relations to the thing. This hypothesis I say removes the strangeness of the fact that observations however different yield one identical result. It removes the strangeness of this fact by putting it in a form and under an aspect in which it resembles other facts with which we are familiar. We are accustomed very rightly to think that causes always precede their effects and to disbelieve in fate, which is a fancied necessity by which some future event as it were forces the conditions which precede to be such as would bring it about. That there is no such intrinsic and unconditional necessity to bring about events Western nations are fully and rightly convinced. This is why it seems strange to assert that the final conclusion of the investigation is predestined and why it is satisfactory to the mind to find a hypothesis which shall assign a cause preceding the final belief which would account for the production of it, and of the truth of this conception of external realities there can be no doubt. Even the idealists, if their doctrines are rightly understood have not usually denied the existence of real external things. But though the conception involves no error and is convenient for certain purposes, it does not follow that it affords the point of view from which it is proper to look at the matter in order to understand its true philosophy. It removes the strangeness of a certain fact by assimilating it to other familiar facts; but is not that fact that investigation leads to a definite conclusion really of so different a character from the ordinary events in the world to which we apply the conception of causation that such an assimilation and classification of it really puts it in a light which, though not absolutely false, fails nevertheless to bring into due prominence the real peculiarity of its nature? That observation and reasoning produce a settled belief which we call the truth seems a principle to be placed at the head of all special truths which are only the particular beliefs to which observation and reasoning in such cases lead. And it is hardly desirable to merge it among the rest by an analogy which serves no other purpose.

§4. Reality †10

336. The question is, "Whether corresponding to our thoughts and sensations, and represented in some sense by them, there are realities, which are not only independent of the thought of you, and me, and any number of men, but which are absolutely independent of thought altogether." The objective final opinion is independent of the thoughts of any particular men, but is not independent of thought in general. †11 That is to say, if there were no thought, there would be no opinion, and therefore, no final opinion.

337. All that we directly experience is our thought — what passes through our minds; and that only, at the moment at which it is passing through. We here see thoughts determining and causing other thoughts, and a chain of reasoning or of association is produced. But the beginning and the end of this chain, are not distinctly perceived. A current is another image under which thought is often spoken of, and perhaps more suitably. We have particularly drawn attention to the point to which thought flows, and that it finally reaches: a certain level, as it were — a certain basin, where reality becomes unchanging. It has reached its destination, and that permanency, that fixed reality, which every thought strives to represent and image, we have placed in this objective point, towards which the current of thought flows.

338. But the matter has often been regarded from an opposite point of view; attention being particularly drawn to the spring, and origin of thought. It is said that all other thoughts are ultimately derived from sensations; that all conclusions of reasoning are valid only so far as they are true to the sensations; that the real cause of sensation therefore, is the reality which thought presents. Now such a reality, which causes all thought, would seem to be wholly external to the mind — at least to the thinking part of the mind, as distinguished from the feeling part; for it might be conceived to be, in some way, dependent upon sensation.

339. Here then are two opposite modes of conceiving reality. The one which has before been developed at some length, and which naturally results from the principles which have been set forth in the previous chapters of this book is an idea which was obscurely in the minds of the medieval realists; while the other was the motive principle of nominalism. I do not think that the two views are absolutely irreconcilable, although they are taken from very widely separated stand-points. The realistic view emphasizes particularly the permanence and fixity of reality; the nominalistic view emphasizes its externality. But the realists need not, and should not, deny that the reality exists externally to the mind; nor have they historically done so, as a general thing. That is external to the mind, which is what it is, whatever our thoughts may be on any subject; just as that is real which is what it is, whatever our thoughts may be concerning that particular thing. Thus an emotion of the mind is real, in the sense that it exists in the mind whether we are distinctly conscious of it or not. But it is not external because although it does not depend upon what we think about it, it does depend upon the state of our thoughts about something. Now the object of the final opinion which we have seen to be independent of what any particular person thinks, may very well be external to the mind. And there is no objection to saying that this external reality causes the sensation, and through the sensation has caused all that line of thought which has finally led to the belief.

340. At first sight it seems no doubt a paradoxical statement that, "The object of final belief which exists only in consequence of the belief, should itself produce the belief"; but there have been a great many instances in which we have adopted a conception of existence similar to this. The object of the belief exists it is true, only because the belief exists; but this is not the same as to say that it begins to exist first when the belief begins to exist. We say that a diamond is hard. And in what does the hardness consist? It consists merely in the fact that nothing will scratch it; therefore its hardness is entirely constituted by the fact of something rubbing against it with force without scratching it. And were it impossible that anything should rub against it in this way, it would be quite without meaning, to say that it was hard, just as it is entirely without meaning to say that virtue or any other abstraction is hard. †12 But though the hardness is entirely constituted by the fact of another stone rubbing against the diamond yet we do not conceive of it as beginning to be hard when the other stone is rubbed against it; on the contrary, we say that it is really hard the whole time, and has been hard since it began to be a diamond. And yet there was no fact, no event, nothing whatever, which made it different from any other thing which is not so hard, until the other stone was rubbed against it.

341. So we say that the inkstand upon the table is heavy. And what do we mean by that? We only mean, that if its support be removed it will fall to the ground. This may perhaps never happen to it at all — and yet we say that it is really heavy all the time; though there is no respect whatever, in which it is different from what it would be if it were not heavy, until that support is taken away from it. The same is true in regard to the existence of any other force. It exists only by virtue of a condition, that something will happen under certain circumstances; but we do not conceive it as first beginning to exist when these circumstances arise; on the contrary, it will exist though the circumstances should never happen to arise. And now, what is matter itself? The physicist is perfectly accustomed to conceive of it as merely the centre of the forces. It exists, therefore, only so far as these forces exist. Since, therefore, these forces exist only by virtue of the fact, that something will happen under certain circumstances, it follows that matter itself only exists in this way.

342. Nor is this conception one which is peculiar to the physicists and to our views of the external world. A man is said to know a foreign language. And what does that mean? Only that if the occasion arises, the words of that language will come into his mind; it does not mean that they are actually in his mind all the time. And yet we do not say that he only knows the language at the moment that the particular words occur to him that he is to say; for in that way he never could be certain of knowing the whole language if he only knew the particular word necessary at the time. So that his knowledge of the thing which exists all the time, exists only by virtue of the fact that when a certain occasion arises a certain idea will come into his mind.

343. A man is said to possess certain mental powers and susceptibilities, and we conceive of him as constantly endowed with these faculties; but they only consist in the fact that he will have certain ideas in his mind under certain circumstances; and not in the fact of his having certain ideas in his mind all the time. It is perfectly conceivable that the man should have faculties which are never called forth: in which case the existence of the faculties depends upon a condition which never occurs. But what is the mind itself but the focus of all the faculties? and what does the existence of the mind consist in but in these faculties? Does the mind cease to exist when it sleeps? and is it a new man who wakes every morning?

344. It appears then that the existence of mind equally with that of matter according to these arguments which have led to this view which is held by all psychologists, as well as physicists, depends only upon certain hypothetical conditions which may first occur in the future, or which may not occur at all. There is nothing extraordinary therefore in saying that the existence of external realities depends upon the fact, that opinion will finally settle in the belief in them. And yet that these realities existed before the belief took rise, and were even the cause of that belief, just as the force of gravity is the cause of the falling of the inkstand — although the force of gravity consists merely in the fact that the inkstand and other objects will fall.

345. But if it be asked us, whether some realities do not exist, which are entirely independent of thought; I would in turn ask, what is meant by such an expression and what can be meant by it. What idea can be attached to that of which there is no idea? For if there be an idea of such a reality, it is the object of that idea of which we are speaking, and which is not independent of thought. It is clear that it is quite beyond the power of the mind to have an idea of something entirely independent of thought — it would have to extract itself from itself for that purpose; and since there is no such idea there is no meaning in the expression. †13 The experience of ignorance, or of error, which we have, and which we gain by means of correcting our errors, or enlarging our knowledge, does enable us to experience and conceive something which is independent of our own limited views; but as there can be no correction of the sum total of opinions, and no enlargement of the sum total of knowledge, we have no such means, and can have no such means of acquiring a conception of something independent of all opinion and thought.

§5. Time and Thought †14

346. Any mind which has the power of investigation, and which therefore passes from doubt to belief, must have its ideas follow after one another in time. And if there is to be any distinction of a right and a wrong method of investigation, it must have some control over the process. So that there must be such a thing as the production of one idea from another which was previously in the mind. This is what takes place in reasoning, where the conclusion is brought into the mind by the premises.

347. We may imagine a mind which should reason and never know that it reasoned; never being aware that its conclusion was a conclusion, or was derived from anything which went before. For such a mind there might be a right and a wrong method of thinking; but it could not be aware that there was such a distinction, nor criticise in any degree its own operations. To be capable of logical criticism, the mind must be aware that one idea is determined by another.

348. Now when this happens, after the first idea comes the second. There is a process which can only take place in a space of time; but an idea is not present to the mind during a space of time — at least not during a space of time in which this idea is replaced by another; for when the moment of its being present is passed, it is no longer in the mind at all. Therefore, the fact that one idea succeeds another is not a thing which in itself can be present to the mind, any more than the experiences of a whole day or of a year can be said to be present to the mind. It is something which can be lived through; but not be present in any one instant; and therefore, which can not be present to the mind at all; for nothing is present but the passing moment, and what it contains. The only way therefore in which we can be aware of a process of inference, or of any other process, is by its producing some idea in us. Not only therefore is it necessary that one idea should produce another; but it is also requisite that a mental process should produce an idea. These three things must be found in every logical mind: First, ideas; second, determinations of ideas by previous ideas; third, determinations of ideas by previous processes. And nothing will be found which does not come under one of these three heads.

349. The determination of one thing by another, implies that the former not only follows after the latter, but follows after it according to a general rule, in consequence of which, every such idea would be followed by such a second one. There can therefore be no determination of one idea by another except so far as ideas can be distributed into classes, or have some resemblances. But how can one idea resemble another? An idea can contain nothing but what is present to the mind in that idea. Two ideas exist at different times; consequently what is present to the mind in one is present only at that time, and is absent at the time when the other idea is present. Literally, therefore, one idea contains nothing of another idea; and in themselves they can have no resemblance. They certainly do not resemble one another except so far as the mind can detect a resemblance; for they exist only in the mind, and are nothing but what they are thought to be. Now when each is present to the mind the other is not in the mind at all. No reference to it is in the mind, and no idea of it is in the mind. Neither idea therefore when it is in the mind, is thought to resemble the other which is not present in the mind. And an idea can not be thought, except when it is present in the mind. And, therefore, one idea can not be thought to resemble another, strictly speaking.

350. In order to escape from this paradox, let us see how we have been led into it. Causation supposes a general rule, and therefore similarity. Now so long as we suppose that what is present to the mind at one time is absolutely distinct from what is present to the mind at another time, our ideas are absolutely individual, and without any similarity. It is necessary, therefore, that we should conceive a process as present to the mind. And this process consists of parts existing at different times and absolutely distinct. And during the time that one part is in the mind, the other is not in the mind. To unite them, we have to suppose that there is a consciousness running through the time. So that of the succession of ideas which occur in a second of time, there is but one consciousness, and of the succession of ideas which occurs in a minute of time there is another consciousness, and so on, perhaps indefinitely. So that there may be a consciousness of the events that happened in a whole day or a whole life time.

351. According to this, two parts of a process separated in time — though they are absolutely separate, in so far as there is a consciousness of the one, from which the other is entirely excluded — are yet so far not separate, that there is a more general consciousness of the two together. This conception of consciousness is something which takes up time. It seems forced upon us to escape the contradictions which we have just encountered. And if consciousness has a duration, then there is no such thing as an instantaneous consciousness; but all consciousness relates to a process. And no thought, however simple, is at any instant present to the mind in its entirety, but it is something which we live through or experience as we do the events of a day. And as the experiences of a day are made up of the experiences of shorter spaces of time so any thought whatever is made up of more special thoughts which in their turn are themselves made up by others and so on indefinitely.

352. It may indeed very likely be that there is some minimum space of time within which in some sense only an indivisible thought can exist and as we know nothing of such a fact at present we may content ourselves with the simpler conception of an indefinite continuity in consciousness. It will easily be seen that when this conception is once grasped the process of the determination of one idea by another becomes explicable. What is present to the mind during the whole of an interval of time is something generally consisting of what there was in common in what was present to the mind during the parts of that interval. And this may be the same with what is present to the mind during any interval of time; or if not the same, at least similar — that is, the two may be such that they have much in common. These two thoughts which are similar may be followed by others that are similar and according to a general law by which every thought similar to either of these is followed by another similar to those by which they are followed. If a succession of thoughts have anything in common this may belong to every part of these thoughts however minute, and therefore it may be said to be present at every instant. This element of consciousness which belongs to a whole only so far as it belongs to its parts is termed the matter of thought.

353. There is besides this a causation running through our consciousness by which the thought of any one moment determines the thought of the next moment no matter how minute these moments may be. And this causation is necessarily of the nature of a reproduction; because if a thought of a certain kind continues for a certain length of time as it must do to come into consciousness the immediate effect produced by this causality must also be present during the whole time, so that it is a part of that thought. Therefore when this thought ceases, that which continues after it by virtue of this action is a part of the thought itself. In addition to this there must be an effect produced by the following of one idea after a different idea; otherwise there would be no process of inference except that of the reproduction of the premises.

§6. Belief †16

354. We have seen that an inference is the process by which one belief determines another. But a belief is itself a habit of the mind by virtue of which one idea gives rise to another. When I say that I know the French language, I do not mean that as long as I know it I have all the words which compose it in my mind, or a single one of them. But only that when I think of an object, the French word for it will occur to me, and that when a French word is brought to my attention I shall think of the object it signifies. What is true of knowledge is equally true of belief, since the truth or falsehood of the cognition does not alter its character in this respect. I believe that prussic acid is poison, and always have believed it. This does not mean that I have always had the idea of prussic acid in my mind, but only that on the proper occasion, on thinking of drinking it, for example, the idea of poison and all the other ideas that that idea would bring up, would arise in my mind.

355. Thus there are three elements of cognition: thoughts, the habitual connection between thoughts, and processes establishing a habitual connection between thoughts. We have seen already that an idea cannot be instantaneously present, that consciousness occupies time, and that we have no consciousness in an instant. So that at no time have we a thought. But now it further appears that in reference to a belief not only can we not have it in an instant, but it can not be present to the mind in any period of time. It does not consist in anything which is present to the mind, but in an habitual connection among the things which are successively present. That is to say, it consists in ideas succeeding one another according to a general rule; but not in the mere thinking of this general rule, nor in the mere succession of ideas one upon another, nor in both together. A thought must therefore be a sign of a belief; but is never the belief itself. The same thing is obviously true in regard to an inference; and even a simple idea is of intellectual value to us not for what it is in itself but as standing for some object to which it relates. Now a thing which stands for another thing is a representation or sign. So that it appears that every species of actual cognition is of the nature of a sign. It will be found highly advantageous to consider the subject from this point of view, because many general properties of signs can be discovered by a set of words and the like which are free from the intricacies which perplex us in the direct study of thought.

356. Let us examine some of the characters of signs in general. A sign must in the first place have some qualities in itself which serve to distinguish it, a word must have a peculiar sound different from the sound of another word; but it makes no difference what the sound is, so long as it is something distinguishable. In the next place, a sign must have a real physical connection with the thing it signifies so as to be affected by that thing. A weather-cock, which is a sign of the direction of the wind, must really turn with the wind. This word in this connection is an indirect one; but unless there be some way or other which shall connect words with the things they signify, and shall ensure their correspondence with them, they have no value as signs of those things. Whatever has these two characters is fit to become a sign. It is at least a symptom, but it is not actually a sign unless it is used as such; that is unless it is interpreted to thought and addresses itself to some mind. As thought is itself a sign we may express this by saying that the sign must be interpreted as another sign. †16 Let us see however, whether this is true of thought itself that it must address itself to some other thought. There are some cases in which it is not difficult to see that this must be the case. I have no belief that prussic acid is poisonous unless when the particular occasion comes up I am led to the further belief that that particular acid is poisonous; and unless I am further led to the belief that it is a thing to avoid drinking. For all these things are necessary to my acting on my belief. A belief which will not be acted on ceases to be a belief.

357. It may be that I shall finally come to a belief which is a motive for action directly without the intervention of a more special belief. In this case how does the belief address itself to a sign? When a person is said to act upon a certain belief the meaning is that his actions have a certain consistency; that is to say, that they possess a certain intellectual unity. But this implies that they are interpreted in the light of thought. So that even if a belief is a direct motive to action it still is a belief only because that action is interpretable again. And thus the intellectual character of beliefs at least are dependent upon the capability of the endless translation of sign into sign. An inference translates itself directly into a belief. A thought which is not capable of affecting belief in any way, obviously has no signification or intellectual value at all. If it does affect belief it is then translated from one sign to another as the belief itself is interpreted. And therefore this character of signs that they must be capable of interpretation in every sense belongs to every kind of cognition. And consequently no cognition is such or has an intellectual significance for what it is in itself, but only for what it is in its effects upon other thoughts. And the existence of a cognition is not something actual, but consists in the fact that under certain circumstances some other cognition will arise.

§7. Pragmatism †17

358. In every logical mind there must be 1st, ideas; 2nd, general rules according to which one idea determines another, or habits of mind which connect ideas; and, 3rd, processes whereby such habitual connections are established.

359. A belief is an habitual connection of ideas. For example, to say that I believe prussic acid is a poison is to say that when the idea of drinking it occurs to me, the idea of it as a poison with all the other ideas which follow in the train of this will arise in my mind. Among these ideas, or objects present to me, is the sense of refusing to drink it. This, if I am in a normal condition, will be followed by an action of the nerves when needed which will remove the cup from my lips. It seems probable that every habitual connection of ideas may produce such an effect upon the will. If this is actually so, a belief and an habitual connection of ideas are one and the same.

360. In a mind which is capable of logical criticism of its beliefs, there must be a sensation of believing, which shall serve to show what ideas are connected. The recognition that two objects present belong together as one is a judgment. All ideas arise in judgments. This is clearly the case if they are caused by previous ideas. If they are sensations then they at once cause other ideas and are connected with these in judgments. The intellectual value of ideas lies evidently in their relations to one another in judgments and not to their qualities in themselves. †18 All that seems blue to me might seem red and vice versa and yet all that I now find true of those objects I should equally find true then, if nothing else were changed. I should still perceive the same distinctions of things that I do now. The intellectual significance of beliefs lies wholly in the conclusions which may be drawn from them, and ultimately in their effects upon our conduct. For there does not seem to be any important distinction between two propositions which never can yield different practical results. †19 Only the difference in the facility with which a conclusion can be reached from two propositions must be regarded as a difference in their effects upon our actions.

361. It appears then that the intellectual significance of all thought ultimately lies in its effect upon our actions. Now in what does the intellectual character of conduct consist? Clearly in its harmony to the eye of reason; that is in the fact that the mind in contemplating it shall find a harmony of purposes in it. In other words it must be capable of rational interpretation to a future thought. Thus thought is rational only so far as it recommends itself to a possible future thought. Or in other words the rationality of thought lies in its reference to a possible future. †20

Book 3: Philosophy of Mind

Chapter 1: Psychognosy †1

§1. Introduction

362. The next business before us is to run through the Subclass of Psychognosy once more, and note its Families, etc. †2 The first order is Nomological Psychognosy, which coincides with what is called Psychology, except that under this latter head, sundry classificatory studies, such as of Criminals, Insects, Great Men, Devil-fishes, Insanity, Sexual, Professional, and Racial characters, are usually included. Such studies cannot be pursued to advantage without a good knowledge of psychology; and here and there, they do contribute a few useful facts to the psychologist. Still, they are not generally pursued by the regular psychologists; nor is the elucidation of the laws of mind their aim, — unless it be a distant and dubious one; so that to a fair and discriminating mind they hardly appear to belong naturally to psychology. It is merely the influence of the abstract definition which has caused them to be called psychological; and we must be on our guard against the deceptions of abstract definitions.

363. We have already recognized two Suborders of Psychology, — General Psychology and Special Psychology. †3 But here we meet with the serious difficulty that we find ourselves in disaccord with the psychologist's conception of his own science. Not that the psychologist will have any objection to a division into General and Special Psychology. But he will draw the line in quite another place from that in which we have drawn it. We have conceived of General Psychology as the study of the law of final causation. The psychologists will disapprove of that. They will say that purpose is characteristic only of a special department of mind, and that what they are studying is the phenomenon of consciousness generally. Now it is my intention in another chapter to examine seriously the question which of us is right. †4 I do not think that such a discussion would be quite relevant here. But when an author (it is my case), having for many years pushed a line of investigation over a path, very old indeed, — uralt, as the Germans say, — yet for centuries unused and grown over with brush, finds that in order to set forth his results, he has to persuade the reader to look at matters from points of view from which everything must seem to him unfamiliar and paradoxical; it will be an advantage, when the two come to the serious argumentation, if the author has already made the reader somewhat acquainted with the propositions he desires to defend. He will do well (so it has seemed to me) to expose what he has to offer to the sunlight, that its garish colors may fade a little, before the time comes for deciding whether it is to be accepted or rejected. To be sure, this will involve considerable repetition; but the repetition will not be without a purpose, and I hope not without its convenience for both parties. Let it be understood, then, that what I say here on the subject of my difference with the modern psychologists, for the scientific character of whose work I have a high degree of respect, is not my argument. That will be presented later; it is not needed here. All I wish to bring before the reader here is the fact that there is a very different opinion from that now current among the psychologists, and an opinion which a man who has anxiously examined into the question, fully alive to the perils of pet-theories and knowing well that no other force than that of the truth that comes from observation can possibly cause an opinion to endure, can entertain with modest confidence as the more conformed to the facts. †5

§2. Consciousness and Purpose

364. To begin with the psychologists have not yet made it clear what Mind is. I do not mean its substratum; but they have not even made it clear what a psychical phenomenon is. Far less has any notion of mind been established and generally acknowledged which can compare for an instant in distinctness to the dynamical conception of matter. Almost all the psychologists still tell us that mind is consciousness. But to my apprehension Hartmann has proved conclusively that unconscious mind exists. What is meant by consciousness is really in itself nothing but feeling. Gay and Hartley were quite right about that; and though there may be, and probably is, something of the general nature of feeling almost everywhere, yet feeling in any ascertainable degree is a mere property of protoplasm, perhaps only of nerve matter. Now it so happens that biological organisms, and especially a nervous system are favorably conditioned for exhibiting the phenomena of mind also; and therefore it is not surprising that mind and feeling should be confounded. But I do not believe that psychology can be set to rights until the importance of Hartmann's argument is acknowledged, and it is seen that feeling is nothing but the inward aspect of things, while mind on the contrary is essentially an external phenomenon. The error is very much like that which was so long prevalent that an electrical current moved through the metallic wire; while it is now known that that is just the only place from which it is cut off, being wholly external to the wire. Again, the psychologists undertake to locate various mental powers in the brain; and above all consider it as quite certain that the faculty of language resides in a certain lobe; but I believe it comes decidedly nearer the truth (though not really true) that language resides in the tongue. In my opinion it is much more true that the thoughts of a living writer are in any printed copy of his book than that they are in his brain.

365. What the psychologists study is mind, not consciousness exclusively. Their mistake upon this point has had a singularly disastrous result, because consciousness is a very simple thing. Only take care not to make the blunder of supposing that Self-consciousness is meant, and it will be seen that consciousness is nothing but Feeling, in general, — not feeling in the German sense, but more generally, the immediate element of experience generalized to its utmost. Mind, on the contrary, when you once grasp the truth that it is not consciousness nor proportionate in any way to consciousness, is a very difficult thing to analyze. I am not speaking of Soul, the metaphysical substratum of Mind (if it has any), but of Mind phenomenally understood. To get such a conception of Mind, or mental phenomena, as the science of Dynamics affords of Matter, or material events, is a business which can only be accomplished by resolute scientific investigation. But the psychologists have been prevented from making that investigation by their delusion that Mind is just Consciousness, a simple affair, as far as the mere phenomenon goes, about which there is no room for error or doubt.

366. The psychologists say that consciousness is the essential attribute of mind; and that purpose is only a special modification. I hold that purpose, or rather, final causation, of which purpose is the conscious modification, is the essential subject of psychologists' own studies; and that consciousness is a special, and not a universal, accompaniment of mind. Von Hartmann, as long ago as 1869, proved conclusively that unconscious mind exists. †6 True, we may suppose that, in the cases instanced by him, there is a rudiment of consciousness; but such an objection would not meet his argument, which goes to show that the mental phenomena may be strong where the consciousness, if there be any, is almost nil, and where there is reason to believe that more consciousness would be rather unfavorable than otherwise to the action of mind. A psychologist cuts out a lobe of my brain (nihil animale me alienum puto) and then, when I find I cannot express myself, he says, "You see your faculty of language was localized in that lobe." No doubt it was; and so, if he had filched my inkstand, I should not have been able to continue my discussion until I had got another. Yea, the very thoughts would not come to me. So my faculty of discussion is equally localized in my inkstand. It is localization in a sense in which a thing may be in two places at once. On the theory that the distinction between psychical and physical phenomena is the distinction between final and efficient causation, it is plain enough that the inkstand and the brain-lobe have the same general relation to the functions of the mind. I suppose that if I were to ask a modern psychologist whether he holds that the mind "resides" in the brain, he would pronounce that to be a crude expression; and yet he holds that the protoplasmal content of a brain-cell feels, I suppose: there is every evidence that it does so. This feeling, however, is consciousness. Consciousness, per se, is nothing else: and consciousness, he maintains, is Mind. So that he really does hold that Mind resides in, or is a property of, the brain-matter. The early students of electricity, who assumed that an electrical current resides in the metallic circuit, had infinitely more reason for their mistaken opinion. Yes, without exaggeration, infinitely more; for the ratio of something to nothing is infinite.

367. No doubt, it seems an extraordinary piece of presumption for a man to tell a large body of scientific men for whom he professes high respect that they do not know what are the problems which they are endeavoring to solve; that while they think they are trying to make clear the phenomena of consciousness, it is really something quite different that they are trying to do. †7 I admit that the notion that phenomena of consciousness are the objects of psychology has caused a disproportionate development of certain departments, and has caused other departments to be much neglected. Nevertheless, I hold my ground. For if psychology were restricted to phenomena of consciousness, the establishment of mental associations, the taking of habits, which is the very market-place of psychology, would be outside its boulevards. To say of such departments of psychology, — from every point of view, the most essential parts of it, — that they are studies of phenomena of consciousness, is as if an ichthyologist were to define his science as a study of water.

§3. Mind and Body

368. There can be no better touch-stone of a psychology than the question of the relation between soul and body. Here the current psychology, instead of producing a scientific theory, finds itself driven into metaphysics. If you want to know how the doctrine of psychophysical parallelism will appear when it comes to be viewed [from] a distance of a couple of centuries, there is a closely similar theory from which the lesson may be learned, — the theory of Pre-established Harmony. What does good sense say to this today? The doctrine of Parallelism, which is that that which when viewed from the outside appears as material, when viewed from the inside appears as mental, encounters apparently insuperable difficulties when it is examined in its application to details. It has been adopted as the only means of reconciling the contradiction that the law of dynamics is never violated and that the law of mind is never violated. Neither of the members of this contradiction are rigidly proved to be true. Here, then, are two pretty serious defects in this theory of parallelism. Still, it is conceivable that satisfactory answers should be found to both objections. There is, however, a third objection which seems to knock the ground from under it, once for all; and this is that the two propositions which are supposed to be in contradiction with one another, unless metaphysics is brought in to reconcile them in a superphenomenal manner, can, in fact, be seen to be not in the least in conflict with one another, if we scrutinize them with a logical microscope. The facts which are supposed to conflict with one another are these. First, ideas produce material effects. A whisper in the ear may cause motions on the earth's surface sufficient to attract the attention of the inhabitants of the planet Venus. And reciprocally motions of matter affect ideas. That is one side of the truth; and no sane man can question it. But, secondly, according to the law of dynamics, no change of motion can take place except through accelerations which are dependent exclusively upon the mutual positions of particles or parts of matter; and according to the law of mind, no idea can arise except by virtue of an association. These propositions cannot properly be said to be proved; but they are postulated; and for the sake of argument we may admit that they are strictly true. Indeed, we should not be justified in believing that they are so very false as it would be necessary to suppose them to be, if this were the only way of preventing their clashing with the obvious fact of the reaction between mind and matter. But in point of fact, there is no contradiction in the propositions stated.

369. Let us imagine a case where matter, the external world, acts upon mind and where mind responsively acts upon matter. Let it be an extremely simple case, yet not so rudimentary as not to display the principal features of such cases. Suppose that while I am sitting writing in my study, which has an outside door, my dog comes and touches me with his nose; which I know is his sign that he wishes to go out. I do not mind the slight interruption of getting up and opening the door for him; but there is a newly made garden-patch out there, where I do not wish him to go; and I object to standing at the door to watch him. However, I know that the first thing he will do, if he is allowed to go out, will be to run to another door to see if my wife is there, so that he can greet her; and I remember that on this day of the week, at this hour, it being a fine day, she will be seated on a certain balcony where she will hear the dog; and I further know that, under those circumstances, she will look out and call him away from the garden-patch, if he starts to go there. Consequently, I get up, and go to the door, let the dog out, shut the door, and return to my table and to my writing. Now I ask the reader whether he will believe that those motions of my body were purely automatic, my mental reflexions being mere surplusage, provided I can show him that there is no necessary violation of the laws of dynamics in supposing that the mental operations were an essential factor of the phenomenon? Do not ask me in return whether I hold it to be inconceivable that an automaton should be made that would act like that; because that is not the question, for two reasons. The first is, that if such an automaton were to be constructed, a vast expenditure of thought would be necessary to design it. While here, the question being whether or not mind is an essential factor in the motions of matter, the theory of parallelism requires us to suppose, not that such an automaton gets constructed, but that it comes into being without any design at all, or automatically and independently of any design. The second reason why the supposed question would not be relevant is that the true question is not what is conceivable but what is credible. Here am I counting upon what the dog will do, and upon what my wife will do. That is, future events determine my present action. True, it is possible that something may interfere to falsify my expectation; but still experience assures us that such expectations are reasonably sure. Such being the fact, those modes of inference upon which we always rely in science lead us, lead the man whose good sense is not sophisticated by a metaphysical theory, to believe that it was my reflections which caused me first to hesitate and then to go and open the door. Nobody would doubt that that was the true account of the matter, were it not that it is contrary to the law of dynamics that mind should act on matter and contrary to the law of purpose that matter should act on mind. Grant that it is so: but the man who regards that as an objection to the common sense theory is simply allowing himself to be taken in by the Achilles sophism.

370. Which do you prefer; one of those ghost-like hypotheses about things-in-themselves which anybody can set up but nobody can refute; or a flesh-and-blood hypothesis that nothing prevents you from wrestling with and flinging it to the ground by any one of a hundred experimental tricks, except that, when you come to try them, they one and all unexpectedly turn out just the other way? I will bring you a hypothesis that is ready to try a bout with you, if you like. This hypothesis may prove false in all its details; I rather guess it will. But in one respect, it certainly is not false; namely, insofar as it shows that matter's acting immediately solely on matter and mind's acting immediately solely on mind in no wise conflicts with matter's truly and literally acting on mind and mind's acting on matter. I will suppose, then, — and this is only one of innumerable hypotheses of the same general type, and leading to the same conclusion, — that when the dog touches his nose to my person, he sets up sound waves in the matter of my body, which, of course, will be propagated with the velocity of sound. I will suppose, however, that, owing to the viscosity of the matter in which these waves reside, a part of the motion is quickly converted into heat, which is a motion of the molecules, atoms, and corpuscles of this matter. But these atoms are really vortices in an ether, and along with the heat there will be vibrations of this ether, which will constitute light and be propagated with the velocity of light. I will further suppose that this ether is not devoid of viscosity, so that part of this vibratory and vortical motion will be converted into what we may call a heating of the ether, a motion of its atoms. But these atoms, I will suppose, are really vortices in an ether's ether; and along with this heat of the ether, vibrations of this ether's ether will be excited, and be propagated at a velocity as much greater than that of light as the velocity of light is greater than that of sound. I will further suppose that this ether's ether is not devoid of viscosity; so that a part of those vibrations will be converted just as before. I will suppose that there is an endless series of these ethers below ethers, and that in consequence of the increase of velocity as the motion passes from each to the next, the entire infinite series of transformations of motion will be accomplished in a fraction of a second of time. All this motion will be purely dynamical; the mind will have nothing to do with it.

371. The third of our diagrams of spirals will be useful here, in helping the reader to grasp my meaning. †8 Let the radius vector measure the time, beginning at the outermost point, as the instant when the dog's nose touches me and proceeding inwards. Let each coil of the spiral represent the transformation of the motion from one ether to the next. At the end of the period of time represented by one inch of the radius, all that infinite series of transformations will be complete. Now let us suppose that the inner series of coils of the spiral, which, instead of being endless, is beginningless in terms of the coils, though not in time, represents operations governed exclusively by final causation, and therefore purely mental. Let us suppose that, although mental, they are not noticeably conscious until the innermost end of the coil is approached. Here begin those reflections of which I am able to give any account, although from ever so early in the second series of coils the mind was acting rationally, in the sense in which unconscious, and therefore uncritical, action can be called rational. Finally, at the innermost end of the spiral will occur my volition to let the dog out. Another similar diagram would be required to show what happens next. If the dog is to be let out, the door must be opened; if the door is to be opened, I must open it. But if I am to open it, I must go to it; if I am to go to it, I must walk; if I am to walk, I must stand; if I am to stand, I must rise; if I am to rise, I had better put down my pen; and there consciousness becomes dim. But there must be an infinite series of such ratiocinations if the mind only acts rationally. Take any instant after the work of the mind has been done, and at that instant, an infinite series of dynamical transformations will have taken place which are to terminate in the door being opened.

372. I repeat that I will not here argue the question. All I have said is not intended as argument. But neither is it vain talk. It is the necessary preparation for an inquiry. How the inquiry itself is to be conducted shall be shown in another chapter. †9 All I wish now to convince the reader of is that, notwithstanding the admirable, conscientious, and most useful studies for which we have to be grateful to Wilhelm Wundt and his hundreds of disciples, — for all modern psychologists are his loyal disciples, — the science is still too unsettled even to understand its own motives; so that a classification which should not look at all beyond the present state of the study could hardly be expected to be really helpful. In this place, therefore, by exception, I shall allow myself to anticipate, as far as such a thing is possible, a state of the science in the near future.

§4. Nomological Psychognosy

373. I shall, then, recognize that Nomological Psychognosy must separate into two Suborders; the first of General Psychonomy, the second of Special Psychonomy, or Nomological Psychology. The former will study the law of final causation and seek to formulate it with exactitude, while the latter will study subordinate laws of mind, of which that of Association is the first.

374. General Psychonomy will have four Families. †10 Family 1 will define the essence of Mind and the law of final Causation, together with its application to non-biological phenomena. We may term it phenomenalistic Pneumatology. Family 2 will show how final causation works in the development of biological stocks. Family 3 will study the law in its application to biological individuals and to consciousness. Family 4 may be called Demonomy, although it should study the application of the law, not merely to Societies, but also to mere Associations, such as that of a profession. This Family has a truly remarkable analogy to that Family of Dynamics which treats of stationary motion. One Subfamily (or possibly only a Genus) of it will work out the general laws of concert and strife. A second will apply these principles to special phenomena. One Genus will apply them to Law and the Constitution of Society, in Subgenera; another to Wealth.

375. Nomological Psychology will treat of laws of mind subordinate to the general principles of final causation. I recognize in it but two Families, of which the one is devoted to the study of the great law of Association (including, of course, Fusion) or that of the mutual attraction of all ideas, the analogue of Gravitation in the Physical world, while the other analyzes the laws of the connection of body and mind. The former Family seems to involve three Subfamilies of which one treats of Association per se, a second association as modified by dissociation, etc., and a third, the laws of the growth of mind in individual and in society or stock. The second of these Subfamilies will have Genera relating, the first to Habit, the second to Imagination and Vividness, the third to Generalization and Reason, the fourth to Recognition and Belief. The Subfamily of the laws of Growth of Mind must have four Genera relating, the first to General Laws; the second to growth, the morphogeny, etc.; the third to growth in the conscious mind, with three Subgenera relating to natural immaturity (with Infant Psychology and Child Psychology as species), to growth under education, and to growth by experience; and the fourth Genus to the laws of growth of the Social Consciousness. Family 2 will have two Subfamilies treating respectively of elementary laws and of the laws of peculiar states of mind. The first Subfamily will have three Genera. Genus 1 will study the general law of the reaction between Body and Mind. Genus 2, Psychophysics, will treat of Sensation and whatever may be analogous to it. Genus 3 will treat of Volition, with three species relating to Impulse, Control, and Controlled Volition, each of these having one Subspecies for direct, or outward volition, another for attention. Perhaps the first of these species must have a third Subspecies for Emotion. The Subfamily relating to laws of special states of mind would have three Genera. Genus 1 will treat of the laws of dissolution and double consciousness, with five Subgenera studying the general law per se, studying fatigue, studying sleepiness and sleep, normal and abnormal, studying dreams and hallucinations, normal and abnormal, and studying double consciousness, normal and abnormal. For it is commonly recognized that there is a multiple personality that is perfectly normal. Genus 2 will treat of the laws of "credenciveness," including what is carelessly called "suggestion," a term which was already preoccupied for one of the general phenomena of association. Genus 3 will treat of the laws of the Passions.

§5. Psychology

376. All this is but a preliminary sketch of what I should imagine might be the division of a psychology of the future, subject to modifications to adapt it to existing psychology. The usual division now is into Introspective, Experimental, and Physiological Psychology. These divisions exist; but they are unimportant, and can only be regarded as constituting species under several of the genera. Let us consider them a moment, beginning with Physiological Psychology. This term may be taken in a strict sense; but it is almost invariably understood in a loose sense. In a strict sense, Physiological Psychology means making experiments on the brain, and from the results of these experiments drawing inferences concerning the Mind. The one fair inference to be drawn from those experiments is that the connection between the mind and the brain is an accidental one. When a lobe of the brain is extirpated, we find that the connection between certain organs of the body is deranged or broken. Of course, for the time being, that prevents mental action, just as if you abstracted my inkstand you would find me transformed for a time from a student working sixteen hours a day into an ardent devotee of amusement. The injury may be such that there is no recovery. But usually recovery does take place. Other parts of the brain are made to do the work, after a fashion, with perhaps other parts of the body. The remarkable thing is, that those very actions, now performed with other organs, show the same mental idiosyncrasies, down to minute details that they did before. The man who has had to learn to write with his other hand directed by another part of the brain, may write pretty badly, but his very handwriting will show the same inimitable characteristics it had before. A few such general truths as that may be established by Physiological Psychology proper. They may be summed up in the proposition: The brain has no radically peculiar relation to mind. But this is only a negative proposition, and, as such, of no positive importance. But what is ordinarily meant by physiological psychology is not these supremely difficult and uncertain experiments, but work done very commodiously with a diagrammatic figure of the brain and its connections. What psychology thus derives from anatomy rather than from physiology is suggestions of theories. When it is conscious mind that is to be studied, no doubt those suggestions are often of great value. In other departments of psychology, they are largely fallacious. But in any case, it is not a method of investigation, but only a help in forming those hypotheses from which investigation takes its start. It cannot, then, constitute one of the higher groups of psychology. As for Experimental Psychology, it is commonly said that this can only be practised in conjunction with introspection. I cannot admit the truth of this. In many experiments there is nothing that any form of statement can torture into introspection. †11 In others, there is no introspection unless nice observation, — such as saying for example which of two colors is the brighter, — is introspection. But this is in reality nothing but the attentive observation of an outward object. It is nonsense to call attention to an outward object by the name of introspection. Introspection is direct observation of the operations of the mind as mental operations; because, as for feelings, they are always referred to some object, and there is no observation of feelings except as characters of objects. I will say a word more about this presently. The type of true psychological experiment consists of putting a man in peculiar and carefully defined conditions, requesting him to do something, typically, of a natural and ordinary kind, and then carefully measuring a certain feature of his action. That will be a scientific observation which may serve to explode a psychological hypothesis. It is the only scientific basis of psychology. There is no introspection in it. Introspective Psychology is the old false psychology which ought not to be countenanced. It is true that a good deal is known about the mind from ordinary observation. There is a considerable store of wisdom concerning man before scientific psychology begins its work. But so far as this is anything more than instinctive knowledge, it really rests on experiments. Only, they are such experiments as any man can perform, by simply resolving to watch all cases in his experience where certain conditions are fulfilled, and noting how far certain results accompany them. As for the mind's watching its own operations, no such thing is possible. It is pure delusion. Take, for example, a train of ideas. A man may recall some of the ideas of the train. But what are they? They are objects, imaginary objects, — products of the mind's operation, but not the movement of mind itself. Whether even these objects can afterward be described or known as they actually presented themselves during the process, — whether they are not really subsequent creations, — is usually very doubtful. It is certain that unless the train of thought was arrested at any one of them long enough to make such an object as can be described, in which case it is not at all the operation of the mind but only an elaborate product that is known, then we cannot afterward know them as they were in the fleeting thought. And even our falsified knowledge of them is not knowledge of thought's movement, but only of a product which it stops in order to throw off. Moreover, even of these, it is experimentally certain that only a small part can be recovered. Thus, the real operation of thought is something purely inferential, at best; and I shall give reason for thinking that it is commonly mistaken. But the Introspective Psychologists, while they acknowledge that there is some force in these objections, though not so much as I think, insist that we have an introspective knowledge of the characters of feelings. They say, for example, that we can perceive that red and green are simple sensations, that yellow is a third simple sensation, not a mixture of the sensations of red and green, but that orange is not a simple sensation, but is a mixture of red and yellow. In weighing the truth of this assertion, the first thing to be clearly understood is that red, orange, yellow, and green, are not pure feelings, but are generalizations of feelings. Red and green lights falling together upon the fovea do produce the sensation of yellow. It is commonly supposed that this is only very roughly true. But this is because proper precautions are not taken in performing the experiment. If it is accurately done, although there is a slight whitishness in the yellow produced, it is only slight. It is very likely, however, that this varies with different eyes, because it probably depends upon the number of rods in that part of the retina. If there were no rods, it might likely be exactly true. For some reason we put the yellow into a different class from red or green. The introspectionists, however, admit that yellow is more like red and more like green than red and green are like one another. If that be so, then we class red and yellow together, and see in them some common element, and we also class yellow and green together, and see in them some common element. Therefore, in yellow we do see a mixture of an element of red and an element of green. They therefore fall into self-contradiction when they say that we perceive that yellow is a simple sensation. It is true that we do not see red in yellow, nor do we see green in it, but only an element of red-likeness and an element of green-likeness; and furthermore we see something peculiar in yellow which predominates over its red-likeness and its green-likeness. But then this is more or less the case whenever from any motive we are led to regard a certain class of phenomena as a class by itself. Any collection of objects in the world, no matter how artificial, has some character common and peculiar to its members. It must be so, or we could not have thought of them as forming a collection. Now in cases where it seems important to regard the objects as a class, this character in which they are utterly dissimilar from all other objects, assumes a mental predominance. But yellow is an important kind of sensation for the reason that any color when highly illuminated looks more yellow. Now since the illumination of surfaces is constantly changing, this yellowishness has to be allowed for specially in classing the color of the surface; and thus it is very natural that the peculiar character yellow should acquire a special importance. But this does not constitute any simplicity of it as a feeling which does not belong to any class of sensations in proportion as it acquires importance. It must be so, in accordance with the general laws of mental phenomena. Orange, on the contrary, is not particularly significant, and therefore its reddishness and its yellowishness seem to us sufficiently to describe it. But if we look at it accurately, we shall see that it is not red and not yellow, but only red-like and yellow-like, and with a peculiar character of its own. The truth is that the phrase simple sensation is devoid of all meaning, unless by simple be meant important. For if the phrase simple sensation means anything, it must mean that no other two sensations are like this in different respects; that is, all others can only differ from it in one way. For if sensations vary along a continuous line, tell me if you can, what it can mean to take a single point of that line and say it is more simple than any of the other points. If you mean that some circumstance gives it a special importance, that I can understand. But that circumstance is probably some fact of astronomy or geognosy, not essentially related to consciousness. If, then, the psychologists wish me to admit merely that yellow seems to be a peculiar color, I grant it is a fact about our minds that they are educated to regard it so. But in that same sense, the sensation of nakedness is a simple sensation; and the sensation of a letter of the alphabet is a simple sensation. These considerations ought to convince anybody who has carefully gone through the introspectional psychology of the present day that it never can again be an important department of the science. It is merely a preliminary study in several Genera.

377. In the rough sketch given above of my impression of what psychology ought to be, I have omitted, by negligence partly, several topics upon which books enough have been written to bend our shelves. The remarkable thing is how valuable they are on the average. It shows what virgin soil psychology is that with so little exertion of strength good fruit can be obtained in this field. Reviewing my preliminary scheme and comparing it with current ideas, the first thing that strikes me is the absence of the terms relating to association which the Germans and their lackeys have introduced; such as Fusion, Assimilation, Synthesis, Complication, Apperception. These are connected with valuable contributions to psychology, no doubt. But I think that the conceptions of the English Associationalists, which are now met with a smile, are of vastly greater importance; such as the distinction between the radically different processes, now generally overlooked, between association and associative suggestion, and the capital distinction between Association by Resemblance and Association by Contiguity, which goes down to the root of the matter as none of the distinctions based on speculations about the brain begin to do. †12 Another modern term that I miss is synesthesia, a trifling variety of imagination. But there is Memory, concerning which there is a whole library of books of exceptional average foolishness. No doubt, under the Genus of Imagination and Vividness, a Species must be devoted to Memory. Attention is a faculty which many excellent psychologists regard as of fundamental importance, not at all to be relegated to subspecies of Volition, as I have relegated it. Of course, I may be wrong; but I adhere to my opinion on this point. I have not said a word about Telepathy; and in general I have not admitted that abnormal phenomena differ deeply from normal phenomena. I cannot admit that there is any special nomology of the abnormal. It is the condition of a science of laws that it is restricted to what it can find to be regular. †13

§6. Classificatory Psychognosy †14

378. Of Classificatory Psychology, which for brevity I term Psychotaxy, two Suborders have already been designated, studying respectively Kinds of Performances and Kinds of Individuals. The word performance must here be taken in a broad sense to include actions that are simple and involuntary. I have been tempted to substitute the word "faculties" and have not done so because this word would certainly be positively misunderstood, while "performance" has no greater fault than unintelligibility at first sight. The Classification of Performances seems, on the whole, to consist of two Families, the one of Elements of Performance, the other of Systems of Performance. But this is one of those cases in which my conclusion is reached by that process of balancing one consideration with another which the history of science, and, as we shall find, the theory of logic, alike stamp as extremely apt to lead to error. †15 The first Family consists (such is my hesitating conclusion) of two Genera relating respectively to Kinds of Sensation and their relations, and to Kinds of Emotion and their relations. It [is] questionable, I admit, whether I ought thus cut the studies of Sensation and of Emotion into two parts belonging to different Orders. If I am wrong about this, I would, at any rate, retain the two Genera of the Classificatory Order. Whether, however, they are separate Genera, rather than Subgenera of one Genus, is another question which I may have answered wrongly. One naturally baulks, too, at admitting that this Family has no Genera studying any other mental faculties than those of Feeling; yet this is a point upon which I permit myself a certain degree of confidence. The second Family, that of Systems of Performance, has quite clearly two Subfamilies. Both the one and the other are, substantially, and in the gross, confined to animal and human performances, including organized associations. One Subfamily studies those systems of performance which are mainly confined to the brutes, to the lower animals generally, being in the instinctive stage of development; so that there is an inborn faculty by virtue of which the performance is determined in almost all its details. The Instincts are said to be all adaptive, although it would seem to be in very small measure that play is so. However, the instincts seem to be of two distinct kinds, those which are adapted to the preservation of the stock, if at all, †16 through preserving the individual in whom the instinct acts, and those which are social, and therefore, so far as they are adaptive, are adaptive primarily to the advantage of some other individual or individuals than the agent. Association may happen to be of advantage to the associating individuals; but each individual's instinct brings no more advantage to him than the sum of all the advantages that it brings to so many others. It is double-entry book-keeping; and the sides of the ledger must balance. But then, over and above this, association is generally connected with reproduction, and is therefore advantageous to the stock quite independently of its advantage to the individual. In many cases, the social instincts are expensive to the individual, even dangerous, sometimes fatal. It appears to me that this Subfamily has but one Genus and that this Genus has two Subgenera relating to the two kinds of instincts. There is a certain difficulty in the fact that instincts for war are on the one hand social, since war is a sort of social reaction, and is moreover often dangerous, sometimes certainly fatal, yet on the other hand, it seems improper to distinguish war from preying, and preying is generally an affair of bread-winning, adapted to the preservation of the agent. It seems to me, however, that in war the enemy is not looked upon as fellow-creatures, but is treated as a thing, and I believe that though the instinct brings danger, it is nevertheless a selfish one, and ought to be classed with those which go to preserve the agent. This is inconvenient, it is true, as regards duels motived by jealousy, which is the chief kind of fighting among herbivora. The leading instincts studied in the first Subgenus are those of Feeding and Food Getting. The study of these will make the first Species. The study of instincts of War will be the second, with two Subspecies, the study of instincts of active war making one, the study of self-preservation including the instincts of self-concealment being the other. Other species will study the minor instincts, such as those of personal Cleanliness, of Medicine (dogs eating grass, etc.), of hibernation, and the singular instinct for collecting and hoarding all sorts of useless things, as seen in rats, in mag-pies, and some other animals, a genuine collecting mania, apparently quite useless. Then I am inclined to think that we must admit a Species for the study of instincts of working materials, such as the tree-felling instinct of beavers, the instinct of the wood-pecker. With this I would reckon all instinctive mechanical skill.

379. The Subgenus of Social Instinct has as its nucleus, so to speak, the Reproductive Instincts proper, to which the first Species will be devoted. Next in importance will be the Instincts of Communication; for some kind of language there is among nearly all animals. Not only do animals of the same species convey their assertions, but different classes of animals do so, as when a snake hypnotizes a bird. Two particularly important varieties of this Species of study will relate to Cries and Songs (among mammals and birds chiefly) and to facial expression among mammals. †17 As belonging to this Species I would include all studies of Instincts for understanding mind. But the subdivision of this Species requires much further study. A third Species will relate to the Architectural Instincts which I place here, although they are sometimes a bachelor establishment or even only a machine, like a cobweb. Passing by as unimportant the Instincts for Clothing, a fourth species will study Instincts of Locomotion and Migration. A fifth Species will relate to Instincts for Games; a sixth, to [the] Instinct for Adornment and Decoration, an Instinct which though associated with the Reproductive Instinct is quite distinct from it. The horse is delighted with a handsome harness. The poodle just trimmed goes to display himself to all his human friends without any teaching.

380. Passing to the second Subfamily of the Psychotaxy of Systems of Performance which relates to such systems in minds that are too highly developed for much wealth of Instinct, let me say, at once, that I doubt very much whether the Instinctive mind could ever develop into a Rational mind. I should expect the reverse process sooner. The Rational mind is the Progressive mind, and as such, by its very capacity for growth, seems more infantile than the Instinctive mind. Still, it would seem that Progressive minds must have, in some mysterious way, probably by arrested development, grown from Instinctive minds; and they are certainly enormously higher. The Deity of the Théodicée of Leibniz is as high an Instinctive mind as can well be imagined; but it impresses a scientific reader as distinctly inferior to the human mind. It reminds one of the view of the Greeks that Infinitude is a defect; for although Leibniz imagines that he is making the Divine Mind infinite, by making its knowledge Perfect and Complete, he fails to see that in thus refusing it the powers of thought and the possibility of improvement he is in fact taking away something far higher than knowledge. It is the human mind that is infinite. One of the most remarkable distinctions between the Instinctive mind of animals and the Rational mind of man is that animals rarely make mistakes, while the human mind almost invariably blunders at first, and repeatedly, where it is really exercised in the manner that is distinctive of it. If you look upon this as a defect, you ought to find an Instinctive mind higher than a Rational one, and probably, if you cross-examine yourself, you will find you do. The greatness of the human mind lies in its ability to discover truth notwithstanding its not having Instincts strong enough to exempt it from error. †18 This comes out strongly in almost any concrete instance. Frederic the Great is a notable example. Kant's power of making use of confused conceptions and working out so much truth as he did in spite of them illustrates this virtue. Hardly any really great inventor thoroughly comprehends his own invention until long after it is achieved.

381. The conception of the Rational Mind as an Unmatured Instinctive Mind which takes another development precisely because of its childlike character is confirmed, not only by the prolonged childhood of men, but also by the fact that all systems of rational performances have had instinct for their first germ. Not only has instinct been the first germ, but every step in the development of those systems of performance comes from instinct. †19 It is precisely because this Instinct is a weak, uncertain Instinct that it becomes infinitely plastic, and never reaches an ultimate state beyond which it cannot progress. Uncertain tendencies, unstable states of equilibrium are conditions sine qua non for the manifestation of Mind.

382. It does not appear that all the animal instincts have produced great systems of human performance. †20 In a general way we can see that, in much the same sense in which it would be true that, according to the theory of Natural Selection, every step of the development from the moner to man has been due to fortuitous variations in reproduction, we can equally say that every step of the progress of physiognosy has been due to a guess prompted by one of those instincts studied in the First Subgenus of the science of Instinct, or as we may call them, the mechanical instincts, and that every step in the progress of psychical science has been due to a guess prompted by one of the social instincts. But science is, after all, but a small part of the rational developments that have had instinct for what we may call their efficient cause; that is, their cause so long as we consider them only as aggregates of their smallest parts, neglecting all that we do neglect when we say that Natural Selection makes man the result of fortuitous variations at birth; in one word, neglecting the rational, the integral, element altogether.

383. But the importance of the different Intellectual Systems of Performance which have developed from the different instincts have had not the slightest relation to the strength or to the adaptiveness of those instincts. In a general way, the useful arts have mostly developed from the Selfish Instincts. But of all these instincts perhaps those of Food getting and Feeding are the strongest. What has developed from these? Agriculture is by far the most respectable of their offspring. The Instincts of War have given rise to the Arts of War. Mechanical Instincts connected with the human hand, and therefore peculiar to man, have probably affected tool-making. But it is a general mechanical instinct, common to almost all animals, which has produced physics and the physical arts generally. Self-preservation has been a motive, or final cause, of the Art of Medicine; but it does not seem to have contributed anything to Medicine as an efficient effect of this instinct.

384. The Social Instincts were more sympathetic to Reason; and it is they that have been the efficient cause of most human performances, and of the higher ones. For although it happens that perspective at this time makes Physiognosy seem very great, it is not in the nature of things that it should be so. True, [it] is pure; it is unblotted by all the ignoble passions which disfigure other elements of civilization. That is its most admirable feature; and it is not a merely negative one. But at the end of the twenty-first century that will no longer be the achievement upon which man can most plume himself. Of the Social Instincts, by far the most violent are of course the Reproductive Instincts; and in man they strongly color all but one of the Social Instincts, to such a degree as almost to weld them all together. The earliest Art of man, after that of trapping animals, was doubtless the Art of making a home. A cluster of arts there are there; as architecture, heating, lighting, etc. Families became communities; and there gradually arose a notion of what customs and behaviour were tolerable. It must have been early in this state of things when men were leading an easy and joyous life, — perhaps in the flush of some great victory which brought them slaves, — or perhaps having recently domesticated cows, — that language began to take a grammatical form, so that sentences could be constructed, and to acquire a relatively copious vocabulary. I have never seen a satisfactory account of how it came about; but the time is ripe for such an account. Next month's Popular Science Monthly may tell us that some Italian has accomplished the feat. Language gave man distinct conceptions, and awakened in him the idea of understanding things. The first fruit of the scientific spirit must have been a Theology, and some confused Cosmogony; †21 for it is man's way to attack the most difficult questions first, and attempt detailed answers to them. What the first religion was like one would give something to know. To tell us would be a suitable task for a Shakespeare and a Browning, in collaboration with a Darwin, a Spencer, and a Hegel. Records we have none of any faith that has not undergone corruption and reform; senility and rejuvenation by fards, hair-dyes, and false teeth; revolution and restoration; death and galvanization, over and over again.

385. Let us see how far we can utilize such reflexions in classifying the Classificatory Sciences of Intellectual Systems of Performance. In the light of what has been said, there seem to be about seven Genera. The first embraces studies of the kinds of purely Material Arts; the second, studies of Ways of Individual Life; the third, studies of Customs and Laws and of Constitutions of Society; the fourth, of Religions; the fifth, of Classifications of Sciences, the very subject upon which we are now engaged, so that we are in the somewhat embarrassing position of having to criticize the very thing we are doing before it can get done; the sixth, of Fine Arts; the seventh, of Language . . . . †22

386. The second Suborder of Classificatory Psychognosy deals with kinds of minds. This, very evidently, if we exclude the minds of plants, and of communities, divides into two Families treating respectively of Animal Instinct and of Types of Men. A fair beginning has been made of the study of animal minds. We really seem to be penetrating the psychical nature of the Hymenoptera, — souls so utterly unlike our own. It is most desirable that we should add to this an understanding of some third kind of mind different from both the others, — say, for example, that of the octopus, whose passions are betrayed by the waves of color that pass over his person. For one can hardly make a beginning of generalization until three instances are at hand. The worms, echinoderms, coelenterates and sponges do not seem to be very interesting psychically. But the squids have a sort of horrible fascination . . . .

387. Of types of men, serious investigations have been made of genius, of criminals, of men of science, and of great men, generally. †23 Theophrastus began the study of types of character; and different authors have, in various ages and countries, displayed the most splendid power for this sort of research. But unfortunately, they have all been seduced by the glamour of literary glory, — even St. Simon, (the ancestor, I mean), whose memoirs were not published until three quarters of a century after his death; so that a field of science of whose cultivation there is the most urgent need, both theoretically and practically has been for millennia lying fallow ground awaiting a conscientious ploughman. †24

Chapter 2: Association †1

§1. General Characteristics of Mental Action

388. In the absence of external impressions of interest, thoughts begin to dance through the mind, each leading in another by the hand, like a train of Bacchants on a Grecian vase, as Hegel says. After a while the clear train of thought breaks, and for a time ideas are scattered, soon, however, to take places again in another train.

There is a law in this succession of ideas. We may roughly say it is the law of habit. It is the great "Law of the Association of Ideas," — the one law of all psychical action.

389. Many psychologists hold that this law as strictly necessitates what idea shall rise on a given occasion as the law of mechanics necessitates how a body in a given relative position to other bodies endowed with given forces shall have its motion altered. This is a theory hard to disprove; but it is a mere forejudgment, or prejudice: no observed facts afford the slightest warrant for it. I do not mean to condemn the trial of it, in psychology, as a working hypothesis: on the contrary, logic fully approves of it in that sense. But many things are worth trial, which do not seem at any time probably true. What is, far more than unyielding uniformity, characteristic of the phenomenon of suggestion, as the calling up of an idea through association is called, †2 is its gentleness. There is another natural operation that, from every point of view, seems much nearer allied to the psychological sequence than is mechanical causation; I mean heredity. Now heredity, powerful as it is, leaves room for sporting, or variations. Remark that the development of species, whether by Natural Selection or by Artificial Breeding, would be impossible were variations not to occur in the teeth of heredity; and in like manner without the element of spontaneous originality, or something acting like it, the development of thought would be instantly arrested. †3 Hume, whose cogitations led up to the recognition of Association as the one law of mind, most judiciously remarks, "This uniting principle among ideas is not to be considered as an inseparable connexion; for that has been already excluded from the imagination: Nor yet are we to conclude, that without it the mind cannot join two ideas; for nothing is more free than that faculty: but we are only to regard it as a gentle force, which commonly prevails." †4 That phrase "a gentle force which commonly prevails" describes the phenomenon to perfection.

390. But it is hopeless to expect men to agree about the question of spontaneity. The observed facts all tend to support it; but some men will deny it, because they are disinclined to that view; thus exercising that very freedom that they refuse to recognize.

§2. Contiguity and Resemblance

391. Psychologists differ in regard to what they call the primary principles of association; but the usual doctrine is that suggestion takes place either by Contiguity or by Resemblance. These are Hume's terms, which psychologists have agreed to retain as convenient names, although as descriptions they are acknowledged to be faulty enough. Suggestion by contiguity means that when an idea is familiar to us as part of a system of ideas, that idea may call the system to our minds, and from the system, one of the other ideas may, for some reason, detach itself and come to be thought of by itself. Thus, mention "the judicial branch of government," and you suggest the idea of a government composed of an executive, a legislature, and a judiciary; and shortly after, the person to whom you are speaking, if you are boring him, will have his ideas running, it may be, upon executive power, it may be upon the conduct of a legislative assembly. So, mention a wife, and your hearer will think of husband and wife, and thereupon, most likely, of a married man. Mention a knife-blade and the whole knife will be thought of, and thence a knife-handle. Thus, suggestion by contiguity may be defined as the suggestion by an idea of another, which has been associated with it, not by the nature of thought, but by experience, or the course of life. †5

392. Suggestion by resemblance is easily enough understood, as soon as the conception is once grasped that the similarity of two ideas consists in the fact that the mind naturally joins them in thought in a certain way. For instance, yesterday I saw a blue color; and here is a blue color. I recall that sensation of yesterday, and I observe that of today. I find myself disposed to say the two are closely allied; in that disposition their similarity consists. For they are two different ideas. One was in my mind yesterday, and consequently that identical idea is not present now. However, I accept the impression it has left on my memory as probably about right. I look again at the color before me. The idea of yesterday and that of today are two ideas; they have nothing in common, unless it be that the mind naturally throws them together. Some beginner may object that they have both a blueness in them; but I reply that blueness is nothing but the idea of these sensations and of others I have had, thrown together and indistinctly thought at once. Blueness is the idea of the class. It is absurd to say that different things which cannot be compared are alike, except in the sense that they act alike. Now, two ideas are compared only in the idea of the class, lot, or set to which they belong; and they act alike only in so far as they have one and the same relation to that connecting idea. Resemblance, then, is a mode of association by the inward nature of ideas and of mind. †6 There are other modes of such association. Thus, contrary ideas are thrown into pairs by [the] inward nature of ideas and of mind. Numbers run into a succession, or sequence, by the same force. inline image What does this figure show? The answer will be a broken star. That answer shows how the mind naturally looks at those lines from the point of view of a set, or regular figure, to which they do not even conform. As experience clusters certain ideas into sets, so does the mind too, by its occult nature, †7 cluster certain ideas into sets. These sets have various forms of connection. †8 The simplest are sets of things all on one footing and agreeing in each belonging to the set. Such a set is a class. The clustering of ideas into classes is the simplest form which the association of ideas by the occult nature of ideas, or of the mind, can take. Now, just as in association by contiguity an idea calls up the idea of the set in which experience has placed it, and thence one of the other ideas of that set, so in association by resemblance an idea calls up the idea of the set in which the mind's occult virtue places it, and that conception perhaps gives, owing to some other circumstance, another of the particular ideas of the same set. Everybody has heard in conversation a person remark, "What you say puts me in mind of a similar occurrence." That is suggestion by resemblance. Association by contrast is a case of association by resemblance, which is so called after its most prominent variety. Suggestion by resemblance means, let it be repeated, the indirect suggestion by one idea of another which has, by virtue of the occult nature of ideas or of the mind, been associated with it into one set. All the suggestions of pure mathematics, of which there is a vast body, are associations by resemblance. Some psychologists refuse to acknowledge association by resemblance. The reason is that they conceive that two different principles of association break the law of association into two; now the idea that there must be one law for a given group of phenomena is an idea so natural to the mind, that for the sake of it, those psychologists allow themselves to wrench all the facts, thus illustrating by their own action the strength of the kind of association which they refuse to acknowledge . . . . †9

§3. Defence of Author's Opinions Stated in Art. 2 [Sec. 2]

393. The reader, having thus been railroaded through the history of the doctrine of association, will perceive that the present writer differs from an important minority of the authorities in holding to two principles of association, and that he differs from all the English psychologists while agreeing with the Herbartians, in splitting the suggestion of B by A into two operations, one leading from A to AB and the other from AB to B.

394. As a sufficient defence of association by resemblance, as a fundamental mode of association, he offers the remark that resemblance consists in an association due to the occult substratum of thought.

395. The defence of the division of suggestion into two steps cannot be quite so summary. In the first place, there are many cases in association in which parts of the train of thought do not appear in memory. Different psychologists have different ways of treating this difficulty. Some maintain that they are performed with lightning rapidity and also with a low degree of consciousness. This is very improbable. Others, as Leibniz, Hamilton, Hartmann, †10 Samuel Butler, †11 and others maintain that they are totally unconscious, or practically so. The present writer will not countenance the rejection of a theory because of metaphysical difficulties. The great object of the metaphysics of Duns Scotus is so to state the results of ordinary experience, that it shall not close any positive experimental inquiry, or pronounce anything possibly observable to be a priori impossible. In Scotus, this naturally led to loyalty to Authority, then the recognized fountain of truth; in our day it will produce unfaltering faith in Observation. Still others are of opinion that parts of a train of association may be altogether suppressed. We cannot deny the possibility of such a thing.

396. The present writer has made a good many quantitative experiments to ascertain what he could of the nature of consciousness and of attention. It would not be convenient to set these forth in this place. †12 But the conclusions to which they lead will be mentioned. An excitement of the nerves will spread, and affect more and more nerve matter. The total excitement may considerably increase, in this. No equation is preserved. It may also wear itself out. Considerable excitements expend themselves out of the spinal nerves, either in contractions of voluntary muscles, attended mostly with a sober activity of mind, or in glandular secretions, actions on involuntary muscles, probably through the sympathetic nerves, and these cases are apt to be accompanied by emotional excitement of the soul. Ideas tending to either of these modes of suggestion present the phenomenon of interest. The intensity of ideas is of two kinds, an objective and a subjective intensity. A high color, a loud sound, a burn have, per se, high objective intensity. I have not been to Niagara for three or four years. But I well recall the tremendous roar; objectively the intensity of the idea is great, as great as it was when it was present (possibly more so), but subjectively my memory of it is getting now a little dim. I remember some time about 37 years ago sitting in the dark room of my class-mate, Albert Stickney, he having just carried away the lamp, I believe. I suddenly saw everything lit up and quickly looking out the window I caught sight of a great meteor. Objectively, my memory of it is of an intense light; subjectively, it is very dim. †13 Ideas of great objective intensity have their subjective intensity, other things being equal, greatly reinforced; but the distinction is unmistakable. The word interest probably means suggestiveness of action or emotion; but it is accompanied with considerable subjective intensity of direct consciousness. The phenomenon of the heightening of the subjective intensity of an idea as it draws into the vortex of an interesting suggestion, is called attention. Ribot and others wish to make attention a fundamental element of consciousness. I grant the fundamental element that they are groping for really exists, and that to some extent it affects attention; but attention itself does not consist in that, nor does that element show out with remarkable clearness in attention. When we try to say what is immediately in consciousness, we have a difficult task. We have to tear down a whole structure which the mind has built round it; and throw that away, while leaving the original elements. Nothing requires greater energy, and energetic determination to be passive; nothing is more fatiguing; and no mental process is so slow. Suppose, you are asked of two colors which is the more agreeable. If you have no training in introspective observation, you may answer quickly; so you may, if there is a marked difference in agreeability. But otherwise, it may take a minute or more of fatiguing strain to reply. Of two pressures brought upon the skin, which seems the stronger, is a direct question of introspective observation. But it is difficult. Sensations differing so slightly, that an exhausting effort of attention, under the most favorable surroundings, leaves us a feeling of utter inability to make out any difference, can, nevertheless, be proved to affect the mind. For instance, it is found that in such cases, if the observer forces himself to say which is the stronger sensation, though his answer seems to him to be given at random, yet taking a dozen sets of a hundred answers, in each set there will be a decided preponderance of true answers. †14 Pass now to sensations differing quite markedly, — or which according to the difference of excitations ought to do so, — and try thousands of times asking which is the stronger. It will be found that erroneous answers are given, oftener than anybody would believe possible in advance of the experiment. That this is not due entirely to the sensations not being what the excitations ought to produce is shown by other mental effects they produce. Take a series of efforts of given degree; for instance, in frames of mind which are marked by the observer on a scale as seeming to have about the same vigor, let a given time say 30 seconds be given to an introspective effort; let this effort be applied to the attempt to discriminate two sensations, and let the resulting feeling of confidence that they are correctly distinguished be marked on a scale. Now out of a thousand observations, where the difference of excitations was the same, the mean difference of sensations will be less than in another thousand observations where the difference of excitations was twice as great. We can then count the proportion of cases in which the degree of confidence in the reply reached a certain point on the scale. Thence, we can, by the usual mathematical methods, find a formula connecting the proportion of cases in which the given degree of confidence is reached with the difference of excitation. Then, we uniformly find that if that degree of confidence is not so high as to invalidate the formula, owing to the small number of cases in which it is observed, [then] it makes no difference what its degree may be in respect to this: that the proportion of cases in which it occurs only sinks to zero when the difference of excitations sinks to zero. It follows, I think, that there is no sensation which can affect the mind at all, which cannot be detected in consciousness by a sufficient exertion of attention.

397. The result of the study of the above formulae and of many others (which I have never published, because no psychologist has paid the slightest attention to those I have published) is that the contents of immediate consciousness range all the way from feelings which an indefinitely great effort is required to reduce to [a] given grade of subjective intensity to feelings which an indefinitely great effort is required to magnify to any given grade of subjective intensity. If we assume, as a convenient scale of measurement, that the measure of subjective intensity of an idea before such effort is applied to it is, other things being equal, proportional to a base raised to a power expressing the degree of effort required to lower its subjective intensity to an assumed standard, then I find that no feelings affecting the mind have the measures of their subjective intensities 0 or ∞; but that they approach indefinitely to those limits. Without any effort of attention at all, certain feelings have sufficient subjective intensity to affect us in certain ways, for instance, to cause us, in an off-hand answer, to reply that we are affected by them. The subjective intensity of many a feeling is sufficient for that without being sufficient to rouse us to decided exertion. On the other hand, the subjective intensity of many a feeling, though insufficient for that, is sufficient to affect our actions and color our emotions strongly.

398. Ideas become subjectively intense, if they are objectively intense. They become for a moment subjectively intense and directly after dim, if their suggestions are interesting. They become subjectively intense in small sets, especially sets of two; and become subjectively faint in large sets. They rapidly lose subjective intensity with time, while at the same time they spread into sets.

399. It follows from the above that the compound idea AB may be operative as an intermediate stage between A and B, notwithstanding our seldom being able to detect it in contiguous suggestion.

Very often this intermediate stage can be directly detected. In others, [it] is demonstrably there, as in ideas of motion where the preservation of the identity in idea of the mobile [is such] that one stage must have been imagined before the imagination of the previous stage was relinquished.

In other cases, whether the compound is present as intermediacy or not can only be a matter of hypothesis. That theory must be adopted which (1) best and (2) most simply explains the observed facts, is (3) in the closest analogy with the rest of our knowledge, and (4) is attributable to causes known to operate or most likely to be operative.

400. The theory here advocated is called, for convenience, the "new" theory. It is not really new; but it has been furbished up so as to be as good as new; and the designation is handy. †15

401. (1) It is true that the new theory does not so well explain the observed facts in the majority of suggestions by contiguity, because it supposes an idea to pass unnoticed. See (11), below.

But it has the advantage in those cases of contiguity where it is observed that A suggests AB. For this kind of suggestion does not come under the old formula. And it is difficult to explain how AB should be sometimes suggested by A and not always suggested.

In the case of association by resemblance, on the other hand, all the testimony of consciousness is that A almost always suggests AB, and perhaps never directly B. See (12), below.

402. (2) In regard to the simplicity of the theory a trifold distinction has to be made. In the sense of presenting many more features requiring study, and suggesting many more questions, the new theory is infinitely more complicated than the old one. See (21), below.

In the sense of being a more natural conception, it is doubtful which theory is superior. But this point is not an important one. See (22), below.

In the sense [of] giving a more unitary account of all the facts, the new theory is superior. See (23), below.

403. (3) In the general analogy with attraction the superiority is with the new theory. See (31), below.

In the general analogy with other changes of state, the superiority is with the new theory. See (32), below.

The new theory is more in conformity with current views of philologists about changes in the signification of words. See (33), below.

The new theory is favored by those modern psychologists who have made the most thorough study of association. See (34), below.

404. (4) There is a psychological cause which would probably produce the process supposed in the new theory. See (41), below.

405. Let us now consider the ten points just mentioned a little more closely. †16

406. (11) The new theory supposes a fact of consciousness usually to pass unnoticed in suggestions by contiguity, namely that when A suggests B, the compound idea AB intervenes.

But, then, it is to be observed that this is a sort of fact of consciousness very likely to pass unnoticed. It is well-known that ideas containing peculiar elements often do pass through the mind unnoticed. But in this case, there is no peculiar element. What is supposed is that instead of A jumping out of consciousness at the very instant B opens the door, quicker than a mouse could run into its hole, it stays until it finds itself de trop. Since it is necessary to suppose that the star of A is on the wane, very little interest would be had in it; and its remaining would not be noticed at the time, and still less be remembered. When you are entertaining a bore, if a visitor of consequence enters the room; and the bore behaves modestly, nobody can say afterwards whether he took his departure at that moment or not. It is, therefore, certain that the number of cases in which we remember positively that A did suggest AB and only later B, which cases are after all numerous, cannot, according to known principles of attention, be but a small percentage of all the cases in which this happened. But dividing the observed frequency of the intermediate suggestion by this small percentage we certainly get a large percentage, and it may be unity. Not knowing the percentages numerically, we cannot positively say that the quotient is unity; but it is not at all unlikely that it is so.

407. (12) We have seen †17 that Bain, as high an authority as any desultory observer can be, and there are as yet too few scientific observations of association to be of much importance, holds that generalization is the direct effect of "an effort of similarity." Why not say, at once, it is the first half of a suggestion by similarity? I am trying to recall the precise hue of a certain emerald that my mother used to wear. A sequence of shades runs through my mind. Perhaps they run into a continuum; but that makes no difference. They are a multitude of colors suggested by that one color. Conceived under what Kant imperfectly describes as a rule or schema, they constitute a general conception of a green something like that emerald. The old-fashioned nominalists would say nothing was in my mind but a word, or other symbol. For my part, I am not quite prepared to say what precisely is in my consciousness; but of this I am sure, that every memory of a sensation is more or less vague, that is, general. Every memory! Why, the sensation itself, when present for a few moments, is so; as every person who has made careful photometric measures is aware. In working with a photometer, I have confined myself to observations of a square centimetre some 10 inches from the eye; and have found the most elaborate arrangements hardly adequate to make the illumination of that small surface sensibly uniform. What, then, must be the vagueness of our observation when we look at a whole sheet of paper and pronounce it to be of one shade throughout? How is it possible to reconcile our notions of the origin of errors of observation with the doctrine that the sensation is absolutely free from all vagueness, all generality? But if it be granted that every memory of a sensation is more or less general, the distinction of intuitive and symbolical knowledge breaks down, as an absolute distinction. The vague memory of a sensation is just an aggregate, whether continuous or not makes no difference, of ideas which are called up together by a suggesting idea. The apparent direct suggestion of a single, or anything that can be taken for a single, idea by resemblance, is so rare, if not altogether dubious, a phenomenon, that William James declares that "there is no tendency on the part of simple ideas or qualities to remind us of their like." †18

408. (21) If A remains in consciousness after it has called in B, we have to inquire in what form A and B coexist in consciousness at such times and what their relation is, a question which we escape, of course, if A vanishes in the act of bringing in B. Nor is this question so innocent and easy as it may appear at first blush; on the contrary, it leads to considerable discussion and creates an extensive theory. Moreover, when A and B are both present, a new problem presents itself. Namely, how A drops out; and that phenomenon, examined closely, turns out to be far from the simple thing one might fancy it would be. Besides, the cases are few in which the set of associated ideas †19 consists of a pair. Most often it is what the country-people in my neighborhood call "quite a few," that is, almost a good many. At other times, though more rarely, it is three or more. Now if A calls up ABCD etc., it is a serious question how all these coexist in consciousness, and another why and how ACD etc. all disappear. Do they all depart in company, or do they sneak out one by one? And in the latter case, do those that remain have to rearrange themselves at each departure? And why should this desertion take place? And what determines who is to be left as IT, to use the terminology of children's games? All these questions are avoided on the old theory.

409. (22) In a question like this, it really makes little difference whether the hypothesis adopted is a natural one or not. We ought to give high authority to natural, instinctive conceptions of the mind, so far as they are of any practical utility. For natural selection, or whatever the principle of evolution may be, is there to adapt them to the welfare of the species. But in questions like that now on the tapis, natural psychology is quite beyond its depth. We will not stop, therefore, to argue this question.

410. (23) The purpose of a theory may be said to be to embrace the manifold of observed facts in one statement, and other things being equal that theory best fulfils its function which brings the most facts under a single formula. Besides, it will be shown in the chapter †20 devoted to the reckoning of the probabilities about such reasoning that the credibility of the more unitary hypothesis is far superior.

Now the new theory makes the whole action of the soul, so far as it is subject to law, consist of nothing but taking up and letting drop in ceaseless alternation. The old theory is obliged to recognize the same processes, and besides supposes, quite unnecessarily, an additional elementary process of passing over from A to B by a saltus. Entia non sunt multiplicanda praeter necessitatem is a maxim of science, which, we shall find, applies to forbid all unnecessary elements of hypothesis.

411. (31) Several philosophers of high rank consider the analogy between association and attraction to be a true and intrinsic one. Whether it really is so or not is doubtful; besides attraction is a little out of fashion among the physicists of our day. Studies of elasticity, in particular, have undermined its philosophical ascendancy. Still, taking the analogy for what it is worth, it is certainly much closer with the new theory. For according to the old theory, while A attracts B, B not only repels A, but repels it with such violence that A goes as soon as B begins to appear. The law of action and reaction would forbid such a phenomenon in physics. We there see one thing strike against another and knock it out; but we do not see it do this by virtue of the attraction of that second thing. On the new theory on the other hand, a wave of condensation brings B up to A, when the completion of the undulation carries A away.

412. (32) Of a good deal more significance are analogies with physical changes in general; and these are two. Under (321), we consider the saltus involved in the old theory; under (322) the rhythm involved in the new theory.

413. (321) Nowhere in nature is there the slightest reason to believe that any saltus takes place during changes. The more we learn of physics, the more we are led to exclude such hypotheses. Nor is there the slightest appearance of the phenomena of the mind being more sudden than those of matter. On the contrary the general evidence of experimental psychology is that mental actions are particularly gradual and gentle.

The old theory, understood as opposed to the new, supposes that at every instant up to a certain instant A is present and B absent, and at every instant after the same instant A is absent and B present.

According to the doctrine of limits, used in the calculus, that is, according to the geometer's conception of time and space, it would follow that at the limiting instant A and B were both present and absent. Now, it may be that time is not really continuous in the way in which the mathematician takes it to be; but logic will not justify the hypothesis that it is not continuous.

Everywhere in nature things that appear and disappear do so little by little. For instance, we can suppose the idea A fades out of attention and out of consciousness, while B quickly grows prominent. But, there, both must be present at once, or else A must be entirely extinct before B begins to appear. It is far more rational to suppose both are present, at once; first, because it is more natural and analogical to suppose A acts as a cause while it is in existence, second, because quantitative experiment shows that A would not naturally fade out quickly until B is already present to accelerate the fading.

414. (322) Everywhere in the world of life there is an alternating motion, an inspiration and expiration. Now according to the new theory, the whole activity of the mind consists of a drawing in and dropping out. One thing's moving in just as another moves out might be supposed in the case of an incompressible fluid not subject to diffusion; but there is no reason to think it really takes place in any case.

415. (33) The changes in the significations of words obey, of course, the law of association; and having been studied until of comparatively recent years as facts of observation, in themselves, without prejudice from psychological theory, they are independent evidence. Now, philologists, from their observations of such changes, have reduced them to successive broadenings and narrowings. The broadenings consist in the taking in of new ideas, the narrowings in the dropping out of little-used ideas.

416. (34) The Herbartians have made the most elaborate and minute studies of association of any psychologists, except the somewhat desultory but very extended studies of the English associationalists. Now, the Herbartian theory of apperception is precisely the theory that A suggests AB. It perfectly agrees with the present theory, only that the Herbartians do not admit that A is ever dropped, again. AB becomes what may be figured as AB, the A becoming faint; but even this is, according to them, unusual. They hold that the ordinary phenomenon is rather AB.

417. (41) Finally, there is a good reason why A should not disappear, until B has been present for some time. For ideas persist in consciousness for a long time after they are gone from the field of easy attention. See Hartley's Proposition 3, a doctrine elaborately studied by the modern school. †21

§4. Psychological Truths Needed in Logic

418. Reasoning is performed by the mind. Hence, the logician must not be entirely neglectful of the science of mind. This science, more than any other, is embarrassed by metaphysical puzzles. The attempt to avoid these only leads to careless and noxious solutions of them. What are the observed facts of psychology? They are the behaviour of men, especially what they say, together with our observation of what takes place within us, termed introspection.

419. What is the nature of introspection? The pre-scientific psychologists, such as Hamilton, believed that introspection was infallible. "To know, and to know that we know, are one and the same thing," said that philosopher. †22 They also had the naïve opinion that the things which are immediately present to consciousness are the things which introspection reveals. If those psychologists had been at all acquainted with the experimental sciences, they would have seen (what they would, doubtless, readily have acknowledged) that in these respects psychology, as they conceived it, was radically unlike any other observational science. The things we observe in a physical science, say in astronomy, are not the elementary facts, at all. Kepler, for example, was not, as even J.S. Mill seems to fancy, provided, in the observations of Tycho, with the real places of the planet Mars, by the study of which he made out two of his three laws. No astronomer can directly observe the situation of a planet relatively to the sun. He only observes, the secondary and derivative fact, that the planet as viewed from the earth, and subject to aberration and the equation of time, is in such and such a direction at such a time. According to the method of observation, this direction will be more or less affected by refraction, etc. Moreover, the astronomer is forced to recognize that every single observation he makes is more or less affected by error. Those errors have to be corrected by reasoning whose only premises are the erroneous observations themselves.

420. Now the truth is that the data of introspection are in these respects altogether analogous to those of external observation. Introspection does not directly reveal what is immediately present to consciousness, at all; but only what seems to have been present from the standpoint of subsequent reflection. It does not even tell what the normal appearance from this subsequent standpoint is, without its testimony being falsified at all times with serious accidental errors. †23

We cannot directly observe even so much as that there is such a thing as present consciousness.

421. We set out with a mass of opinions about the mind, which are not testified to by introspection. They are simply man's natural psychology. It is instinctive, no doubt, in part; for we can see that the lower animals have virtually such a psychology. In part also, it grows up nearly the same in all men as the natural result of similar experiences acting upon similar understandings. There is not the smallest reason for supposing that that natural psychology is at all accurately true; on the contrary, it probably involves great errors. At the same time, its authority must be allowed to be very high indeed in regard to all features which are of importance in the conduct of life; for, on the whole, man has prospered under such beliefs.

422. A part of this instinctive science, as we may call it, is that events succeed one another in time, that the past, when not too remote, is remembered, that the future, when not too remote, can be with some probability conjectured or anticipated, and that a single moment between the past and the future, (that is, some facts belonging to that moment), is directly before the mind.

423. This is the first item of our instinctive psychology. It makes a distribution of knowledge which has the closest bearing upon practical life; and to doubt its practical truth would be idle. At the same time, we have no reason at all for presuming it to be minutely true. Indeed, criticism shows that minutely examined it will not hold water; it is at issue with itself. The justification for this statement will be adduced in a subsequent chapter.

424. Meantime, we shall have to assume that, practically speaking, there is a flow of ideas through the mind, that is, of objects, of which we have the barest glimpse while they are with us, but which are reported by memory after they have been associated together and considerably transformed; and this report, though not very accurate, is substantially acceptable as correct.

425. Still, we must never forget that when we say, this idea is the same [that] I had yesterday, this idea resembles that, this idea involves or contains that, these are not things that are true of the ideas in their presentation. They suppose a mind, — our mind, — in which it seems that the workings of ideas involve those judgments. Perhaps, some of them would be true for all minds, and in that sense of the ideas themselves; but that cannot be averred at the outset. The point to remember is, that whatever we say of ideas as they are in consciousness is said of something unknowable in its immediacy. The only thought that is really present to us is a thought we can neither think about nor talk about. "Of thine eye I am eyebeam," says the Sphinx. We have no reason to deny the dicta of introspection; but we have to remember that they are all results of association, are all theoretical, bits of instinctive psychology. We accept them, but not as literally true; only as expressive of the impression which has naturally been made upon our understandings.

426. By the time we can examine our ideas at all, we find the process of combining them into sets has begun. But we seem to be able to discriminate roughly between a matter of cognition, as Kant calls it, forced upon us by the mysterious power without and within, and a skeleton of a set, in providing which we feel as if we have had a comparative freedom, which skeleton is nearly what Kant means by the form of cognition. For example, I hear at this moment a bird calling. I think he is on a lilac-tree close by the verandah. Every time he calls, I seem to see the bird. It is not much like seeing, but still it is a visual idea. Now that visual idea I think of as the bird itself, and the call I think of as something appertaining to that idea. Though the association is quite involuntary, I could banish the visual idea if I chose. Yet that, I recognize as forced upon my belief by experience. I cannot help believing there is a bird there, that would look something as I imagine it to look. But I have besides the visual idea of the bird and the sound of the call, a skeleton idea of connection between two things. It is a dim idea in itself; but if I want to think about it, I have a visual idea inline image of two dots connected by a line, or of a knot in a string. However, when I just think of the bird calling, I do not think the idea of connection so distinctly. Nevertheless, I do think it, and think of the call and the visual bird as belonging to it. Under ordinary circumstances, I might not remark the idea of connection; but potentially it would be there, that is, it would be all ready to be called into existence, as soon as there should be need of it. Before me on the table is a nearly cubical box, containing a photometer. As I look at it, I see three faces. I not only see them, at once, which associates them in contiguity; but I regard them as coming up to form a square corner, and thus associate them by means of a skeleton idea inline image of a triplet.

427. In all association, even by contiguity, the potential idea of the form of the set is operative. It is the instrument without which the association would take no hold upon the mind. It is not necessary that the formal idea should be clearly apprehended. As to the metaphysics of the causation, I do not care a straw for that. If any nominalist fancies it is more philosophical to say that the force of mind which can produce the idea of the set, has to operate to produce the association, I am not concerned at present to enter into that discussion. Only this must be insisted upon, that the skeleton of the set is something of which a mathematical diagram can be made. It is something in itself intelligible; though it is not necessary that it should emerge into the field of easy attention. For example, if a mind is under the influence of the skeleton idea of connection shown in the accompanying figure of the ten dots, inline image then upon seeing two triangles in perspective, †24 without thinking at all of this figure, or much of any form of connection, that mind will be pretty sure to regard the six rays making the two triangles, the three rays to the eye, or centre of perspective, and the ray of intersection of the two planes as forming a set of ten rays, an idea which certainly would not occur to a mind which was not so dominated by the form of connection.

By subsequent examination of the set of associated ideas, namely, the ten lines, the form of their connection might be perceived.

428. Looking out of the window, I see the cow whose milk we generally drink. There are certain difficulties which have occasioned a good deal of thought, so that I imagine I see a boy sitting by the cow milking her. The boy, and the stool, and the pail are added to my idea. Thence, I imagine that boy carrying the pail to the house. The cow and stool have dropped out. The straining of the milk presents itself to my imagination. A bowl is there and the pail. The boy is standing by; but I lose sight of him. I am following along the train dramatically, that is, following the interesting history.

429. As I followed that series of events in my mind (as I did; for I do not take make-believe observations), there was always something identical carried along. The boy going up to the house with the pail, was thought as that same boy, the pail that same pail, and the occasion that same occasion that I had just before been thinking of. The new ideas must, therefore, have always been taken in before the old ones were allowed to drop. By the time the milk was straining in imagination I had already begun to think that it would be good for my wife, who is threatened with nervous prostration.

430. To one skeleton-set another is added to form a compound set. Then, the first, perhaps, is dropped and the ideas which remain are viewed in a new light.

431. I saw a lady yesterday. I had not seen her since one evening when she and her husband drove up as my wife and I were standing at the well. A handsome man! He and she are both very fond of his nephew who seems to us too a charming fellow; and only yesterday my wife showed me a newspaper-paragraph that he had been arrested for debt. So his centi-millionaire cousin paid his tailor's bill of $5000. The last time I saw him he was hardly presentable. So my thoughts ran on in spite of me. First, the lady. Then, she in a set with her husband, my wife, myself, the buggy, and the well. Then mingles with this set another, the lady, her husband, my wife, myself, the nephew, and his agreeability; now that nephew brings in something concentrating him, my wife, myself, the newspaper. I forget the others. Then, him, and that Newport house, and the Croesus cousin. The skeleton-sets themselves I do not think particularly about; but they are operative. The marriage relation, the familiar intercourse of people in the country, the relation of handsome nephew to a message; newspaper-publications about people; the relation of a man of stupendous fortune to his cousins. All of these skeleton-sets, though not attended to, influenced my thought; and they followed one another by the same alternating process of taking up and dropping.

432. When these skeleton-sets were joined intermediately to the passage from one to another, these connections of them had their skeleton-sets. But these latter were all of that simple form expressible by the sign +, and had no specific character. There are, however, cases in which the connections of the skeleton-sets have skeleton-sets of more interest.

§5. Theoretical Interest

433. Interest has been spoken of as either connected with voluntary action or as emotional. We must not, however, lose sight of the fact that there is such a thing as theoretical interest, which has reference not to outward action but to the voluntary agency we put forth in directing our own ideas. Whether or not this is muscular is, as far as I can see, of no great importance for our purpose. It would be a pretty large hypothesis to suppose that we could contract and expand the arteries of our brains by a direct exertion. Let us rather content ourselves with acknowledging that this sort of voluntary action is of a nature not understood. It exists; there is a corresponding kind of interest referring to it; and there is a kind of attention, or heightening of consciousness in the initial stage of suggestions interesting in that way.

434. An immense number of associations are formed, and remain as long as they endure, in the background of consciousness, that is, in subjective obscurity. But as soon as a cerebro-motor suggestion is made, — that is a suggestion of the idea of voluntarily exercising thought, — the whole set brightens up. At the same time the action of forming and annulling sets, — say the metabolism of thought, — becomes more active. So that our instinctive psychological explanation is that the heightened consciousness is an agent that performs the action. If there is nothing in this but a word, we need not quarrel about it; but it would seem that as a matter of dynamics heightened consciousness, or attention, is nothing but a concomitant of the idea of voluntary action, and that it is the approach to a discharge of the excitement out of the cerebro-spinal nerves (although upon the same nerves again,) which accelerates the movement of thought, somewhat as the current of a stream is accelerated in approaching a cataract.

435. But when we undertake to give an account of any train of thought, as I have done in a few examples, when we say such and such ideas occurred to us, it is not at all true that they then came into consciousness. All that is true is, that at those moments they became connected with the idea of a voluntary act of thought, and consequently, became subjectively vivid enough to find a place in our narrative. In my train of thought about the cow, I have no doubt the idea of doing something to help my wife was what made me notice the creature at all, and caused my thought to be active in that direction. The set wife-milk was in the deeper shaded part of consciousness. The set cow-milk joined itself to this and gave wife-milk-cow, and thence wife-cow. This did not emerge into the glare of attention but was working all the time.

436. The subjective vividness which an idea gets from exciting interest is very transient. If it connects itself permanently with an enduring interest, it is very soon found that it has less vividness than it would naturally have had if it had not been connected with that interest. For instance, we have the most erroneous notions of how words sound in our own mouths and those of others. If we did not know the language the mere total impression of the peculiarity of sound, I do not say the analysis of the articulations, but the general character of the noise, would be much more vividly apprehended. This may be explained by remembering that the impression we speak of means our recollection of the impression; now this is the sum of the effect it makes while it is present. But if the idea is interesting, it suggests another so quickly, that it is present itself but a very short time; and its total effect does not amount to much. It is like a thermometer dipped for a moment into very hot water and immediately withdrawn. It is hardly affected at all. Still, however the fact be explained, it remains true that old ideas, while they have generally gained in interest and suggestiveness, have lost subjective vividness. On the other hand, an idea that is new and fresh seems quickly to gain vividness from that circumstance. Hence we say that as the excitation spreads it loses intensity.

§6. Experience and Inference

437. The examples which have hitherto been dwelt upon are instances of the free play of imagination. But in order to become aware of the whole range of association, or of that side of it which is of most interest to the logician, we have to consider experience.

Experience may be defined as the sum of ideas which have been irresistibly borne in upon us, overwhelming all free-play of thought, by the tenor of our lives. The authority of experience consists in the fact that its power cannot be resisted; it is a flood against which nothing can stand. The maxim that we ought to be "guided" by experience amounts to this, that what we have got to yield to at last we shall economically do well to be submissive to from the first. "Guided" is too egotistical a word.

438. We naturally make all our distinctions too absolute. We are accustomed to speak of an external universe and an inner world of thought. But they are merely vicinities with no real boundary line between them. It comes to this: there are some ideas, —objects, be it remembered, — which will have their own way, and we cannot swerve them much, and the little effect we can produce upon them we only produce indirectly. They make up or indicate the outward world. There are other ideas which seem very docile, they are just as we think they ought to be. They form the inner world. Yet it will be found that the inner world has its surprises for us, sometimes. It isn't so exactly as we would have it as we fancy. It is rather our wishes which conform to it, Mahomet that repairs to the mountain. Neither is the moderate amount of control which we exercise upon the world of ideas nearly so direct as we fancy it to be. We go about instinctively, and without being aware how circuitously we proceed to change the current of thought. There is an intermediate world, our own neighborhood, household, and persons, which belongs to us, which we sometimes feel inclined to class with the outer world and sometimes with the inner world.

439. Experience being something forced upon us, belongs to the external type. Yet in so far as it is I or you who experiences the constraint, the experience is mine or yours, and thus belongs to the inner world.

440. Experience is double, as much as reality is. That is, there is an outward and an inward experience. Under the latter head ought particularly to be reckoned a mathematical experience, not usually so called, which has compelled the development of pure thought to take a determinate course.

441. There is also an emotional experience, which has all the authority of any experience, provided it is equally irresistible. But experience and its irresistibility has a public character, which we shall study in another chapter.

442. Under the influence of association, the lash of experience needs only to be shown to us to cause us to submit. Now, there are indications by which we recognize the experiential character of certain ideas. One of these is the glowing blaze of their subjective vividness; but there are others, besides.

443. When an idea bearing the stamp of experience suggests another, that other in many cases itself carries that same stamp, which is carried forward in suggestion and thus a derivative authority from experience is conferred upon an idea which may have neither the vividness nor the other marks of directer experience. This sort of suggestion is inference. The law of association will divide inference into inferences by contiguity and inferences by resemblance, meaning by these latter inference from the occult inward nature of ideas or of the soul.

§7. Uncontrolled Inference

444. All inferences are really performed under the influence of the law of association. But all psychical actions divide into two great classes, those which are performed under the uncontrolled governance of association and those in which by the "agency" of consciousness, — whatever that may mean, — the actions come under self-criticism and self-control. The latter class of actions may be pronounced good or bad; the former could not be otherwise than they were.

445. Uncontrolled inference from contiguity, or experiential connection, is the most rudimentary of all reasoning. The lower animals so reason. A dog, when he hears his master's voice, runs expecting to see him; and if he does not find him, will manifest surprise, or, at any rate, perplexity.

446. Inference from resemblance perhaps implies a higher degree of self-consciousness than any of the brutes possess. It involves somewhat steady attention to qualities, as such; and this must rest on a capacity, at least, for language, if not on language, itself. Primitive man is very industrious in this sort of reasoning. Mythology, says Major Powell, is the philosophy of the Savage. It is certainly composed of inferences from resemblance. Our ancestors saw something man-like in the Sun, and could even tell what sort of a character the Sun-God's was.

447. Our daily life is full of involuntary determinations of belief. It is the egotism of the ego, or field of attention, which imposes upon [us] with its High German modest conviction that whatever is known is known through it. It is not so. I converse with a man and learn how he is thinking: I fancy he has told me, that is, has "stated" the fact in accurate forms of speech. But he has not, and how I have found out his thought is too subtle a process for this psychologist writing to find out. You hear a new slang word: you never ask for a definition of it; and you never get one. You do not get even any simple example of its use; you only hear it in ironical, twisted, humorous sentences whose meaning is turned inside out and tied in a hard knot; yet you know what that word means much better than any abstract definition could have informed you. In riding a horse; rider and ridden understand one another in [a] way of which the former can no more give an account than the latter.

448. Such inferences are beyond the jurisdiction of criticism. It is the part of psychology to explain their processes as it can; but, as long as they are out of the focal plane of consciousness, they are out of our control; and to call them good or bad were idle. The ordinary business of life is, however, best conducted without too much self-criticism. Respiration, circulation, and digestion are, depend upon it, better carried on as they are, without any meddling by Reason; and the countless little inferences we are continually making, — be they ever so defective, — are, at any rate, less ill performed unconsciously than they would be under the regimen of a captious and hypochondriac logic.

449. Quite otherwise is it with the actions which carry out our grander purposes. Here all must be voluntary, thoroughly conscious, based on critical reflection. Logic is wanted here, to pull inferences to pieces, to show whether they be sound or not, to advise how they may be strengthened, to consider by what methods they ought to proceed.

450. Intermediate between the lesser and the greater inferences lies a class which are best governed by habits, yet by habits formed or corrected under conscious criticism. Within a man's own special profession, his habits of thinking will in the natural course of things have been subjected to a good deal of criticism, — perhaps not remarkably intelligent, yet at all events based on experience. Outside of that narrow beaten path, if he has not studied logic, his habits of thinking will have been carelessly formed. If he has been educated under the traditional logic, they will have been formed under an influence positively baleful.

§8. Association and Inference †25

451. In the absence of external impressions, thoughts chase one another through the mind in a sort of Bacchic train. Each suggests another. After a while, the clear train of thought is broken, the ideas remain scattered for a time, and then reconcentrate in another train. Psychologists recognize that the suggestion of one idea by another may take place according to either one of two different principles; for an idea may suggest another like it, or it may suggest another which has been connected with it in experience. Thus, the thought of Niagara may suggest a hero or anything else that is grand, and so similar to the cataract, or it may suggest a crowd of importunate hackdrivers, which is connected with the place in every visitor's experience.

452. Association of the latter kind, association by contiguity as it is called, is the more typical. In it the characteristics of mental association are more strongly marked. Association by similarity is related to association by contiguity somewhat as our inward consciousness is related to outward experience; the one association is due to a connection in outward experience, the other to a connection in our feelings. Many psychologists have proposed to reduce association by similarity to a special kind of association by contiguity; few have been inclined to reduce the latter principle to the former.

453. Suggestions of these two kinds characterize not merely dreams and dreamy meditations, but also thoughts referred to the real world, or in technical language categorical judgments. Association is the only force which exists within the intellect, and whatever power of controlling the thoughts there may be can be exercised only by utilizing these forces; indeed, the power, and even the wish, to control ourselves can come about only by the action of the same principles. Still, the force of association in its native strength and wildness is seen best in persons whose understandings are so little developed that they can hardly be said to reason at all. Believing one thing puts it into their heads to believe in another thing; but they know not how they come by their beliefs, and can exercise no control over the inferential process. These unconscious and uncontrolled reasonings hardly merit that name; although they are very often truer than if they were regulated by an imperfect logic, showing in this the usual superiority of instinct over reason, and of practice over theory. †26 They take place like other mental suggestions according to the two principles of similarity and connection in experience.

454. Inference from connection in experience is most rudimentary of all reasoning. The lower animals plainly reason in this way. The dog, when he hears the voice of his master runs expecting to see him, and if he does not find him will manifest surprize, or at any rate perplexity. This is as good an example of inference from connection in experience as could easily be given.

455. Inference from resemblance probably implies a higher degree of self-consciousness than any of the brutes possess. It involves a somewhat steady attention to qualities as such; and this must rest on the capacity for language, if not on language itself. Primitive man, however, reasons in this way; for mythology is built of such inferences. Our ancestors saw something manlike in the sun, and could even tell what kind of a man the sun-god was.

456. But we need not go to the lower animals nor to savages for examples of associational determinations of belief. Our daily life is full of such phenomena. We have the naïve idea that our beliefs are principally determined by the exercise of our conscious intellect; but it is not so. I converse with a man and learn how he is thinking: I fancy that he has told me, but he has not. I hear a new slang word, but I need not ask for a definition of it; I understand its meaning much better without a definition, I know not how, than I should with one. In riding a horse, I understand him and he understands me; but how we understand one another I know hardly better than he.

457. All such inferences are, of course, beyond the jurisdiction of criticism. It is the part of psychology to explain their processes as it can; but as long as they are out of consciousness, they are out of our control and it is idle to call them good or bad. We may, however, say that the ordinary business of life is best conducted without too much self-criticism. Just as our respiration, circulation, and digestion are far better carried on by involuntary than they could possibly be by voluntary actions, so the countless little reasonings which we are continually making, — although they may often be defective, — are nevertheless much better performed unconsciously than they would be if we were to try to interfere with them by a captious and hypochondriac logic. It is very different with the actions which we undertake in order to carry out our grander purposes. Here, all must be voluntary, thoroughly conscious, and based upon the most critical reflection. Here logic is wanted, to pull to pieces our inferences, to show whether they are good or bad, how they can be strengthened, and by what methods they ought to proceed. Intermediate between the lesser and the greater inferences, lies an intermediate class which are best governed by habits, yet by habits formed or corrected under conscious criticism. Within a man's own special profession, his habits of thinking will have been subjected to a good deal of criticism (not necessarily the most intelligent, but based on experience); outside of that, if he has not studied logic, his habits of thinking will have been carelessly formed, or if he has studied the traditional logic, they will have been formed under an influence truly baleful.

458. Reasoning unconsciously can hardly be called reasoning at all. As long as I simply find myself seized with a belief, without being able to give any account of how I came by it, logic has nothing to say except to warn me of the extreme danger that I shall err.

459. Reasoning proper begins when I am conscious that the judgment I reach is the effect in my mind of a certain judgment which I had formed before. The judgment which is the cause is called the premise, that which is the effect is called the conclusion. When I am aware that a certain conclusion which I draw is determined by a certain premise, there are three things which I have more or less clearly in my mind. First, I have a peculiar sense of constraint to believe the conclusion, connected with a sense that that constraint comes from the premise; second, I have a conception that there is a whole class of possible analogous inferences (though I may not be able to define the class) in which a similar constraint would be felt by me; and third I have a present belief that all of these inferences, or at least the great body of them would be true.

460. The lowest kind of conscious reasoning is where I know what the premise is from which my belief in the conclusion follows, and I feel that it follows upon some principle, — technically called the leading principle of the inference, — but I do not distinctly know what that principle is. Such an inference is called a simple consequence.

461. Such inferences are common enough. Uneducated people seldom reason in a higher way; and educated people reason so very often. Since the object of reasoning is merely to arrive at the truth, if the leading principle of our inference be really true, it is not necessary for us to know it, for in that case the mode of inference based upon it can in no case carry us away from a true premise to a false conclusion. Such a mode of inference is valid, that is, its leading principle is true; but it is only materially valid, that is, valid because as a matter of fact the leading principle happens to be true; it is not logically valid, that is, the leading principle might be false. Although the simple consequence may be valid, logic condemns it. A conclusion may be true, though the inference by which it was reached was invalid; that is, it may chance to be true. But the inference is condemned because other conclusions similarly drawn may be false. In the same way, a simple consequence may happen to be valid; but since the leading principle is not recognized, there is no security for its validity, and the next simple consequence drawn, though indistinguishable from the first (the leading principle being unrecognized), may very likely fail.

462. Simple consequences have occasionally been introduced into philosophy. The most remarkable instance is the Cogito, ergo sum of Descartes, who wished every philosopher to begin by doubting everything without exception. But even in doubting everything he must, says Descartes, be aware that he doubts, that he thinks. Now from this belief that he thinks he is led by a blind but irresistible constraint to believe in his own existence. This inference, "I think, therefore I am," is a simple consequence, for as long as the philosopher doubts everything he can have no fuller reason to give. He cannot, for example, say that thought supposes a thinker, for he is bound as a Cartesian to doubt that among other things at the outset. Such is the doctrine of Descartes. Of course, were there nothing to check the absolutely resistless force of a belief, logic must be silent, Leges silent inter arma. But in point of fact, no belief is found thus absolutely irresistible. There is always room for the reflection that an error may have been committed. †27 †28

§9. Association and the Law of Mind †29

463. In reflecting upon the work which has hitherto been done upon association, we are led to remark how many writers have been led astray by futile attempts to seek guidance for their psychological studies in physiological hypotheses. Their idea has, no doubt, been that physical facts are more tangible, certain, and easily intelligible than psychical facts; and that knowledge of the less easily ascertained truths ought to be based upon an acquaintance with more easily ascertained truths. How far is this just? The present writer holds that in advance of positive knowledge, the presumption ought to be that there is such a unity in the universe that the difference between mental and natural phenomena is only a difference of degree. Presumably, the same elements are in both; and if so, so far there is no essential difference in their intelligibility. But upon the opposite supposition, namely that the phenomena of mind are essentially more complicated than those of matter, the study of mind through physiology must necessarily be misleading. It may be said that, at all events, we do understand physical phenomena the best. This, however, is open to doubt. Those physical phenomena which we really understand, the motions of the planets and the like, are quite exceptionally simple; and the assumption that all physical phenomena are regulated by the laws of mechanics, which since Helmholtz has been the ruling idea of science, appears in the light of the logical rules to be developed in this treatise, as a good "working hypothesis," but as a dogmatic proposition, — in which way it is used, when a method of psychological investigation is founded upon it, — as exceedingly improbable. Nothing is less understood than the action of the nerves, in the sense in which they would require to be understood for such a purpose. The psychological phenomena, on the other hand, are revealed to us in the complicated process of "introspection," in language, in behaviour, and in our instinctive, and (we may presume) approximately correct, notions of the way of the mind, with an eminent degree of clearness. This method is far more accurate and scientific than the other, at least, in the present stage of the inquiry.

464. Our object is to formulate the law of mind. We have to consider all mental action whatsoever and, generalizing it, to say not what all the elements of it are, but what that element of it is which is legislative. "Generalization," is the old answer. Pretty well that for a first essay; but open to the following objections. First, it is logical, it contemplates only the product, while what we aim at is the psychological law, relating to the action itself; second, it confines itself to the logic of non-relative terms, and is therein very imperfect, indeed; third, it is a meagre word, while we want the whole process with all its characteristics at large. Still, we remark that all attempts to say what mind does, that it reduces the manifold of sense to unity, that it assimilates, that it shapes action to purposes, have one thing in common.

465. A feeling is an element of consciousness just as it immediately is in the moment when it is there for itself and not as delegate of some other feeling not present. Such a feeling is not a psychological datum. The data are highly complex. That there is a cream colored surface with black characters on it is as near as I can readily describe the datum of my consciousness at this minute, — but in truth the moment I pick it to pieces, as I must do to describe it, it ceases to be a datum. As for the pure feeling, that is a hypothetical entity, and is as completely veiled from me by its own immediacy as a material particle, as it exists in itself, is veiled by the somewhat absurd requirement that it shall be considered in itself. The truth is there are no data. We have a lot of inferences from data, liable to error, and these we have to correct as best we can by putting them together. The state of the case is quite similar to that of a physical science, say astronomy. All we have to go upon in astronomy is observations, and all those observations are erroneous. But we collect them and take their means and find a general description of the path of the observed object; and from this we can calculate an ephemeris, and finally, if there is any interest in doing so, ascertain what those observations ought to have been. We can no more start with immediate feelings in psychology than we can start with accurate places of the planets, as affected by parallax, aberration, refraction, etc. in astronomy. We start with mediate data, subject to error, and requiring correction.

466. The mind pronounces that what I see now resembles something I saw yesterday. The whole aspect of things as flowing in time is, it is plain, virtually a theory of the mind's creation. But, for the present, we take that theory as true, that is, as a stable one. Taking it as true, it seems to provide no possible means by which the mind could compare what is present to it now with what is past and gone and done with. This compels us to say that the time idea, — at least, in its first crude shape, — needs correction, like an erroneous observation in astronomy. Examining it more carefully, we observe that the idea is that the series of instants of time is continuous. Analyzing this idea of continuity, as we shall do in a future chapter with the most minute accuracy which an improved art of logic puts at our disposition, †30 we find that it implies that there are instants infinitesimally close together; that is that there are durations of time so short, that every one such starting with a given date has a character exactly like the one before it in some respect, without any limitation to this rule, while yet a time a little later does not possess that character. This enables us to suppose that the consciousness is not limited to a single instant but that it immediately and objectively extends over a lapse of time, without thereby extending over any sensible lapse of time. We are thus able to suppose that consciousness is carried along from one time to another, and is able to compare what is present to it at different times. Such we may suppose to be the process of memory; and this is the account of it which best squares with those natural beliefs which are all the data the psychologist can possibly have upon which to found his science, corresponding, as they do, to the observations of the astronomer.

467. But granting that memory is thus justified, — while errors may, of course, creep in during the process, — it still remains that when the mind declares that what it sees now, or remembers to have seen yesterday, is like what it remembers to have seen last week, the likeness, which though accompanied like all mental processes with a peculiar and characteristic sensation, is mainly a fact, a mental fact, and the sensation of it is of no consequence except as an advertisement of that fact. That fact is that by virtue of the occult working of the depths within us, those two feelings coalesce into one notion. For the sake of calling this by a familiar name, I call this association by similarity. But the ideas united by virtue of an occult inward power, are not always regarded as similar. Contraries are also so joined. Ideas and feelings are so joined which are neither merely declared by the mind to be similar nor to be contrary. Such, for instance, are length, breadth, and thickness. The mind delights in triads. In general, what the mind pronounces is that the feeling or idea of yesterday and that of today belong to one system, of which it forms a conception. A concept is not a mere jumble of particulars, — that is only its crudest species. A concept is the living influence upon us of a diagram, or icon, with whose several parts are connected in thought an equal number of feelings or ideas. The law of mind is that feelings and ideas attach themselves in thought so as to form systems. But the icon is not always clearly apprehended. We may not know at all what it is; or we may have learned it by the observation of nature.

Chapter 3: Habit †1

§1. Laws of Physics

468. The books on physics are replete with examples of what they call "empirical laws," that is to say, formulas which are satisfied as nearly as men have succeeded in observing the facts and under certain limited circumstances, but which nobody supposes go down to the roots of existence, or to exhibit the general forms of all phenomena. They are, on the contrary, supposed to be merely special modifications which the universal formulæ assume under special conditions. Of such a pseudo-law centrifugal force affords a good example. When a railway-train moves round a curve, there is always a pressure away from the centre of curvature. It must be so; for since a body not subjected to any force naturally moves in a right line, while this railway-train does not so move, it follows that the guiding rail exerts a force upon it in a direction toward the centre of curvature; and consequently by virtue of the law of action and reaction, the train must exert an equal and opposite force upon the rail. This is a perfectly real force. Namely, it is the elastic force of the iron rail which is strained by the tendency of the train to preserve a rectilinear motion. If you examine the rail you will detect manifestations of the reality of the centrifugal pressure; or if you whirl a sling, you will actually feel the centrifugal force. But now certain natural philosophers extend the formula of centrifugal force, which is a genuine force where the motion is constrained by a rigid guide to cases where there is no such constraint. They say that a planet is held to its circular orbit by the balance between centrifugal and centripetal forces. In this case, centrifugal force is a mere formula, — a formula which is undoubtedly quite correct as far as the effect goes, while yet the centrifugal force is a merely formal affair with nothing at all corresponding to it in nature. It is very much as if between two men, A and B, there has been a single transaction consisting in A lending B $5. Now if B were to keep his books in such a manner that the state of the account as entered on those books made A owe him $100 with $105 on the opposite side of the account, the entries would in effect be correct; but yet that hundred dollars would be a fiction of bookkeeping. In like manner the centrifugal force of a planet is a fiction due to using polar coördinates in place of rectangular coördinates. It is true that were the gravitation of the sun suddenly to be annihilated there would be at the first instant an acceleration of the planet away from the circular orbit equal to the centrifugal force; and it is certainly true that what we call force in Dynamics is nothing more than the product of an acceleration multiplied by a mass. Only, this acceleration away from the circular motion of the natural motion of the planet were it suddenly emancipated from gravitation is nothing in the world but the entry we have to make on one side of our accounts to balance that fictitious entry which we have virtually made on the other side when we took the circular motion as the standard or origin from which to reckon accelerations.

469. Now the question is, whether or not there is any ratiocinative method by which we can assure ourselves that any law which we may discover by the observation of nature is not like centrifugal force a mere fiction of bookkeeping but represents a real and a living action in nature. Many nominalistic logicians will deny at once that any such distinction can be made; but in doing so, they will be merely adhering to preconceived metaphysical opinions. They have no real evidence to offer upon the subject. Of absolute knowledge there can be no question. But if we see that as soon as circumstances are somewhat varied, the form of the law is lost, the inference would seem to be that it is not a universal or living mode of action. If on the other hand, we find that as soon as the form is prevented from manifestation in one shape it immediately reappears in another shape, and especially if it shows a power of spreading and of reproducing itself, these phenomena may be considered as evidence of genuine vitality and fundamental reality in the form of the law.

But I confess I think it will, and ought to be, harder to convince you of the truth of this general principle than it will be to assure you of the consequence which leads me to formulate it. Namely, what I wish to show is that causation, as distinct from the action of conservative force, is a real, fundamental, and vital element both in the outer and in the inner world.

470. As to those explanations which the physicists propose for irreversible phenomena by means of the doctrine of chances as applied to trillions of molecules, I accept them fully as one of the finest achievements of science. Judge Stallo †2 performed an acceptable service in his earnest assault upon them, which was conducted with as much ability as so poor a cause could possibly be expected to command. Other writers have recently attempted to reinforce the attack, one of them with some understanding of the subject. But the judgment of a really scientific logic must be altogether in favor of the accepted theory. Its explanation of the facts is altogether admirable and is fortified by a variety of new phenomena which were not known at the time the theory was first proposed, but which fit into their places like the pieces of a boy's dissected map, after he has once begun to put a few of them rightly together. This explanation demonstrates that the agency of energy is disseminated through every department of physical phenomena. But in one thing it fails; namely, it fails to show the absence of a very different kind of agency; and it not only fails to show its absence, but even supplies the means of proving its presence.

§2. Non-Conservative Actions

471. Those non-conservative actions which seem to violate the law of energy, and which physics explains away as due to chance-action among trillions of molecules, are one and all marked by two characters. The first is that they act in one determinate direction and tend asymptotically toward bringing about an ultimate state of things. If teleological is too strong a word to apply to them, we might invent the word finious, to express their tendency toward a final state. The other character of non-conservative actions is that they are irreversible. †3 If a falling stone, which moves under the conservative force of gravity, were suddenly to strike a perfectly elastic horizontal fixed surface, its motion would be reversed and it would move upwards to the point from which it fell with precisely the velocities it had in falling, only in reverse order. So it would be if every planet in the solar system suddenly had its motions reversed. Whatever motion conservative forces can effect, the very reverse of that motion they are equally capable of effecting.

472. There is some objection to taking either of the two characters of finiosity and irreversibility as criteria of the conservative or non-conservative character of an action. That which strictly constitutes an action as conservative is that the forces depend solely on the relative positions of the particles, and do not depend on the velocities. But theoretically that which makes an action irreversible is that the forces do not depend upon odd powers of the velocities. Practically, however, the irreversibility is an infallible criterion. For example, the friction of sliding motion is altogether independent of the velocity; so that according to the definition it is a conservative action. The velocity of a sliding motion is retarded by friction according to precisely the same formula as the velocity of a body shot vertically upwards. The only difference is that when the instantaneous state of rest is reached, a new kind of friction, rest-friction, suddenly begins to act and breaks the continuity of the motion. Sliding friction is a unique example of a non-conservative action that simulates conservative action. The reason that it does so undoubtedly is that conservative action enters into it in a singularly uniform manner. When one solid body is set down upon another, there will be many points at which they come into contact, and where this occurs the paths of the atoms, — for I do not half believe in the molecules of solids, will begin to be interlaced. The result is that when one begins to slide over the other, many ruptures have to be made, and before the ruptured parts have attained their positions of equilibrium they will on the average come into new contacts with the other body and thus there is a perpetual average state of elastic strain. The elastic stress of this strain is the friction, and it really is a conservative force. The parts of the action which are non-conservative are two, first and most important the ruptures, by which the elastic potential is at once converted into heat, and second and less important the contacts. You will observe that by friction the energy of molar motion is not immediately converted into heat but into elastic potential and it is only after the action is over that this becomes converted into heat, and that fact explains why friction acts like a conservative force.

473. The resistance of a fluid according to the analysis of Newton and his contemporaries is proportional to an even power of the velocity, namely the square. It ought therefore to be reversible; and probably it would be so in part for a moment. But the truth is [that] the whole analysis is an example of the unskillful application of mathematics, the hypotheses being too unlike the real facts to be useful. Of course, no resistance proper can be reversible.

474. The other character of non-conservative action, namely, its finiosity, is, as a criterion, open on the theoretical side to still more serious objection. Namely, it is not true that only non-conservative forces can bring about enduring states of things.

475. In the first place, let me remark that it is not generally true that a particle moving about an attracting centre describes any fixed orbit. In order that that should be the case, it is requisite that the law of the force should be subject to peculiar numerical conditions. We know that if the attraction is inversely as the square of the distance, and the velocity is not too great, the moving particle will describe an ellipse having the attracting centre at the focus. If, however, at the smaller distances the attraction is a little greater than the law of the inverse square of the distance requires, the result will mainly be that the ellipse itself will revolve slowly about the centre in the same direction in which the moving particle revolves. If there is any commensurable ratio between the periods of the two revolutions, the motion will finally return into itself; otherwise not.

476. If the attraction is inversely as the cube of the distance, the revolving orbit will make infinitely many revolutions while the moving body is making one-half revolution in that orbit; so that it will describe a spiral line having in general an outer and an inner boundary. The outer boundary may however be at an infinite distance or even further away. Here then we have a case in which conservative action asymptotically moves toward a final and ultimate state of things. Suppose the inner limit be distant from the centre by an insensibly minute interval. Then, it will appear to remain fixed in one spot, although it will really be in tremendously rapid motion. The fact that tremendously rapid or even infinitely rapid motion may simulate rest is what makes the conservative action simulate the finiosity of non-conservative action.

477. The attraction may vary according to such a law that the moving body winds in indefinitely near to the centre without ever passing out or passing through the centre. It certainly seems as if the atoms of the chemical elements may have been formed by some such aggregation. For in that way Prout's law could be accounted for.

478. It is important to remark that even if the attraction varies inversely as the cube of the distance, and still more easily if it varies more rapidly, the moving particle may pass through or, at any rate, to the centre. And this it will generally do by performing infinitely many revolutions in an infinitesimal moment of time. What the motion will be when it does arrive at the centre it is hard to say. My father †4 in his Analytic Mechanics says that after that the body will proceed in a straight line. This, of course, would violate the principle of areas. He does not mention the circumstance that the direction of that straight line would in many cases be indeterminate. It appears to me that a general law being essentially continuous, to suppose an infinite velocity, or any other discontinuity in the action is to suppose that general law to be violated. If therefore a general law is such that it essentially involves such a phenomenon, the law is, in so far, self-contradictory. Still, the contradiction only amounts to this, that there is a point of discontinuity in the continuum. It is only a slight departure from generality in one particular instance. It is not that the state of facts supposed is self-contradictory; but only that it is self-contradictory to suppose such a phenomenon to be a result of a perfectly general law.

479. If such an event can happen then it follows as a necessary consequence that there is such a thing as an absolutely chance event. For even an infinitesimal variation in the conditions will make a finite difference in the result.

480. But as to whether or not there is any such law, inquiry in that direction is absolutely barricaded and brought to an eternal standstill, unless there has been some logical process in nature whereby the laws of nature have been brought about. Since, therefore, it is a corollary from the First Rule of Reasoning †5 that we must not make hypotheses that will absolutely stop inquiry, it follows that we are bound to hope that such a logical process of the evolution of law in nature may be discovered and that it is our duty as scientific men to search for it.

481. But let us return to those spiral motions which reach the centre only at the end of an infinite time. It must be confessed that here the simulation of non-conservative action by a conservative action is not a false or extrinsic simulation, but is true and intrinsic. It is just one of those extreme cases which throw the most light on philosophical problems and to which a powerfully solvent method of reasoning must pay particular attention. We note in the first place that the simulation depends in part on the bringing together into one infinitesimal moment motions which undo one another, and in declining to analyze this moment because it is absolutely infinitesimal. Thus the velocities in that moment, though instantaneously infinite are in their resultant zero; and with the attractive forces the same thing is true. From this point of view, it becomes absurd to say that an attraction varies inversely as the cube or any higher power of the distance down to the very centre of attraction. Indeed, a somewhat similar difficulty arises whenever there is any attraction at all at the centre.

482. This leads me to remark that the finiosity of non-conservative action is also manifested in hyperbolic orbits under the attraction inversely as the square of the distance. inline image That is to say a moving body which starts from an infinite distance in one direction reaches at the end of infinite time an infinite distance in another direction. This finiosity might be regarded as due to the circumstance that time has an absolute limit. For could the motion continue beyond the infinitely distant instant of time it would continue through the infinitely distant line in the plane and complete the closed hyperbolic orbit. But I do not think that this simple way of solving the difficulty ought to be regarded as satisfactory. At any rate, if a similar solution be sought for the spiral, one is led to imaginaries, which seems to show that the mathematical hypothesis does not correspond to the facts.

483. It will be remarked that both these cases, that of the spiral orbit and that of the hyperbolic orbit, are connected with angular displacements. Any kind of rectilinear motion is continued by virtue of momentum, and from this circumstance arises the result that conservative forces affect not directly the velocities, but only the accelerations; and in the fact that such forces depend upon the relative positions of the particles lies their conservative character. But it is different with rotations. There is no momentum continuing an angular displacement as such, but only so far as that angular displacement involves rectilinear displacements. The mere rotation of an absolute particle, strictly occupying a single point, has no momentum at all. So if a rectilinear displacement is effected as in the hyperbolic orbit by means of motions which in their limits become radial, the momentum has no tendency to continue the angular motion. Thus angular motion per se is not a conservative action. If, for example, atomicules are Boscovichian points, the attractions of those atomicules may be different on different sides of them. Many facts in elaterics, crystallography, and chemistry render it almost certain, for reasons which it would be too long here to discuss, that, as far as atoms are concerned, this is actually true. Suppose for the moment that it be also true of atomicules. What would be the result? As far as the mutual action of two atomicules was concerned, they would instantly turn those sides to one another which gave the minimum potential energy; and in the absence of all momentum, there would be no tendency to swing beyond that point. Those two sides would always be turned toward one another. But when there were three such points, the face which one atomicule turned toward another, and consequently its attraction for that other, would depend in part upon the position of the third atomicule. In this case, although the motions of translation would be conservative, the rotations of the atomicules would be regulated by the old formula of causation.

§3. Relative and Absolute Motion

484. Now from our modern point of view of the non-Euclidean geometry, it appears that, strictly speaking, there is no kind of motion having the properties which we associate with translation. That is to say there is no motion which is merely relative. It would not be convenient to attempt to explain this here, before we have examined further into the nature of Continuity.

485. But let me here say a word about the attempt of Ernst Mach to show that all motion, even rotation, is merely relative. Mach belongs to that school of soi disant experiential philosophers whose aim it is to emancipate themselves from all metaphysics and go straight to the facts. This attempt would be highly laudable, — were it possible to carry it out. But experience shows that the experientialists are just as metaphysical as any other philosophers, with this difference, however, that their pre-conceived ideas not being recognized by them as such, are much more insidious and much more apt to fly in the face of all the facts of observation.

486. Newton in his Principia maintains that Time and Space are substances, or in the jargon of French philosophers that they are Entities. The doctrine was a new one, well-recognized as such by Newton. Mach seems to think it was a blunder which Newton fell into inadvertently. It was nothing of the sort. We have historical testimony to show that Newton himself and his contemporaries regarded it as a peculiar, definite, and deliberate theory. Newton does not overtly argue the question in the Principia for the reason that he was a stickler for the traditions of mathematical exposition; and that tradition compelled him to confine himself to demonstrations and comments upon demonstrations. But he contrives to make his reason plain enough. That reason is that the laws of motion make velocity of rotation to be something absolute and not merely relative. Now velocity is the ratio of the amount of a space-displacement to the amount of time in which this displacement takes place. If therefore, argued Newton, velocity is not merely relative, neither is a displacement in space nor a lapse of time relative; and therefore Space and Time are not mere relations but are absolute subjects or substances. Now this reasoning is founded on positive facts of observation; and it appears to me to be sound reasoning. I will not say that it draws a necessary conclusion; but I do say it is an excellent hypothesis to account for the facts.

487. Mach on the other hand lays it down as an Axiom that Space and Time are merely relative. No facts lend any support whatever to such an assertion. The most that could be said, — more than is really true, — is that facts concerning the composition of motions of Translation go to show that space-position has an element that is merely relative. Mach's struggles to define angular motion as motion relative to the mean position of all the bodies in the universe are not only struggling against all observation, and not only involve the absurdity that the centrifugal force of sling would be influenced by the angular motion of stars very far away, and more influenced by the more remote than by the nearer stars, contrary to his own conception of space as an image of dynamical relations; but, what is still worse, this gratuitous theory is in mathematical contradiction to the point he most insists upon, namely that rectilinear motion is purely relative.

488. It is true that Space, in so far as it is a continuum, is a mere law, — a mere Thirdness. †6 But that does not stand in the way of its being a thing too. If besides its continuity it presents arbitrary thisness, †7 we must admit that it is something more than a mere law. The question of the relativity of motion is a question of the measurement of space, not of the nature of space itself; and therefore, although motion be not relative, it would not necessarily follow that space itself is non-relative, however good the inference may be, considered as a retroduction. But there are characters belonging to space per se which seem to involve thisness, such as its having three dimensions, — which is an arbitrary limitation. Its cyclosis and periphraxis, †8 whether these be supposed equal to 0 or to 1 are apparently arbitrary Facts. You cannot reduce them to mere formalities without supposing that space has some kind of topical singularity, — which is still more manifestly an arbitrary fact of existence. As to the Fourth Listing number, all must admit that its value is 1. That is to say, a body filling all space could not by gradual degrees shrink to a point without being ruptured, while the slightest explosion which should separate the body entirely from a single place however small, — the smallest vacuous cist in it, — would suffice to enable the collapse to take place. This I believe nobody who has carefully considered the matter has doubted or is likely to doubt, — at least unless it be supposed that space has modes of connection of which observation affords not the slightest trace. Here again, then, is an arbitrary existential fact about Space, which is simply the way it insists upon being, without any logical necessity. Now insistence upon being in some quite arbitrary way is Secondness, which is the characteristic of the actually existing thing. It is its self-willedness.

489. Now if you examine the matter more closely than I have time to do in this lecture, you will find that it is precisely in those respects in which Space shows such indications of Secondness that motions act as though governed by the law of causality, while in those respects in which Space preserves all its Thirdness the motions preserve their dynamical character.

490. Let us next consider actions of which the space-element is not an intrinsic part. For example, I slip a nickel into the hand of a mendicant. One might say that this was a space motion. But the non-conservative friction is so great that neither the beggar nor the giver remarks any effects of momentum. The coin is not thrown but pushed along, and the dynamical part of the action is altogether insignificant. The fact that there is any space motion at all is accidental as far as the determination of the events goes. The money is caused to become the beggar's and remains his. Take the purest kind of temporal action. The very flow of time itself. The event passes out of the problematical state of futury into the state of a fait accompli. All psychical action has this character. A question is answered, and answered it remains. A mere duality, a passage from a first state into a second state, here takes the place of that determination of a relation between three states which characterizes physical dynamics.

491. My father, Benjamin Peirce, drew my attention to the psychological peculiarity of an experiment which I am going to show you. I do not now remember how he formulated the matter. It is that a mathematical analysis of the conditions of motions often gives an expression of what happens conceived under one aspect; while anybody looking at the experiment would instinctively express what he saw under quite another aspect. The dictum of the eye is that one of the pendulums is ahead of the other in its oscillations by half an oscillation, i.e. by a quarter of a vibration, and that the oscillations [of] this pendulum are continually losing their amplitude and transferring it to the other. This is quite true, too. But analytic mechanics looks upon the fact from quite a different point of view. According to it each pendulum oscillates in two different ways at once. One of the components of its oscillation has the period of the two pendulums when they are swinging together and both pendulums partake equally of this component, while the other has the period of the two pendulums swinging opposite ways and the two pendulums are opposite one another in the phases of this component. I remember distinctly that my father remarked that while the view of analytic mechanics corresponds to the formula {theta}1 = {theta} cos [(a-b)t] + {Theta} cos [(a+b)t] {theta}2 = {theta} cos [(a-b)t] - {Theta} cos [(a+b)t] the instinctive, or intuitional, view corresponds to the formula {theta}1 = 2 {Theta} cos at . sin (bt+90°) {theta}2 = 2 {Theta} sin at . sin bt. And I further remember his remarking that the decided choice of this last view showed a peculiarity of our mental constitution. But I cannot remember that he attempted to formulate this peculiarity. It is, however, clear to me that it is nothing but our natural tendency to prefer the formula of causation. We regard the pendulum which is ahead as the agent and the one which lags behind as the patient.

492. To the reason of the mathematician the intuitional mode of conception is singularly crooked and unphilosophical. It happens to be pretty simple because the two pendulums are of equal weight and equal length. Were they not so, the phenomenon would appear very complicated from that point of view, though almost as simple as before from the point of view of analytical mechanics.

§4. Psychical Action

493. It is now time to inquire whether psychical action be of the conservative or the causational type. You know I make no pretension to competing with the profound psychologists under whom you sit here in Harvard; and I do not promise to bring the question to a satisfactory conclusion. But I shall hope in the few minutes that I can devote to it to make you all understand what the question is, and I hope the provisional reply I make to it may recommend itself as provisional good sense.

494. I read out to you the rules of philosophical terminology that seem to me to recommend themselves at once to the logic of science and to the ethics of science. †9 Those reasons for adopting them were so weighty, that I would not range any other consideration alongside of them. But now that I am no longer arguing the question, let me add that I for one entertain a deep feeling of reverence for the traditions of the English language. It has not the amazing psychical and especially emotional wealth of German. It has not half as many words for tools and manipulations as French; nor has it the delightful social finesse of French. But in all that concerns logic and reasoning, it has a spirit of accuracy which is due to the fact that the language spoken in State Street and other market places preserves to an extraordinary degree the sharp distinctions of the scholastic lore of the middle ages; and where those distinctions are not available, our vernacular language still preserves the spirit of them. I regret very much that those who of late years have written in English upon philosophy and psychology seem most of them to have a contempt for all English thought and English speech so great that it produces an utter insensibility to the distinctions of the language. The French language has long been cut off from medieval traditions; and moreover it is the genius of the French to rely upon skillful phraseology to express their precise thoughts rather than upon accurate terminology. But notwithstanding this, large numbers of French words which happen to be spelled like English words but which bear quite different meanings have by recent writers been used in their French meanings threatening an utter break-down of the spirit of English speech and of English thought. For example, the word Entartung, having been translated into French by dégeneration, becomes "degeneration" in English, although what is meant is degeneracy, which is an entirely different thing. So spontanée becomes in this new lingo spontaneous, which is almost the reverse of the correct English meaning of spontaneous. Suggestion becomes "suggestion," regardless of the fact that suggestion was already an exact term of philosophy in English in a different sense. The German Association is rendered by "association," although if ever there was a school of writers who by the clearness of their definitions and the accuracy of their thought deserved to have their usage of terms respected, it was the English Associationalists. I might expend the rest of the hour on this theme. When these neologists have succeeded in thus dishonoring their mother-tongue, till no vestige of her pristine virtue remains, they will by the same act have hopelessly corrupted all the old virility and health of English thought.

495. However, putting aside all such regrets, which are probably futile, — and saying no more about vernacular speech, I am still obliged in the interest of the logic of science to employ a scientific terminology; and this must follow the only rules by which confusion can possibly be avoided. According to those rules I am bound to use scientific terms in the senses in which they first became terms of science. Accordingly, the English associationalists having first made association a term of science, and they having been careful never to extend it to the operation or event whereby one idea calls up another into the mind, but to restrict it primarily to a habit or disposition of mind in consequence of which an idea of one description is likely to bring into comparative vividness of consciousness an idea of another description, or, when they applied the term association to any operation or event, to designate by it only that process of habituation by which such a habit or disposition of mind acquires strength, they having been punctilious in this matter, my code of rules obliges me logically and morally, to follow them. As for that mental event which corresponds, as we suppose, to the nervous discharge of one part of the cortex upon another, — or the action of one idea to render another idea which is associated with it vivid, — for that they employed the term suggestion. This word is now applied mostly to motor phenomena or to such manifestations of mind as can be observed from without; and therefore, although the two meanings doubtless are in real facts connected together, the meanings themselves are different. But here a compromise is possible; for I shall violate no rule of terminology by speaking of the "suggestion" of the associationalists as associational suggestion and that of the hypnotists as nervous suggestion. The adjectives may be dropped, — especially the former, — in cases where there is no possibility of the meaning being mistaken.

496. I next remark that different sense-qualities have different degrees of intensity. The sound of thunder is more intense than the sound of a dozen people clapping their hands; and the light of an electric arc is more intense than that of a star. It is also true that the sound of thunder is more intense than the light of a star, and that the electric arc light is more intense than the sound of a dozen people clapping their hands. It is not at random that I say this. Besides this intensity of the sense-qualities, ideas have another mode of intensity, — their vividness. The contrary of vividness we call dimness. Although my personal imagination and memory of colors is very dim compared with that of most persons, yet it is decidedly above the average in accuracy; and in matching a color by memory I am no more likely to select a paler or darker color than I am to select a higher or more luminous color. This vividness, which is so much more intense in my memory of the red pencil which I saw this afternoon than it is in my memory of a certain red fan which I possessed when I was nine years old, appears, as far as I have been able to experiment, to be entirely distinct from the intensity of the qualities remembered; although, no doubt, other things being equal my memory of an intense sensation is likely to be more vivid than my memory of a faint sensation. It does not belong to the Firstness of the quality, but to the Secondness or insistency of the particular apparition of that quality.

497. At any one time I have a great multitude of ideas in my consciousness of different degrees of vividness. How vivid the most vivid of them are depends upon how wide awake I am. In any given state of mental wakefulness or alertness, there is a certain maximum limit of vividness which none of my ideas surpass, but which a few of them always attain. There is only room in my consciousness for a few at this highest level of vividness. If others force themselves up, some of those that were at the surface must subside. Below these there are others less vivid, and still deeper others that are so dim that only by intense effort, perhaps by no effort that I can possibly exert, can I assure myself of their presence. And yet it may be proved indirectly that they are really there. For example, I have occupied myself for weeks in answering questions about the relative intensity of excitations of sense when with the most vigorous effort I could not seem to detect the slightest difference between them, so that my answers seemed quite random guesses; and yet the decided majority of the answers would be right every day, thus proving that sensations were capable of affecting my answers although I could not seem to be aware of them at all. †10 Moreover, ideas of which we do not seem to be aware will sometimes suggest or call up others by association, these others being vivid enough. I have endeavored to ascertain whether there is in any ordinary state of consciousness a definite minimum degree of vividness, as there certainly is a maximum degree. But all my experiments upon careful mathematical discussion point to the presence of ideas so very dim, or wanting in vividness, that I am strongly inclined to say, as a first approximation at any rate, that the vividness ranges all the way down to zero, and that every cell that ever can be sentient is in some degree sentient as long as it is alive at all.

§5. Association

498. Association is of two kinds. †11 For, on the one hand, it may be a natural disposition, which was from birth destined to develop itself whatever the child's outward experiences might be, so long as he was not maimed nor virtually maimed, say by being imprisoned. This sort of association by virtue of which certain kinds of ideas become naturally allied, as crimson and scarlet, is called association by resemblance. The name is not a good one, since it implies that the resemblance causes the association, while in point of fact it is the association which constitutes the resemblance. In themselves considered any two sense-qualities are what they are to themselves alone and have no relation to one another. But could they be compared by a mind that brought no tinge of its own nature into the comparison, any two ideas would appear somewhat alike and somewhat different. But the human mind attaches a peculiar value and emphasis to some resemblances, and that consists in this, that when one quality is brought vividly to consciousness, others will at once have their vividness increased, some more, some less. Thus, an idea which may be roughly compared to a composite photograph surges up into vividness, and this composite idea may be called a general idea. It is not properly a conception; because a conception is not an idea at all, but a habit. But the repeated occurrence of a general idea and the experience of its utility, results in the formation or strengthening of that habit which is the conception; or if the conception is already a habit thoroughly compacted, the general idea is the mark of the habit. Some psychologists deny the existence of association by resemblance, or say that it is at bottom merely a special case of association by contiguity. To the arguments in defence of its fundamental character which are to be found in common books, I will add three. The first is that it is incredible that man is so constituted that no paths of nervous discharge between parts of the cortex are naturally more or less resistant than others. But those that are less resistant must correspond to natural associations, and ideas naturally associated will resemble one another. The second argument is that without association by resemblance there could be no general ideas and no resemblances. The third argument is this. Suppose I have long been puzzling over some problem, — say how to construct a really good typewriter. Now there are several ideas dimly in my mind from time, none of which taken by itself has any particular analogy with my grand problem. But someday these ideas, all present in consciousness together but yet all very dim deep in the depths of subconscious thought, chance to get joined together in a particular way such that the combination does present a close analogy to my difficulty. That combination almost instantly flashes out into vividness. Now it cannot be contiguity; for the combination is altogether a new idea. It never occurred to me before; and consequently cannot be subject to any acquired habit. It must be, as it appears to be, its analogy, or resemblance in form, to the nodus of my problem which brings it into vividness. Now what can that be but pure fundamental association by resemblance?

499. On the other hand, the association, instead of being a natural disposition of mind, may be an acquired habit of mind. That supposes that similar ideas have been conjoined in experience until they have become associated. That is termed association by contiguity. Of course, psychologists have not been wanting who sought to show that there is no such thing as association by contiguity, or that it is merely a special case of association by resemblance. It is a long time since I read the work of Gay who first gave the idea of associationalism to Hartley. But I seem dimly to remember that he had a notion of that kind. A number of other principles of association have been proposed, such as contrast and causation. Association by contrast ought to be regarded as a case of association by resemblance, not in the narrow sense in which the reduction is often made, but by generalizing the conception of resemblance in accordance with the logic of relatives until it embraces all high degrees of logical relations between ideas. Contrast is a particular form, an especially prominent and familiar form, of what may be called relational resemblance by which I do not mean a resemblance of relations, but a connection of the kind which in the logic of relatives is shown to belong to the same class of relations to which the relation of resemblance belongs. Association by causation is an ill-defined conception embracing associations of different natures. But besides that reiterated coöccurrence which helps to consolidate an association by contiguity, another factor which plays a great part in accomplishing the association, is the experience that the combination of the ideas has important consequences. When we learn that white cats with blue eyes are deaf and have peculiar habits, such as that of following their masters like dogs, we no sooner see a white cat than we want to know what colored eyes she has. This may be called association by relational contiguity. That is to say not only have the two ideas frequently been experienced together, but their union has often been accompanied in experience with a third idea of an interesting kind. Another kind of association which is very important is that which makes an idea interesting. I propose to term it association by interest. An idea occurs to us in such a way that it would, other things being equal, be very dim. For example, it may result from a fortuitous putting together of two other ideas both of which are sunk deep in the subconscious mind. But if the new idea happens to be interesting, it will promptly become vivid. Why is this? Clearly it is because the objective self-consciousness, or the idea which a man has of himself, consists in large measure of what may be roughly described as a composite of ideas of his aims and purposes, including all problems which exercise him. Now the separate components of this composite may for the most part be dim; but the total idea is perhaps the most vivid in consciousness at all times. Now an interesting idea is one which has an analogy, or resemblance in form, to this composite of the man's aims. It is, therefore, drawn into vividness by the vividness of that composite.

§6. Law of Action of Ideas

500. Let us now make an attempt to formulate the law of action of ideas. In the first place, an idea left to itself does not retain its vividness but sinks more and more into dimness. In the second place associated ideas in consciousness together soon undergo alterations of vividness, the dimmer ones becoming more vivid, and the more vivid ones dimmer, according to the strength of the associations. The dimmer idea never becomes more vivid than the more vivid idea had been before the change; but it may become more vivid than the idea originally the more vivid is after the change; for otherwise it would hardly be possible to explain idea chasing after idea. But in the third place the action of associative suggestion does not take place instantly as soon as the two ideas are in consciousness together. There are continual changes going on in the connections of ideas in consciousness; and the action of associative suggestion does not take place until chance has brought the two ideas into suitable connection for acting upon one another. Thus, I stand before an emblem wondering what it means. It is vividly in my mind. Perhaps the meaning is dimly in my consciousness; but it is not until by the movements in consciousness, chance has thrown the idea of the emblem and the idea of its meaning into the right sort of connection, that they suddenly change in vividness, the idea of the emblem becoming much dimmer and that of its meaning much more vivid.

501. In the fourth place, this interchange of vividness is accompanied by another event which takes place altogether outside my consciousness, though there is a sign of it in consciousness. Namely, the association between the two ideas becomes strengthened, in such a way that the more vivid idea becomes more likely to call up the less vivid one on another occasion. At the same time, in the fifth place, certain other associations become weakened.

502. Now that the mental action, as so described, is upon the surface, at least, causational and not conservative is quite obvious. There is no reversibility in it, and the traces of anything like momentum are slight and doubtful. At the same time, it would be possible to suppose that it was a conservative action affected to such a degree by resistances, that the momentum had no sensible effect.

503. The established cerebral theory will easily account for all the five features of mental action which I have mentioned; and that theory is favorable to the view that while the action is of a mixed nature, the non-conservative elements are the predominant ones. For there can hardly be a doubt that the peculiar properties of protoplasm depend upon the enormous complexity of its molecules, upon those molecules being frequently broken up and reunited in new connections, and upon the circumstance that in the quiescent state the molecules are in stationary motion, while in the active state they are partly broken up and the fragments are wandering. Now all this may be summarized by saying that its properties depend upon Bernoulli's law of high numbers, and every action depending upon that law is, so far as it is so dependent, purely causational and not conservative.

504. Although the cerebral theory is established and although it is of priceless value to psychology in its present stage of development, it by no means follows that it will never be superseded. That method may perhaps lead to a purely psychical way of investigating the mind. We must wait and see whether it will or not; but meantime for various reasons which I cannot now enter upon that is what I am inclined to expect.

§7. Physics and Psychics

505. We have, then, these two modes of action, the conservative and the causational, the former rather the dominant one in pure physics, the latter dominant in psychics. Our logical impulse, which prompts us to try to understand the universe, and as an essential condition of doing so to bring all its action under a single principle, this impulse, I say, compels us to hope that it may in some way be shown either that all causational action is conservative at bottom or that all conservative action is causational at bottom.

506. But I am quite sure that, as far as I personally am concerned, if I had not been moved by any consideration which touched me more nearly than such a vast and shadowy hope can do, I never should have been moved to do all the hard work I have done for the last fifteen years in trying to reason this matter out. I must confess that for me a living motive must have smaller dimensions than that very general hope. But I am a physicist and a chemist, and as such eager to push investigation in the direction of a better acquaintance with the minute anatomy and physiology of matter. What led me into these metaphysical speculations, to which I had not before been inclined, I being up to that time mainly a student of the methods of science, was my asking myself, how are we ever going to find out anything more than we now [know] about molecules and atoms? How shall we lay out a broad plan for any further grand advance?

507. As a first step toward the solution of that question, I began by asking myself what were the means by which we had attained so much knowledge of molecules and ether as we already had attained. I cannot here go through the analysis, although it is very interesting. But that knowledge has been based on the assumption that the molecules and ether are like large masses of ordinary matter. Evidently, however, that similarity has its limits. We already have positive proof that there are also wide dissimilarities; and furthermore it seems clear that nearly all that method could teach has been already learned.

508. We now seem launched upon a boundless ocean of possibilities. We have speculations put forth by the greatest masters of physical theorizing of which we can only say that the mere testing of any one of them would occupy a large company of able mathematicians for their whole lives; and that no one such theory seems to have an antecedent probability of being true that exceeds say one chance in a million. When we theorized about molar dynamics we were guided by our instincts. Those instincts had some tendency to be true; because they had been formed under the influence of the very laws that we were investigating. But as we penetrate further and further from the surface of nature, instinct ceases to give any decided answers; and if it did there would no longer be any reason to suppose its answers approximated to the truth. We thus seem to be reduced to this alternative. Either we must make some very broad generalization as to the character of Nature's ways, which may at least tell us that one theory about molecules and ether is better worth trying than another theory, or else we had better abandon altogether a line of inquiry, — I mean into the inmost constitution of matter, — which is likely to prove a mere waste of time.

509. But meantime our scientific curiosity is stimulated to the highest degree by the very remarkable relations which we discover between the different laws of nature, — relations which cry out for rational explanation. That the intensity of light should vary inversely as the square of the distance, is easily understood, although not in that superficial way in which the elementary books explain it, as if it were a mere question of the same thing being spread over a larger and larger surface. I cannot stop to give the true explanation, but I will just give you two hints. The first is that the basis of the measurement of light is the convention that we will call the light of two candles double the light of one. The other hint is that according to the superficial explanation of the school-books, you would expect the brightness of the image of a star made by a perfect lens to be proportional to the area of the lens, while in point of fact it is proportional to the square of that area. But grant that the law of variation of light with the distance is known, what an extraordinary fact it is that the force of gravitation should vary according to the same law! When both have a law which appeals to our reasons as so extraordinarily simple, it would seem that there must be some reason for it. Gravitation is certainly not spread out on thinner and thinner surfaces. If anything is so spread it is the potential energy of gravitation. Now that varies not as the inverse square but simply [as] the distance. Then electricity repels itself according to the very same formula. Here is a fluid; for electricity is really something like a fluid. It is not a mode of motion. Here is a fluid repelling itself but not at all as a gas seems to repel itself, but following that same law of the inverse square. I have not time to instance other extraordinary relations between laws of nature. But I cannot refrain from alluding to that most extraordinary law of Mendeléef.

510. According to the strictest principles of logic these relations call for explanation. In order to find such explanation, you must deduce the fundamental laws of the physical universe as necessary consequences of something. That is you must explain those laws altogether.

511. Now were it merely a question of the form of the law, you might hope for a purely rational explanation, — something in Hegel's line, for example. But it is not merely that. Those laws involve constants. Light for example moves over 300,000,000 centimetres per second. A mass at a distance of one centimetre from a gramme of matter receives in consequence of gravitation an increment of velocity toward that mass every second of . . . †12 centimetre per second. The explanation of the laws of nature must be of such a nature that it shall explain why these quantities should have the particular values they have. But these particular values have nothing rational about them. They are mere arbitrary Secondnesses. The explanation cannot then be a purely rational one. And there are numberless other facts about nature which, if my logic is not quite at fault, absolutely and decisively refute the notion that there can be any purely rational explanation.

§8. Evolution of the Laws of Nature

512. What kind of an explanation can there be then? I answer, we may still hope for an evolutionary explanation. We may suppose that the laws of nature are results of an evolutionary process. In the course of this process of evolution, light, let us suppose, age by age moves faster and faster, and we have now arrived at the stage of the process in which it moves just so fast. Now logic does not demand any further explanation than that. The same applies to gravitation. You might ask me whether the relation between the velocity of light and the modulus of gravitation does not require explanation. I answer that it does not because the dimensions of the quantities are different. One involves the unit of mass and the other does not. But two universal constants are as many as can be allowed without explanation of their relations, except that there may be besides a constant of space.

513. By a process of reasoning, then, of the nature of which I thus give you some hint, though given in full it would be seen to be drawn from a great variety of different evidences, I reached the conclusion that a theory of the evolution of the laws of nature must be sought. †13

514. But if the laws of nature are the result of evolution, this evolutionary process must be supposed to be still in progress. For it cannot be complete as long as the constants of the laws have reached no ultimate possible limit. Besides, there are other reasons for this conclusion. But if the laws of nature are still in process of evolution from a state of things in the infinitely distant past in which there were no laws, it must be that events are not even now absolutely regulated by law. It must be that just as when we attempt to verify any law of nature our observations show irregular departures from law owing to our errors, so there are in the very facts themselves absolutely fortuitous departures from law trillions of trillions of times smaller no doubt, but which nevertheless must manifest themselves in some indirect way on account of their continual occurrence. I do not mean to say that it is a strictly necessary consequence that there should be this element of absolute chance in nature, and my first theory attempted to avoid it. But as I went on, I found other reasons to support this view of which I will endeavor to give you some idea in the next lecture. †14

515. But if the laws of nature are results of evolution, this evolution must proceed according to some principle; and this principle will itself be of the nature of a law. But it must be such a law that it can evolve or develope itself. Not that if absolutely absent it would create itself perhaps, but such that it would strengthen itself, and looking back into the past we should be looking back through times in which its strength was less than any given strength, and so that at the limit of the infinitely distant past it should vanish altogether. Then the problem was to imagine any kind of a law or tendency which would thus have a tendency to strengthen itself. Evidently it must be a tendency toward generalization, — a generalizing tendency. But any fundamental universal tendency ought to manifest itself in nature. Where shall we look for it? We could not expect to find it in such phenomena as gravitation where the evolution has so nearly approached its ultimate limit, that nothing even simulating irregularity can be found in it. But we must search for this generalizing tendency rather in such departments of nature where we find plasticity and evolution still at work. The most plastic of all things is the human mind, and next after that comes the organic world, the world of protoplasm. Now the generalizing tendency is the great law of mind, the law of association, the law of habit taking. We also find in all active protoplasm a tendency to take habits. Hence I was led to the hypothesis that the laws of the universe have been formed under a universal tendency of all things toward generalization and habit-taking.

516. The next problem was to find a method of reasoning by which I could deduce with mathematical certainty the exact nature and formulae of the laws which would be formed under the influence of such a tendency and having deduced them to compare them with nature and thus see whether the theory was tenable or not.

517. Now I have had some remarkable successes in this line; and have also been led to make some remarkable predictions which remain yet to be compared with observation. Of the method of reasoning I have used I shall give you some slight idea in the next lecture. †15

§9. Chance and Law †16

518. Uniform distribution presents to a superficial view diverse characters. There are just so many suicides every year; of children born every year just so many develope into giants and just as many into dwarfs. An insurance company stakes almost its existence upon the expectation that just so many losses will occur each year. The relation between temperature, pressure, and volume upon which the whole cosmos of business reposes, insofar as it depends on the regular working of steam-engines, is another case of a uniformity which is simply a necessary corollary of a fortuitous distribution. But in many cases of uniform distribution, so far as we can see, fortuitous distribution plays no part. Thus, the two kinds of electricity tend to unite in a certain fixed proportion. This is simply because one kind attracts what the other repels and these two forces vary with the distance in precisely the same way. Both are conservative forces; and the uniform distribution of the two electricities is due to the very peculiarly adjusted relation between the two conservative forces. In chemical combinations we have a very marked example of uniform distribution. We do not know by what sort of forces chemical compounds are held together. Even apart from the circumstance that some of the most readily formed bodies, such as acetylene, are endothermic, there are other considerations which show that those forces are not altogether conservative. But the bonds of atoms and their atomicities are sufficient warrant for the assertion that the forces must be exceedingly complicated and specially related to one another. I might say much more both about chemical forces and about the conditions of uniform distribution in general; but in the limits of one lecture I think it best to confine myself to the two clearer cases.

519. I have said that a uniformity, or regular law, may be a mere consequence of a fortuitous distribution. But if you examine any such case critically, you will find that after all, this only results because of some regularity in the conditions. Take, for example, Boyle's law that if the density of a gas is doubled its pressure will be exactly doubled. This is because if there are twice as many molecules in the space, twice as many in a given time will pound upon the wall of the receptacle. But this results not from fortuitous distribution alone, but from fortuitous distribution conjoined with the circumstance that the paths of the molecules are all very nearly rectilinear. I will not stop to prove this, which you will find set forth both in Watson's little treatise and in the more generally interesting volume of Oscar Emil Meyer. Suffice it to say that it is an essential condition. Now this is something which, being true of all the molecules, is a regularity. The simplicity of the law is due to the simplicity of this regularity. You will find, if you analyze the problem, that it must always be the case when a regularity results from a fortuitous distribution that some uniformity of the objects of the collection must come into play, and further that any simplicity the resulting law may exhibit must be due to the simplicity of that uniformity.

520. On the other hand, in regard to fortuitous distribution, while you may undoubtedly suppose that it arises simply from the absence of any sufficient reason to the contrary, — not that I accept the principle of sufficient reason as a general one by any means, but in this case, it amounts merely to supposing the fortuitous distribution is a pure First, without any cause or reason whatsoever, — while this you may of course suppose, yet if you suppose it to have been in any case a necessary result, this necessity certainly implies that some law of uniformity is at work, but for all that it will be quite evident that the uniformity has not per se of its own nature produced the irregularity, but that this irregularity is due to some other irregularity, some other fortuitous distribution, in the initial conditions.

521. Thus it is that uniformity, or necessary law, can only spring from another law; while fortuitous distribution can only spring from another fortuitous distribution. Law begets law; and chance begets chance; and these elements in the phenomena of nature must of their very nature be primordial and radically distinct stocks. Or if we are to escape this duality at all, urged to do so by the principle of retroduction, according to which we ought to begin by pressing the hypothesis of unity as far as we can, the only possible way of doing so is to suppose that the first germ of law was an entity, which itself arose by chance, that is as a First. For it is of the nature of Chance to be First and that which is First is Chance; and fortuitous distribution, that is, utter irregularity, is the only thing which it is legitimate to explain by the absence of any reason to the contrary.

522. These things having become clear to us, let us now, remembering that the whole aim of this discussion is to find some clue by which physical and psychical action may be unified, examine, a little, certain other features of the two classes of phenomena governed respectively by conservative forces and by the principle of causality, and see how bright or how darkling a light is shed upon them by what we have thus far made out.

523. Looking first at conservative forces, we remark that they govern nothing but the space relations of particles. They are the law of the mutual reactions of particles in space. And the first fact that demands our attention is that, other things being equal, particles react upon one another more strongly the nearer they are to one another. How shall we explain this fact? We shall get the right hint if we ask ourselves what would happen in case all this were suddenly reversed and particles were to act most and most directly on those particles which were most distant from them.

Chapter 4: Consciousness

§1. Categories of Experience †1

524. If the whole business of mathematics consists in deducing the properties of hypothetical constructions, mathematics is the one science to which a science of logic is not pertinent. For nothing can be more evident than its own unaided reasonings. On the contrary logic is an experiential, or positive, science. Not that it needs to make any special observations, but it does rest upon a part of our experience that is common to all men. Pure deductive logic, insofar as it is restricted to mathematical hypotheses, is, indeed, mere mathematics. But when logic tells us that we can reason about the real world in the same way with security, it tells us a positive fact about the universe. As for induction, it is generally admitted that it rests upon some such fact. But all facts of this sort are irrelevant to the deduction of the properties of purely hypothetical constructions.

525. But there is a part of the business of the mathematician where a science of logic is required. Namely, the mathematician is called in to consider a state of facts which are presented in a confused mass. Out of this state of things he has at the outset to build his hypothesis. Thus, the question of topical geometry is suggested by ordinary observations. In order definitely to state its hypothesis, the mathematician, before he comes to his proper business, must define what continuity, for the purpose of topics, consists in; and this requires logical analysis of the utmost subtlety. Mathematicians still survive who are so little versed in reasoning as to deny that we can reason mathematically about infinity, although the hypothesis of an endless series of whole numbers involves infinity and the hypothesis of transcendental irrational quantities involves an infinity of another kind. If we cannot reason mathematically about infinity, a fortiori we cannot reason mathematically about continuity, and any exact mathematics of topical geometry becomes impossible. To clear up these difficulties, some consideration of logical matters is indispensable.

526. Logic is a branch of philosophy. That is to say it is an experiential, or positive science, but a science which rests on no special observations, made by special observational means, but on phenomena which lie open to the observation of every man, every day and hour. There are two main branches of philosophy, Logic, or the philosophy of thought, and Metaphysics, or the philosophy of being. Still more general than these is High Philosophy which brings to light certain truths applicable alike to logic and to metaphysics. It is with this high philosophy that we have at first to deal.

527. What is the experience upon which high philosophy is based? For any one of the special sciences, experience is that which the observational art of that science directly reveals. This is connected with and assimilated to knowledge already in our possession and otherwise derived, and thereby receives an interpretation, or theory. But in philosophy there is no special observational art, and there is no knowledge antecedently acquired in the light of which experience is to be interpreted. The interpretation itself is experience. Even logic, however, the higher of the two main branches of philosophy, draws a distinction between truth and falsehood. But in high philosophy, experience is the entire cognitive result of living, and illusion is, for its purposes, just as much experience as is real perception. With this understanding, I proceed to make evident the following proposition.

528. All the elements of experience belong to three classes, which, since they are best defined in terms of numbers, may be termed Kainopythagorean categories. †2 Namely, experience is composed of

1st, monadic experiences, or simples, being elements each of such a nature that it might without inconsistency be what it is though there were nothing else in all experience;

2nd, dyadic experiences, or recurrences, each a direct experience of an opposing pair of objects;

3rd, triadic experiences, or comprehensions, each a direct experience which connects other possible experiences.

529. In order to prove this proposition I have, first, to invite every reader to note certain phenomena in experience and make certain simple generalizations from those observations; second, to point out in those generalized phenomena the essential characters in the above definitions of the categories; third, to point out certain other characteristics of those phenomena and show how they are related to the essential characters of the categories; fourth, to exemplify the wide range of each category in experience; fifth, to show by comparison of the characters already ascertained that none of the categories can be resolved into the others, but that all are distinct from one another; sixth, and most difficult, to prove that there can be no element in experience not included in the three categories.

530. A quality of feeling, say for example of [a] certain purple color, might be imagined to constitute the whole of some being's experience without any sense of beginning, ending, or continuance, without any self-consciousness distinct from the feeling of the color, without comparison with other feelings; and still it might be the very color we see. This is a conclusion which anybody can reach by comparing his different states of feeling; but we cannot actually observe a quality of feeling in its purity; it is always mixed with other elements which modify it greatly. Were a feeling thus to usurp the whole consciousness, it would necessarily be perfectly simple; for the perception of different elements in it is a comparison of feelings. Moreover, with us every feeling has its degree of vividness, which does not affect its quality, but is apparently the degree of disturbance it produces. It is necessary to speak vaguely, because it is not settled precisely what vividness consists in. But [were] the feeling uncomplicated by anything else, no particular degree of vividness would attach to it. The quality of feeling would then be the whole feeling. Qualities, then, constitute the first category. A quality of feeling is perfectly simple, in itself; though a quality thought over and thus mixed with other elements, may be compared with others and analyzed. A quality of feeling, in itself, is no object and is attached to no object. It is a mere tone of consciousness. But qualities of feeling may be attached to objects. A quality of feeling, in itself, has no generality; but it is susceptible of generalization without losing its character; and indeed all the qualities of feeling we are able to recognize are more or less generalized. In a mathematical hypothesis the qualities of feeling are so subordinate as to be scarcely noticeable.

531. That we cannot have an experience of exertion without a direct experience therein of resistance to our exertion is plain. By an experience of exertion, I do not mean a consciousness of resolving to do something, nor the collection of our force preparatory to an effort, but merely what we experience in the very act of doing. This being understood, I contend that it is equally true that we cannot have an experience of being affected by anything without having therein a direct experience of our resisting the effect. Take hold of one end of a lexicon and lift it, while one edge remains on the table or floor. You experience its resistance. But when the centre of gravity has passed beyond the vertical plane of stationary edge, what you feel is that the dictionary is acting upon you. Yet the only difference is that different muscles are now called into play, which are elongating instead of contracting. Lay your forearm on the table and place the book on your palm. Though the sensation is somewhat different, you still have an experience of being overborne, and thus of holding out against the compression. A series of such experiments, with variations needless to describe, will convince the reader that there is a common character in the experience of acting upon anything by a muscular contraction and an experience of being acted on whether by a relaxation of a muscle or by a sensation received upon the organs of sense. That experience gives us at once a direct consciousness of something inward and an equally direct consciousness of something outward. In fact, these two are one and the same consciousness. They are inseparable. The same two-sided consciousness appears when by direct effort I bring to the surface of recollection a name that I dimly remember, and when I make distinct to myself a confused conception. †3 If the purple color which we just supposed made up the whole consciousness of a being were suddenly to change, then, still supposing the idea of continuance is either absent or not prominent, that being will have a two-sided consciousness. The sense of what has been will be a rudimentary ego, the sense of what comes about will be a rudimentary non-ego. For past experience is for each of us ours, and that which the future brings is not ours, which becomes present only in the instant of assimilation. That being could have no sense of change except by experiencing the two colors together. The instant change would involve a sort of shock consisting in the two-sided consciousness. This experience of reaction is the second Kainopythagorean category. It is impossible to find any element of experience directly involving two objects, and no more, — those two embraced in any third, such as a pair, but standing in their naked otherness, — other than an experience of reaction.

532. A reaction is something which occurs hic et nunc. It happens but once. If it is repeated, that makes two reactions. If it is continued for some time, that, as will be shown below, involves the third category. It is an individual event, and I shall show that it is the root of all logical individuality. A reaction cannot be generalized without entirely losing its character as a reaction. A generalized reaction is a law. But a law, by itself without the addition of a living reaction to carry it out on each separate occasion, is as impotent as a judge without a sheriff. It is an idle formula entirely different from a reaction. A reaction may be ever so conformable to law or reason, that is, it may occur when law or reason calls for it. But, in itself, as reaction it is arbitrary, blind, and brute exertion of force. To express the fact that a reaction thus resists all generalization, I say that it is anti-general. In this respect it contrasts with a quality of feeling, which though not in itself general is susceptible of generalization without losing its character as quality of feeling. It is remarkable that Reaction, which is the Dyad category, should have an aggressive unity that Quality, the Monad category, does not exhibit. But the explanation of it is that the quality involves no reference to anything else and so is one without any special emphasis, since it could not be otherwise; while reaction consists in the congress of two things, that might not come together, and every concurrence of them makes a distinct reaction. It will be found that the third category also has a mode of unity which does not belong to either of the others.

533. A quality of feeling does not in itself involve any reaction. But an experience of reaction does involve two qualities of feeling. It consists in the conjunction of two qualities of feeling; and in this conjunction those two qualities of feeling become more than mere qualities. In being thus set over against one another they acquire the concreteness and actuality of feelings. The one purple color absorbing the entire consciousness of our supposed being was a mere tone of life. But when a sudden change occurs setting two against one another, they become objects.

534. Although in all direct experience of reaction, an ego, a something within, is one member of the pair, yet we attribute reactions to objects outside of us. When we say that a thing exists, what we mean is that it reacts upon other things. †4 That we are transferring to it our direct experience of reaction is shown by our saying that one thing acts upon another. It is our hypothesis to explain the phenomena, — a hypothesis, which like the working hypothesis of a scientific inquiry, we may not believe to be altogether true, but which is useful in enabling us to conceive of what takes place.

535. Now if we ask ourselves what else we observe in every experience (taking experience in its broadest sense to include experience of ideal worlds and of the real world as we interpret its phenomena) besides qualities and reactions, the answer will readily come that there remain the regularities, the continuities, the significances. These are essentially of one kind. That continuity is only a variation of regularity, or, if we please so to regard it, that regularity is only a special case of continuity, will appear below, when we come to analyze the conception of continuity. It is already quite plain that any continuum we can think of is perfectly regular in its way as far as its continuity extends. No doubt, a line may be say an arc of a circle up to a certain point and beyond that point it may be straight. Then it is in one sense continuous and without a break, while in another sense, it does not all follow one law. But in so far as it is continuous, it everywhere follows a law; that is, the same thing is true of every portion of it; while in the sense in which it is irregular its continuity is broken. In short, the idea of continuity is the idea of a homogeneity, or sameness, which is a regularity. On the other hand, just as a continuous line is one which affords room for any multitude of points, no matter how great, †5 so all regularity affords scope for any multitude of variant particulars; so that the idea [of] continuity is an extension of the idea of regularity. Regularity implies generality; †6 and generality is an intellectual relation essentially the same as significance, as is shown by the contention of the nominalists that all generals are names. Even if generals have a being independent of actual thought, their being consists in their being possible objects of thought whereby particulars can be thought. Now that which brings another thing before the mind is a representation; so that generality and regularity are essentially the same as significance. Thus, continuity, regularity, and significance are essentially the same idea with merely subsidiary differences. That this element is found in experience is shown by the fact that all experience involves time. Now the flow of time is conceived as continuous. No matter whether this continuity is a datum of sense, or a quasi-hypothesis imported by the mind into experience, or even an illusion; in any case it remains a direct experience. For experience is not what analysis discovers but the raw material upon which analysis works. This element then is an element of direct experience.

536. It remains to be shown that this element is the third Kainopythagorean category. All flow of time involves learning; and all learning involves the flow of time. Now no continuum can be apprehended except by a mental generation of it, by thinking of something as moving through it, or in some way equivalent to this, and founded upon it. For a mere dull staring at a superficies does not involve the positive apprehension of continuity. All that is given in such staring is a feeling which serves as a sign that the object might be apprehended as a continuum. Thus, all apprehension of continuity involves a consciousness of learning. In the next place, all learning is virtually reasoning; that is to say, if not reasoning, it only differs therefrom in being too low in consciousness to be controllable and in consequently not being subject to criticism as good or bad, — no doubt, a most important distinction for logical purposes, but not affecting the nature of the elements of experience that it contains. In order to convince ourselves that all learning is virtually reasoning, we have only to reflect that the mere experience of a sense-reaction is not learning. That is only something from which something can be learned, by interpreting it. The interpretation is the learning. If it is objected that there must be a first thing learned, I reply that this is like saying that there must be a first rational fraction, in the order of magnitudes, greater than zero. There is no minimum time that an experience of learning must occupy. At least, we do not conceive it so, in conceiving time as continuous; for every flow of time, however short, is an experience of learning. It may be replied that this only shows that not all learning is reasoning, inasmuch as every train of reasoning whatever consists of a finite number of discrete steps. But my rejoinder is that if by an argument we mean an attempt to state a step in reasoning, then the simplest step in reasoning is incapable of being completely stated by any finite series of arguments. For every step in reasoning has a premiss, P, and a conclusion, C; and the reasoning consists in the perception that if P is found true as it has been found true, then must C be always or mostly true; and this "must" means that not only [is] C true (or probable) unless P is false (or not found true in the way supposed) but that every analogous premiss and conclusion are in the same relation. That is to say, in the reasoning we observe that P has a certain general character and C is related to it in a certain general way, and further that given any proposition whatever of that general character, the proposition related to it in that general way is true unless the former proposition is false; whence it necessarily follows of C and P, that either the former is true or the latter is false. But this is a second argument involved in the reasoning. For the first argument was P is true, Hence, C must be true; while the second argument is P has a general character P' and C has a relation r to P; But given any proposition having the character P', the proposition having the relation r to it is true unless the former is false; Hence, C is true unless P is false.

Thus, every reasoning involves another reasoning, which in its turn involves another, and so on ad infinitum. Every reasoning connects something that has just been learned with knowledge already acquired so that we thereby learn what has been unknown. It is thus that the present is so welded to what is just past as to render what is just coming about inevitable. The consciousness of the present, as the boundary between past and future, involves them both. Reasoning is a new experience which involves something old and something hitherto unknown. The past as above remarked is the ego. My recent past is my uppermost ego; my distant past is my more generalized ego. The past of the community is our ego. In attributing a flow of time to unknown events we impute a quasi-ego to the universe. The present is the immediate representation we are just learning that brings the future, or non-ego, to be assimilated into the ego. It is thus seen that learning, or representation, is the third Kainopythagorean category.

537. There are no more Kainopythagorean categories than these three. For the first category is nonrelative experience, the second is experience of a dyadic relation, and the third is experience of a triadic relation. It is impossible to analyze a triadic relation, or fact about three objects, into dyadic relations; for the very idea of a compound supposes two parts, at least, and a whole, or three objects, at least, in all. On the other hand, every tetradic relation, or fact about four objects can be analyzed into a compound of triadic relations. This can be shown by an example. Suppose a seller, S, sells a thing, T, to a buyer, B, for a sum of money, M. This sale is a tetradic relation. But if we define precisely what it consists in, we shall find it to be a compound of six triadic relations, as follows:

1st, S is the subject of a certain receipt of money, R, in return for the performance of a certain act As;

2nd, This performance of the act As effects a certain delivery, D, according to a certain contract, or agreement, C;

3rd, B is the subject of a certain acquisition of good, G, in return for the performance of a certain act, Ab;

4th, This performance of the act Ab effects a certain payment, P, according to the aforesaid contract C;

5th, The delivery, D, renders T the object of the acquisition of good G;

6th, The payment, P, renders M the object of the receipt of money, R. Or we may define a sale as the execution of contract of sale. The contract of sale has two clauses. The first clause provides for a giving and a receiving. The giving is by the seller of the commodity; the receiving is by the buyer of the same commodity. The second clause provides for a giving and a receiving. The giving is by the buyer of the price; the receiving is by the seller of the same price. The execution is of the first clause and of the second, etc. But I do not think this latter definition as good as the other, since it introduces several unnecessary elements and also covertly brings in four pentadic relations, such as the relation of the buyer to the first and second clauses of the contract and to the separate executions of them.

538. Let me now resume the argument. To begin with, it is to be remarked that I use the word "experience" in a much broader sense than it carries in the special sciences. For those sciences, experience is that which their special means of observation directly bring to light, and it is contrasted with the interpretations of those observations which are effected by connecting these experiences with what we otherwise know. But for philosophy, which is the science which sets in order those observations which lie open to every man every day and hour, experience can only mean the total cognitive result of living, and includes interpretations quite as truly as it does the matter of sense. Even more truly, since this matter of sense is a hypothetical something which we never can seize as such, free from all interpretative working over. Such being what is here meant by experience, my argument is of the utmost simplicity. It consists merely in begging the reader to notice certain phenomena which he will find, I believe, in every corner of experience and to draw the simplest generalizations from them. The first phenomenon that I ask him to observe is, that he can detect elements in experience which are whatever they are each in its own simplicity. Namely, he will perceive that this is true of colors, smells, emotions, tones of mood, the characteristic flavors, if I may use this expression, attaching to certain ideas. Look, for instance, on anything yellow. That yellow quality is not in itself, as that mere quality, to be explained by anything else, or defined in terms of anything else; nor does it involve or imply anything else. This is surely evident. True, we know by experiment that a yellow color can be produced by mixing green and red light. But the yellow, as a quality of feeling, involves no reference to any other color. Every quality of feeling, as such, is perfectly simple and irrespective of anything else. The second phenomenon that I ask the reader to observe is that there are in experience occurrences; and in every experience of an occurrence two things are directly given as opposed, namely, what there was before the occurrence, which now appears as an ego, and what the occurrence forces upon the ego, a non-ego. This is particularly obvious in voluntary acts; but it is equally true of reactions of sense. If the latter are intense, or violent, the sense of reaction is particularly strong. There is a certain quality of feeling here, a brute arbitrariness, as I may call it, though it cannot be described any more than yellow can be described. But it is not this quality of feeling to which I wish to direct attention as peculiar, but the actual taking place. This actual taking place essentially involves two things, what there was before and what the occurrence introduces. I ask the reader to remark that such an occurrence cannot possibly be resolved into qualities of feeling. For in the first place, a quality of feeling is, in itself, simple and irrespective of anything else; so that anything compound necessarily involves something besides a quality of feeling. Secondly, a quality is merely something that might be realized, while an occurrence is something that actually takes place. The character of brute exertion that attaches to every occurrence is, no doubt, a quality of feeling; but experience of the occurrence itself, is something else. Such an element of experience I term a reaction in order to emphasize its essentially dual character. Thirdly, a reaction has an individuality. It happens only once. If it is repeated, the repetition is another occurrence, no matter how like the first it may be. It is anti-general. A quality, on the other hand, has no individuality. Two qualities are different only so far as they are unlike. Individuality is an aggressive unity, arising from an absolute refusal to be in any degree responsible for anything else. This a quality cannot have since it is too utterly irrespective of anything else even to deny it. A reaction, on the other hand, is an opposition, or pairedness of objects that are existentially correlative, neither existing except by virtue of this opposition.

§2. Forms of Consciousness †7

539. I propose to review the ideas of the Nineteenth Century; and as an introduction to that review it will be well to glance at the general tendencies of the times in their influence upon human nature in general. In order to do that it will be convenient first to enumerate the departments of mental action.

540. Almost all the philosophers of this century have agreed to name Feeling, Knowledge, and Will, as the parts of the mind, or to speak more accurately as the three classes of states of mind. Few of those who make use of this enumeration pretend that it is exactly scientific; but it has served a good purpose. It is usually attributed to the Father of German philosophy, Immanuel Kant, who died in the last year of the last century. Kant borrowed it from his master Tetens; but in doing so he quite changed the boundaries of the department of Feeling. Take whatever is directly and immediately in consciousness at any instant, †8 just as it is, without regard to what it signifies, to what its parts are, to what causes it, or any of its relations to anything else, and that is what Tetens means by Feeling; and I shall invariably use the word in that same sense. For example, here we are in this pleasant room, sitting before the fire, listening to my reading. Now take what is in your consciousness at any one single moment. There is in the first place a general consciousness of life. Then, there is the collection of little skin-sensations of your clothes. Then, there is the sense of cheerfulness of the room. Then, there is a social consciousness, or feeling of sympathy with one another. Then, there is the light. Then, there is the warmth of the fire. Then, there is the sound of my voice, which in any one instant will merely be a note. In addition, there [are] a hundred things in the background of consciousness. This is the best way in which I can describe what is in your consciousness in a single moment. But it has taken me a considerable time to describe them. I cannot, therefore, have described them as they are in your mind; for precisely what I am trying to describe is the consciousness of a moment. By the very nature of language, I am obliged to pick them to pieces to describe them. This requires reflection; and reflection occupies time. But the consciousness of a moment as it is in that very moment is not reflected upon, and not pulled to pieces. As it is in that very moment, all these elements of feeling are together and they are one undivided feeling without parts. What I have described as elements of the feeling are not really parts of the feeling as it is in the very moment when it is present; they are what appears to have been in it, when we reflect upon it, after it is past. As it is felt at the moment itself these parts are not yet recognized, and therefore they do not exist in the feeling itself. I have assured myself that this is so, by frequent repetitions of the following experiment. Namely, sitting in a perfectly dark room with my eyes directed to a piece of paper upon which some pretty simple figure had been drawn, I knew not what, I have caused the paper to be instantaneously illuminated by a single electric spark. The spark was practically instantaneous; but the impression upon the retina would last nearly a quarter of a second. But I always found I had to sit reflecting for several seconds before I could tell at all what I had seen. Undoubtedly, the feeling was actually present for a good quarter of a second; and it was followed by a vivid memory that for some seconds was, I will not say nearly as intense as the feeling itself, but yet very perfect for a memory. But until I had had time to pick the memory to pieces, I found I could not say what I had seen. After experimenting in this way for some time, I became struck with the fact that there was, after all, conclusive proof of the thing, without the experiment. In the very moment of receiving an impression, it is impossible that we should say what the parts of it are, because in order that we should do that we must attend to one part and another separately, and to carry the attention from one part to another requires time. The third of a second is sufficient time for me to say that I have seen a light, not felt a jab; for some reflection can be accomplished in a third of a second, or much less. For in watching a pendulum swing over twenty millimetres with a scale of millimetres behind it, I can accurately observe the extreme point of the swing to a millimetre and estimate to a tenth part the fraction of the millimetre, although the pendulum is not there for a twentieth of a second. Now this requires reflection. So that it is proved that a not very simple reflection can be performed in the twentieth part of a second. But reflection cannot be performed instantaneously; and the evidence is quite satisfactory that the feeling of a moment cannot be at all analyzed in that moment. I trust then that I have made clear what I mean, and what Tetens meant by Feeling. It is the consciousness of a moment as it is in its singleness, without regard to its relations whether to its own elements or to anything else. Of course, this feeling although it can exist in a moment, can also be protracted for some time. For example, if we are close to an engine with a powerful whistle, and this suddenly shrieks, the intensity of it seems to paralyze me; and for several seconds my mind seems to have hardly anything in it but that shriek. Even when our thoughts are active, at each instant we have a feeling; and in the midst of changes of thought not a whole feeling but an element of feeling, which I shall also call a Feeling, may endure. Kant, in order to make the enumeration of Tetens fit into his own philosophical system, limited the word Feeling to feelings of pleasure and pain; and the majority of philosophical writers of this century have followed him in this. I think this has been unfortunate, and has hindered the perception of the real relations of [the] triad.

541. It may be asked where Tetens got his idea that Feelings, Cognitions or Knowledges, and Volitions or acts of willing made up the mind. I have never seen this question answered. Yet the answer is not far to seek. He took it from the ancient writers upon rhetoric. For they instruct the orator to begin his discourse by creating a proper state of feeling in the minds of his auditors, to follow this with whatever he has to address to their understandings, that is, to produce cognitions, and finally to inflame them to action of the will. For the rhetoricians, therefore, the triad names three states of mind; and most of the psychologists of our century have considered Feeling, Cognition, and Volition to be three general states of mind. †9

542. But in my opinion, by a slight modification the triad may be made to stand for three radically different kinds of elements of all consciousness, the only elements of consciousness, which are respectively predominant in the three whole states of mind which are usually called Feeling, Knowing, and Willing. It is thus raised from a mere loose grouping into a scientific and fundamental analysis of the constituents of consciousness.

543. The modification which I propose relates to the department to which Sensation is to be assigned. It will be best to explain what I mean by sensation. If you look at a flame, you observe that it is orange, and that orange color as it was seen on that particular occasion and was attributed to a reality then and there before you, and not called up in memory, was a sensation. So if you hear a cry, whether it is real or a hallucination, if you take it for a reality then and there present, every vowel and consonant of it is a separate sensation. But if it is only called up by your own act of imagination it is not a sensation. A sensation is not a feeling; but an element of feeling is one part of it. Here is a little bottle with some green spicular crystals in it. When I look at it, I experience a sensation of greenness. Were that greenness to fill my whole field of vision, while I became momentarily deaf, lost my skin-sensations, and my memory, it would be a total feeling. For it would be my life for the moment, and would not be attributed to anything in particular without me or within me. As it is, it is an element of my feeling while I am looking at the bottle. But to make up the sensation, along with this feeling there is a consciousness of being irresistibly compelled to see it when I look at it. I cast my eyes upon it, without any intention of imagining such a thing, and there it is more vivid than any imagination could be. The sight forces itself upon me. The sensation has two parts: first, the feeling, and second, the sense of its assertiveness, of my being compelled to have it. The consequence is that remembering a sensation is not at all the same thing as having it. For though there is some vestige of compulsiveness, even in the memory, it is not at all comparable to the compulsiveness of the actual sensation. But if I remember, or imagine a feeling, whatever I remember or imagine is a feeling, and I cannot remember or imagine or anywise represent to myself a feeling without having that very feeling then and there. All the existence a feeling can have is had the moment it is thought. But a sensation is not had until I am really acted upon by something out of my control. I have, thus, made clear, I hope, what I mean by a sensation. It is an event which has to happen at a particular moment. For that reason there is great need of a verb to correspond with the noun; and I shall use the expression to sense the greenness. It translates the German verb empfinden. The verb to feel is quite superfluous; for to think a feeling at all is to feel it. But the verb to sense is indispensable, because to actually sense a sensation is very different from remembering or imagining it. Now, it is usual to put sensation under the head of Knowledge. This may or may not be correct language; I do not propose to be led into any verbal dispute. But I refuse to classify sensation in that way, because I aim to enumerate the different kinds of elements of consciousness. Now, sensation contains two radically different kinds of consciousness. One part is feeling and the other part is the consciousness of being compelled to feel upon that particular occasion. This consciousness of compulsion has a general resemblance to the consciousness of willing. Willing is the consciousness of exerting a force upon something without the consciousness, or at least outside of that part of consciousness. But the consciousness of exerting force and the consciousness of suffering the effect of a force are one and inseparable. Suppose I try to exercise my strength in lifting a huge dumb-bell. If I strive to lift it, I feel that it is drawing my arm down. If I suffer no consciousness of having my arm pulled down, I can have no consciousness of exerting force in lifting the dumb-bell. To be conscious of exerting force and to be conscious [of] having force used upon me are the same consciousness. Hence, the compulsive element of sensation must be classed along with the consciousness of willing. Both are particular events which must happen at definite times; and to dream of exercising the will is as different from actually willing as dreaming of a sensation is from actually sensing. Feeling is neither over against me nor in me. If I have any momentary consciousness of self, that is a part of the feeling. So that I am, or at any rate my immediate self-consciousness is, a part of my total feeling. Any element of feeling has the same relation to self-consciousness that it has to any other element of the same total feeling; that is to say, it is quite independent of it. An element of Feeling is neither a part of self-consciousness nor is set up over against self-consciousness. But the consciousness of compulsion in sensation as well as the consciousness of willing necessarily involves self-consciousness and also the consciousness of some exterior force. The self and the not-self are separated in this sort of consciousness. The sense of reaction or struggle between self and another is just what this consciousness consists in. Hence, to give it a name, I propose to call it altersense. To avoid circumlocution, I will speak of the altersense element of sensation, as Sensation simply. Thus, Altersense has two varieties, Sensation and Will. The difference between them is that Sensation is an event in which a feeling is forced upon the mind; while Volition or Willing, is an event in which a desire is satisfied, that is, an intense state of feeling is reduced. In Sensation, a feeling is forced upon us; in Willing, feeling forces its way out from us.

544. The removal of sensation from the department of cognition, or Knowledge, leaves nothing remaining in that department except what are called Mediate Cognitions, that is, Knowledges through some third idea or process different from either the Knowing self or the Known object. For the sake of giving this Mediate Cognition, or rather the peculiar kind of element of consciousness it involves a single name, I will call it medisense, that is, the consciousness of a middle term, or process, by which something not-self is set up over against the consciousness. All consciousness of a process belongs to this medisense. It has several varieties. In the first place there is a separative process, the centrifugal tendency of thought, by which any idea by following out its own development becomes separated from those with which it is connected. We see this in attention. When we see the little bottle with green crystals, the green idea detaches itself from the remaining ideas, the spicular form, the being bunched together in a little tube, etc. and leads to a thought which is accurately expressed by the sentence "these crystals are green," where the green stands off from the remaining ideas which remain confused together. It is the liveliness of the green idea which brings this about. And in all cases it is the idea which has vigor which spontaneously detaches itself from the rest. We may call this variety of medisense by the name of Abstraction.

545. Before I go further, there are one or two points which require explanation. Everybody knows that recollections gradually become "dim"; and also that attention makes Feelings "vivid," which before attention was applied to them were relatively "dim." This does not mean that we recollect a bright color as a dull color, or a loud sound as a faint sound; nor that attention makes an olive color seem an apple green or a whisper seem to be a bellow. It is several years since I was at Niagara Falls; but I have no doubt my recollection of the roar is of its being about as loud as it really is. I remember when I returned from a long absence, I found my old room was much smaller than I had recollected it. The first cup of coffee I tasted more than fifty years ago seems to me of a higher flavor than any coffee in the world really is. Though my imagination is very much the reverse of a vivid one, I can carry colors in my mind with more than usual accuracy. Dim as my imaginations and memories are, they do not represent high colors by low colors. We must say then that feelings have two kinds of intensity. One is the intensity of the feeling itself, †10 by which loud sounds are distinguished from faint ones, luminous colors from dark ones, highly chromatic colors from almost neutral tints, etc. The other is the intensity of consciousness that lays hold of the feeling, which makes the ticking of a watch actually heard infinitely more vivid than a cannon shot remembered to have been heard a few minutes ago. I shall not stop to discuss the difficult question of what the distinction between those two kinds of intensity consists in, about which three or four opinions are held. I shall simply say that in my opinion the first kind of intensity, distinguishing bright colors from dim ones, is the intensity of feeling-consciousness; while the second kind, distinguishing sensation from imagination, is the intensity of altersense or of the assertiveness of the feeling. I shall call this second vividness.

546. Now, in order that you may understand what I am about to say, I must tell you about some experiments which I have conducted. †11 They have been several times repeated. But each series of experiments lasted for from three to five weeks, at a time when the weather was steady and my health or that of the subject of experiment was good; and I or he, as the case might be, took pains to lead a regular, cheerful life without agitation. The experiments would last for an hour, in some series for an hour and a half, at the same time every day. Extraordinary precautions were taken to have all the mental influences, light, warmth, etc. precisely the same every day, and the same throughout the time of experimentation. The attention would be exercised for seven minutes, in some series for ten; and then five minutes, sometimes three minutes, rest would be taken of just the same kind, generally a little conversation about the experiments. A habit was acquired of making two different efforts of attention of just the same degree of effort of attention at every experiment. One of these would be a very light effort, the other a vigorous one. I did not assume that these two degrees of attention would remain exactly the same throughout the month, but I did assume, first, that they would not change extravagantly, and second, that if, say, six or eight kinds of experiments were made, each ten times every day, then on the average of the whole month, the degree of effort made would be the same in one kind of experiment as in another, especially when the subject could not tell which were which. In that way, I was able to produce a fixed average intensity of attention. That attention was directed to certain differences of sensation. The sensations were of two general kinds in different series, some being colors and others sensations of pressure. In each case, there was a very carefully devised apparatus for producing the precise sensations desired, and for measuring them. I may mention that my color-box cost me $2000. The pressure apparatus was cheap; but there no conceivable refinement was left out of account. I have mentioned that the sensations were measured. Now many psychologists deny that sensation can be measured. That is because they are not mathematicians, and are unacquainted with the mathematical theory of measurement; of which they have the crudest notions. I repeat that the sensations were scientifically measured, and on such a scale that zero meant no sensation. To show how accurate they were I may say that a piece of specially selected fuzzy black paper much blacker than black velvet was found to be 30 measurable degrees from absolute blackness. To get absolute blackness a closet about ten feet by ten was constructed and painted with lamp black in the inside. This was placed in a large hall with little light in it. Then, a small hole about the size of a cent in the thin wall of the closet when looked at from the outside appeared to be absolutely black. Now the experiments would be like this. The subject would put his eye to the eye-piece of the color-box and would see a small rectangle which at first sight would appear to be all one color. inline image But after an effort of attention continuing from 5 seconds to a minute, he would see that it was not all one color, that it was sharply divided into two parts whose colors were different. inline image One part might be a very little yellower than the other. After he had exerted his attention for a certain number of seconds, the whole would disappear and he would tell a second person, the operator, what he thought he had seen, and would also give a number marking his degree of confidence that he had seen it. The operator would record the result, in absolute silence without the slightest sign and without being seen. A tap mechanically made of precisely the same intensity would inform the subject that another rectangle was to be seen, and he would say "tp" when he put his eye to the eyepiece. I need not describe exactly how the pressure-experiments were made. †12 As a result there would be several thousand experiments showing the effect of two degrees of attention exerted for several different lengths of time upon discriminating between sensations differing by several known amounts. The results of experiments would all be expressed in two sets [of] numbers, one showing the percentage of errors and the other the feeling of confidence, in the attempts at discrimination under different circumstances. Those numbers were then subjected to mathematical discussion, according to the established principles of such work; and from them a law was deduced. It was found that the feeling of confidence did not begin to show itself at all until the real power of discrimination had reached a considerable strength. There were a very large number of cases in which the confidence was zero, so that the answers given appeared to the subject to be mere random guesses. Yet a decided majority of them were, in all cases, correct. It was also found that during the period of attention, the difference of sensation was continually increasing in vividness. Sensations that differed less, no matter how little, could still be discriminated just as well as sensations that differed more, if the effort of attention were greater, or if it were longer continued. The law was so accurately fulfilled, that it was safe to infer that the point at which infinite attention would be required for the slightest preponderance of right answers over wrong ones was just the point where the two sensations differed not at all. The difference of sensation for the discrimination of which no attention whatever would be required appeared to be infinite; though this result was less certain than the other.

547. The general upshot of all these experiments, together with others which I have not time to describe, was that when you ask yourself what is in your mind at any moment, and give yourself an answer, even after a searching scrutiny of the field of consciousness, you have not begun to tell yourself the whole truth. For it is one thing to feel a thing and it is another thing to have a reflex feeling, that there is a feeling; and my experiments conclusively show that the consciousness must reach a considerable vividness before the least reflex feeling of it is produced. That it is really felt is shown by the fact that a greater effort of attention would detect it. There is as it were, an upper layer of consciousness to which reflex consciousness, or self-consciousness, is attached. A moderate effort of attention for a second or two only brings a few items into that upper layer. But all the time the attention lasts, thousands of other ideas, at different depths of consciousness, so to speak, that is, literally, of different degrees of vividness, are moving upwards. These may influence our other thoughts long before they reach the upper layer of reflex consciousness. There are such vast numbers of ideas in consciousness of low degrees of vividness, that I think it may be true, — and at any rate is roughly true, as a necessary consequence of my experiments, — that our whole past experience is continually in our consciousness, though most of it sunk to a great depth of dimness. I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way. But in this water there are countless objects at different depths; and certain influences will give certain kinds of those objects an upward impulse which may be intense enough and continue long enough to bring them into the upper visible layer. After the impulse ceases they commence to sink downwards. †13

548. I have spoken †14 of the first kind of medisense, abstraction, which breaks one idea away from another. There is an opposite influence by which when one idea has its vividness increased it gives an upward impulse to a number of other ideas with which it is connected so that it forms one set with them. The law of this is often called the law of the association of ideas. That is well enough. But it is inaccurate to call this phenomenon association, as Germans especially often do. Association is a different thing. †15 More accurate German writers call the action of which we are now speaking reproduction. But even that is not free from objection. For the idea which receives an upward impulse, making it grow more vivid, was not necessarily ever so near the surface of consciousness before; or if it was, that circumstance has nothing to do with it. It is a great mistake to suppose that ideas only become associated into sets in the upper layer of consciousness, although such action is more lively there. Most English and American psychologists of today use the term Reproduction; but I prefer the older English word Suggestion, to which some of the very best writers still adhere. The only objection to it is that the word is used in another sense in reference to the phenomena of hypnotism.

549. What takes place in suggestion is that an idea when it rises gives an upward motion to all other ideas belonging to the same set. For example, if the idea of husband is mentioned, since husband and wife form a set, the idea of wife will receive an upward motion and a few minutes later when fatigue has caused the husband idea to commence sinking, that is to become dim, the wife idea will be uppermost. I will some other day talk to you about this action of suggestion.

550. At present I hurry on to the third form of medisense which is that of the formation of sets of ideas, or association proper. A great many associations of ideas are inherited. Others grow up spontaneously. The rest depend upon the principle that ideas once brought together into a set remain in that set. Many associations are merely accidental. A child acquires a distaste for a particular kind of food merely because it ate it when it was sick. The idea of that food and the feeling of sickness are brought into a set; and the consequence is that every time the idea of that food reaches a high degree of vividness, the feeling of sickness gets a swift upward motion. Other associations cannot be called accidental because it was in the nature of things that they should appear in sets. Thus, light and warm get associated in our minds because they are associated in Nature.

551. There are no other forms of consciousness except the three that have been mentioned, Feeling, Altersense, and Medisense. They form a sort of system. Feeling is the momentarily present contents of consciousness taken in its pristine simplicity, apart from anything else. It is consciousness in its first state, and might be called primisense. Altersense is the consciousness of a directly present other or second, withstanding us. Medisense is the consciousness of a thirdness, or medium between primisense and altersense, leading from the former to the latter. It is the consciousness of a process of bringing to mind. Feeling, or primisense, is the consciousness of firstness; altersense is consciousness of otherness or secondness; medisense is the consciousness of means or thirdness. Of primisense there is but one fundamental mode. Altersense has two modes, Sensation and Will. Medisense has three modes, Abstraction, Suggestion, Association. †16

552. The only element of the mind that this enumeration omits is the phenomenon of Fatigue. It is a highly important matter. Our mental life and health depend to a far greater extent than would at first be guessed upon the action of fatigue. But it finds no place in this system. The only defence that I can offer for this is that there is no direct consciousness of fatigue. Whether that is an adequate excuse or not, I am not yet quite decided.

§3. Consciousness and Reasoning †17

553. We are going to shock the physiological psychologists, for once, by attempting, not an account of a hypothesis about the brain, but a description of an image which shall correspond, point by point, to the different features of the phenomena of consciousness. Consciousness is like a bottomless lake in which ideas are suspended at different depths. †18 Indeed, these ideas themselves constitute the very medium of consciousness itself. †19 Percepts alone are uncovered by the medium. We must imagine that there is a continual fall of rain upon the lake; which images the constant inflow of percepts in experience. All ideas other than percepts are more or less deep, and we may conceive that there is a force of gravitation, so that the deeper ideas are, the more work will be required to bring them to the surface. This virtual work, which the mathematicians call the 'potentials' of the particles, is the negative of the 'potential energy'; and the potential energy is that feature of the image which corresponds to the degree of vividness of the idea. Or we may see that the potential, or depth, represents the degree of energy of attention that is requisite to discern the idea at that depth. But it must not be thought that an idea actually has to be brought to the surface of consciousness before it can be discerned. To bring it to the surface of consciousness would be to produce a hallucination. Not only do all ideas tend to gravitate toward oblivion, but we are to imagine that various ideas react upon one another by selective attractions. This images the associations between ideas which tend to agglomerate them into single ideas. Just as our idea of spatial distance consists in the sense of time that it would take with a given effort to pass from one object to another, so the distance between ideas is measured by the time it will take to unite them. One tries to think of the French for shark or for linchpin. The time that it will take to recover the forgotten word depends upon the force of association between the ideas of the English and French words and upon circumstances which we image by their distance. This, it must be confessed, is exceedingly vague; as vague as would be our notion of spatial distance if we lived in the body of an ocean, and were destitute of anything rigid to measure with, being ourselves mere portions of fluid.

554. Consciousness is rather like a bottomless lake in which ideas are suspended, at different depths. Percepts alone are uncovered by the medium. The meaning of this metaphor is that those which [are] deeper are discernible only by a greater effort, and controlled only by much greater effort. These ideas suspended in the medium of consciousness, or rather themselves parts of the fluid, are attracted to one another by associational habits and dispositions, — the former in association by contiguity, the latter in association by resemblance. An idea near the surface will attract an idea that is very deep only so slightly that the action must continue for some time before the latter is brought to a level of easy discernment. Meantime the former is sinking to dimmer consciousness. There seems to be a factor like momentum, so that the idea originally dimmer becomes more vivid than the one which brought it up. In addition, the mind has but a finite area at each level; so that the bringing of a mass of ideas up inevitably involves the carrying of other ideas down. Still another factor seems to be a certain degree of buoyancy or association with whatever idea may be vivid, which belongs to those ideas that we call purposes, by virtue of which they are particularly apt to be brought up and held up near the surface by the inflowing percepts and thus to hold up any ideas with which they may be associated. The control which we exercise over our thoughts in reasoning consists in our purpose holding certain thoughts up where they may be scrutinized. The levels of easily controlled ideas are those that are so near the surface as to be strongly affected by present purposes. The aptness of this metaphor is very great.

555. If the question is asked in what the processes of contemplation and of fixation of the attention consist, this question being psychological, it is necessary, before answering it, to describe some phenomena of the mind. Be it known, then, that consciousness, or feeling, has been ascertained by careful observations mathematically discussed to have the properties now to be stated. †20 Feeling, by which is here meant that of which we are supposed to be immediately conscious, is subject to degrees. That is to say, besides the objective intensity which distinguishes a loud sound from a faint sound, there is a subjective intensity which distinguishes a lively consciousness of a sound, from a dull consciousness of it. Though the two kinds of intensity are apt to go together, yet it is possible for a person at the same time to recall the tick of a watch and the sound of a neighboring cannon, and to have a livelier consciousness of the former than of the latter, without however remembering the latter [as] a fainter sound than the former. Feelings of slight subjective intensity act upon one another, undergo transformations, and affect the emotions and the voluntary actions; although they do all this less decisively than they would do if they were more intense. They are also, other things being equal, much less under control than more subjectively intense feelings. This remark needs explanation. A feeling may be forced upon the mind through the senses, or by experience, directly or indirectly, and bear down the power of the will; and those feelings are the most subjectively intense we have. Why they should be so, will soon be explained. †21 But when a feeling is not thus forced upon us our being conscious of it sufficiently to attract attention makes it act more upon us, and at the same time enables us to affect its transformations, more than if it were scarcely perceptible. Now there are certain combinations of feelings which are specially interesting. These are those which tend toward a reaction between mind and body, whether in sense, in the action of the glands, in contractions of involuntary muscles, in coördinated voluntary deeds, or, finally, in discharges of an extraordinary kind of one part of the nerves upon another. Interesting combinations of ideas are more active than others, both in the way of suggestion, and in the way of subjective intensity. The action of thought is all the time going on, not merely in that part of consciousness which thrusts itself on the attention, and which is the most under discipline, but also in its deeply shaded parts, of which we are in some measure conscious but not sufficiently so to be strongly affected by what is there. But when in the uncontrolled play of that part of thought, an interesting combination occurs, its subjective intensity increases for a short time with great rapidity. †22 This is what constitutes the fixation of the attention. Contemplation consists in using our self-control to remove us from the forcible intrusion of other thoughts, and in considering the interesting bearings of what may lie hidden in the icon, so as to cause the subjective intensity of it to increase.

556. The observation of the icon may be ordinary direct observation, or it may be scientific observation aided by the apparatus of logical algebra and other technical means.

557. A third step in inference is performed upon the indices. Thus, an index may be dropped from consideration. If there are two selective indices, one universal, the other particular, and the latter selection is made last, the order of the selections can be reversed. But all these changes in the indices are justified only by considering icons. We may, therefore, say that excepting the colligation of different beliefs the whole of inference consists in observation, namely in the observation of icons. Even the colligations well up from the depths of consciousness in precisely the same manner as that in which the special features of icons are remarked.

558. Thus, all knowledge comes to us by observation, part of it forced upon us from without from Nature's mind and part coming from the depths of that inward aspect of mind, which we egotistically call ours; though in truth it is we who float upon its surface and belong to it more than it belongs to us. Nor can we affirm that the inwardly seen mind is altogether independent of the outward mind which is its Creator.

§4. What is the Use of Consciousness? †23

559. In the last chapter, †24 I assumed the reader would occupy the position of Common Sense, which makes the real things in this world blind unconscious objects working by mechanical laws together with a consciousness as idle spectator. I pointed out that this spectator cannot have part or lot even in the intelligence and purpose of the business; for intelligence does not consist in feeling intelligently but in acting so that one's deeds are concentrated upon a result.

560. This makes the universe a muddle. According to it consciousness is perfectly impotent and is not the original of the material world; nor on the other hand can material forces ever have given birth to feeling, for all they do is to accelerate the motions of particles. Nay, that they should so much as give rise to sensations in that consciousness is more than incomprehensible, it is manifestly impossible. There is no room for reaction between mind and matter. The only consistent position for such a philosophy is flatly to deny that there is any such thing as consciousness. Even were that denial made, the question would be insoluble — not for us merely, but in its own nature, — how all the laws of mechanics came about, or why they should have the curious relationships they exhibit. Then, were that impossibility disregarded, just look out of your window, reader, and see this world in all its infinite manifoldness, and say whether you are content to take it wholly unaccounted for, as something that always has been, and always has been as complex as it is now. For mechanical forces never produce any new diversity, but only transform one diversity into another diversity.

561. The whole of this suicide of Common Sense results from its incautious assumption that it is one thing to look red or green and another thing to see red or green. Now metaphysicians never have agreed, or at least never have perceived that they agreed, about anything; but I believe that every man who has ever reflected deeply about knowledge has come to the conclusion that there is something wrong about that assumption. †25

562. Grant that that assumption is somehow wrong, though we may not, at first, see how exactly, and the muddle begins to clarify itself. The spectator is no longer on one side of the footlights, and the world on the other. He is, in so far as he sees, at one with the poet of the piece. To act intelligently and to see intelligently become at bottom one. And in the matter of auditing the account of the universe, its wealth and its government, we gain the liberty of drawing on the bank of thought.

563. This method promises to render the totality of things thinkable; and it is plain there is no other way of explaining anything than to show how it traces its lineage to the womb of thought.

564. This is what is called Idealism. As soon, however, as we seek preciser statement, difficulties arise, — by no means insuperable ones, yet calling for patient study based upon a thorough understanding of logic. All this must be postponed. Yet one very obvious and easily answered objection may be noticed. It will be said that the identification of knowledge and being threatens to deprive us of our Ignorance and Error. Let me hasten to swear that no act of mine shall lay hands on those sacramenta.

§5. Synechism and Immortality †26

565. The word synechism is the English form of the Greek {synechismos}, from {synechés}, continuous. †27 For two centuries we have been affixing -ist and -ism to words, in order to note sects which exalt the importance of those elements which the stemwords signify. Thus, materialism is the doctrine that matter is everything, idealism the doctrine that ideas are everything, dualism the philosophy which splits everything in two. In like manner, I have proposed to make synechism mean the tendency to regard everything as continuous. †28

566. For many years I have been endeavoring to develope this idea, and have, of late, given some of my results in the Monist. †29 I carry the doctrine so far as to maintain that continuity governs the whole domain of experience in every element of it. Accordingly, every proposition, except so far as it relates to an unattainable limit of experience (which I call the Absolute,) is to be taken with an indefinite qualification; for a proposition which has no relation whatever to experience is devoid of all meaning.

567. I propose here, without going into the extremely difficult question of the evidences of this doctrine, to give a specimen of the manner in which it can be applied to religious questions. I cannot here treat in full of the method of its application. It readily yields corollaries which appear at first highly enigmatic; but their meaning is cleared up by a more thoroughgoing application of the principle. This principle is, of course, itself to be understood in a synechistic sense; and, so understood, it in no wise contradicts itself. Consequently, it must lead to definite results, if the deductions are accurately performed.

568. Thoroughgoing synechism will not permit us to say that the sum of the angles of a triangle exactly equals two right angles, but only that it equals that quantity plus or minus some quantity which is excessively small for all the triangles we can measure. †30 We must not accept the proposition that space has three dimensions as certainly strictly accurate; but can only say that any movements of bodies out of the three dimensions are at most exceedingly minute. We must not say that phenomena are perfectly regular, but only that the degree of their regularity is very high indeed.

569. There is a famous saying of Parmenides {esti gar einai, méden d' ouk einai}, "being is, and not-being is nothing." This sounds plausible; yet synechism flatly denies it, declaring that being is a matter of more or less, so as to merge insensibly into nothing. How this can be appears when we consider that to say that a thing is is to say that in the upshot of intellectual progress it will attain a permanent status in the realm of ideas. Now, as no experiential question can be answered with absolute certainty, so we never can have reason to think that any given idea will either become unshakably established or be forever exploded. †31 But to say that neither of these two events will come to pass definitively is to say that the object has an imperfect and qualified existence. Surely, no reader will suppose that this principle is intended to apply only to some phenomena and not to others, — only, for instance, to the little province of matter and not to the rest of the great empire of ideas. Nor must it be understood only of phenomena to the exclusion of their underlying substrates. Synechism certainly has no concern with any incognizable; but it will not admit a sharp sundering of phenomena from substrates. That which underlies a phenomenon and determines it, thereby is, itself, in a measure, a phenomenon.

570. Synechism, even in its less stalwart forms, can never abide dualism, properly so called. It does not wish to exterminate the conception of twoness, nor can any of these philosophic cranks who preach crusades against this or that fundamental conception find the slightest comfort in this doctrine. But dualism in its broadest legitimate meaning as the philosophy which performs its analyses with an axe, leaving as the ultimate elements, unrelated chunks of being, this is most hostile to synechism. In particular, the synechist will not admit that physical and psychical phenomena are entirely distinct, — whether as belonging to different categories of substance, or as entirely separate sides of one shield, — but will insist that all phenomena are of one character, though some are more mental and spontaneous, others more material and regular. Still, all alike present that mixture of freedom and constraint, which allows them to be, nay, makes them to be teleological, or purposive.

571. Nor must any synechist say, "I am altogether myself, and not at all you." If you embrace synechism, you must abjure this metaphysics of wickedness. In the first place, your neighbors are, in a measure, yourself, and in far greater measure than, without deep studies in psychology, you would believe. Really, the selfhood you like to attribute to yourself is, for the most part, the vulgarest delusion of vanity. In the second place, all men who resemble you and are in analogous circumstances are, in a measure, yourself, though not quite in the same way in which your neighbors are you.

572. There is still another direction in which the barbaric conception of personal identity must be broadened. A Brahmanical hymn begins as follows: "I am that pure and infinite Self, who am bliss, eternal, manifest, all-pervading, and who am the substrate of all that owns name and form." This expresses more than humiliation, — the utter swallowing up of the poor individual self in the Spirit of prayer. All communication from mind to mind is through continuity of being. A man is capable of having assigned to him a rôle in the drama of creation, and so far as he loses himself in that rôle, — no matter how humble it may be, — so far he identifies himself with its Author.

573. Synechism denies that there are any immeasurable differences between phenomena; and by the same token, there can be no immeasurable difference between waking and sleeping. When you sleep, you are not so largely asleep as you fancy that you be.

574. Synechism refuses to believe that when death comes, even the carnal consciousness ceases quickly. How it is to be, it is hard to say, in the all but entire lack of observational data. Here, as elsewhere, the synechistic oracle is enigmatic. Possibly, the suggestion of that powerful fiction "Dreams of the Dead," recently published, †32 may be the truth.

575. But, further, synechism recognizes that the carnal consciousness is but a small part of the man. There is, in the second place, the social consciousness, by which a man's spirit is embodied in others, and which continues to live and breathe and have its being very much longer than superficial observers think. Our readers need not be told how superbly this is set forth in Freytag's Lost Manuscript. †33

576. Nor is this, by any means, all. A man is capable of a spiritual consciousness, which constitutes him one of the eternal verities, which is embodied in the universe as a whole. This as an archetypal idea can never fail; and in the world to come is destined to a special spiritual embodiment.

577. A friend of mine, in consequence of a fever, totally lost his sense of hearing. He had been very fond of music before his calamity; and, strange to say, even afterwards would love to stand by the piano when a good performer played. So then, I said to him, after all you can hear a little. Absolutely not at all, he replied; but I can feel the music all over my body. Why, I exclaimed, how is it possible for a new sense to be developed in a few months! It is not a new sense, he answered. Now that my hearing is gone I can recognize that I always possessed this mode of consciousness, which I formerly, with other people, mistook for hearing. In the same manner, when the carnal consciousness passes away in death, we shall at once perceive that we have had all along a lively spiritual consciousness which we have been confusing with something different.

578. I have said enough, I think, to show that, though synechism is not religion, but, on the contrary, is a purely scientific philosophy, yet should it become generally accepted, as I confidently anticipate, it may play a part in the onement of religion and Science.

§6. Consciousness and Language †34

579. Philosophy is the attempt, — for as the word itself implies it is and must be imperfect — is the attempt to form a general informed conception of the All. All men philosophize; and as Aristotle says we must do so if only to prove the futility of philosophy. Those who neglect philosophy have metaphysical theories as much as others — only they [have] rude, false, and wordy theories. Some think to avoid the influence of metaphysical errors, by paying no attention to metaphysics; but experience shows that these men beyond all others are held in an iron vice of metaphysical theory, because by theories that they have never called in question. No man is so enthralled by metaphysics as the totally uneducated; no man is so free from its dominion as the metaphysician himself. Since, then, everyone must have conceptions of things in general, it is most important that they should be carefully constructed.

580. I shall enter into no criticism of the different methods of metaphysical research, but shall merely say that in the opinion of several great thinkers, the only successful mode yet lighted upon is that of adopting our logic as our metaphysics. In the last lecture, †35 I endeavored to show how logic furnishes us with a classification of the elements of consciousness. We found that all modifications of consciousness are inferences and that all inferences are valid inferences. At the same time we found that there were three kinds of inference: 1st, Intellectual inference with its three varieties Hypothesis, Induction and Deduction; 2nd, Judgments of sensation, emotions, and instinctive motions which are hypotheses whose predicates are unanalyzed in comprehension; and 3rd, Habits, which are Inductions whose subjects are unanalyzed in extension. This division leads us to three elements of consciousness: 1st, Feelings or Elements of comprehension; 2nd, Efforts or Elements of extension; and 3rd, Notions or Elements of information, †36 which is the union of extension and comprehension. I regret that the time does not permit me to dwell further upon this theory; but I wish to pass to a loftier and more practical question of metaphysics in order to put in a still stronger light the advantages of the study of logic. The question which I shall select is "what is man?" I think I may state the prevalent conception thus: Man is essentially a soul, that is, a thing occupying a mathematical point of space, not thought itself but the subject of inhesion of thought, without parts, and exerting a certain material force called volition. I presume that most people consider this belief as intuitive, or, at least, as planted in man's nature and more or less distinctly held by all men, always and everywhere. †37 On the contrary, the doctrine is a very modern one. All the ancients and many of the scholastics, held that man is compact of several souls; three was the usual number assigned, sometimes two, four, or five. Every attentive reader of St. Paul is aware that according to him, man has a threefold being. We derive the notion of the soul's being single from Descartes. But with him, thought itself makes the man; whereas with us consciousness is not the man but is in man. Descartes, also, does not admit that the will of man exerts any force upon matter; as we mostly believe. In fact, the prevalent view of the present day is a heterogeneous hodgepodge of the most contradictory theories; its doctrines are borrowed from different philosophers while the premisses by which alone those philosophers were able to support their doctrines are denied; the theory thus finds itself totally unsupported by facts and in several particulars at war with itself. And this is admitted by most of those who have subjected it to rigid criticism. †38

581. One source of all this diversity of opinion, has been the want of an accurate discrimination between an inductive and a hypothetic explanation of the facts of human life. We have seen that every fact requires two kinds of explanation; the one proceeds by induction to replace its subject by a wider one, the other proceeds by hypothesis to replace its predicate by a deeper one. †39 We have seen that these two explanations never coincide, that both are indispensable, and that quarrels have sprung up even in physical science where there are so few disagreements in consequence of trying to make one theory perform both functions. Let us take care that we do not confound these two separate inquiries in reference to the soul. The hypothetic explanation will inform us of the causes or necessary antecedents of the phenomena of human life. These phenomena may be regarded internally or externally. Regarded internally they require an internal explanation by internal necessary antecedents, that is by premisses; and this explanation was given in the last lecture. If they are regarded externally or physically they require a physical explanation by physical antecedents, and this inquiry must be turned over unreservedly to the physiologists. They will find the truth of the matter, and we may rest satisfied that no explanation which is based squarely upon legitimate hypothesis from the facts of nature, can possibly conflict with a purely inductive explanation of man. It is true that the question for the physiologist is what are the physical antecedents of man's actions, that is what sort of an automaton is man; so that it is assumed as the condition of the problem that man is an automaton. For, automatism in this connection, consciousness being of course admitted, means nothing but regular physical antecedence; — implies only that nature is uniform; and this as we have seen is not a mere law of nature or fact of observation, but is a postulate of all thought, which no man consistently or persistently denies. †40 Yet this automatism seems, no doubt, to many to conflict with the notion of man as a RESPONSIBLE and IMMORTAL soul. But, then, we should remember that in our minds, the essential conceptions of responsibility and immortality are covered over with a mass of parasitical reflection derived from every philosophy and every religion of past time; so that if we cannot reconcile the doctrines of responsibility and immortality with the postulates of thought or with themselves, this is sufficiently accounted for by the obscurity and confusion of our notions on this subject, and we are by no means forced to adopt that which is the only other alternative and say that these doctrines are essentially false. These doctrines are a part of our religion; and one [of] them — if not both — are among its most precious consolations, which it would be difficult indeed to wring from the breast of a people which has entertained them for a thousand years. Talk as they please, of the weariness of unceasing day, of the balm of an eternal sleep, of the nobility lent to humanity by regarding it as capable of struggling and suffering for that which transcends its own responsibility and life-time; we still cling by nature original or acquired, to the dear hopes of our ancient religion. But while I have thought it proper to dwell for a moment upon the possibility of our being unable to reconcile responsibility and immortality with physical necessity, I must add that in fact we are not driven to that point, at all. On the contrary the philosophers of the Brownist school have shown uncontrovertibly that they are capable of being reconciled, and their arguments are very forcibly stated in an American work called Liberty and Necessity, written by Judge [Henry] Carleton of Louisiana and published in Philadelphia in 1857. There may be other modes of reconciling these conceptions †41 besides that which they have pointed out but still they have shown that a rational reconciliation is possible.

582. Thus, the hypothetic explanation of human nature stands by itself and will present no contradiction to the inductive explanation, which is what we desire when we ask what is man? To what real kind does the thinking, feeling, and willing being belong? We know that externally considered man belongs to the animal kingdom, to the branch of vertebrates, and the class of mammals; but what we seek is his place when considered internally, disregarding his muscles, glands, and nerves and considering only his feelings, efforts, and conceptions.

583. We have already seen that every state of consciousness [is] an inference; so that life is but a sequence of inferences or a train of thought. At any instant then man is a thought, and as thought is a species of symbol, the general answer to the question what is man? is that he is a symbol. To find a more specific answer we should compare man with some other symbol.

584. I write here the word Six. Now let [us] ask ourselves in what respects a man differs from that word. In the first place, the body of man is a wonderful mechanism, that of the word nothing but a line of chalk. In the second place, the meaning of the word is very simple, the meaning of a man a very Sphinx's question. These two differences are very obvious, — they lie upon the surface. But what other difference is there?

585. A man has consciousness; a word has not. †42 What do we mean by consciousness, for it is rather an ambiguous term. There is that emotion which accompanies the reflection that we have animal life. A consciousness which is dimmed when animal life is at its ebb, in age or sleep, but which is not dimmed when the spiritual life is at its ebb; which is more lively the better animal a man is, but is not so the better man he is. You can all distinguish this sensation I am sure; we attribute it to all animals but not to words, because we have reason to believe that it depends upon the possession of an animal body. And, therefore, this difference is included under the first that we mentioned and is not an additional one. In the second place, consciousness is used to mean the knowledge which we have of what is in our minds; the fact that our thought is an index for itself of itself on the ground of a complete identity with itself. But so is any word or indeed any thing, so that this constitutes no difference between the word and the man. In the third place, consciousness is used to denote the I think, the unity of thought; but the unity of thought is nothing but the unity of symbolization; consistency, in a word — the implication of being — and belongs to every word whatever. It is very easy to think we have a clear notion of what we mean by consciousness, and yet it may be that the word excites no thought but only a sensation, a mental word within us; and then because we are not accustomed to allow the word written on the board to excite that sensation, we may think we distinguish between the man and the word when we do not. "Most ignorant of what we're most assured Our glassy essence!"

586. Consciousness is, also, used to denote what I call feeling; as by Mr. Bain whom I mention in order to say that he recognizes the unity of sensation and emotion under this term although he has not carried out the conception consistently. Has that word feeling? Man, say the sensationalists, is a series of feelings; at any one moment, then, is a feeling. How is it with the word? Feelings, we all know, depend upon the bodily organism. The blind man from birth has no such feelings as red, blue, or any other colour; and without any body at all, it is probable we should have no feelings at all; and the word which has no animal body probably therefore has no animal feelings, and of course if we restrict the word feeling to meaning animal feeling the word has no feelings. But has it not something corresponding to feeling? Every feeling is cognitive — is a sensation, and a sensation is a mental sign or word. Now the word has a word; it has itself; and so if man is an animal feeling, the word is just as much a written feeling.

587. But is there not this difference. Man's feelings are perceptions, he is affected by objects. He sees, hears, etc. A word does not. Yes; that is true, but perception, plainly, depends upon having an animal organism and therefore there is here no further difference beyond the obvious two mentioned at first. Yet even here, there is a correspondence between the word and the man. Perception is the possibility of acquiring information, of meaning more; now a word may learn. How much more the word electricity means now than it did in the days of Franklin; how much more the term planet means now than it did in the time [of] Hipparchus. These words have acquired information; just as a man's thought does by further perception. But is there not a difference, since a man makes the word and the word means nothing which some man has not made it mean and that only to that man? This is true; but since man can think only by means of words or other external symbols, words might turn round and say, You mean nothing which we have not taught you and then only so far as you address some word as the interpretant of your thought. In fact, therefore, men and words reciprocally educate each other; each increase of a man's information is at the same time the increase of a word's information and vice versa. So that there is no difference even here.

588. You see that remote and dissimilar as the word and the man appear, it is exceedingly difficult to state any essential difference between them except a physiological one. A man has a moral nature, a word apparently has none. Yet morals relate primarily to what we ought to do; and therefore as words are physiologically incapacitated to act we should not consider this as a separate point of distinction. But if we consider morality as the conformity to a law of fitness of things, — a principle of what is suitable in thought, not in order to make it true but as a prerequisite to make it spiritual, to make it rational, to make it more truly thought at all; we have something extremely analogous in the good grammar of a word or sentence. Good grammar is that excellence of a word by which it comes to have a good conscience, to be satisfactory not merely [with] reference being had to the actual state of things which it denotes, not merely to the consequences of the act, but to it in its own internal determination. Beauty and truth belong to the mind and word alike. The third excellence is morality on the one hand, Grammar on the other.

589. Man has the power of effort or attention; but as we have seen that this is nothing but the power of denotation, it is possessed by the word also.

590. Perhaps the most marvellous faculty of humanity is one which it possesses in common with all animals and in one sense with all plants, I mean that of procreation. I do not allude to the physiological wonders, which are great enough, but to the fact of the production of a new human soul. Has the word any such relation as that of father and son? If I write "Let Kax denote a gas furnace," this sentence is a symbol which is creating another within itself. Here we have a certain analogy with paternity; just as much and no more as when an author speaks of his writings as his offspring, — an expression which should be regarded not as metaphorical but merely as general. Cuvier said that Metaphysics is nothing but Metaphor; an identity which is prettily typified in those acted charades, [in] the first of which two doctors come in at opposite sides of the stage, shake hands and go out for the first scene, then repeat the same thing for the second scene and again for the whole word; and then do the same thing three times for the three scenes of the second word; the two words are of course metaphysician and metaphor; and their identity suggests that the characters must have been the invention of some one who thought with Cuvier that Metaphysics is another term for Metaphor. If metaphor be taken literally to mean an expression of a similitude when the sign of predication is employed instead of the sign of likeness — as when we say this man is a fox instead of this man is like a fox, — I deny entirely that metaphysicians are given to metaphor; on the contrary, no other writers can compare with them for precision of language; but if Cuvier was only using a metaphor himself, and meant by metaphor broad comparison on the ground of characters of a formal and highly abstract kind, — then, indeed, metaphysics professes to be metaphor — that is just its merit — as it was Cuvier's own merit in Zoölogy . . . .

591. Enough has now been said, I think, to show a true analogy between a man and a word. I dare say this seems very paradoxical to you; I remember it did to me, at first. But having thought it over repeatedly, it has come to seem merest truism. A man denotes whatever is the object of his attention at the moment; he connotes whatever he knows or feels of this object, and is the incarnation of this form or intelligible species; his interpretant is the future memory of this cognition, his future self, or another person he addresses, or a sentence he writes, or a child he gets. In what does the identity of man consist and where is the seat of the soul? It seems to me that these questions usually receive a very narrow answer. Why we used to read that the soul resides in a little organ of the brain no bigger than a pin's head. Most anthropologists now more rationally say that the soul is either spread over the whole body or is all in all and all in every part. But are we shut up in a box of flesh and blood? When I communicate my thought and my sentiments to a friend with whom I am in full sympathy, so that my feelings pass into him and I am conscious of what he feels, do I not live in his brain as well as in my own — most literally? True, my animal life is not there but my soul, my feeling thought attention are. If this be not so, a man is not a word, it is true, but is something much poorer. There is a miserable material and barbarian notion according to which a man cannot be in two places at once; as though he were a thing! A word may be in several places at once, Six Six, because its essence is spiritual; and I believe that a man is no whit inferior to the word in this respect. Each man has an identity which far transcends the mere animal; — an essence, a meaning subtile as it may be. He cannot know his own essential significance; of his eye it is eyebeam. But that he truly has this outreaching identity — such as a word has — is the true and exact expression of the fact of sympathy, fellow feeling — together with all unselfish interests — and all that makes us feel that he has an absolute worth. Some one will ask me for proof of this. It seems to me that I have already given both the proof and the confirmation. The whole proof is very long but its principal lemmas were these: 1st, "What is man?" is an inductive question in its present sense; 2nd, The inductive explanation is only the general expression of the phenomena, and makes no hypothesis; 3rd, Whatever man is he is at each instant; 4th, At each instant the only internal phenomena he presents are feeling, thought, attention; 5th, Feelings, thought, attention are all cognitive; 6th, All cognition is general, there is no intuition; †43 7th, A general representation is a symbol; 8th, Every symbol has an essential comprehension which determines its identity. The confirmation I offered was the fact that man is conscious of his interpretant, — his own thought in another mind — I do not say immediately conscious — is happy in it, feels himself in some degree to be there. So that I believe that nothing but an undue ascendency of the animal life can prevent the reception of this truth.

592. This essence of which I speak is not the whole soul of man; it is only his core which carries with it all the information which constitutes the development of the man, his total feelings, intentions, thoughts. When I, that is my thoughts, enter into another man, I do not necessarily carry my whole self, but what I do carry is the seed of [the] part that I do not carry — and if I carry the seed of my whole essence, then of my whole self actual and potential. I may write upon paper and thus impress a part of my being there; that part of my being may involve only what I have in common with all men and then I should have carried the soul of the race, but not my individual soul into the word there written. Thus every man's soul is a special determination of the generic soul of the family, the class, the nation, the race to which he belongs . . . .

593. The principle that the essence of a symbol is formal, not material, has one or two important consequences. Suppose I rub out this word (Six) and write Six. Here is not a second word but the first over again; they are identical. Now can identity be interrupted or ought we to say that the word existed although it was unwritten? This word six implies that twice three is five and one. This is eternal truth; a truth which always is and must be; which would be though there were not six things in the universe to number, since it would still remain true that five and one would have been twice three. Now this truth is the word, six; if by six we mean not this chalk line, but that wherein six, sex, {hex}, sechs, zes, seis, sei agree. Truth, it is said, is never without a witness; and, indeed, the fact itself — the state of things — is a symbol of the general fact through the principles of induction; so that the true symbol has an interpretant so long as it is true. And as it is identical with its interpretant, it always exists. Thus, the necessary and true symbol is immortal. And man must also be so, provided he is vivified by the truth. This is an immortality very different indeed from what most people hope for, although it does not conflict with the latter. I do not know that the Mohammedan paradise is not true, only I have no evidence that it is. Animal existence is certainly a pleasure, though some speak of being weary of it; but I think it is confessed by the most cultivated peoples that it is not immortal; otherwise, they would consider the brutes as immortal. Spiritual existence, such as a man has in him, whom he carries along with him in his opinions and sentiments; sympathy, love; this is what serves as evidence of man's absolute worth — and this is the existence which logic finds to be certainly immortal. It is not an impersonal existence; for personality lies in the unity of the I think — which is the unity of symbolization — the unity of consistency — and belongs to every symbol. It is not an existence, cut off from the external world, for feeling and attention are essential elements of the symbol itself. It is, however, a changed existence; one in which there are no longer any of the glories of hearing and vision, for sounds and colors require an animal eye; and in the same way all the feelings will be different.

594. This immortality is one which depends upon the man's being a true symbol. If instead of six, we had written Jove we should have had a symbol which has but a contingent existence; it has no everlasting witness in the nature of things and will pass away or remain only in men's memories without exciting any response in their hearts. It is, indeed, true so far as it means a supreme being; its generic soul is true and eternal, but its specific and individual soul is but a shadow.

595. Each man has his own peculiar character. It enters into all he does. It is in his consciousness and not a mere mechanical trick, and therefore it is by the principles of the last lecture a cognition; but as it enters into all his cognition, it is a cognition of things in general. It is therefore the man's philosophy, his way of regarding things; not a philosophy of the head alone — but one which pervades the whole man. This idiosyncrasy is the idea of the man; and if this idea is true he lives forever; if false, his individual soul has but a contingent existence.

596. Gentlemen and ladies, I announce to you this theory of immortality for the first time. It is poorly said, poorly thought; but its foundation is the rock of truth. And at least it will serve to illustrate what use might be made by mightier hands of this reviled science, logic, nec ad melius vivendum, nec ad commodius disserendum.

Chapter 5: Telepathy and Perception †1

§1. Telepathy

597. A little passage at arms between a physicist of standing and a celebrated psychologist has lately focussed the public glance once more for a moment upon this subject. †2 The remarks of Prof. Trowbridge express, more or less successfully, the typical physicist attitude toward the hypothesis of telepathy and toward psychical research. I shall consider rather that typical attitude than the special points which this excellent physicist has made. For I was trained from boyhood in physics, have mostly associated with physicists, and fully share their prejudices, whether legitimate or illegitimate. Upon the formation of the Society for Psychical Research, I disapproved of physicists lending it their countenance, on the ground that in doing so they would be encouraging young men to devote the best years of their lives to an inquiry of little promise in which those men would be in great danger of compromising themselves, since it would appear that they must either have some positive result to defend after so much time had been spent or else be reduced to a distressing acknowledgment of failure. When the large book "Phantasms of the Living" appeared, I wrote a long and minute criticism of it, †3 arguing that it only showed that no scientific conclusion could be reached by the examination of stories of sporadic and unanalyzed phenomena. Thus I have little need of consulting with others to do full justice to the typical physicist's disapproval of the hypothesis and the methods of the telepathists. On the other hand, ever since Wundt inaugurated the modern science of psychology about 1862 (the date of the collected publication of his Beiträge zur Theorie der Sinneswahrnehmung,) I have pursued that study both experimentally and speculatively, and am thus better able than some physicists to appreciate the opinions of the psychologists.

598. Let me endeavor to explain the attitude of the physicist. Many people imagine that there is a certain class of facts which it is repugnant to the physicist to acknowledge. This is not so. If there were such a class of facts, the phenomena connected with radium would fall within it. Yet there has been no disposition to ignore these phenomena. But the physicist recognizes that a phenomenon is of no use to him unless both it and its conditions can be subjected to exact analysis. Moreover, the only theories that can have any value for him are those from which can be deduced exact predictions capable of exact verification. As long as a fact stands isolated and strange, it is next to impossible to make sure that it is a fact, and quite impossible to render it useful to science. Physicists are doubtless inclined to discredit facts of which they, as physicists, could make no use. But that is a mere matter of personal belief with them. It cannot affect their conduct as physicists. Thus, in regard to aerolites, as long as there were merely scattered tales of stones having fallen from heaven at long intervals, although some of them were very strongly attested, as when a shower of them were dashed into a public square of Siena, it must be admitted that physicists of the very highest genius were too much inclined to pooh-pooh the matter. But this they did not do in their character as physicists, since there seemed to be no way by which a physicist could inquire into the matter. It was merely a "belief." One physicist, however, Chladni, bethought him to draw up a catalogue of all these tales, — using, not "post-card evidence," since post-cards were not yet in use, but testimonies that, taken singly, were mostly far from affording satisfactory scientific security. The result was that it appeared that stones fall from heaven every day (we now know that thousands fall daily). Thus, the subject became opened to scientific investigation, and the personal adverse "beliefs" of the physicists, gave way to the general acknowledgment that the fact had been established.

599. Suppose we knew nothing at all about electricity except for the stories of fire-balls. Then it could make no difference to physicists, as physical inquirers, whether those stories were true or not, since there would be no way by which further physical inquiry into their nature could be pursued. It would not be their concern, professionally; but personally their "belief" would mostly be that they were fancies.

600. The theory of telepathy is that in some cases one mind acts upon another, whether directly or not, at any rate by means fundamentally different from those that every-day experience renders familiar. As a scientific theory, this almost condemns itself. For to say that a phenomenon is fundamentally different from anything in ordinary experience is almost to say that it is of such a nature as to preclude the deduction from it of manifold exact predictions verifiable by ordinary perception. Pretty nearly the sole support claimed for this theory consists of certain tremendous experiences that are said to have happened to a minute fraction of mankind. If such be the only facts in the case, they are facts with which science can have nothing to do, since science is the business of finding out Law, i.e., what always happens.

601. Suppose it were true that those marvellous stories proved the doctrine of telepathy; then what would it be that had been proved? Why, that very rarely mind acts upon mind in a way utterly unlike the normal way. This would be no contribution to science. It would, in the case supposed, have been ascertained that sometimes a marvel, an impenetrable mystery, occurs. The concern of science, however, is with intelligible facts. Science no more denies that there are miracles and mysteries than it asserts them. But it is a Postulate, — a hope, — of science and of all sound reasoning that any given fact to which our attention may be directed shall turn out to be intelligible. †4 It is justly held criminal for a commander-in-chief to "despair of the republic"; and it would be as monstrous for an inquirer to despair of the comprehensibility of his problem. The psychicists are fond of reminding us that the most familiar facts are full of mystery. So they are, in a metaphysical sense; and that is the very reason why the physicist eschews metaphysical inquiry and seeks to understand phenomena only in the sense of establishing their exact relations to one another. Hence, what is absolutely severed and sundered from the body of ordinary experience is absolutely beyond scientific comprehension.

602. Sharing these sentiments common to all physicists, when 'Phantasms of the Living' appeared, — that vast collection of well-sifted stories by which Messrs. Gurney, Myers, and Podmore endeavored to prove the theory of telepathy, — I felt that I would far sooner believe in spiritualism. For according to this latter theory, we all pass into another life; nor would this experience common to us all be much more wonderful than the development that we all undergo when the child becomes a grown person. If telepathy be a fact, why should it have the strange character of being excessively infrequent, so contrary to the ubiquity of all the other agencies of nature? One cannot suppose it otherwise than extremely infrequent without having long ago become well-known and beyond doubt. Nor have the psychicists succeeded in making out the slightest trace of it in ordinary people. If, on the other hand, we suppose there are communications from the other world, there is nothing surprising in their being infrequent. For with what disgust and indifference must the departed spirit recall the pettiness and blindness of the ends, the villainy, meanness, and filth of the methods of the inhabitants of this [world], who, as he well sees, are at the bottom of their hearts glad to get rid of him, and who have to work out their own salvation without interference, — the nasty little imps. †5 Surely, the canyon that spiritualism has to suppose between the two worlds has a gentle slope compared with the abyss that telepathy opens in the midst of experience between the ordinary and extraordinary intercommunion between minds.

603. Messrs. Gurney, Myers, and Podmore in asking human reason to admit that a class of phenomena was sundered from ordinary experience vastly more than any phenomena had been believed to be, seemed to me to be all but asking reason to admit that its hope of understanding things, — its only aim, — was futile; and I was accordingly moved to write an elaborate criticism of their book to show that hallucinations were so very common, while hallucinations coincident with truth beyond the ken of sense were so very rare, after the suspicious cases had been weeded out, that these coincidences might very well be supposed to be fortuitous. At the same time, I essayed to determine by logical analysis what were the conditions to which a census of hallucinations must conform in order to afford sound support to the contention of the telepathists that the veridical †6 hallucinations were too numerous to be accounted chance coincidences. The Society at once set about making a new census. I wish I could pay them the compliment of averring that, in doing so, they were influenced by my reasons or by any better considered reasons. But I am obliged to say that they so far failed to conform to the conditions which I had shown to be requisite, — and in the direction of favoring their doctrine of telepathy, — that now the question stands as it did before, a question which each man will answer according to his predilections, whether these owe their birth to his general experience of the ways of nature or to some episode of his private life.

§2. The Scientific Attitude

604. I am sorry. For the question at issue between the physicist and the psychologist in the recent passage of arms was how far the psychical researchers have the character of men of science. Now however much ratiocinative analysis may help toward a decision upon this point, the answer must ultimately rest, like every other judgment concerning men's character, upon the testimony of instinctive impressions; and one of my purposes in this article is to render the testimony of my own impressions upon the matter. Thus finding myself in a situation that calls for truth-telling, truth will I tell, without exaggeration or extenuation, as accurately as I can, whatever it costs me.

605. There are two qualifications which every true man of science possesses, and which, if a man possesses them, he is sure to develop into a scientific man in the course of time, if he ought not fairly to be called such already. First, the dominant passion of his whole soul must be to find out the truth in some department, regardless of what the color of that truth may be. Secondly, he must have a natural gift for reasoning, for severely critical thought. Perhaps a man who had drunk of the fountain of perpetual youth need not, at the outset of his career, possess either of those qualifications: he would infallibly become a man of science at last, because the incessant action of experience would ultimately produce those two qualities in him. For we see that, in a measure, that effect has been produced in the course of history upon civilized man at large.

606. In a measure, I say, for the love of truth is still far from mighty; and a gift for reasoning is still as rare a talent as a gift for music. Most men are incapable of strong control over their minds. Their thoughts are such as instinct, habit, association suggest, mainly. Their criticism of their thoughts is confined to reconsideration and to asking themselves whether their ideas seem reasonable. I do not call this reasoning: I call it instinctive reflexion. For most purposes it is the best way to think; for instinct blunders far less than reason. Reasoners are in danger of falling into sophistry and pedantry. Our instinctive ways of thinking have become adapted to ordinary practical life, just as the rest of our physiology has become adapted to our environment. Wisdom lies in nicely discriminating the occasions for reasoning and the occasions for going by instinct. Some of my most valued friends have been almost incapable of reasoning; and yet they have been men of singularly sound judgment, penetrating and sagacious. So much more important is it, on the whole, to feel right than to reason deeply. But in science instinct can play but a secondary rôle. The reason of this is that our instincts are adapted to the continuance of the race and thus to individual life. But science has an indefinite future before it; and what it aims at is to gain the greatest possible advance in knowledge in five centuries or ten. Instinct not being adapted to this purpose, the methods of science must be artificial. As Professor Trowbridge hints, pure science has nothing to do with belief. What I believe is what I am prepared to go on today. Imagine a general besieging a city. He sits in his tent at night preparing the details of his plan of action for the morrow. He finds that what his orders ought to be and perhaps the whole fate of his army depend upon a certain question of topography concerning which he is in need of information. He sends for his best engineer officer, — a highly scientific man, — and asks how he is to ascertain the fact in question. The officer replies, "There is only one possible way of ascertaining that. So and so must be done." "How long will that take?" "Two or three months." The general dismisses the man of science, — as Napoleon dismissed Laplace, — and sends for another officer, not half so scientific, but good at guessing. What this officer shall say, the general will go by. He will adopt it as his belief.

607. Beyond the two general qualifications mentioned, every scientific man needs a special training in his particular branch of research; and moreover this branch will probably call for the possession of some special mental, physiological, and instrumental advantages for the acquisition of a special line of facts. I do not set down "power of observation" among the general qualifications, because this phrase covers a variety of capacities having nothing in common, of which a naturalist will want one, an astronomer another, a linguist a third, a psychologist a fourth, and so on. Besides, there has been some exaggeration about the observing powers of scientific men; and in that quality which the phrase seems best to fit, the power of noting one's precise sensations unaffected by any interpretation of them, the scientific men of most branches are decidedly inferior to the artists. I should not, therefore, attribute any very high importance to great general powers of observation as distinguishing men of science. But I must say that the best psychical researchers rank high in this respect as compared with scientific men generally.

608. In considering how far they possess the essential characters of scientists, I first note that amateurs, idlers, and people not extra wise naturally flock to the Society for Psychical Research and make up an even greater proportion of it than they do of other large scientific associations. But these are not the persons under consideration. It is only the men who have devoted all the strenuous energies of their lives to the work, some of whom have succumbed to the strain of it, whom I am to endeavor to class.

609. As to their devotion to truth, I have to remember that, as I have known them, they have been serious and foreseeing men who would not embark upon any enterprise without carefully reckoning up its contingencies. Therefore, at the moment when any one of those men deliberately devoted his life and his whole being to this inquiry, as several have done, he certainly had distinctly before his mind the following considerations: that it would be hard and incessant work, mostly drudgery, requiring him to be occupied mostly with knaves and fools; that it would cost him a great deal of money, considering all that it would prevent him from earning; that it would never bring him much honor, but would put a certain stamp of obloquy upon him; that even among the company of those who professed to love the truth, and who ought to press him to their hearts as a brother, there would be found in the more richly endowed sciences, individuals who would treat him in the narrowest and most despicable spirit of the east wind; that after his whole life had been poured out into the inquiry, it was not unlikely that he might find that he had not found out anything.

610. These considerations go to show that, whatever those men have been aiming at, they have aimed at in a single-hearted manner. Were they desirous of believing in the particular doctrine of telepathy, or were they bent on finding out the truth, whatever it might be?

611. I cannot see that there is anything particularly comfortable about a belief in telepathy. To be sure, it cuts off, or greatly weakens, the force of such evidence as there might seem to be for spiritualism; and, no doubt, for many reflecting persons, the prospect of another life is rather unpleasant. But who will believe that the main motive of the telepathists has been to escape thoughts of another world? Such thoughts are not troublesome enough for that.

612. I had a somewhat prolonged controversy with Edmund Gurney which was only interrupted by his death; and this brought me into fine touch with the spirit of the man. I was most strongly impressed with the purity of his devotion to truth. This impression has been thoroughly convincing in the cases of others whom I have met personally, but whom I do not name because they are still living.

613. The power of reasoning of the leaders is certainly much above that of the average of men. It does not seem to me to have been altogether sufficient for their problem. The hypothesis of telepathy does not seem to me to have much merit, as a specimen of scientific method. I believe that if the researchers had been better reasoners they would not have spent so much time in sifting tales of extraordinary happenings but would rather have thrown their energies into an endeavor to connect the dubious extraordinary phenomena with ordinary experience. In this direction, the little that they have done seems to me feeble and to show defect of analysis.

614. As for scientific training and special qualifications, the psychicists seem to me to have been amply provided with all that their method gave room for. Their exposure of several frauds has been neat and workmanlike, and they have made use of numbers as far as numbers have been applicable. Prof. Trowbridge complains that they make no measurements; and that coincides with my complaint that they have not sufficiently endeavored to bring their marvels into relation to ordinary experience. For, in order to do that, the phenomena would have had to be analyzed; and then, and not before, would measurements have been applicable. Prof. Trowbridge will not forget that in the early stages of physics, there were no measures. Galileo, Gilbert and others made considerable progress before they arrived at a stage at which they were able to make any measurements to speak of. But they did exhibit great skill in analyzing the phenomena; and I agree that the psychicists have not exhibited signal ability in doing that. It must be remembered, however, that they are only breaking ground in a perfectly virgin soil intractable and thicket-tangled. They are doing good honest work, not shrinking from labor, and proceeding intelligently, if not with high genius. The farm of physics has long been under cultivation, the costliest implements and the most refined methods are here in use. Here have come these new settlers, occupying land not easy to till and poor in resources. Come, let us turn up our noses at them, gossip about their suspicious ways, and let them feel the difference between them and us. Who knows whether they are honest?

§3. Perception

615. If there were only some way of reconciling the usual order of nature, as it is familiar to us, with the possibility of rare cases of quasi-vision beyond the ken of sense, then I grant that the testimonies adduced in "Phantasms of the Living" would suffice to render it extremely likely that such rare quasi-vision actually takes place. For, after all, the theory of chance coincidence puts a certain strain upon our instinct of receiving testimony; and natural instinct is not a thing to be lightly disregarded.

616. Is it quite certain that such an occasional, but very rare, determinedly veridical vision of things beyond the senses' ken would be altogether unlike every-day experience? As to that I have a suggestion to make.

617. It is not uncommon to hear a man or woman say, "I believe what I see, and nothing more." But little cross-questioning would commonly be needed to show that it is an exaggeration. There are not many persons, even though they boast themselves to be materialists, who do not really believe much that they do not themselves think that they directly perceive by any sense, peripheral or visceral; — polonium, the sacred city of Thibet, George Washington, the glacial period, that motions will tomorrow conform to Newton's three laws. But I myself happen, in common with a small but select circle, to be a pragmatist, or "radical empiricist," †7 and as such, do not believe in anything that I do not (as I think) perceive: and I am far from believing in the whole of that.

618. Only, the question arises, What do we perceive? It would not serve our turn to answer scholastically with an arbitrary definition which might be ill-considered. Let us rather set out from familiar instances, and having noticed what their relation is to the formation of scientific opinions, found upon that a definition which shall cover all that is so related to knowledge and shall cover nothing else.

619. Let us say that, as I sit here writing, I see on the other side of my table, a yellow chair with a green cushion. That will be what psychologists term a "percept" (res percepta). They also frequently call it an "image." With this term I shall pick no quarrel. Only one must be on one's guard against a false impression that it might insinuate. Namely, an "image" usually means something intended to represent, — virtually professing to represent, — something else, real or ideal. So understood, the word "image" would be a misnomer for a percept. The chair I appear to see makes no professions of any kind, essentially embodies no intentions of any kind, does not stand for anything. It obtrudes itself upon my gaze; but not as a deputy for anything else, not "as" anything. It simply knocks at the portal of my soul and stands there in the doorway.

620. It is very insistent, for all its silence. It would be useless for me to attempt to pooh-pooh it, and say, "Oh come, I don't believe in the chair." I am forced to confess that it appears. Not only does it appear, but it disturbs me, more or less. I cannot think the appearance is not there, nor dismiss it as I would a fancy. I can only get rid of it by an exertion of physical force.

621. It is a forceful thing. Yet it offers no reason, defence, nor excuse for its presence. It does not pretend to any right to be there. It silently forces itself upon me.

622. Such is the percept. Now what is its logical bearing upon knowledge and belief. This may be summed up in three items, as follows:

1st, it contributes something positive. (Thus, the chair has its four legs, seat, and back, its yellow color, its green cushion, etc. To learn this is a contribution to knowledge.)

2nd, it compels the perceiver to acknowledge it.

3rd, it neither offers any reason for such acknowledgment nor makes any pretension to reasonableness. This last point distinguishes the percept from an axiom. I am a total disbeliever in axioms; but so far as the proposition, say, that a straight line is the shortest distance between two points even so much as seems to be self-evident, it seems to be reasonable. It is as founded in reason or in the nature of things, or as founded in something, that it recommends itself. The percept, on the contrary, is absolutely dumb. It acts upon us, it forces itself upon us; but it does not address the reason, nor appeal to anything for support.

623. Let us say, then, that anything is, for the purposes of logic, to be classed under the species of perception wherein a positive qualitative content is forced upon one's acknowledgment without any reason or pretension to reason. There will be a wider genus of things partaking of the character of perception, if there be any matter of cognition which exerts a force upon us tending to make us acknowledge it without any adequate reason.

But in order fully to satisfy ourselves of the justice of classing in this species and in this genus all that I propose to refer to them, it is desirable to examine a little more closely the characters of the percept.

624. A visual percept obtrudes itself upon me in its entirety. I am not therein conscious of any mental process by which the image has been constructed. The psychologists, however, are able to give some account of the matter. Since 1709, they have been in possession of sufficient proof (as most of them agree,) that, notwithstanding its apparent primitiveness, every percept is the product of mental processes, or at all events of processes for all intents and purposes mental, except that we are not directly aware of them; and these are processes of no little complexity. The psychologists very reasonably argue that the first impressions made upon sense must have been feelings of sense qualities, — say colors, sounds, etc. — disconnected from one another, and not appearing to stand over against a self as objects; and it would seem that this must have been true of the very first impressions ever made upon sense in the history of mental development, however far the sense of the individual man of today may have been rendered capable of immediately apprehending the complex. But this is quite inferential. We are, of course, directly aware of positive sense-qualities in the percept (although in the percept itself they are in no wise separate from the whole object); but as for their being at first disconnected and not objectified, that is psychological theory.

625. Thus, two utterly different kinds of elements go to compose any percept. In the first place, there are the qualities of feeling or sensation, each of which is something positive and sui generis, being such as it is quite regardless of how or what anything else is. On account of this self-sufficiency, it is convenient to call these the elements of "Firstness." †8 In the percept, these elements of Firstness are perceived to be connected in definite ways. A visual percept of a chair has a definite shape. If it is yellow with a green cushion, that is quite different from being green with a yellow cushion. These connectives are directly perceived, and the perception of each of them is a perception at once of two opposed objects, — a double awareness. In respect to each of these connections, one part of the percept appears as it does relatively to a second part. Hence, it is convenient to call them elements of "Secondness." The vividness with which a percept stands out is an element of secondness; because the percept is vivid in proportion to the intensity of its effect upon the perceiver. These elements of secondness bring with them the peculiar singleness of the percept. This singleness consists in a double definiteness. For on the one hand, the percept contains no blank gaps which, in representing it, we are free to fill as we like. What I mean will be seen if we consider any knowledge we can have of the future. I heard somebody say that the Brooklyn bridge would fall some day. The only way in which he could even think he knew that would be by knowing that any bridge I might select that should be constructed in a certain way would fall. There is no such universality about the percept. It is quite individual. On the other hand, the definiteness of the percept is of a perfectly explicit kind. In any knowledge of the past something is, as it were, held in reserve. There is an indicated gap which we are not free to fill but which further information may fill. We know that the Sphinx was made by some king of Egypt. But what one? The percept, however, exhibits itself in full. These two kinds of definiteness, first, that the percept offers no range of freedom to anybody who may undertake to represent it, and secondly, that it reserves no freedom to itself to be one way or another way, taken together, constitute that utter absence of "range" which is called the singularity, or singleness, of the percept, the one making it individual and the other positive. The percept is, besides, whole and undivided. It has parts, in the sense that in thought it can be separated; but it does not represent itself to have parts. In its mode of being as a percept it is one single and undivided whole.

626. The percept is not the only thing that we ordinarily say we "perceive"; and when I professed to believe only what I perceived, of course I did not mean percepts, since percepts are not subjects of belief or disbelief. I meant perceptual judgments. Given a percept, this percept does not describe itself; for description involves analysis, while the percept is whole and undivided. But once having a percept, I may contemplate it, and say to myself, 'That appears to be a yellow chair'; and our usual language is that we "perceive" it to be a yellow chair, although this is not a percept, but a judgment about a present percept.

627. The perceptual judgment is all but in the same relation to knowledge and belief as is the percept. It is true that I may, by an effort of will, abstain from thinking about the color of the chair, so that the judgment 'the chair appears yellow' is not unconditionally forced upon me, and thus might seem not quite fully to partake of the character of perception. One can, however, escape the percept itself by shutting one's eyes. If one sees, one cannot avoid the percept; and if one looks, one cannot avoid the perceptual judgment. Once apprehended, it absolutely compels assent. Its defect in forcefulness is thus excessively slight and of no logical importance.

628. To about the same degree its forcefulness falls short of the utter irrationality of that of the percept. The perceptual judgment professes to represent the percept. A logical defence of it would therefore have to be founded either on the percept as a premiss of that logical defence, or else on the percept as a fact represented by such premiss. But the percept cannot be a premiss, since it is not a proposition; and a statement of the character of the percept would have to rest on the perceptual judgment, instead of this on that. Thus, the perceptual judgment does not represent the percept logically. In what intelligible manner, then, does it represent the percept? It cannot be a copy of it; for, as will presently appear, it does not resemble the percept at all. There remains but one way in which it can represent the percept; namely, as an index, or true symptom, just as a weather-cock indicates the direction of the wind or a thermometer the temperature. There is no warrant for saying that the perceptual judgment actually is such an index of the percept, other than the ipse dixit of the perceptual judgment itself. And even if it be so, what is an index, or true symptom? It is something which, without any rational necessitation, is forced by blind fact to correspond to its object. To say, then, that the perceptual judgment is an infallible symptom of the character of the percept means only that in some unaccountable manner we find ourselves impotent to refuse our assent to it in the presence of the percept, and that there is no appeal from it. Thus, the forcefulness of the perceptual judgment falls short of the pure unreasonableness of the percept only to this extent, that it does profess to represent the percept, while the perfection of the percept's surdity consists in its not so much as professing anything.

629. The perceptual judgment, then, does not quite accurately fulfill the condition of forcefulness nor that of irrationality, as it should do to be strictly entitled to be considered a product of perception. But the differences are so minute and so unimportant logically that it will be convenient to neglect them. Perhaps I might be permitted to invent the term percipuum †9 to include both percept and perceptual judgment.

630. I promised to show that a perceptual judgment is entirely unlike a percept. If it be true, as my analysis makes it to be, that a percept contains only two kinds of elements, those of firstness and those of secondness, then the great overshadowing point of difference is that the perceptual judgment professes to represent something, and thereby does represent something, whether truly or falsely. This is a very important difference, since the idea of representation is essentially what may be termed an element of "Thirdness," that is, involves the idea of determining one thing to refer to another. The element of secondness in the percept consists in one part being relative to another. But the percept presents itself ready made, and contains no idea of any state of things being brought about. There is a rigid mathematical demonstration (which I cannot give here) that the idea of Firstness, or that of a positive suchness, and the idea of Secondness, or that of one thing's referring to another, can in no way be combined so as to produce the idea of one thing A, referring to a second, B, in the very act of referring to a third, C. †10 This is the element of Thirdness, or mediation, which the conception of the representation of something to somebody obviously involves. In a perceptual judgment the mind professes to tell the mind's future self what the character of the present percept is. †11 The percept, on the contrary, stands on its own legs and makes no professions of any kind.

631. There are several other points of contrast between the perceptual judgment and the percept that are calculated to exhibit their disparateness. The judgment, "This chair appears yellow," separates the color from the chair, making the one predicate and the other subject. The percept, on the other hand, presents the chair in its entirety and makes no analysis whatever.

632. We have seen that the "singularity" of the percept is a composite of two modes of definiteness. The first consists in this, that its faithful and full interpreter has no freedom allowed to him, but all is prescribed. But the perceptual judgment 'This chair appears yellow' has vaguely in mind a whole lot of yellow things, of which some have been seen, and no end of others may be or might be seen; and what it means to say is, 'Take any yellow thing you like, and you will find, on comparing it with this chair, that they agree pretty well in color.' It thus directly invites the exercise of a freedom of choice on the part of the interpreter (any one yellow thing answering as well as any other) which freedom the percept sternly and stupidly precludes.

633. The other mode of definiteness of the percept consists in its being perfectly explicit. The perceptual judgment carelessly pronounces the chair yellow. What the particular shade, hue, and purity of the yellow may be it does not consider. The percept, on the other hand, is so scrupulously specific that it makes this chair different from every other in the world; or rather, it would do so if it indulged in any comparisons.

634. It may be objected that the terms of the judgment resemble the percept. Let us consider, first, the predicate, 'yellow' in the judgment that 'this chair appears yellow.' This predicate is not the sensation involved in the percept, because it is general. It does not even refer particularly to this percept but to a sort of composite photograph of all the yellows that have been seen. If it resembles the sensational element of the percept, this resemblance consists only in the fact that a new judgment will predicate it of the percept, just as this judgment does. It also awakens in the mind an imagination involving a sensational element. But taking all these facts together, we find that there is no relation between the predicate of the perceptual judgment and the sensational element of the percept, except forceful connections.

635. As for the subject of the perceptual judgment, as subject it is a sign. But it belongs to a considerable class of mental signs of which introspection can give hardly any account. It ought not to be expected that it should do so, since the qualities of these signs as objects have no relevancy to their significative character; for these signs merely play the part of demonstrative and relative pronouns, like "that," or like the A, B, C, of which a lawyer or a mathematician avails himself in making complicated statements. In fact, the perceptual judgment which I have translated into "that chair is yellow" would be more accurately represented thus: "inline image is yellow," a pointing index-finger taking the place of the subject. On the whole, it is plain enough that the perceptual judgment is not a copy, icon, or diagram of the percept, however rough. It may be reckoned as a higher grade of the operation of perception.

636. In order not to prolong the discussion, I leave some possible objections to what I have said unanswered. The most serious of these is that a perceptual judgment may be revised; so that there is a certain check upon it. The examination of this point would be lengthy, and it does not seem to me likely to appear to anybody to be of fundamental importance. Full justice to it would involve complications which few would have the patience to follow. †12

§4. A Programme

637. Having thus formed some acquaintance with the characteristics of perception, we go on to a line of thought of which the programme may be set down in advance.

638. No scientifically valuable classification can draw a line of demarcation between forms which differ indefinitely little. I shall begin by showing that this principle, which I shall refer to as the "serial principle," †13 obliges us to class as perceptions many ideas not popularly regarded as belonging to this class.

639. By the continued application of the same principle, I shall widen more and more our notion of what perception includes. In particular, I shall endeavor to bring into a clear light the truth that although what I have already said implies the truth of that doctrine of the direct, or "immediate," perception of the external world which is taught by the Aristotelians, by Kant, and by the philosophers of the Scotch school, yet we cannot refuse the name of perception to much which we rightly reject as unreal; as indeed, dreams and hallucinations are quite commonly classed as perceptions.

640. In this way, I shall lead up to the consideration of a certain group of ideas, — I beg permission to withhold the specification of what group it is, for the moment, — which ordinary instinctive language speaks of as perception, but which, as soon as one undertakes to be extra precise in one's speech, one usually never thinks of so classing; and I hope to give good reason for holding that, in this particular, instinct is right and pedantry wrong. Of this group of ideas, however, the great majority are illusory, the small minority determinedly veridical and not merely true by chance coincidence. The physicist would stultify himself if he were not the last of all men to call this into question.

641. With this group of ideas I proceed to compare the entire host of hallucinations, which there is no good reason to separate into the veridical and the non-veridical, and which there is good reason to account far more frequent than the census of the Society for Psychical Research admits. They shade off into bévues of which ordinary people commit from one to dozens daily. In view of this comparison and of all the characteristics that have been developed of ordinary perceptions in their now enlarged domain, I shall inquire, to begin [at] the end, whether it will be more in accordance with general experience to expect that some fraction of hallucinations should have a pronounced tendency to being determinedly veridical or that none should be so. Thence I shall go on to the two questions that are really pertinent to the present positions of opinion, first, whether, in case we were to admit, what is very far from commanding any reasonable assent, that all the stories which the telepathists consider marvellous and that are supported by testimony of real weight are real histories, there would be any ground for admitting a mode of communication between minds, in those cases, differing radically from modes that are ordinary; secondly, whether it be consonant with ordinary experience to be so extremely sceptical about the determinedly veridical character of occasional visions of what is beyond the ken of the senses as the rank and file of the physicists are apt to be.

§5. The Percipuum

642. If there is any novelty in the suggestion I am about to make, — and I must confess I fear there is, — it lies only in the juxtaposition of ideas. The facts which I shall adduce are to the psychologist the merest commonplaces. In the classification of them I endeavor to eliminate the pedantries and formalisms which are retained in the books for convenience, but to which psychologists attach no particular importance; and this I do by the application of the above principle of forming almost continuous series, which principle is the principal clew of which the biological taxonomists, — the great masters of classification and of terminology, — are accustomed to avail themselves. Addressing, as I do, a reader who I dare say has read a book or two about psychology but who has not dwelt enough upon the subject to prevent his being impressed by the more tangible, wooden, and dead ideas, — or corpses of ideas, — rather than by the more elusive, fluid, and living ones, my principal care will be to correct such notions. If the reader comes with a fresh mind unsophisticated by any such reading, he will follow my meaning all the easier.

643. We know nothing about the percept otherwise than by testimony of the perceptual judgment, excepting that we feel the blow of it, the reaction of it against us, and we see the contents of it arranged into an object, in its totality, — excepting also, of course, what the psychologists are able to make out inferentially. But the moment we fix our minds upon it and think the least thing about the percept, it is the perceptual judgment that tells us what we so "perceive." For this and other reasons, I propose to consider the percept as it is immediately interpreted in the perceptual judgment, under the name of the "percipuum." The percipuum, then, is what forces itself upon your acknowledgment, without any why or wherefore, so that if anybody asks you why you should regard it as appearing so and so, all you can say is, 'I can't help it. That is how I see it.' For example, one of the foolish questions with which treatises on physics used to abound was why things look right side up, when the images on the two retinas are upside down; and sundry sapient reasons more or less abstruse were given for their looking as they do. Now such arguments might have proved that things really are right side up, or perhaps they might have shown what physiological and psychical agencies cause us to regard them as right side up; but if anybody were to ask you why you should regard the visual images as right side up like the things themselves, rather than upside down like the optical images on the retinae, how you were justified in doing so, your only possible answer would be "They do look so, and I cannot make them look otherwise," whether it is reasonable for them to look so or not. Sometimes when I have been seated in a railway-car that was stationary and another train has been slowly passing by, I have been vexed at the unreasonableness of its appearing to me that our train was moving and the other train was at rest. I have reasoned with my perception. I have asked, "Is there jarring such as there is when one is in a moving car?" No. "Is there any noise of the wheels?" No. "Is there anything at all in the looks of either train that is more as if we were moving rather than they?" Quite the reverse. "Then why do I have the idea that that train is at rest and that we are moving?" There is no answer except that such is the percipuum, and I cannot help it.

644. There is no difference between a real perception and a hallucination, taken in themselves; or if there be, it is altogether inconsiderable. The difference is that rational predictions based upon the hallucination will be apt to be falsified, — as for example, if the person having the hallucination expects another person to see the same thing; while truly sound predictions based on real perceptions are supposed never to be falsified, although we have no positive reason for assuming so much as that. But this difference between hallucinations and real perceptions is a difference in respect to the relations of the two cases to other perceptions: it is not a difference in the presentations themselves. For the purposes of physiological psychology it may be proper and needful to put them into different classes. That is a branch of science with which I am not concerned. But for logical purposes, that is, in regard to their relations to knowledge and belief, which is the concern of this whole paper, they should be regarded as one and the same phenomenon, in themselves.

645. So likewise all hallucinations, the non-veridical, the fortuitously veridical, and the determinedly veridical, are, for our purposes, all one and the same phenomenon, in themselves.

646. But this is not all. The serial principle will not permit us to draw a hard and fast line of demarcation between perception and imagination. Physiological psychology may be justified or compelled to separate them, for aught I know or care. But, in regard to their relation to knowledge and belief, the percipuum is nothing but an extreme case of the fancy.

647. We all know, only too well, how terribly insistent perception may be; and yet, for all that, in its most insistent degrees, it may be utterly false, — that is, may not fit into the general mass of experience, but be a wretched hallucination. In other cases, the insistence of the percipuum may be something of a sham. That is, it may resist all unskillful attempts to overthrow it, be they ever so energetic; and yet when one knows the right trick it will be curious to see how easily it is downed. For example, that moving train that appears stationary will not move however one may try to force it to do so. Yet if one only looks down and watches the wheels turn, in a very few seconds it will seem to start up. The percipuum, insistent as it is, is not nearly so persistent and thing-like as one is apt to think. There is a well-known outline figure of a straight flight of steps against a wall seen in perspective from the side. It is called 'Schroeder's Stair.' †14 When you look at it you seem to be looking at the stairs from above. You cannot conceive it otherwise. Continue to gaze at it, and after two or three minutes the back wall of the stairs will jump forward and you will now be looking at the under side of them from below, and again cannot see the figure otherwise. After a shorter interval, the upper wall, which is now nearer to you, will spring back, and you will again be looking from above. These changes will take place more and more rapidly, the aspect from above always lasting longer, until at length, you will find you can at will make it look either way. But put it aside for a quarter of an hour or less and you will find you have lost this power. Doubtless frequent repetition of the experiment would give one complete control over it. You will thus have converted an uncontrollable percipuum into a controllable imagination by a brief process of education. It is one of the recognized difficulties of all psycho-physical measurement that the faculties rapidly become educated to an extraordinary degree. Thus, contrast-colors, when properly exhibited, are incredibly vivid. One is not easily persuaded that they are not real. Yet the experimenter becomes, in time, almost incapable of perceiving them. This is a case in which the same educational course which gives control over appearances which sometimes do and sometimes do not accord with the mass of experiences, only serves to strengthen the forcefulness of those appearances which always do so accord.

648. It is a difficult question whether the serial principle permits us to draw sharp lines of demarcation between the percept and the near anticipation, or say the antecept, and between the percept and the recent memory (may I be permitted to call this the ponecept, a distant and dubious memory being perhaps quite another thing?), or whether the percept is at once but an extreme case of an antecept and an extreme case of a ponecept. Or rather, — I beg the reader's pardon for my awkwardness of statement, — the precise question is not about percept, antecept, and ponecept, but about percipuum, antecipuum, and ponecipuum, the direct and uncontrollable interpretations of percept, antecept, and ponecept. There can surely be no objection to our beginning the discussion by asking what the deliverance of a flow of time, say for example of the motion of a shooting star, is concerning the matter; for this inquiry cannot result in our knowing less about the main question than we did before. The psychologists think it will not cause us to know any more, either; because the question is not what the percipuum represents the nature of the transformations of antecipuum into percipuum and of percipuum into ponecipuum to be, but what in fact they really are. It will be observed that, in so putting the question, the psychologists are assuming that time really is as our common-sense metaphysics, or rather as their own interpretation of common-sense metaphysics, represents it to be. What they doubt is whether the percipuum accords with the facts; that is, with their interpretation of the general mass of experience; or, since experience is nothing but the interpretation of the percipua, what they doubt is whether the percipuum accords with an interpretation of an interpretation of itself, just as one asks whether the Greek testament faithfully accords with the Authorized Version, whether Jesus was a sound christian and could sign the thirty-nine articles, whether Plato, Isocrates, Thucydides and the rest of the prosaists of that period wrote good grammar, and the like. †15 I fear I shall not be able to follow them far into this deep and dark exploration.

649. If we wish to know what the percipuum of the course of time is, all we have to do is to abstain from sophisticating it, and it will be plain enough. No more than the present moment directly confronts us. The future, however little future it may be, is known only by generalization. The past, however little past it may be, lacks the explicitness of the present. Nevertheless, in the present moment we are directly aware of the flow of time, or in other words that things can change. †16 Several other points are clearly delivered in the percipuum, but they are implied in what has been stated. Sundry schools of philosophy hold this testimony of the percipuum to be contrary to sound reason, and accordingly either set it down as false, or conclude that the facts really are absurd, or both. But it strikes me that while it is not the business of facts to conform to what M or N may approve as sound reasoning, it is the business of M's and N's logic to conform to facts.

650. Fully to unfold all the implications of the deliverance of the percipuum so as to demonstrate the accuracy of the interpretation would require a small treatise, if written in the English style, or three stout octavos in German. But I will endeavor to summarize what the upshot of the discussion would be so as to render it tolerably perspicuous.

651. Kant squarely hit the nail on the head when he said that every part of a lapse of time was a lapse of time. But here as in many parts of his philosophy, Kant did not quite understand himself, and imagined that in saying that every part of a time is a time he had only said that time was infinitely divisible. †17 . . . †18

652. But although Kant unwarily confused the idea that time, as "intuited" (to use his language, for he himself translates his Anschauung by the Latin intuitus), has no parts that are not themselves times with the very different idea that there is a way of dividing time so as never to reach an ultimate part (though such parts there may be), yet his reasoning, taken as a whole, is consistent only with the idea that time as intuited has no ultimate parts, or instants. That opinion I share, substituting the percipuum for his intuition. Thus, that which the mathematicians call "continuity" becomes, for me, "pseudo-continuity."

653. Of course, if there is no such thing as an absolute instant, there is nothing absolutely present either temporarily or in the sense of confrontation. In fact, we are thus brought close to the doctrine of Synechism, which is that elements of Thirdness cannot entirely be escaped. The present moment will be a lapse of time, highly confrontitial, when looked at as a whole, seeming absolutely so, but when regarded closely, seen not to be absolutely so, its earlier parts being somewhat of the nature of memory, a little vague, and its later parts somewhat of the nature of anticipation, a little generalized. It contains a central part which is still more present, still more confrontitial, but which presents the same features. There is nothing at all that is absolutely confrontitial; although it is quite true that the confrontitial is continually flowing in upon us.

654. I aver, but do not show, that if my statement of what I call the essential part of the delivery of the percipuum be true to it, then the interpretation given is demonstrably the only one possible. But though I do not actually demonstrate it, I will mention some secondary features of the deliverance of the percipuum which strongly tend to confirm the interpretation.

655. One such deliverance is that any multitude of changes not too great to be successive in any sense might take place in any lapse of time however short. Now two things are demonstrable (although again I withhold the demonstrations). One is that no multitude is so great as to prevent a collection of objects of that multitude from being linearly arranged. †19 The other is that there is no maximum multitude. It follows, then, from the deliverance just stated, that the possible mutually exclusive divisions of any time, however short, exceed all multitude. In that case, time can not only not have merely the pseudo-continuity of quantity, — since the multitude of quantities †20 is well-known to be only the second of an endless series of grades of infinite multitude, — but it cannot be composed of instants at all (as it might very well be and still enormously exceed the differentiation of quantity) since the entire collection of such instants would have a multitude.

656. Another plain deliverance of the percipuum is that moment melts into moment. That is to say, moments may be so related as not to be entirely separate and yet not be the same. Obviously, this would be so according to our interpretation. But if time consists of instants, each instant is exactly what it is and is absolutely not any other. In particular, any two real quantities differ by a finite amount.

657. Still another deliverance of the percipuum is that every interval of time has a beginning and an end, an initial moment and a terminal moment; that is, a moment before which there is no moment of the interval and a moment after which there is no moment of the interval. This again is obviously true of our interpretation; and were the terminal moment thrown off, that is, not reckoned as belonging to the interval, still what was left would have a terminal moment. If only one moment were thrown off at the end, the new terminal moment would not be altogether different from what had been the terminal moment. Of course, the expression "only one moment" can only be understood in a relative sense. This precisely agrees with the percipuum, according to which if from a terminated line, the terminal point be thrown off, what remains still has a terminal which is substantially identical with the old terminal. I appeal to the reader's consciousness to say if that be not so. But if time is composed of instants, and the last instant of an interval be thrown off, the interval will be left without any last. For if it had any, then before the last was thrown off, there would be no instant between this original last and the instant which becomes the last after the throwing off. But to say that there is not a moment between any two distinct moments is too monstrously in conflict with the percipuum for any reasoning man to maintain. Such a notion would be exploded in a dozen ways.

658. By this time, while I have not exhausted my stock of reasons for thinking that the deliverance of the percipuum concerning the flow of time must be interpreted as I say, yet I have said enough to convince any superior reasoner, — or as nearly to convince him as his caution will allow him to be convinced until he has had time for reconsideration. Further confirmation will soon appear; but we may turn now to the question of whether the testimony of the percipuum is truthful or not. It is obvious that a percept cannot be false, since it makes no assertion and is not a proposition, whether indicative, interrogative, optative, imperative, or in any mood whatever; and few philosophers will today think otherwise. It is indeed one of the stock remarks that even a hallucination is not false. It would save me trouble in my present argumentation if I could take that short cut to the truth; but I fear I cannot quite do so.

659. We must enter for a few moments into the field of metaphysics. For we are inquiring how things really are whatever we may think. What is reality? There would not be any such thing as truth unless there were something which is as it is independently of how we may think it to be. †21 That is the reality, and we have to inquire what its nature is. We speak of hard facts. We wish our knowledge to conform to hard facts. Now, the "hardness" of fact lies in the insistency of the percept, its entirely irrational insistency, — the element of Secondness in it. That is a very important factor of reality. But this factor is not confined to the percept. We can know nothing about the percept, — but only experience it in its totality, — except through the perceptual judgment, and this likewise compels acceptance without any assignable reason. This indefensible compulsiveness of the perceptual judgment is precisely what constitutes the cogency of mathematical demonstration. One may be surprised that I should pigeon-hole mathematical demonstration with things unreasonably compulsory. But it is the truth that the nodus of any mathematical proof consists precisely in a judgment in every respect similar to the perceptual judgment except only that instead of referring to a percept forced upon our perception, it refers to an imagination of our creation. There is no more why or wherefore about it than about the perceptual judgment, "This which is before my eyes looks yellow." To show this I must take an example of a mathematical proof; and for the reader's comfort I will take an extremely simple one. At the same time it must be of as abstract a nature as possible, or it might be said that whether intuitional mathematics were perceptual or not, this was not the nature of all mathematics.

660. I will start with the following premiss, which is true of whole numbers: If any predicate, P, be true of the number 0, zero, but not of all numbers, then there must be two numbers M and N such that N is next greater than M, and P, while true of M, is not true of N.

661. From this I proceed to prove, first, that there is no number except zero that is not next greater than some number other than itself. For if there were any such number, call it A. Then the predicate "is not A" would be true of 0 (since A is supposed other than 0) but not of all numbers (since it would not be true of A). Yet there would be no number of which it would be true that it was not A while there was a number next greater than this number of which this was not true (since A is, by hypothesis, not next greater than any other number than itself).

662. I will further prove from the same premiss that there is no number except zero that cannot be reached from zero by a finite multitude of successive steps, each passing from a number to [a] number next greater than it. By a "finite" multitude is meant the multitude of any collection [for which, that collection] being substituted for "Hottentot" in the following syllogism, this syllogism would be valid: Every Hottentot kills a Hottentot; No Hottentot is killed by more than one Hottentot; Therefore every Hottentot must be killed by a Hottentot.

663. I will first demonstrate that if a single individual is joined to a finite collection, the collection will remain finite. For that purpose, I first remark that the premisses of the above syllogism say nothing about the individual differences of the single Hottentots; and therefore if a newcomer were substituted for one of the Hottentots and the conclusion logically followed from the premisses before the substitution, so they would after the substitution. (There are other ways of making this evident.) Now suppose the tribe were increased by a new man. If the collection thereby ceased to be finite, the premisses might continue to be true of the new Hottentots (that is, of the tribe as so increased) and yet some man might escape being killed. We may suppose for convenience that this is the newcomer (since we have seen that a mere substitution as to who kills who makes no difference). Then no Hottentot kills the newcomer; but every Hottentot still kills some Hottentot. Hence he must kill one of the old Hottentots. So as before every old Hottentot kills an old Hottentot and the old Hottentots being a finite collection, every old Hottentot gets killed by an old Hottentot. But no man is killed by two different men; so that there is nobody for the newcomer to kill. Thus the premisses cannot be true of the increased collection unless the conclusion be true; which is as much as to say that the collection remains finite.

664. Now, to return to the numbers, suppose there be such a number as I undertake to prove there is not. Call it A (or if there be more than one, call any one of them A). Let the predicate, P, be "is either zero or can be reached from zero by a finite collection of steps from [a] number to [a] next greater number." This predicate is true of zero, but not of A. Yet there is no number of which it is true and yet not of a next greater, since to suppose this would be to suppose a finite collection of steps would cease to be finite on the adjunction of one more. Thus the supposition that there is such a number as A is absurd, and the proposition is proved.

665. These proofs are founded on nothing but an abstract proposition. But an abstract proposition is a subject for observation as much as anything else. The proofs consist in remarking implications which were not thought of in the proposition as first adopted. Our premiss said that no matter what predicate and what number be chosen, either that predicate is true of that number or not true of zero or else two numbers could be found of one of which, which was next greater than the other, the predicate would not be true while it would be true of the other. In thinking this, we did not think whether or not it was possible that there should be a number not greater than any other. But when this is suggested, we are led to remark that being not next greater than any number and yet not zero is itself a predicate and the negative of a predicate. This is the kind of observation peculiar to mathematics, the looking at things substantively that have only been regarded transitively, or transitorily, the operation of abstraction. †22 How do we know that is a predicate? Precisely as we know that what is before our eyes is yellow. We can, after the fact, invent a formula to cover the case; but it will still leave something undefended. It is really a compulsion similar to that of the perceptual judgment with which we have to do.

Both the arguments happen to be stated in the form of the reductio ad absurdum, which is very appropriate to mathematics as bringing out its ultimately irrational character. But it is a mere form of statement. Every reductio ad absurdum can be stated as a direct argument. The reduction of the figures of [the] syllogism illustrates, if it does not virtually demonstrate, this truth.

666. But it is not in respect to this immediate insistence alone that the real is as it is independently of how we think it to be. The future is real, as well as the present, in so far as it is predetermined; and who but a mad man will deny that it largely is predetermined, at least to some degree, if not irrevocably. Indeed, the tendency of modern philosophy has been to follow the stoical doctrine that the future is what it is to be, independently — of something; I do not think it is clearly said of what. The explanation of this state of mind, as far as the stoics were concerned, is not difficult. The early stoics in their efforts to make the universe comprehensible endeavored to discard elements of Thirdness, with a more or less unconscious feeling of Ockham's razor. The resulting hard dualism suited the hard lot of slaves and of the oppressed; and as time went on and this class and their descendants became more influential, a stern morality, which is essentially dualistic, naturally flourished amid the hideous riot of that age, while thirdness was utterly shoved into the background. The chief rival of stoicism, Epicureanism, sought to get along in its philosophy even without elements of secondness. About 1600, it was the scholastic realists who were the defenders of thirdness, and their dunsical opposition to the new learning and their dreadful corruption of the university disgusted the new men. Hence the fight was between Gassendi, the Epicurean, and Descartes, the real though unconscious stoic. I refuse to believe the future is entirely predetermined; but it certainly is so in great measure; and in so far as it is so, it is independent of all that we can think, wish, or do. It has the kind of compulsiveness that belongs to inductive reasoning, or experimental inquiry, really the most mighty cogency there is. For experimental inquiry sets out with a hypothesis; upon which it bases predictions as to the issue of experiments, and it is left to the future experiment to bring forth the conclusion from the womb of the future. This factor of reality is specially prominent in the reality of personality. It is what the man is destined to do, what of the future is wrapped up in him, that makes him what he is.

667. The difference between the insistency of what is before us and the power of predestination is manifest enough. But there is a third factor of reality, different from either of those. The past also is real, — something in it, at least. The future weeds it out; but the positive element is peculiar. Memory would be nothing but a dream if it were not that predictions are based on it that get verified. When we think how slight and entangled must be the ultimate bits of feeling out of which memory constructs her mosaic, we are compelled to liken it to conjecture. It is a wonderful power of constructing quasi-conjectures or dreams that will get borne out by future experience. The power of performing this feat, which is the power of the past, is a gentle compulsiveness.

668. There are the three elements of reality: that by which ideas spring up that have concealed within them an accord with the mass of ideas; that by which one idea acts directly on another; that force from without that weeds out a part of the ideas and strengthens the rest.

669. To state the matter otherwise: An idea, a surmise springs up in my mind. It recommends itself to me more or less forcibly as reasonable. The fact that it recommends itself to me more or less surely warrants its pretty near accord with what will recommend itself to reasonable minds as well as to the quasi-mind behind the issues of the future. That idea acts upon other ideas and absolutely forces me to say that it requires certain things to happen in the future. The future events come to pass and in part negative my surmise, in part confirm it. I do not know what idea we can form of reality except that it is that threefold force; or what the real can be except that which the whole process tends, as we hope, to induce our thoughts to rest upon.

670. Such being the nature of the real, since the percipuum confesses itself to contain a soupçon of memory, — that is, of conjecture, — as well as a soupçon of onsight, or watching to see if the future comes as expected, it must be confessed that according to the percipuum's own account of itself, not only may this or that percipuum be false, — and should be so regarded in the case of blunders, if not of hallucinations, — but it is even conceivable that all percipua should contain a false element, perpetually refuted by oncoming fresh percipua, although these fresh percipua perpetually introduce the like falsity anew.

671. But it is remarkable that in case we do not accept the percipuum's own account of itself, but maintain that time is composed of absolute instants, then it would seem that there is nothing that empirical truth can mean except accordance with what is given in those instants, which in this case, in no way testify concerning one another or in any way refer to one another. If that be so, a percept must be absolutely true. Here, then, we have a witness who testifies, "There is a certain dose of falsity in my testimony, I know," and a large and influential party of philosophers who protest, "Oh, no such thing! Whatever you testify to is absolute truth."

672. Suppose, however, that some fallacy lurks here, and that the doctrine of instantaneous consciousness does not logically require absolute assent to all the representations of perception. Still, it must be admitted that the only method of ascertaining the truth is to repeat this trio of operations: conjecture; deductions of predictions from the conjecture; testing the predictions by experimentation (not necessarily what is technically so called, but essentially the same thing, — trial). †23 We, thus, necessarily repose upon man's power of guessing the truth. Let him analyze the question as far as practicable; and give him guesses enough (not very many) upon each simple item and eventually he will guess right. Since we thus unavoidably assume that the mind has a certain power of evolving the truth from its own entrails, natural ideas, such as the deliverances of the percipua, have a right of precedence, and should be adhered to until fact flatly contradicts them. But thus far all the facts of observation are in remarkable accord with the deliverance of the percipuum as it is above stated.

673. If my view is right, time is of the nature of a general. That is, it may be a day; and a day is, by virtue of there being a forenoon and an afternoon; and a forenoon or afternoon is, by virtue of the different hours; the hour, by virtue of its minutes; and so on endlessly. But you never can find an indivisible time.

674. It is true that we may imagine a pendulous motion. The motion to the right ceases and the motion to the left begins. If the pendulum is an absolutely rigid body all whose parts are constrained to move in precisely the same way, then, were time composed of rational dates only, there need not be any date at which the right hand motion ended and the left hand motion began. In a true continuum there must be a common moment, but not an absolute instant, independent of all that is before and after. Looking at matters through the wrong end of a telescope, as it were, — that is, aggregating the parts, — there certainly is something in a moment altogether independent of past and future. But examining the moment under a microscope we find this independent element divided up into portions, less independent of one another. Finally, we come to this, that while there are elements of secondness, — of irrational compulsion — they flow in upon us continuously, thus being subjected from the very first to thirdness. Take away considerable time, — as a day; — and doubtless much therein happens that could not have been expected. But if we divide the day into hours, we find that much that was unexpected on the whole is no more than might have been anticipated from a part; and so we are led to say that the unexpected comes, not only in driblets, but in inappreciable flow.

675. On the whole, then, the percipuum is not an absolute event. There is no span of present time so short as not to contain something remembered, that is, taken as a reasonable conjecture, not without containing something expected for the confirmation which we are waiting. The peculiar element of the present, that it confronts us with ideas which it forces upon us without reason, is something which accumulates in wholes of time and dissipates the more minutely the course of time is scrutinized.

676. There is no percipuum so absolute as not to be subject to possible error.

677. The percipuum is a recognition of the character of what is past, the percept which we think we remember. The interpretation is forced upon us; but no reason for it can be given.

678. But just so when we experience a long series of systematically connected phenomena, suddenly the idea of the mode of connection, of the system, springs up in our minds, is forced upon us, and there is no warrant for it and no apparent explanation of how we were led so to view it. You may say that we put this and that together; but what brought those ideas out of the depths of consciousness? On this idea, which springs out upon experience of part of the system we immediately build expectations of what is to come and assume the attitude of watching for them.

679. It is in this way that science is built up; and science would be impossible if man did not possess a tendency to conjecture rightly.

680. It is idle to say that the doctrine of chances would account for man's ultimately guessing right. For if there were only a limited number n of hypotheses that man could form, so that 1/n would be the chance of the first hypothesis being right, still it would be a remarkable fact that man only could form n hypotheses, including in the number the hypothesis that future experimentation would confirm. Why should man's n hypotheses include the right one? The doctrine of chances could never account for that until it was in possession of statistics of the hypotheses that are inconceivable by man. But even that is not the real state of things. It is hard to say how many hypotheses a physicist could conceive to account for a phenomenon in his laboratory. He might suppose that the conjunctions of the planets had something to do with it, or some relation between the phases of variability of the stars in {ö} Centauri, or the fact of the Dowager empress having blown her nose 1 day 2 hours 34 minutes and 56 seconds after an inhabitant of Mars had died. The truth is that very few hypotheses will appear to the physicist to be reasonable; and the one true hypothesis is usually of this small number. Why is that? It may be answered, very truly, that experience has taught us that astrology, correspondences, magic, and many hypotheses formerly considered reasonable are to be put aside. Yes, but if primitive man had not had, at the very outset, some decided tendency toward preferring truthful hypotheses, no length of time, — absolutely none, — would have been sufficient to educate him even to the state of mind of Aristotle in his Book of Physical Auscultations, ridiculous as all that now seems to us. No, it is absolutely necessary to admit some original connection between human ideas, and the events that the future was destined to unfold.

681. But that is something very like telepathy. What would telepathy amount to, if it were an established fact. It would then be proved that people not very infrequently have hallucinations, and that one hallucination out of a great number (but more frequently than chance coincidence could account for) coincides with subsequent experience to such a degree as to attract attention; for even if there really be telepathy we must suppose, from what we know of human nature, that the accordance with truth is apt to be greatly exaggerated. In this case, telepathy would be a phenomenon somewhat more remote from perception than the conjectures by which physicists so often hit upon the truth.

§6. Conclusion

682. Very well, then; what does all this rambling lead to? Nobody, of course, denies the phenomena, which the telepathists bring before us; that is to say, that such and such stories are told. The only question is whether they are to be accounted for by the operation of causes usually active in such phenomena.

683. The doctrine of telepathy is not established, nor far on the way toward establishment, as a scientific truth. For understood as the telepathists make a point of defining it, it denies the hope on which all science is based. If, however, we amend it, in order to avoid that positively anti-scientific character, what does it amount to? That very rarely a person at a distance from another has a hallucination or a positive conviction apparently irrational which represents something as having happened to that other person, and this turns out to be veridical with a frequency and to a degree which we know not how to explain, and which seems mysterious. But science can make no use of a proposition so vague as that. Where is the phenomenon, or the feature of a phenomenon, in which, if we examine closely, we shall not find much that our science cannot yet explain?

684. There is, however, no part of the work of science that ought to rank higher than that which brings a phenomenon to the cognizance of science. That sort of work, which Chladni did for the falling stones, is what the psychicists are endeavoring to do for veridical hallucinations and the like; and they will no doubt persevere until they succeed. I do not think they have displayed great genius for research; but they ought to be respected for the thorough single-heartedness, conscientiousness, and constancy with which they have pursued this purpose.

685. The general public has no accurate conception of what the work of a scientific investigator consists in; for the books of "popular science" give no idea of it. But the general public is no fool in judging of human nature; and the general public is decidedly of the opinion that there is such a thing as a scientific pedantry that swells with complaisance when it can sneer at popular observations, not always wisely. I must confess that in the past generations scientists of great eminence have sometimes been betrayed into this fault; but it will not be so hereafter. As for Sir William Crooks his most exquisite experimental researches were still in the future when he first displayed an openness of mind more admirable still. Neither Newcomb nor Langley was a worn-out and super-annuated physicist when he took a prominent position in the Psychical Research Society; neither had at that time achieved his most brilliant experimental triumphs.

686. What school of philosophers is it that attributes to the human mind the most wonderful powers? One might guess that it would be the idealists and spiritualists; but strange to say it is those who boast themselves to be materialists and who insist that nothing is real except mass and motion. For in order to maintain that, they are obliged to say that law is nothing but a figment of the human mind. Now law can certainly not be jammed into the pigeon-hole of mass, nor into that of motion. That indeed is their real reason for making it a fiction. Now is it not of all things the most wonderful, that the mind should be able to create an idea for which there is no prototype in nature, nor anything in the least resembling it, and that by means of this utter fiction it should manage to predict the results of future experiments and by means of that power should during the nineteenth century have transformed the face of the globe? Telepathy, with its infrequency and usual deceptiveness (for there is no reason for separating veridical from non-veridical hallucinations, as phenomena essentially different,) would be an insignificant faculty in comparison.

687. For my part, I cannot accept such a theory. It attributes to man powers which he knows too well that he does not possess. It seems to me that the only admissible view is that the reasonableness, or idea of law, in a man's mind, being an idea by which objective predictions are effected, — for all physical theories originate in human conjectures, and experiment only lops off what is erroneous and determines exact values, — must be in the mind as a consequence of its being in the real world. Then the reasonableness of the mind and that of nature being essentially the same, it is not surprising that the mind, after a limited number of guesses, should be able to conjecture what the law of any natural phenomenon is. How far this power of conjecture may go we certainly do not know. We do know that it goes far enough to have enabled men to make already considerable progress in science. Whether or not it extends so far that very rarely one mind can know what passes in another at a distance, would seem to be a question to be investigated as soon as we can see our way to doing so intelligently. I do not believe that questions can be permanently settled by pooh-poohing one or another alternative.

688. It is curious to see how the materialists, — or those who are flattered at being so called, — plume themselves on being free from "beliefs." Really, one would suppose they imagined it possible for a man to conduct his life on a basis of scientifically established doctrine. It is true that an engineer, civil, mechanical, electrical, or chemical, is able to do this in the present advanced state of science, so far as he has to deal with materials. But even a member of one of those four professions, the only ones that can be called thoroughly reduced to the applications of scientific principles, even he still finds that exact science fails him in dealing with men, — that is to say in considering the use to which his construction is to be put, in considering financial questions, in considering his relations to those who are to execute his plans. For everything else in life unscientific beliefs have to be relied upon for the present; and in particular, it is precisely what we are to believe about telepathy that we all are curious to know. †24


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The Collected Papers of Charles Sanders Peirce. Electronic edition.
Volume 7: Science and Philosophy
Endmatter
Endnotes
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Endnotes

xi

†1 He was employed by the Coast Survey from September 21, 1859, to June 1, 1860, and from July 1, 1861, to December 31, 1891.

xi

†2 See the Bibliography in Vol. VIII, especially the years 1872 through 1886; Peirce produced little in the way of results for the Coast Survey after he moved to Milford, Pa., in the spring of 1887.

xii

†3 Cf. 6.44, 6.46. Peirce's most original contribution to geodetics was the discovery of a new source of error in gravity measurement; this is described at 7.1-12. Peirce also did research for the Coast Survey on standards of measurement.

3

†1 (Ed.) From pp. 359-361 of Appendix 14, "On the Flexure of Pendulum Supports," [CS 1881] 1883, pp. 359-441.

3

This gives a succinct account, in Peirce's own words, of his most original work in the field of pendulum measurements.

4

†2 Thus, Bessel's idea of directly measuring the position of the center of mass was supposed by the Swiss savans to belong to M. Cellerier.

5

†3 (Ed.) [Bibliography] G-1875-5. The quotations from the circular by Baeyer, given in 7.6, and from the reports, given in this paragraph, are in [International Geodetic Comm., Paris, 1875] 1875, pp. 90-91, 93, and 96.

6

†4 (Ed.) See [Bibliography] G-1875-5. The quotation in this paragraph from Hirsch is in [International Geodetic Comm., Brussels, 1876] 1877, p. 18.

6

†5 (Ed.) [Bibliography] G-1877-3.

7

†6 (Ed.) See [Bibliography] G-1877-3.

8

†7 (Ed.) "Six Reasons for the Prosecution of Pendulum Experiments," pp. 506-508 of Appendix 22, "Report of a Conference on Gravity Determinations, Held in Washington, in May, 1882," [CS 1882] 1883, as corrected from a reprint marked "Copy read by C. S. Peirce," Widener IC2c.

8

This is reprinted here because it is a good statement by Peirce of what he thought the value of his pendulum work to be.

9

†8 (Ed.) J. E. Hilgard was Superintendent of the United States Coast and Geodetic Survey at this time.

10

†9 (Ed.) Cf. [Bibliography] G-1879-1, G-1881-5, G-1882-12.

13

†1 (Ed.) "On Small Differences of Sensation," Memoirs of the National Academy of Sciences 3, Part I (1884) 73-83, with corrections from a reprint marked, "Prof. John W. Langley, With the regards of C. S. Peirce," Widener IC1a.

13

The article was written with Joseph Jastrow, a student of Peirce at Johns Hopkins University. In The Nation 98 (14 May 1914) 571 Jastrow says of it: "It was Mr. Peirce who introduced me to the possibility of an experimental study of a psychological problem. He provided the problem, the instruments which I set up in my room, the method, and the mode of reaching the results; these were printed over our joint names." See also Joseph Jastrow, "Charles S. Peirce as a Teacher," The Journal of Philosophy, Psychology, and Scientific Method 13 (21 Dec. 1916) 724.

13

Edwin G. Boring, in his A History of Experimental Psychology, p. 529, refers to "On Small Differences of Sensation" as "an important paper on the method of determining the differential limen . . ."

13

†2 Elemente der Psychophysik, I, p. 242.

15

†3 The rule for finding this ratio is as follows: Divide the logarithm of the ratio of excitations by the probable error and multiply the quotient by 0.477. Call this product t. Enter it in the table of the integral {th}t, given in most works on probabilities; {th}t is the proportion of cases in which the error will be less than the difference between the given excitations. In all these cases, of course, we shall answer correctly, and also by chance in one-half of the remaining cases. The proportion of erroneous answers is therefore (1-{th}t)/2. In the following table the first column gives the quotient of the logarithm of the ratio of excitation, divided by the probable error, and the second column shows the proportion of erroneous judgments:

0.0 0.50
0.05 0.49
0.1 0.47
0.25 0.43
0.5 0.37
1.0 0.25
To guess the correct card out of a pack of fifty-two once in eleven times it would be necessary to have a sensation amounting to 0.37 of the probable error. This would be a sensation of which we should probably never become aware, as will appear below.
17

†4 The number of errors, when an increase of weight was followed by a decrease, was slightly less than when the first change was a decrease of pressure.

18

†5 The result of our observations on the confidence connected with the judgments is as follows: —————————————————————————————- [Subject, Mr Peirce.] —————————————————————————————- Average Number of Variations. confidence. sets of 50. —————————————————————————————- Grams. 60 ........................... .67 7 30 ........................... .28 6 15 ........................... .15 5 —————————————————————————————- ——————————————————————————————— [Subject, Mr. Jastrow.] ——————————————————————————————— 60............................ .90 13 30............................ .51 12 15............................ .30 12 20............................ .11 12 10............................ .06 12 5............................ .00 10 ———————————————————————————————

18

In 1,125 experiments (subject, Mr. Peirce) — variations 15, 30, and 60 grams — there occurred confidence of 3, 35 times (3 per cent.); of 2, 102 times (9 per cent.); of 1, 282 times (25 per cent.); of 0, 706 times (63 per cent.). In these experiments there were 332 (29 per cent.) errors committed, of which 1 (0.3 per cent.) was made in connection with a confidence 3; 10 (3 per cent.) with a confidence 2; 51 (15 per cent.) with a confidence 1; 270 (81 per cent.) with a confidence 0. From which we find that in connection with a confidence of 3 there occurred 1 error in 35 cases (3 per cent.); with a confidence of 2, 10 errors in 102 cases (10 per cent.); with a confidence of 1, 51 errors in 282 cases (18 per cent.); with a confidence of 0, 270 errors in 706 cases (38 per cent.).

18

In 1,975 experiments (subject, Mr. Jastrow) — variations 15, 30, and 60 grams — there occurred confidence of 3, 62 times (3 per cent.); of 2, 196 times (10 per cent.); of 1, 594 times (30 per cent.); of 0, 1,123 times (57 per cent.). In these experiments there were 451 (23 per cent.) errors committed, of which 2 (0.4 per cent.) were made in connection with a confidence of 3; 12 (3 per cent.) with a confidence of 2; 97 (22 per cent.) with a confidence of 1; 340 (75 per cent.) with a confidence of 0. Again, in connection with a confidence of 3, errors occurred twice in 62 cases (3 per cent.); with a confidence of 2, 12 times in 196 cases (6 per cent.); with a confidence of 1, 97 times in 504 cases (16 per cent.); with a confidence of 0, 340 times in 1,123 cases (30 per cent.).

18

In 1,675 experiments (subject, Mr. Jastrow) — variations 5, 10, and 20 grams — there occurred confidences of 3, none; of 2, none; of 1, 115 times (7 per cent.); of 0, 1,560 times (93 per cent.). In these experiments there were 538 (32 per cent.) errors committed, of which 16 (3 per cent.) occurred in connection with a confidence of 1; 522 (97 per cent.) with a confidence of 0. Again, in connection with a confidence of 1, errors occurred 16 times in 115 cases (14 per cent.); with a confidence of 0, 522 times in 1,560 cases (34 per cent.). Second group. ———————————————————————————- Ratio of weights. Mark 0. Mark 1. Mark 2. Mark 3. ———————————————————————————- 1.015.......{110 right 51 right 3 right 1 right { 66 wrong 17 wrong 2 wrong 0 wrong 1.030.......{106 right 72 right 23 right 2 right { 35 wrong 11 wrong 1 wrong 0 wrong 1.060.......{ 86 right 75 right 54 right 24 right { 8 wrong 1 wrong 2 wrong 0 wrong ———————————————————————————- Third and fourth groups. [Marks 2 and 3 do not occur.] ——————————————————————- Ratio of weights. Mark 0. Mark 1. ——————————————————————- 1.005...............{294 right 2 right {203 wrong 1 wrong 1.010...............{366 right 32 right {192 wrong 30 wrong 1.020...............{395 right 68 right {131 wrong 6 wrong ——————————————————————-

21

†6 At first a short pause was made in the set of 25, at the option of the subject; later this was dispensed with.

22

†7 In the experiments of December, 1883, and January, 1884, the method as above described was not fully perfected, the most important fault being that the total weight instead of being removed and replaced by a mechanical device, was taken off by the operator pressing with his finger upon the beam of the balance.

26

†8 In the tables of the third and fourth groups, there is a marked divergence between the a priori and a posteriori probable error, for the average number of errors in 50, making the observed probable error too small. This can only be partly accounted for by the fact that the subject formed the unconscious habit of retaining the number of each kind of experiment in a set and answering according to that knowledge. In point of fact the plus errors and minus errors separately do not exhibit the singular uniformity of their sums, for which we are quite unable to account. Thus in the fourth group we have: Number of + and - errors. Date. 1.020 1.010 1.005 ———————————————————————————— March 30........ -4,+ 7 -6,+10 -13,+ 8 March 31........ -7,+ 3 -5,+10 - 6,+15 April 2......... -1,+10 -8,+ 9 - 8,+13 April 3......... -4,+ 5 -4,+14 -10,+10 April 6......... -6,+ 6 -8,+ 7 -10,+11 April 7......... -5,+ 9 -8,+ 7 - 8,+ 9 ————————————————————————————

26

†9 The conclusions of this paper are strengthened by the results of a series of experiments on the color sense, made with the use of a photometer by Mr. Jastrow. The object was to determine the number of errors of a given magnitude, and compare the numbers thus ascertained with the theoretical numbers given by the probability curve. A thousand experiments were made. Dividing the magnitude of the errors from 0 to the largest error, made into 5 parts, the number of errors, as observed and calculated, that occur in each part are as follows: Observed ....... 199 181 217 213 190 Calculated ..... 213 197 209 181 200

26

These numbers would be in closer accordance if the probable error were the same throughout, as it is not owing to the effects of practice, etc. Moreover, the experiments were made on different colors — 300 on white and 100 each on yellow, blue, dove, pink, green, orange, and brown. These experiments were not continuous.

27

†10 (Ed.) See the following section of the present chapter.

27

†11 (Ed.) Cf. [Bibliography]G-1887-3, p. 194.

27

†12 (Ed.) From a manuscript, "Guessing," with a quotation in 36n13 from a fragmentary alternative draft. These manuscripts are in Widener IB2-12, and are dated c.1907 on the basis of internal references and statements in the letter referred to in 44n17.

27

The manuscript, "Guessing," was published in The Hound and Horn 2 (April-June 1929) 267-282.

27

In the passages reprinted here Peirce gives a non-technical summary of the previous paper and discusses some philosophical implications of it.

27

†13 (Ed.) The fragmentary manuscript (see 36n12) begins: "All our knowledge starts from perception, and consequently perception ought never to be doubted, and indeed never can be doubted. That is to say, that we cannot doubt that that really seems which seems to seem" and then the manuscript proceeds very much like the version printed above. Cf. 5.157.

29

†14 (Ed.) Cf. 2.638, 2.753, 2.755.

30

†15 (Ed.) Peirce here recounts a personal anecdote, concerning the theft of his coat and a valuable watch from his stateroom on a Boston to New York boat. He says that he made all the waiters stand in a row and after talking briefly with each, but without consciously getting any clue, he made a guess as to which one was guilty. The upshot of the story is that after many difficulties, and by making more successful guesses, he proved that his original guess had been correct.

31

†16 (Ed.) See the first section of this chapter.

32

†17 (Ed.) Reprinted as the first section of this chapter. Peirce says in a letter to William James of 16 July 1907 (Houghton Library) that there were 3389 guesses given with a confidence of "Naught" and about two thirds of these were correct (see 26n5).

37

†1 (Ed.) Paragraphs 49-52 are from manuscript L, undated (but cf. 59n4), Widener IB2-9. Paragraphs 53-58 are from "Of the Classification of the Sciences. Second Paper. Of the Practical Sciences," Widener II. Paragraphs 53-57, 381n19 and 58 come from the manuscript in that order. This manuscript is dated c.1902 on the basis of references in it.

40

†2 (Ed.) This statement appears on page 3 in the edition edited by Alois Höfler, published by C. E. M. Pfeffer, Leipzig, 1900.

43

†3 (Ed.) Cf. 5.340.

43

†4 (Ed.) Paragraphs 59-76 are "Introductory Lecture on the Study of Logic," [JHUC] 2(Nov 1882)11-12, with two preliminary paragraphs omitted. Paragraphs 77-78 are from manuscript N, Widener IB2-9, undated, but the manuscript contains results from the census of 1900. This manuscript and manuscript L (cf. 49n1) are probably parts of the same work.

44

†5 (Ed.) Orbellis (Nicholaus de), Expositio super textu Petri Hispani, Super libro Peryhermenias, Venice, 1500, fol. a3v.

46

†6 (Ed.) See Book I of the present volume.

46

†7 (Ed.) Peirce's main task in the United States Coast Survey was to measure the force of gravity by swinging a pendulum.

46

†8 (Ed.) See the review of Wundt's book in [CP] VIII, Book I, Review 14.

47

†9 (Ed.) See [CP] V.

48

†10 (Ed.) See the rest of the present book and [CP] II for discussions of most of the topics mentioned in this and the following paragraphs.

49

†11 (Ed.) Cf. 5.383ff.

52

†12 (Ed.) Paragraphs 79-88 are "Scientific Method," Dictionary of Philosophy and Psychology (edited by James Mark Baldwin), Vol. II, 1902, pp. 500-503. Paragraphs 89-91 are "Verification," ibid., pp. 761-762.

52

†13 (Ed.) Peirce did not define this term for Baldwin's Dictionary, but see Section 1 of the present chapter (49ff.).

54

†14 (Ed.) See Chapter 2, "Economy of Research," in the present book.

55

†15 (Ed.) See Chapter 3, "The Logic of Drawing History from Ancient Documents," in the present book.

57

†16 (Ed.) Cf. Chapter 5, "Telepathy and Perception," in Book III of the present volume.

57

†17 (Ed.) 2.773-778.

58

†18 (Ed.) 2.783-787.

59

†19 (Ed.) Paragraphs 92-93 are "Parsimony (law of)," Dictionary of Philosophy and Psychology (edited by James Mark Baldwin), Vol. II, 1902, p. 264. Paragraphs 94-96 are from "Theory," ibid., pp. 693-694.

61

†20 (Ed.) "Notes for my Logical Criticism of Articles of the Christian Creed," Widener IB3. Judging by the reference to 1860 in the second paragraph, this is to be dated c.1910.

61

†21 (Ed.) Peirce also uses "Abduction" and "Hypothesis" for what he here calls "Retroduction."

62

†22 (Ed.) That is, in the case of a unit mass, the force is equal to the acceleration, and it is also equal to the derivative of the energy with respect to distance.

62

†23 (Ed.) See [CP] IV, Book II.

64

†24 (Ed.) Peirce's fallibilism, the doctrine that there is no absolute certainty in knowledge, is discussed at 1.8ff., and elsewhere in [CP] I.

64

†25 (Ed.) Cf. the discussion of unreal doubt as contrasted to genuine doubt at 5.265 and elsewhere in [CP] V.

65

†26 (Ed.) From Vol. I of Lecture 7 of the Lowell Lectures of 1903, Widener IB2-4. Cf. 2.755-760 and 7.208-217 for related treatments of the same topic.

67

†27 (Ed.) "The Deductions which we base upon the hypothesis which has resulted from Abduction produce conditional predictions concerning our future experience. That is to say, we infer by Deduction that if the hypothesis be true, any future phenomena of certain descriptions must present such and such characters. We now institute a course of quasi-experimentation in order to bring these predictions to the test, and thus to form our final estimate of the value of the hypothesis, and this whole proceeding I term Induction. I speak of quasi-experimentation because the term experiment is, according to the usage of scientific men, restricted to the operation of bringing about certain conditions. The noting of the results of experiments or of anything else to which our attention is directed in advance of our noting it, is called Observation. But by quasi-experimentation I mean the entire operation either of producing or of searching out a state of things to which the conditional predictions deduced from hypothesis shall be applicable and of noting how far the prediction is fulfilled." From an earlier passage of the same lecture (110n26).

72

†28 (Ed.) From Lecture IV (c.1866) of the same series from which 7.579-596 are taken, Widener IB2-10; cf. 7.579n34.

76

†1 (Ed.) "Note on the Theory of the Economy of Research," [CS 1876] 1879, pp. 197-201, with some corrections from a manuscript version in Widener IC2a. Cf. 5.600ff.; the paper referred to at 5.601n§ is probably this one.

81

†2 (Ed.) In this paragraph the editor has corrected the second formula according to the manuscript, and rewritten the notation somewhat to make it uniform.

82

†3 (Ed.) In the manuscript version (see 139n1) Peirce says that this problem suggested his speculations on the economy of research.

82

†4 (Ed.) See [Bibliography] G-1879-5d, p. 260.

84

†5 (Ed.) "[Memoir] No. 28, On the Economics of Research," from an application by Peirce for a grant from the Carnegie Institution (stamped by the Carnegie Institution 30 July 1902) with an added quotation in the present footnote from an alternative draft, both in Widener VB5. Peirce proposed to write thirty-six memoirs on logic, most of them of approximately 20,000 words, a few much shorter, and some of 50,000 words.

84

The following are quoted from other parts of the application: "Therefore, what I hereby solicit the aid of the Carnegie Institution to enable me to do is to draw up some three dozen memoirs, each complete in itself, yet the whole forming a unitary system of logic in all its parts, which memoirs shall present in a form quite convincing to a candid mind the results to which I have found that the scientific method unequivocally leads, adding, in each case, rational explanations of how opposing opinions have come about; the whole putting logic, as far as my studies of it have gone, upon the undeniable footing of a science," pp. 4-5.

84

"It is my belief that science is approaching a critical point in which the influence of a truly scientific logic will be exceptionally desirable. Science, as the outlook seems to me, is coming to something not unlike the age of puberty. Its old and purely materialistic conceptions will no longer suffice; while yet the great danger involved in the admission of any others, ineluctable as such admission is, is manifest enough. The influence of the conceptions of methodeutic will at that moment be decisive," p. 57.

84

In an alternative draft of this application he says: "What are the researches of which I speak? "They are the work of my life, that which I seem to have been put into the world to do." The application was rejected.

87

†6 (Ed.) Section 1 of the present chapter.

87

†7 (Ed.) See the same quotation in 7.59.

89

†1 (Ed.) From a draft of a report on the meeting of the National Academy of Sciences in November, 1901, Widener IV; see [Bibliography] N-1901-16. Cf. [Bibliography] G-1901-2b and 2c, both of which touch on the topic of the present chapter and which were written about the same time.

90

†2 (Ed.) The remainder of this chapter is from a typed manuscript, "On the Logic of drawing History from Ancient Documents especially from Testimonies," with two quotations added at 182n7 and 220n18. The material from the manuscript includes additions in Peirce's hand and a few minor editorial corrections taken from a corresponding handwritten manuscript; the quotation in 220n18 is from some alternate pages of the handwritten manuscript. These manuscripts are at Widener IB2-12 and are dated c.1901 on the basis of Peirce's National Academy of Sciences paper, [Bibliography] G-1901-4.

99

†3 (Ed.) Cf. 2.19ff.

101

†4 (Ed.) Peirce's theory of probability is presented in [CP] II, Part B of Book III.

105

†5 (Ed.) See 1.188, 1.260, 1.502.

105

†6 (Ed.) See 1.189.

†7 (Ed.) "On five occasions in my life, and on five occasions only, I have had an opportunity of testing my Abductions about historical facts, by the fulfillment of my predictions in subsequent archeological or other discoveries; and on each one of those five occasions my conclusions, which in every case ran counter to that of the highest authorities, turned out to be correct. The last two cases were these. Prof. Petrie published a history of Egypt in which he treated the first three dynasties as mythical. I was just about writing a history of science and in the first chapter I showed why those Dynasties including the name of Menes and other facts ought to be considered historical. Before my book was near completion Petrie himself found the tomb of Menes. Again a few years ago I wrote in the Nation, where there was no room for details, that the Babylonians had high scientific genius and that there was reason to conjecture that Alexander sent home a Babylonian celestial globe dating from 2300 years B.C. Now the newest finds show that at that very date they were accomplished astronomers." From the Lowell Lectures of 1903, Lecture VIII, following shortly after 5.604; Widener IB2-4. See [Bibliography] G-1903-2a.

107

†8 (Ed.) [Bibliography] G-c.1902-2.

107

†9 (Ed.) Cf. [Bibliography] G-1901-2.

112

†10 (Ed.) Cf. [Bibliography] G-1891-1.

116

†11 (Ed.) The Principles of Empirical or Inductive Logic, London, 1889. The quotations given by Peirce in paragraphs 199 and 200 are taken from pages 495 and 498.

119

†12 (Ed.) See R. C. Archibald, Benjamin Peirce, p. 14, for an account of this.

121

†13 (Ed.) These subjects are also treated in [CP] II.

125

†14 (Ed.) See Chapter 2, "Economy of Research," in the present book.

126

†15 (Ed.) Cf. 7.110-130.

126

†16 (Ed.) There follows a long discussion of collections (sets), of which we have printed here only that part necessary to understand the discussion below.

127

†17 (Ed.) [Bibliography] G-1881-7 ([AJM]). See also [Bibliography] G-1885-3 ([AJM]).

138

†18 (Ed.) "[Abduction] alone can propose every proposition. . . . induction is the sole court of last resort in every case.

138

"This being the case, what does it matter how the work of abduction is performed? It matters much, for the reason that it originates every proposition. It is true that, however carelessly the abduction is performed, the true hypothesis will get suggested at last. But the aid which a correct logic can afford to science consists in enabling that to be done at small expenditure of every kind which, at any rate, is bound to get done somehow. The whole service of logic to science, whatever the nature of its services to individuals may be, is of the nature of an economy. So much truth, — and more than this, — I concede to the doctrine of Ernst Mach, although I cannot approve of the extreme length to which he carries the theory of economy. . . .

138

"The principles upon which abduction ought to be conducted ought to be determined exclusively by considerations of what purpose it subserves and how it may best subserve that purpose. Since, therefore, in scientific investigation abduction can subserve no other purpose than economy, it follows that the rules of scientific abduction ought to be based exclusively upon the economy of research." From a fragmentary alternative draft (see 164n2).

138

Cf. Chapter 2, "Economy of Research," in the present book (7.139ff.).

151

†19 (Ed.) The essentials of this story are credited in John Edwin Sandys, A History of Classical Scholarship, Vol. 1, 3rd edition, University Press, Cambridge, 1921, pp. 85-86.

153

†20 (Ed.) Peirce's brackets.

161

†21 (Ed.) Peirce's brackets.

162

†22 (Ed.) Peirce advanced the same theory at 2.776, but at 8.209 (c.1905) he confesses that it is doubtful.

164

†23 (Ed.) Peirce then proceeds to give two more illustrative examples. The first is a problem of the chronology of Plato's dialogues, and the second concerns the life of Pythagoras. This part of the manuscript is more than half as long as the part reprinted here.

165

†1 (Ed.) Paragraphs 256-261 are from one draft of a manuscript on the productiveness of the nineteenth century in great men; paragraphs 262-266 are from an alternative draft. Both drafts are in Widener IC1b, and are dated c.1900 on the basis of their resemblance to [Bibliography] G-1901-5a and internal references to dates.

165

For additional information on Peirce's study of great men see [Fisch-Cope] 290-291 and Joseph Jastrow, "Charles S. Peirce as a Teacher," The Journal of Philosophy, Psychology, and Scientific Method 13 (21 Dec 1916) 724-725.

167

†2 The fact that some of the finest observations of the naturalist were made by a blind man sufficiently shows that that science does not call for any extraordinary amount of the power I have in view.

167

(Ed.) Peirce is probably referring here to François Huber, 1750-1831, a Swiss naturalist who became blind at age fifteen. He was noted for his investigations of bees.

169

†3 (Ed.) [Bibliography] G-1878-6.

170

†4 This vote was probably influenced by religious bias.

172

†5 (Ed.) Cf. Peirce's "Introductory Lecture on the Study of Logic," 7.59-76.

174

†6 (Ed.) Peirce then proceeds to discuss the great men of the nineteenth century. He discusses the century's great men in science in [Bibliography] G-1901-5a.

175

†7 (Ed.) Paragraphs 267-275 are the concluding remarks to a series of lectures on the history of science, Widener IC1b, with quotations added at 267n8. The first paragraph of 267n8 is from Lecture V of this series, Widener IC1b. These are most probably the lectures delivered on "The History of Science" to the Lowell Institute, 1892-1893. On the basis of this probability and internal references, Lecture V is dated c.1892, and the concluding remarks 1893.

175

Paragraphs 276-278 are Section 13, "Varieties of Medisense," of an incomplete manuscript, undated, Widener IB2-10. This manuscript has some resemblance to 7.539-552, [Bibliography] G-undated-9, and may have been written about the same time.

175

Paragraph 279 is from Section 1, "Classification of the Sciences," of Minute Logic, Chapter 2, "Prelogical Notions," Widener IB2-2. The marginal sidehead is "Three Stages of Physical Research." One of the manuscript pages is stamped "Mar 12 1902." This selection lies between 7.374n10 and 7.362; cf. 7.362n1.

†8 (Ed.) In Lecture V of the series (see 267n7), Peirce says: "For my part, I am quite sure that, however it may be with the rank and file of the great army of general readers, those who come here will be interested in the history of science not as a mere Wonder Book, but as an instance, a specimen, of how the laws of growth apply to the human mind. As this Century is drawing to a close, it is interesting to pause and look about us and to ask ourselves in what great questions science is now most interested. The answer must be that the question that everybody is now asking, in metaphysics, in the theory of reasoning, in psychology, in general history, in philology, in sociology, in astronomy, perhaps even in molecular physics, is the question How things grow; and by far the most interesting aspect of the history of science, is that it shows how an important department of human thought has been developed from generation to generation, with a view of comparing this growth with the historical development of art, of religion, of politics, and of institutions generally, and not only with historical development but also with the growth of the individual mind, and not only of mind, but of organisms both in their geological succession and in their individual development, and with the formation of worlds, and even with the gradual coming into being and crystallization of the fundamental laws of matter and of mind, — from all of which facts taken together we are to expect in the future a grand cosmogony or philosophy of creation."

In the "Introduction" to a planned history of science, Widener IC1b (undated), Peirce says: "For that which the author had at heart throughout his studies of the history of science was to gain an understanding of the whole logic of every pathway to the truth."

178

†9 (Ed.) [Bibliography] G-1891-1e (1893).

179

†10 (Ed.) Cf. 7.539-552.

179

†11 (Ed.) Cf. [Bibliography] G-c.1893-4.

180

†12 (Ed.) Cf. [Bibliography] N-1894-4.

181

†13 (Ed.) From "Of the Nature of Measurement," an undated, incomplete manuscript in Widener IA-4. Cf. 4.142-152 which are on the same topic.

184

†14 (Ed.) Cf. 5.389.

186

†15 (Ed.) Cf. 3.567ff., 4.639ff., 6.174ff.

187

†16 (Ed.) Brackets in the original.

190

†17 (Ed.) The proof, which is quite long, and a scholium are omitted. The title, "Of Space Measurement," precedes the following paragraphs.

193

†18 (Ed.) The manuscript continues for several pages and then breaks off in the middle of a sentence.

†1 (Ed.) This chapter is from a set of associated manuscripts in Widener IB2-8, with the addition of a quotation in the present footnote. These manuscripts seem to be a number of partial drafts of a book to be titled "Logic." One set of chapters includes several bearing dates in March, 1873, and one chapter of another set is dated "1873 July 1." Others may have been written in 1872; in a letter to his brother Henry dated November 24, 1872, William James says, "Charles Peirce . . . read us an admirable introductory chapter to his book on logic the other day" ([Perry] I, 332). Some of the manuscripts have no heading, but probably belong to this undertaking. The portions bearing no date are dated here c.1873.

The contents of the present chapter should be compared with "The Fixation of Belief" (1877), 5.358-387, and "How to Make Our Ideas Clear" (1878), 5.388-410. Several pages in the set of manuscripts from which the present chapter is taken contain passages to be found in the first of these two articles. In 1909 and 1910 Peirce worked on a revision of these two articles, to be published under a single title. A draft for this work is titled, "Essays Toward the Interpretation of Our Thoughts (Provisional Title of volume); My Pragmatism (Provisional Title of the Essay), set forth in Two Chapters," Widener IB2-11. On page 1 of the draft, in a preface for the work, Peirce says: "The main part of this Essay, — the characterizations of Belief and of Doubt, the argument as to the effective aim of inquiry, the description of four methods directed toward that aim, with the criticisms of them, the discussion of the proper function of thinking, and the consequent maxim for attaining clear concepts, — reproduces almost verbatim a paper I read, — it must have been in 1872, — to a group of young men who used, at that time, to meet once a fortnight in Cambridge, Mass., under the name of 'The Metaphysical Club,'-a name chosen to alienate such as it would alienate." This page is headed "1909 Apr 6 2AM, MEANING, Pragmatism." Cf. 5.13 and [Bibliography] G-1909-1.

194

†2 (Ed.) Paragraphs 313-314 are "Chapter 1 (Enlarged abstract)," with added quotations at 313n3 and 314n4. Paragraphs 315-316 are from an abstract of the first few chapters. Paragraphs 317-325 are the contents of an untitled manuscript. See 313n1.

195

†3 (Ed.) ". . . the characters of belief are three. First, there is a certain feeling with regard to a proposition. Second, there is a disposition to be satisfied with the proposition. And third, there is a clear impulse to act in certain ways, in consequence." From "Of Reality" (see 313n1).

195

†4 (Ed.) "Doubt has degrees and may approximate indefinitely to belief, but when I doubt, the effect of the mental judgment will not be seen in my conduct as invariably or to the full extent that it will when I believe. Thus, if I am perfectly confident that an insurance company will fulfill their engagements I will pay them a certain sum for a policy, but if I think there is a risk of their breaking, I shall not pay them so much." From a fragment (see 313n1).

195

†5 (Ed.) In the omitted portion of the manuscript Peirce briefly outlines three of his four "methods of effecting a settlement of opinion." The first is "obstinate adhering to whatever happens to be one's existing opinions." The second is by persecution. The third is "by the natural development of opinion," which fails when "one community comes in contact with another. Then it is seen that the result is quite accidental and dependent on surrounding circumstances and initial conditions and belief gets all unsettled.

195

"In this way once more the conviction is forced on man that another's opinion, if derived by the same process as his own, is as good as his own, and that other's opinion is taken by him for his own. Then he says we in the sense of the learned world."

195

Peirce's fourth method is discussed in our following paragraph.

200

†6 (Ed.) From "LOGIC, Chap. 4 (—- draft)" (see 313n1).

201

†7 (Ed.) From "LOGIC, Chap. 4. — Of Reality (1st draft)," with an added quotation in 331n9. See 313n1.

201

†8 (Ed.) See Book III, Chapter 2, "Association," in the present volume.

203

†9 (Ed.) Investigation involves, besides sensation, "the production of new beliefs out of old ones according to logical laws. This process is the logical process, but by an extension of the meaning of a familiar word I call it also inference." From "Of Reality," the same manuscript quoted at 313n3.

207

†10 (Ed.) An untitled manuscript originally in one paragraph, with an added quotation in 336n11. See 313n1.

†11 (Ed.) "The final settled opinion is not any particular cognition, in such and such a mind, at such and such a time, although an individual opinion may chance to coincide with it. If an opinion coincides with the final settled opinion, it is because the general current of investigation will not affect it. The object of that individual opinion is whatever is thought at that time. But if anything else than that one thing is thought, the object of that opinion changes and it thereby ceases to coincide with the object of the final opinion which does not change. The perversity or ignorance of mankind may make this thing or that to be held for true, for any number of generations, but it can not affect what would be the result of sufficient experience and reasoning. And this it is which is meant by the final settled opinion. This therefore is no particular opinion but is entirely independent of what you, I, or any number of men may think about it; and therefore it directly satisfies the definition of reality." From "Logic, Chap. 6th," March 10, 1873 (see 313n1).

209

†12 (Ed.) Cf. 5.403.

211

†13 (Ed.) Cf. 5.255.

212

†14 (Ed.) An untitled manuscript originally in one paragraph. The date is hardly legible, but is probably March 6, 1873. A manuscript dated March 8, 1873, seems to be an alternative draft, but in the opinion of the editor the manuscript printed here is superior to the later draft. See 313n1.

215

†15 (Ed.) "Logic, Chap. 5th," March 10, 1873, originally in one paragraph. See 313n1.

217

†16 Cf. 5.253.

218

†17 (Ed.) Chapter V, "That the significance of thought lies in its reference to the future." A draft of Chapter IV, "The Conception of Time essential in Logic," dated "1873 July 1," seems to belong with this Chapter V as parts of one series. See 313n1.

218

†18 (Ed.) Cf. 5.287ff.

219

†19 (Ed.) Cf. 8.33 (1871) and 5.400 (1878).

219

†20 (Ed.) The manuscript ends without a period.

223

†1 (Ed.) Peirce uses the terms "psychognosy" and "physiognosy" for the psychical and physical sciences, respectively (cf. 1.242).

223

This chapter is from Section 1, "Classification of the Sciences," of Minute Logic, Chapter 2, "Prelogical Notions," including some alternative pages, Widener IB2-2, with a quotation added in 381n19. The manuscript has dates of early 1902 stamped in the margin of several sheets. All but one of Peirce's marginal sideheads are omitted, and some of his marginal notes have been treated as footnotes rather than as insertions in the text.

223

1.203-283 are from the first part of this manuscript. Paragraph 374n10 follows shortly after 1.283. The rest of the present chapter follows considerably after 374n10; in the manuscript between 374n10 and 362, Peirce deals with the subdivisions of Physiognosy. Cf. 7.267n7.

223

†2 (Ed.) Cf. 1.269-272.

224

†3 (Ed.) 1.269-270.

224

†4 (Ed.) No such chapter is among the manuscripts. A list of all the chapters for which there are manuscripts is given at [Bibliography] G-c.1902-2.

225

†5 (Ed.) The text continues at paragraph 366. Paragraph 364 is from some alternative sheets, and 365 is from some other alternative sheets (see 362n1).

226

†6 Not being a German university professor, his arguments were not fairly considered by German university professors, and were treated with contempt by those who pin their faith upon the philosophical fashions that happen for the moment to prevail in those universities. [Peirce's marginal insert.]

227

†7 Professor Baldwin in the preface of his Dictionary distinctly places himself upon the platform that philosophical and scientific questions ought to be settled by majorities. 'We are many: you are one,' he says. But in the history of science majorities short of unanimity have more often been wrong than right. Majorities do not form their opinions rationally. [Peirce's marginal insert.]

231

†8 (Ed.) Cf. 1276, 8.122n19, and 8.274.

232

†9 (Ed.) No such chapter is among the manuscripts. Cf. 363n4.

233

†10 (Ed.) "As the different Orders are distinguished by the different conceptions which govern them, so it has seemed to me that the different Families are distinguished by the differences of their methods of investigation, when these different methods are applied to different problems. For if there are two different methods, both of them sound and scientific, which are applicable to the same problem, they ought to be employed jointly; or if not, they at any rate are too closely associated to make different families of science. Nothing, for example, can be in stronger contrast than the method of investigating ancient history from monuments and from documents. But the only proper course is to use both methods conjointly. It is true that one man may not be strong enough to work in both ways to advantage; but still he will thoroughly know that his own work is only a result of the division of labour and that it has to be joined to another man's work by a third workman, before anything can be settled. On the other hand, a mere difference of problems, where the methods of investigation are identical does not constitute a division that can rank as a division between Families of science.

233

"Different Genera of the same Family of science are studies which have precisely the same general character, but of which each is strongly distinguished by some marked feature. This is a sufficiently vague statement, not to have the effect of imposing an artificial classification, while it is clear enough to be of material service in enabling us to determine whether a given subdivision is a division into Families or into Genera.

233

"Finally, the different Species of one Genus of science, are studies which, though morphologically identical in all their features, even similar in their proportions, and undistinguished by any leading peculiarities, lie nevertheless not so exactly in one path that the man who is everywhere prepared for the pursuit of the one will be quite ipso facto expert in the other, without having anything to learn of new kinds of precaution; in sharpening his attention to unfamiliar observations, in manipulating an instrument that has been strange to him, or in putting a familiar one to unfamiliar uses." From the manuscript, following shortly after 1.283 (see 362n1).

236

†11 Take, as an example, Cattell's observations of the motions of a reader's eyeball. [Peirce's marginal insert.]

240

†12 (Ed.) See the following chapter, "Association."

240

†13 (Ed.) See Chapter 5, "Telepathy and Perception," in the present book.

240

†14 (Ed.) Cf. 1.271.

241

†15 (Ed.) Cf. Chapter 3, "The Logic of Drawing History from Ancient Documents," Book II, present volume.

242

†16 Of course, if they are not so, they are not what the Darwinian means by "adaptive." For example, Weismann says that death is an adaptive character.

243

†17 I can tell by the expression of face the state of mind of my horse just as unmistakably as I can that of my dog or my wife.

244

†18 This is the marvel and admirable in it; and this essentially supposes a generous portion of capacity for blundering. [Peirce's marginal insert.]

†19 (Ed.) "Descriptive Definition of a Human Instinct, as the term will here be used. An animal instinct is a natural disposition, or inborn determination of the individual's Nature (his 'nature' being that within him which causes his behaviour to be such as it is), manifested by a certain unity of quasi-purpose in his behaviour. In man, at least, this behaviour is always conscious, and not purely spasmodic. More than that, unless he is under some extraordinary stress, the behaviour is always partially controlled by the deliberate exercise of imagination and reflexion; so much so that to the man himself his action appears to be entirely rational, so far is it from being merely sensori-motor. General analogy and many special phenomena warrant the presumption that the same thing is true of the lower animals, though they are undoubtedly far less reflective than men. Yet the adaptation of the behaviour to its quasi-purpose in some definite part overleaps all control . . . . So then the three essential characters of instinctive conduct are that it is conscious, is determined to a quasi-purpose, and that in definite respects it escapes all control." From "Of the Classification of the Sciences. Second Paper. Of the Practical Sciences," Widener II, c.1902 (see 7.49n1).

245

†20 (Ed.) The marginal sidehead "Science is but a Development of Instinct" appears opposite this paragraph.

247

†21 As I write, the Monist XII.321 brings me the account of such a thing dating from the XVIth century before Christ, or earlier. Several sciences are known to have been earlier than that; but they were probably looked upon as Useful Arts. This seems purely speculative.

247

(Ed.) The reference is to James H. Breasted, "The First Philosopher," The Monist 12(April, 1902)321-336.

247

†22 (Ed.) We omit a long section on linguistics and anthropology. The following is from an alternate page of this part of the manuscript (see 362n1): "The Indo-European languages are singular in having the common noun distinctly and fully developed as a separate part of speech, and by more or less development even of abstract nouns. I do not mean to say that the common noun is not fully developed in any other language; but only that such a phenomenon is exceptional in every other great family of speech. This requires and evidences considerable power of thought on the part of those who use these languages. With the exercise of a little ingenuity it is possible to express anything in these languages, provided no higher relations than dyadic ones enter. Only very simple propositions can be expressed involving higher relations; and those whose mental education is limited by the powers of these languages are unable to grasp the meaning of a complex triple relation; . . ."

248

†23 (Ed.) Cf. 7.256-266.

248

†24 (Ed.) The manuscript continues, "In Descriptive Psychognosy we have recognized two Suborders, the one relating to Situations, the other to Events." Cf. 1.272. Peirce then discusses bibliography, books of travels, numismatics, metrology, history, etc.

249

†1 (Ed.) Sections 1-7 are "Introduction, Association of Ideas," c.1893, from Grand Logic, Widener IB2-1, with the omission of Art. 3, a long section devoted to the history of the doctrine of association, of which only a few sentences are printed (417n21), and with an added quotation in 392n7. Sections 1 and 2 are Peirce's Art. 1 and 2, respectively, and sections 3 through 7 are Peirce's Art. 4 through Art. 8, respectively. The titles of all these sections, except that of Section 5, are taken from a partial table of contents in Widener IB2-1, with some changes in capitalization.

250

†2 It is now more often called reproduction, which is the German term. I prefer to write English; and certainly no reader will suppose that I am speaking of suggestion in its hypnotic connection.

250

†3 (Ed.) Cf. 6.60.

250

†4 (Ed.) A Treatise of Human Nature. In the Everyman's Library edition, No. 548, 1939, edited by Ernest Rhys, this passage appears in Vol. I, page 19.

251

†5 (Ed.) Cf. 1.383.

252

†6 (Ed.) Cf. 4.157.

†7 (Ed.) "An 'occult property' is a property which is only brought to light by experiment. 'Occult Science' means, therefore, precisely experimental science. The reason these properties were called occult was that they could not be deduced after the manner of Aristotle from the prime qualities hot and cold, moist and dry." A footnote, p. 16, from Peirce's Prospectus of The Treatise of Petrus Peregrinus on the Lodestone, [Bibliography] G-c.1893-4.

252

†8 See Mr. A.B. Kempe's Memoir upon Mathematical Form.

253

†9 (Ed.) Art. 3, on the history of the doctrine of association, is deleted here (see 388n1).

253

†10 Hartmann's account of association is well worth reading.

253

†11 Unconscious Memory.

254

†12 They are written out, but as for seeing the light, even if they were printed, that does in no wise depend on their merit. Men do not want to know the truth and they ought to have their way. (Ed.) But cf. 7.546, 7.215.

254

†13 The distinction is virtually made by James Mill. J.S. Mill, and I think Bain too, mistakenly calls subjective intensity emotional intensity.

255

†14 (Ed.) See Chapter 2, "Small Differences of Sensation," of Book I of the present volume.

257

†15 (Ed.) In the following paragraphs, Peirce shows the inter-relationship between the points he is making by numbering them in a special way. We have placed these numbers in parentheses to separate them from the paragraph numbers. Note that (22) is the second point under (2), (32) is the second point subordinate to (3), (321) the first sub-item under (32), etc.

258

†16 (Ed.) In the manuscript paragraph 404 was inserted between the lines after paragraph 405. We have adopted the present order so that there will be references to ten numbered points, (11), (12), (21), (22), (23), (31), (32), (33), (34), and (41), preceding paragraph 405.

259

†17 (Ed.) In the deleted Art. 3; see 392n9.

260

†18 Professor James seems to think it to the purpose to remark that "the similarity of two things does not exist till both are there." That may be; it is so, in a sense. But how he infers that "it is meaningless to talk of it as an agent of production" I cannot see. Nobody means that the appearance of resemblance is an agent but that what there is in the depths of the soul that makes the appearance also makes the association.

260

(Ed.) The quotation from James in the text is from The Principles of Psychology, Vol. 1, Henry Holt and Company, New York, 1890, p. 579; the quotation in this footnote is from the same volume, p. 591.

261

†19 James wants us to say things. I reply that ideas were always meant as objects, direct objects, not matters of psychology, by those who talked of them. When he says things he cannot mean the real external things; for they are beyond the power of thought. He can only mean the perceived objects, which are precisely what is meant by "ideas." What is perceived is an idea, in contradistinction to a raw sensation.

261

†20 (Ed.) Chapters XVIII (2.645-660) and XIX of the Grand Logic were to be on probability and induction, respectively; no manuscript of Chapter XIX has been found.

264

†21 (Ed.) In the discussion of Hartley in the omitted Art. 3, Peirce says: "Proposition 3: sensations remain in the soul for a brief interval of time after the object is removed. This seems like a genuine psychological observation; and the acuteness of the physician is certainly shown in giving it this foremost place. But the proof offered is perfectly futile."

264

†22 (Ed.) In Discussions on Philosophy and Literature, Education and University Reform, Harper and Brothers, New York, 1861, p. 53, Sir William Hamilton says: "We know; and We know that we know: — these propositions, logically distinct, are really identical; each implies the other . . . . The attempt to analyze the cognition I know, and the cognition I know that I know, into the separate energies of distinct faculties, is therefore vain."

265

†23 (Ed.) Cf. 5.213ff.

268

†24 (Ed.) The editor suggests that the two triangles in perspective constitute a figure distinct from the figure of the ten dots; and that the association is between ten dots in the original figure, and ten rays in the second figure.

275

†25 (Ed.) From Qualitative Logic, a partially completed book intended for young people, Widener IB2-9, undated. Paragraphs 451-457 are a draft of Chapter I, "The Association of Ideas." Paragraphs 458-462 are a draft of Chapter II, "The Simple Consequence."

275

The reader's attention is called to the similarity between 7.454-457 of this section and 7.445-450 which come from Grand Logic. Paragraphs 7.457 and 7.448-450 are nearly identical. This similarity provides some information as to when Qualitative Logic was written.

276

†26 (Ed.) Cf. 1.626ff.

279

†27 Absolute doubt is also impossible.

279

†28 (Ed.) The manuscript then continues with Chapter III, "The Modus Ponens"; Chapter IV, "The Traditional Syllogistic"; etc.

280

†29 (Ed.) From Chapter VI of Grand Logic, Widener IB2-1, coming after 4.52. This is dated 1893 on the basis of 4.21n*.

282

†30 (Ed.) Cf. 4.121ff.

284

†1 (Ed.) Sections 1-8 are "Habit," Widener IB3, c.1898, with a quotation added in 494n9. The manuscript, "Habit," is probably a version of Lecture 7 of the Cambridge series, [Bibliography] G-1898-1. The manuscript from which 494n9 is taken is probably a version of Lecture 2 of this series. Section 9 is from Lecture 4 of the Cambridge series; cf. 518n16.

286

†2 (Ed.) Cf. 6.240.

287

†3 (Ed.) See also 6.23, 6.72, and [Bibliography] N-1890-3.

289

†4 (Ed.) Benjamin Peirce.

290

†5 (Ed.) Cf. 1.135.

294

†6 (Ed.) Cf. 6.82ff. Peirce's categories of First, Second, and Third are discussed especially in [CP] I.

294

†7 (Ed.) See the discussion of indices in [CP] II and elsewhere.

294

†8 (Ed.) Cf. 6.6, 6.211-212.

296

†9 (Ed.) This is probably a reference to the following rules (cf. 2.226): "Rule I. Assign to every scientific conception a scientific name of its own, preferably a new word rather than one already appropriated to an unscientific and dubious conception.

296

"That was the practice adopted by the scholastic doctors, how advantageously every student will testify. The renaissance, on the other hand, condemned the scholastic terms as not being Ciceronian, with the result of making renaissance philosophy as soft and savorless as a sage pudding. There is a rule of good writing higher than Ciceronian purity, that of expressing your thought, both accurately and concisely. More than a rule of good writing, this is a fundamental condition of scientific thinking; for man cannot think at all without formulas, nor think powerfully without concise formulas . . . .

296

"Rule II. The author of a scientific conception has the first right to name it; and his name ought to be accepted, unless there are grave substantial objections to it. But if he fails to give it a scientific name, somebody else must do so; and in that case the earliest good scientific name shall be employed . . . .

296

"Rule III. After a scientific conception has once received a suitable name, let it not be called by any other scientific name, old or new . . . .

296

"Rule IV. As far as practicable, let the terms of philosophy be modelled after those of scholasticism . . . ." From "Detached Ideas; Induction, Deduction, and Hypothesis," Widener IB2-10, c.1898, probably a draft of one of the lectures (possibly the second) on "Detached Ideas on Vitally Important Topics" of the Cambridge series (see 468n1).

300

†10 (Ed.) See Chapter 2, "On Small Differences of Sensation," in Book I of the present volume.

300

†11 (Ed.) See also the preceding chapter, "Association."

307

†12 (Ed.) The dots indicate a blank in the manuscript, where presumably Peirce meant to write in the value of the gravitational constant. This value is approximately 6.7 x 10-8 in the centimeter-gram-second system of units.

308

†13 (Ed.) Cf. [Bibliography] G-1891-1.

309

†14 (Ed.) Presumably Lecture 8, "The Logic of Continuity." There is a manuscript, "The Logic of Continuity," in Widener IB3 which is very probably the lecture referred to; 6.185-213 are from this manuscript.

310

†15 (Ed.) See the preceding footnote.

310

†16 (Ed.) This final section is the four missing manuscript pages referred to at 6.81n* (p. 60); these pages are now with the rest of the manuscript at Widener IB2-10. They are published here to fill the gap in "Causation and Force," 6.66-87, Lecture 4 of the Cambridge series, [Bibliography] G-1898-1. This lecture deals with some of the topics discussed in "Habit," Sections 1-8 above.

313

†1 (Ed.) From Section 2, "Some Logical Prolegomena," the final section of a manuscript, "On Topical Geometry, in General," Widener IA-2, undated, with added quotations in 534n4 and 535n6. A partial draft and a complete draft of Section 2 have a common first page. Paragraphs 524-529 are from the partial draft; paragraphs 530-538 are the last part of the complete draft.

315

†2 (Ed.) These are the psychological versions of Peirce's categories, First, Second, and Third, which are treated in general in [CP] I, Book III.

317

†3 But I do not mean to say that bare striving usually does any more good in these cases than in the case of such a physical difficulty as turning a key that does not fit very well in its lock. If a moderate effort does not suffice, some contrivance has to be employed.

†4 (Ed.) "When the idea of space forms itself in our minds, or being inborn, connects itself with sensations, those things come to be regarded as near together which act strongly on one another, and are intimately related in regard to forces; while those things come to be regarded as remote which, as far as those forces of which we have any primitive experience are concerned, have little to do with one another. Hence, when gravitation was found to act at a distance, and even at vast distances, men were astounded; they thought it could not be. It seemed somehow to involve absurdity. The absurdity which was obscurely felt was that the idea [of] nearness was the idea of close connection; and therefore men felt that immediate connection supposed confinity. But that instinctive idea has been corrected. Any particle may be regarded as extending throughout space. It is where it acts. But it acts extremely little except in a very little space; and its place is peculiarly where it acts the most." From a fragment in Widener IA-8, undated.

319

†5 (Ed.) Cf. 3.567, 4.639-640.

†6 (Ed.) "I begin by defining a part of any whole, in a sense of the [term] much wider [than] any in current use, though it is not obsolete in the vocabulary of philosophy. In this broadest sense, [it] is anything that is (1) other than its whole, and (2) . . . such that if the whole were really to be, no matter what else might be true, then the part must under all conceivable circumstances itself really be, in the same 'universe of discourse,' though by no means necessarily in the same one of those three Universes with which experience makes us all more or less acquainted. Thus, light is a part of vision . . . .

"A perfect continuum belongs to the genus, of a whole all whose parts without any exception whatsoever conform to one general law to which same law conform likewise all the parts of each single part. Continuity is thus a special kind of generality, or conformity to one Idea. More specifically, it is a homogeneity, or generality among all of a certain kind of parts of one whole. Still more specifically, the characters which are the same in all the parts are a certain kind of relationship of each part to all the coördinate parts; that is, it is a regularity. The step of specification which seems called for next, as appropriate to our purpose of defining, or logically analyzing the Idea of continuity, is that of asking ourselves what kind [of] relationship between parts it is that constitutes the regularity a continuity; and the first, and therefore doubtless the best answer for our purpose, not as the ultimate answer, but as the proximate one, is that it is the relation or relations of contiguity; for continuity is unbrokenness (whatever that may be,) and this seems to imply a passage from one part to a contiguous part. What is this 'passage'? This passage seems to be an act of turning the attention from one part to another part; in short an actual event in the mind. This seems decidedly unfortunate, since an event can only take place in Time, and Time is a continuum; so that the prospect is that we shall rise from our analysis with a definition of continuity in general in terms of a special continuity. However, it is possible that this objection will disappear as we proceed." From "Supplement. 1908 May 24," Widener IA-3, an addendum alternative to 4.642 ([Bibliography] G-1908-1b).

325

†7 (Ed.) An untitled manuscript, Widener IB1-2, undated. The quotations in 540n8 and 541n9 are from what appears to be an alternative partial draft, Widener IC1-a,b, undated. In this alternative draft it is stated that the paper was originally written to be read to a group that met Sunday afternoons. It is likely that these manuscripts were written about 1900; see paragraphs 539, 540 and 545 and [Bibliography] G-1901-5, but note that Kant died in 1804 and not "in the last year of the last century," as Peirce says in paragraph 540.

325

†8 (Ed.) "Direct in philosophical language without anything intervening. Thus this house directly abuts upon the street. I am talking to you directly. Immediate involves the same idea carried further. It denies every kind of separation by a boundary, by a difference of place or time. What is immediately in consciousness is what consciousness is made of." A footnote from the alternative draft (see 539n7).

328

†9 (Ed.) "No sharp line of demarcation can be drawn between different integral states of mind; certainly not between such states as feeling, knowing, and willing. It is plain that we are actively knowing in all our waking minutes, and actually feeling, too. If we are not always willing, we are, at least, at all times consciously reacting against the outer world. Strumpell's celebrated experiment, fully confirmed by others, shows that as soon as outward stimuli are entirely removed, the person falls asleep." From the alternative draft (see 539n7).

332

†10 (Ed.) Peirce first had "One is an objective intensity" and then substituted "One is the intensity of the feeling itself." Cf. 555.

332

†11 (Ed.) Cf. 7.215.

334

†12 (Ed.) See Chapter 2, "Small Differences of Sensation," Book I, present volume.

335

†13 (Ed.) Cf. 553-554.

335

†14 (Ed.) In 544.

336

†15 (Ed.) See Chapter 2, "Association," in the present book.

337

†16 (Ed.) See further 7.276-278.

337

†17 (Ed.) Paragraph 553 is an undated fragment; paragraph 554 is from an alternative draft. Both are in Widener IC1-a,b.

337

Paragraphs 555-558 are from Chapter I, "Of Reasoning in General," of the "Short Logic," Widener IB2-10. This manuscript is dated c.1893 in [CP] II. Paragraph 555 follows immediately after the last sentence of 2.443. The part of the manuscript from which 555-558 and 2.444 are taken is not continuous; paragraph 2.444 is from manuscript pages beyond 555-558, but the last paragraph of 2.444 is similar to 558.

338

†18 (Ed.) Cf. 547.

338

†19 (Ed.) "An idea is nothing but a portion of consciousness having in itself no definite boundaries, except so far as it may be of a different quality from contiguous ideas." Peirce's marginal comment.

340

†20 (Ed.) Cf. 546.

340

†21 (Ed.) No such explanation is given in the extant manuscript.

341

†22 It may be remarked that this is a very temporary condition, and shortly after the interesting idea will be found to have a lower subjective intensity than it would have had if it had not been interesting.

341

†23 (Ed.) "What is the Use of Consciousness?" Chapter IV, c.1893, of Grand Logic, Widener IB2-1.

341

†24 (Ed.) "The Materialistic Aspect of Reasoning," 6.278-286.

342

†25 Take, for instance, that superlatively cunning defense of common sense, the doctrine of immediate perception, — a doctrine so subtle that it has eluded the grasp of many a fine logician, — and what is it, after all, but a confession that to see and to be seen are one and the same fact.

343

†26 (Ed.) "Immortality in the Light of Synechism," Widener IB3. "For the Open Court" is written on the manuscript. It is dated c.1892 on the basis of the bibliographic references in the article.

343

†27 (Ed.) Synechism is treated in detail in [CP] VI, Part B of Book I.

343

†28 The Greek word means continuity of parts brought about by surgery.

343

†29 (Ed.) [Bibliography] G-1891-1c (1892). This paper gives a definition of "synechism," 6.103.

344

†30 (Ed.) Cf. Chapter 5, "On Non-Euclidean Geometry," [CP] VIII, Book I.

344

†31 (Ed.) Cf. 1.171.

346

†32 (Ed.) Edward Stanton Huntington, Dreams of the Dead, by Edward Stanton (pseud.), Boston, 1892. Cf. [Bibliography] N-1892-14.

346

†33 (Ed.) Gustav Freytag, Die Verlorene Handschrift, Leipzig, 1869.

347

†34 (Ed.) From Lecture XI of an incomplete series of lectures in Widener IB2-10. The editor has been unable to make a positive identification of these lectures, but the internal references and the general tone of the writing indicate that they are probably the manuscripts for the Lowell Institute lectures of 1866-67 ([Bibliography] G-1866-2a). On this basis Lecture XI is dated c.1867. In Widener IB2-10 these lectures are mixed with the manuscripts of a different series, which are probably those of the Harvard series of 1865-66, [Bibliography] G-1864-3.

348

†35 (Ed.) Lecture X. Only fragments of it have been found.

348

†36 (Ed.) Cf. 2.407ff.

348

†37 (Ed.) The following was pencilled in the margin with a line to indicate that it was to be inserted here: "Most ignorant of what he's most assured His glassy essence."

349

†38 (Ed.) Peirce here inserted "Upon the diversities of theories of the soul there are some pretty lines by Sir John Davies in his poem on Psychology" and referred to Sir William Hamilton's edition of Thomas Reid's Works, p. 203.

349

†39 (Ed.) Induction and hypothesis are discussed in Book II of the present volume and at 2.508ff. (1867).

350

†40 (Ed.) Cf. 7.131-138, which are from Lecture IV of the same series (see 579n34).

351

†41 (Ed.) Cf. 5.339.

351

†42 (Ed.) Compare the following paragraphs with 5.313ff. (1868).

356

†43 (Ed.) Cf. [Bibliography] G-1868-2a (5.213-263).

†1 (Ed.) "Telepathy," including some alternative pages, Widener IC1-a,b, with deletions, and with an added quotation in 597n3. This manuscript is dated 1903 on the basis of the dates given in the next footnote, references to a manuscript on telepathy in the Peirce-James correspondence (James collection, Houghton Library), what appear to be James's handwritten comments in the margin of the first part of the manuscript, and a crossed-out date in the last section of the manuscript. This was a first draft from which Peirce intended to extract a magazine article.

Peirce divided the manuscript into six sections (with no titles); the sections of the present chapter are the same as Peirce's, but the titles have been supplied by the editor.

Cf. 6.548-587 and [Bibliography] G-1887-3 for other writings by Peirce on the subject of psychical research.

359

†2 (Ed.) John Trowbridge, "Telepathy," The Nation 76 (16 April 1903)308309; and William James, "Telepathy Once More," ibid., (23 April 1903) 330.

360

†3 (Ed.) [Bibliography] G-1887-3, "Criticism on 'Phantasms of the Living'. . ." In a fragment in Houghton Library, Peirce says: "Phenomena for which psychical researchers invoke telepathy can be explained by unconscious mental action, after severe scrutiny of testimony, and with aid from the doctrine of chances." Cf. [Bibliography] G-1887-3, p. 194. The fragment concludes, "Eight years ago on the appearance of the laborious work, Phantasms of the Living, I examined the question with care, pronounced it very doubtful, but provisionally rejected the whole theory. Reviewing the state of the question, this year, I find no decided change in either direction." This internal reference dates the fragment as c.1895.

362

†4 (Ed.) Cf. 5.354ff., 2.654ff.

363

†5 It would be different if the theory of Hobbes, LaRochefoucauld, and other thinkers in the boyhood of modern philosophy, were true, and man could not act otherwise than selfishly. But this theory which rests on a logical fallacy is supported by no fact and refuted by many.

363

†6 The word "veridical" was first made a term of art by Mr. Myers in the sense of coinciding with the truth, whether fortuitously or causedly. It is contrary to the ethics of terminology to change the meaning of a term of art without necessity. Its author has no more right to do so than anybody else. Yet in Baldwin's Dictionary, where accuracy of definition ought to have been the first consideration, Mrs. Sidgwick limits the term to that which is determined by a general cause to be true, with no hint that it had ever been used in any other sense. Looseness of speech and looseness of thought are wife and husband. I shall speak of the 'simply veridical' and the 'determinedly veridical,' in the wider and narrower senses.

369

†7 (Ed.) See [CP] V, Pragmatism and Pragmaticism.

371

†8 (Ed.) The psychological versions of Peirce's categories of First, Second, and Third are discussed in 7.524-538, and the categories in general are treated in [CP] I.

374

†9 Formed from percipio on the analogy of praecipuum from praecipio. I am quite sure that it would be well if philosophers were bolder in forming new words instead of giving old ones so many meanings. What if we were to use words ending in -cept for different kinds of acquisition of cognition? There would be of good Latin words accept, antecept, decept, except, incept, intercept, occept, precept, suscept, besides many others quite supportable.

374

†10 (Ed.) Cf. 7.537.

375

†11 There is no objection to saying that 'The chair appears yellow' means 'The chair appears to me yellow'; but the reference to the future self is more pertinent.

376

†12 (Ed.) "It may be objected that a perceptual judgment is not so utterly beyond all control or check as I say; since it may be revised. I may negligently think 'this chair appears scarlet,' when if I had looked more carefully, I should have said 'it appears vermillion.' I reply that no doubt mistakes can arise from inadvertency; and possibly, in order to take due account of that phenomenon, some complication of my statement would be required. But it cannot be that, on this account, it is fundamentally wrong. A perceptual judgment can only refer to a single percept which can never re-exist; and if I judge that it appears red when it did not appear red, it must, at least, be acknowledged that it appeared to appear red. I do not think it worth while to follow out the objection further." From alternate pages of the manuscript (see 597n1).

377

†13 (Ed.) Cf. Peirce's doctrine of synechism, 7.565ff.

381

†14 It was discovered by H.G.F. Schroeder in 1858. Poggendorff Annalen CV, 298.

382

†15 I myself was severely taken to task, sat upon, squelched, marked down to my real insignificance, by an eminent French logician, for presuming to speak disparagingly of so sublime a work of genius as the algebra of dual relatives, this algebra happening to be a thing of my own invention.

383

†16 (Ed.) Cf. 5.205, 6.109-110.

383

†17 In the Monist for July, 1892, I followed him in this misunderstanding, my notion of continuity at that date being far from clear. (Ed.) Cf. 6.120ff.

383

†18 (Ed.) The editor has deleted a long passage on continuity, which presents material already covered in 6.120ff. and 6.174ff.

384

†19 (Ed.) Cf. 3.567, 4.639ff.

384

†20 (Ed.) That is, real numbers.

386

†21 (Ed.) Cf. 8.12ff.

389

†22 (Ed.) Peirce's observational theory of mathematics is discussed also in various places in [CP] IV.

391

†23 (Ed.) See Book II, "Scientific Method," in the present volume.

397

†24 (Ed.) The manuscript breaks off shortly after this point.