THE THOMIST A SPECULATIVE QUARTERLY REVIEW OF THEOLOGY AND PHILOSOPHY EDITORS: THE DoMINICAN Publishers: VoL. FATHERS oF THE PROVINCE oF ST. JosEPH The Thomist Press, Washington 17, D. C. APRIL, 1956 XIX No.2 NEWTONIAN ANTINOMIES AGAINST THE PRIMA VIA T HE proof of God's existence from motion in the universe, as originally proposed by Aristotle 1 and as later presented by St. Thomas, 2 was intended to be understood by physical scientists. The terms in which it was couched were technical terms with clearly defined meanings, and their application was straightforward and rigorous. Yet the proof, for all its technical elegance, no longer convinces the scientific mind. By and large, its terminology is unintelligible to modern scientists, and as a consequence the argument is now commonly :rejected as having no scientific importance or validity. There are many possible explanations for this enigma, most of them reducible to the patent equivocation in the use of the word " science " through the past three centuries. Prior to the ' Physics, Book Vll. 2 Summa Theologiae, I, q. a. 3. 151 152 W. A. WALLACE seventeenth century, science .was commonly understood as a body of certain and evident knowledge known to be true through causes. Physical or natural science was further considered as having two maip. parts: a fundamental or generalized part, dealing with the common features of natural things presupposed to other studies, and a specialized part in which detailed investigation was made of the various types of natural things. The ewtonian revolution drastically affected this understanding; it placed the accent on intensive specialized investigation, minimized the search for causes, and in its place methodology based largely mi. mathematical· correlations.3 From that time· until the present day, the meaning of the term " science " has still not crystallized, but the prevailing modern opinion places the emphasis on specialized investigation using a uniform postulational procedure that engenders only probable kno\vledge. Thus' c'ausality, certitude and truth are no longer the hallmark o..f science. Moreover, there is no fundamental or generalized study of physical reality prior to detailed experimental work. Such considerations, if they are thought of at all, are usually relegated to the broad field of philosophy, and they are not regarded as essential to the intellectual equipment of the scientist. The prima via, or the proof of God's existence from motion, is refractory to the modern mind· simply because it is based upon these fundamental, generalized concepts that are no longer considered a. part of science and hence are not taught to scientists. And the situation is further complicated by the fact that modern specialized terminology frequently employs the same terms as pre-Galilean science, but with more restricted meanings than these terms enjoyed in the traditional fundamental understanding. Thus the modem- scientist finds considerable ambiguity in the classical .statement of the demonstration, and this constitutes an almost insurmountable barrier to his acceptance of its conclusion. , 8 I E. F. Caldin, "Science and the Map of Knowledge," Blackfriara, XXXVI (1955) • /)68-569. NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 153 Yet there is a ray of hope for one who would reinstate the prima via to its rightful place as a classical scientific demonstration. Oddly enough, this springs from the very man whose genius distracted later generations from becoming interested in the fundamental science of nature that rigorously establishes the demonstration, namely, Sir Isaac Newton. Being at the beginning of a new line of thought, Newton appreciated the terminology of his predecessors and properly formulated his own contribution so as not to be misunderstood by his contemporaries. But, as frequently happens, the scientists who are now most indebted to Newton are generally unacquainted with his original works, and thus have lost contact with this valuable part of his writings. They miss the point of the very title of his main contribution, the :fJ1athematical Principles of Natural Philosophy, possibly because they are unaware of any other principles with which Newton might be contrasting the ones he there proposes. Even worse, in some instances they misrepresent his teachings, and use their own misconceptions to argue against the premises of the prima via. This situation has given rise to the so-called Newtonian antinomies against the prima via. 4 They are not Newton's arguments against this classical demonstration, but rather are difficulties that present themselves to those who are acquainted with Newton's laws of motion, and cannot see how these can be reconciled with the analysis of motion presupposed to the proof for God's existence. Although these antinomies appeal immediately to anyone who has only a rudimentary knowledge of Newtonian mechanics, moreover, they are quite difficult to resolve, and have proved extremely bothersome to philosophers and theologians who teach the prima via to students of modern science. The present study is an attempt to remove these difficulties • R. Garrigou-Lagrange, 0. P., has already considered one such antinomy in an appendix to God: Hi8 Existence and Hi8 Nature (London: B. Herder, 1986), II, pp. 447-452. More recently, E. T. Whittaker has invoked a Newtonian antinomy to reject the prima via in his Space and Spirit (London: Thomas Nelson and Sons, 1946). 154 W. A. WALLACE at their source by evaluating them in the light of Newton's original doctrine. It aims to rediscover, for those acquainted with the terminology of modern Newtonian physics, the physical import of the celebrated Principia, to show how this work presupposes a fundamental science of nature based on generalized physical principles, and how in the light of these presuppositions answers can still be given to the basic problems Newton raised about the physical world. And in thus removing the apparent difficulties now contained in the Newtonian antinomies, it proposes to insinuate, at least, that the prima via still remains a classical demonstration for scientists, that it is in fact the monumental achievement of physical science for anyone who can learn the generalized concepts on which it is based and rigorously apply them to all he knows with certitude about the physical world. The three antinomies selected for resolution are based upon each of Newton's three laws of motion. They are directed not only against the conclusion of the prima via, but also against its two basic premises, namely, the motor causality principle which states that whatever is moved is moved by another, and the regress principle which rules out either an infinite series or a re-entrant series of corporeal movers. Thus the first law of motion, which enunciates the principle of inertia, would seem to affirm that the inertia of a body is the sufficient explanation of that body's motion, and therefore invalidates the principle that whatever is moved is moved by another. Again, one consequent of the second law, which itself seems to be an operational definition of force, mass and acceleration, is the inverse-square law of gravitational attraction. This law would seem to affirm that mutually attracting bodies are the sufficient explanation of gravitational motion, and thus they invalidate the regress principle by invoking a closed chain of moved moverso And finally, the third law of motion, stressing the universality of action and reaction between movers and the moved, would seem to exclude the very possibility of an unmoved incorporeal Mover as being the first cause of motiono NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 155 More complex antinomies may have occurred to some readers, and others could undoubtedly be excogitated with little effort, but it is believed that the basic difficulties are contained in these three. These also have the advantage that they can be solved to an appreciable extent by reference to Newton's original writings. From the viewpoint of textual analysis, it matters little in which order these be considered. Their resolution can best be accomplished, however, by first answering the antinomy arising f:rom the law of gravitational attraction, then using the concepts developed therein to reply to the antinomy based on the principle of inertia, and finally by resolving the actionreaction antinomy. * * In gravita.tional motion, all bodies mutually attract each other with a force given by the inverse-square law. But this force adequately accounts for gravitational motion without the presence of an extrinsic mover. Therefore the two or more bodies are the mutual cause of each other's motion, and they form a closed system in which no extrinsic mover is needed, let alone a first unmoved Mover. FmsT ANTINOMY: This antinomy obviously presupposes the reality of gravitational attraction as a physical force that exists outside the mind and is actually the cause of the falling motion otherwise identified as gravitationaL Most scientists today will accept this presupposition, for they commonly refer to the pull of gravity as if it were something real, and some even discuss quite seriously the problem of shielding gravitational attraction in some way analogous to that in which magnetic and electrical fields are shielded. 5 Whether o:r not this is a true presupposition, however, is another question. In fact, whether Newton would subscribe to such an understanding of the attraction concept he proposed presents an even more interesting problem, and one that will be fruitful to investigate at the outset in order to prepare for the resolution of this antinomy. • The Gravity Research Foundation, New Boston, N. H., has repeatedly offered prizes for the best essay on this subject. 156 W. A. WALLACE Newton's conception of gravitational attraction can best be understood in terms of the distinction that he made between physical and mathematical principles at the very beginning of his Principia. In the first sentence he states: "I have in this treatise cultivated mathematics as far as it relates to philosophy." 6 He then goes on to outline the entire content of the work, and stresses the role that mathematical demonstration will play in the science he is presenting: I consider philosophy rather than arts and write not concerning manual but natural powers, and consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore I offer this work as the mathematical principles of philosophy, for the whole burden of philosophy seems to consist in this-from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena; and to this end the general propositions in the first and second Books are directed. In the third Book I give an example of this in the explication of the System of the World; for by the propositions mathematically demonstrated in the former Books, in the third I derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then, from these forces, by other propositions which are also mathematical, I deduce the motions of the planets, the comets, the moon, and the sea. 7 Newton's use here of the term "philosophy" is to be understood in the sense of the term " physics," as they were used interchangeably in his time. He is quite dear in pointing out that he is concerned with natural phenomena, and not merely with calculations that .respect artifacts, such as levers and the like, which were treated mathematically by the ancients. And his mathematical principles are not the abstract principles of pure mathematics; they have an intimate connection with physical reality and are primarily ordered to explaining that reality. He stresses this again in the introduction to the third Book, where he says: • I. Newton, Mathematical Principles of Natural Philosophy (Great Books of the Western World, vol. 34; Chicago: Encyclopedia Brittanica Inc., p. 1. 7 Ibid., pp. Hl. NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 157 In the preceding books I have laid down the principles of philosophy, principles not philosophical but mathematical: such, namely, as we may build our reasonings upon in philosophical inquiries. These principles are the laws and conditions of certain motions, and powers or forces, which chiefly have respect to philosophy .... It remains that, from the same principles, I now demonstrate the frame of the System of the World. 8 Thus Newton's approach to physical reality was not completely physical, nor was it completely mathematical, but it was rather a mixture of the two, and so it would be more proper to designate it as physico-mathematical. Moreover, in his development of this new science, which has with good reason come to be known as mathematical physics, he is not always concerned with purely physical considerations. Since we are interested now in his attitude towards " gravitational attraction," it will be well to trace here his development of the inversesquare law in an attempt to identify the physical and mathematical elements present in his reasoning process. After stating his definitions and laws of motion, Newton begins immediately to treat of the motions of bodies, and the whole of Book I is devoted to this subject. He begins this treatment, however, not with one body attracting another body in any physical sense, but with the notion of one body alone tending to a mathematical center. The first ten sections are thus devoted to theorems which describe mathematically the motion of such a body, and no reference is made whatsoever to any attracting body that might be regarded as the physical cause of the motion. Then, in the eleventh section, he takes up the motions of bodies tending to each othe1·, and it is only in the twelfth section, where he considers the attractive forces of spherical bodies, that he derives the inverse-square law in the second proposition. It should be obvious from Newton's procedure that he considered the mathematical aspects of gravitational motion as something that could be derived while abstracting completely "Ibid., p. 269. 158 W. A. WALLACE from the physical causes of the motion, for otherwise he could not possibly have followed this method of derivation. But the question arises whether he himself actually thought that the " attracting " body was a necessary physical presupposition, or whether the entire derivation could be made rigorously while remaining quite indifferent as to what might be the physical cause of the motion. Or, to put it somewhat more generally, could his new science be developed without necessary reference to physical causes as they might exist in the real world, as long as they did not contravene the mathematical principles that successfully describe such motion? Reference to Newton's original text will again throw light on the matter. At the very outset, in his comments on Definition VIII, he makes quite clear what he intends by the " quantities of forces" to which he will have :reference throughout the three Books: These quantities of forces, we may, for the sake of brevity, call by the names of motive, accelerative, and absolute forces; and, for the sake of distinction, consider them with respect to the bodies that tend to the center, to the places of those bodies, and to the center of force to which they tend; that is to say, I refer the motive force to the body as an endeavor or propensity of the whole towards a center, arising from the propensities of the several parts taken together; the accelerative force to the place of the body, as a certain power diffused from the center to all places around to move the bodies that are in them; and the absolute force to the center, as endued with some cause, without which those motive forces would not be propagated through the spaces round about it; whether that cause be some central body ... or anything else that does not yet appear. For I here design to give only a mathematical notion of those forces, without considering their physical causes and seats. 9 The last sentence of the citation gives express indication that Newton himself was abstracting from physical factors involved in all types of motion attributable to such forces. That he also had in mind gravitational " attraction " is beyond all doubt, for he goes on to say: • Ibid., p. 7. NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 159 I likewise call attractions and impulses, in the same sense, accelerative and motive; and use the words attraction, impulse or propensity of any sort towards a center, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically; wherefore the reader is not to imagine that by those words I anywhere take upon me to define the kind, or the manner of any action, the causes or the physical reason thereof, or that I attribute forces, in a true and physical sense, to certain centers (which are only mathematical points); when at any time I happen to speak of centers as attracting, or as endued with attractive powers. 10 This makes it quite clear that centripetal " attraction," for Newton, was simply a mathematical way of looking at the phenomenon, which in no way was intimately connected with any physical presupposition as to why the phenomenon took place. And he recurs to this theme immediately after deriving the inverse-square law, where he again points out: I here use word attraction in general for any endeavor whatsoever, made by bodies to approach to each other, whether that endeavor arise from the action of the bodies themselves, as tending to each other or agitating each other by spirits emitted; or whether it arises from the action of the ether or of the air, or of any medium whatever, whether corporeal or incorporeal, in any manner impelling bodies placed therein towards each other. In the same general sense I use the word impulse, not defining in this treatise the species or physical qualities of forces, but investigating the quantities and mathematical proportions of them.U This was a point that was evidently misunderstood in Newton's own day, so when he came to write the Optics some years after the Principia, he returned again to the question of gravitational" attraction" at the end of the tract on light, and tried to make his position yet more explicit: How these attractions may be performed I do not here consider. What I call attraction may be performed by impulse, or by some other means unknown to me. I use that word here to signify only Ibid., p. 8. Ibid., pp. 180-181. 12 Optics (Great Books of the Western World, vol. 84), p. 581. 10 11 160 W. A. WALLACE in general any force by which bodies tend towards one another, whatsoever be the cause.12 Thus an unprejudiced study of Newton's presentation of mathematical physics indicates that he thought :it quite valid to discuss the mathematical laws and properties of motion, while abstracting completely from the physical factors that are the adequate cause of such motion. Does this mean that in Newton's mind there were no proper physical causes for the motion, or that these were out of the ambit of scientific consideration? Could his mathematical physics be said to deny causality, or at least to place it in the realm of meaningless questions? Far from committing himself to such an attitude, Newton frankly states that there must be a cause for gravitational motion; indeed, he should like very much to know what it is, but he has never been able to answer the problem to his own satisfaction, and he does not want to venture an explanation that is purely hypothetical. Thus he states at the end of the Principia, in the General Scholium where he summarizes his views on the physical universe: Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause .... But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses. 18 The last words cited, hypotheses non jingo, have often been quoted as Newton's great contribution over that of the scholastic thinkers, but its context seems completely forgotten in the minds of many moderns. The more one studies Newton's works, the more one becomes convinced that Newton.used the "attraction theory" only as a convenient mathematical device for deriving his laws and equations of motion, but that he inclined to the opinien that there was an inherent power in the bodies themselves that caused them to gravitate, and not to be pulled by something 13 Mathematical Principles, p. 371. NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 161 outside. This would seem to be confirmed by his method o£ derivation in the first ten sections of Book I mentioned above, where he starts off initially with the notion of bodies tending towards a center. There are also express indications in his writings that he favored the impulse concept when he was speaking physic&,Uy, as opposed to mathematically, as witness his statement at the beginning of Section XI of Book I: I shall therefore at present go on to treat of the motion of bodies attracting each other; considering the centripetal forces as attractions; though perhaps in a physical strictness they may more truly be called impulses. But these propositions are to be considered as purely mathematical; and therefore, laying aside aU physical considerations, I make use of a familiar way of speaking, to make myself the more easily understood by a mathematical reader. 14 Further, when he comes to mention various causes at the physical level, he first names the action of bodies themselves before considering other possibilities. 15 He also defines motive force " as an endeavor or propensity of the whole towards a center." 16 Later, when speaking of the motions of planets, he prefers to speak actively rather than passively and mentions, "That all the planets gravitate one towards another, we have proved before." 17 These are not absolutely convincing in themselves, but when we consider them with some comments Newton made in a letter to Professor Bentley in which he expressly rejects the " attraction" concept, it seems that they give the best explanation consistent with his other statements. For Newton wrote to Bentley after the first edition of the Principia: That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in Ibid., p. Ill. '"Ibid., p. 130. 16 Ibid., p. 7. 17 Ibid., p. 281. 14 162 W. A. WALLACE philosophical matters a competent faculty of thinking, can ever fall into it.l 8 It is true that Newton's reasoning here is based on his abhorrence of a void, but the overall argument has cogency today in view of the rejection of a Newtonian "ether" on the basis of the Michelson-Morley experiment. The only difficulty in Newton's mind about attributing to bodies an inherent power which caused them to gravitate was that such a power, from all the evidence he possessed, was occult, and he had no predilection whatsoever for occult powers. It is interesting in this connection to read Roger Cotes' implicit answer to this difficulty when he wrote, at Newton's invitation, the Preface to the second edition of the Principia. He there makes this statement: But shall gravity be therefore called an occult cause, and thrown out of philosophy, because the cause of gravity is occult and not yet discovered? Those who affirm this, should be careful not to fall into an absurdity that may overturn the foundations of philosophy. For causes usually proceed in a continued chain from those that are more compounded to those that are more simple; when we have arrived at the most simple cause we can go no farther. Therefore no mechanical account or explanation of the most simple cause is to be expected or given; for if it could be given, the cause were not the most simple. These most simple causes will you then call occult, and reject them? Then you must reject those that immediately depend upon them, and those which depend upon these last, till philosophy is quite cleared and disencumbered of all causes. 19 Cotes here gives implicit preference for the natural impulse explanation for gravitational motion. And this explanation being quite consistent with Newton's various remarks on the subject, we have excellent reason to reject the "attraction" notion as of mathematical utility but of little physical significance, and to look, therefore, for a proper physical cause for gravitational motion. 18 Letter to Bentley, 1692/8, in Eddleston, Correspondence of Sir Isaac Newton and Professor Cotes (London, 1850), p. 159. 19 R. Cotes, Preface to the Second Edition, Mathematical Principles (Chicago: Henry Regnery Co., 1951), p. xviii. NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 168 The foregoing analysis of Newton's work centers attention on the fact that the use of mathematics in this science can well obscure factors that pertain to physical causality. It is well to insist on this, and to make quite clear what the contribution of mathematics is for Newtonian science, for otherwise there is danger in replacing its physical aspects by an all-consuming mathematicism that confers great exactness and rigor on a description, but is not at all sure about what reality is ultimately described. The most significant word in the vocabulary of the mathematician is the term "equation." The use of mathematics in a physical science is immediately directed towards the writing of equations that describe particular classes of phenomena. And this in turn makes it necessary to equate quantities. The only difference between mathematical physics and pure mathematics from the point of view of these quantities is that the former is concerned with quantities that are the result of measurements performable on various physical bodies and their qualities, while the latter is concerned with quantities that are pure numbers. The former considers numbers with a dimensional tag attached, while the latter considers numbers alone. The dimensional specification introduces an additional step into the calculations of the mathematical physicist, for he not only has to be sure that his equations are numerically correct, but also that they equate on the score of dimensional analysis. But he still must equate. H mathematics applied to physical problems can produce no equations, it is sterile and does not generate mathematical physics. It is only in terms of equations that the hybrid science becomes intelligible. Now the peculiar thing about an equation is this: if it does not express a tautology, then the only way it can equal two things that are not identical is by abstracting from certain features that are not common to both. In fact, abstraction must be made from everything that would either disturb the equality, or does not enter into it essentially. An equation that is not a tautology, by the very fact that it is an equation, 164 W. A. WALLACE must of necessity give only a partial account of physical reality. This is not to say that such a partial account may not be an important one; it may well be extremely fruitful and useful in describing the properties and relations that obtain between particular phenomena. But it must abstract from some physical considerations-whether they be known or unknown in the mind of the mathematical physicist is immaterial at this point -it must equate parts, and thus of its nature it gives only a partial account of the physical world. When Newton's second law is given mathematical formulation, for instance, there are only three things that enter the equation: force, mass and acceleration. Whatever be the physical situation to which it is applied, every physical aspect other than those which can be ascertained by these three measurements is unimportant. More than that, every other aspect must be neglected at the price of disturbing the equality. A boy pulling a sled cannot be equated to the sled. There is no doubt that he is the physical cause of the sled's motion, and yet there is no way of showing this in the Newtonian equation. All that the equation can say is F equals ma. Granted the motion, whatever be its physical cause, the relation between certain measurable aspects of the bodies involved will be expressed accurately by the equation. But the price of the very writing of the equation is the neglect of some factors that are physically necessary to an understanding of the phenomenon. The question of physical causality is by-passed at the point where mathematical physics begins. If this were all that could be said for modern physics and its knowledge of the physical universe, however, the prima via would be a quite hopeless undertaking. The fact is that recent years have shed light on the inadequacy of a mathematical physics that equates quantities numerically and dimensionally, and then stops at that. Modern scientists are returning to the concept of a mathematical physics that uses its equations as a tool, as a starting point to ask questions about the physical NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 165 reality that lies beneath the description, which Newton clearly espoused. 20 One sign of this is the tendency, in certain quarters, to distinguish between mathematical physics and theoretical physics. According to this conception, the mathematical physicist may well restrict himself to writing equations, to investigating the consequents of certain postulates and the mathematical formulation of hypothetical constructions, and yet be withal divorced from questions immediately respecting the physical world. He may be two steps closer to that world than the pure mathematician, and one step closer than the applied mathematician who "tailors" equations for him, but he still refrains from passing judgment on the physical reality that lies behind his final results. Not so the theoretical physicist. He now is approaching the classical conception of the integral physicist. He not only knows the final results of the mathematical physicist, but he knows what they mean in terms of the physical world. Mathematics is one of his most powerful tools, but it is only a tool; there are still physical questions that can be asked, and it is his business to find the answers. 21 It is to such a theoretical physics, developed in the light of the principles of a generalized physical science already known to Aristotle and Saint Thomas, that the solution of the problem of gravitational attraction must be referred. 22 The inverse square law, on the face of it, is powerless to say what is the cause of gravitational motion. Recourse must be had to physi20 Mathematical Principles (Great Bocks of the Western World, vol. 34), p. 181: "In mathematics we are to investigate the quantities of forces with their proportions consequent upon any conditions supposed; then, when we enter upon physics, we compare those proportions with the phenomena of Nature, that we may know what conditions of those forces answer to the several kinds of attractive bodies. And this preparation being made, we argue more safely concerning the physical species, causes, and proportions of the forces." 21 Cf. W. H. Kane, B. M. Ashley, J. D. Corcoran, R. J. Nogar, Science in Synthesis (River Forest, Til.: Albertus Magnus Lyceum for Natural Science, 1958), pp. 86, 87. •• Cf. Pope Pius XII, "Science and Philosophy," Address to the Pontifical Academy of Sciences, April 24, 1955. The Pope Speaks, Vol. 2, No. lil (11155), pp. llS-UO. 166 W. A. WALLACE cal concepts to find the answer, and since Newton himself seems to have inclined to the natural impulse explanation, it offers a convenient concept with which to begin the search. Nature, taken in a strict technical sense, is a principle of motion that exists within a primary unit. 23 It is the source from which proceed all movements that are called " natural," and thus such movements are conceived as originating in some way within the moving body, and not imposed on it completely from without. Natural motions are therefore different from compulsory motions, which are the result solely of extrinsic agents acting on the body. 24 When studying the local motions of fishes and birds and other living things, there is no great difficulty in recognizing a natural motion and distinguishing it from a compulsory motion. If a fish is taken and thrown into a bucket, there cannot be much question that its motion, as it flies in a graceful arc through the air, is not natural for a fish; " thrown " motion is compulsory motion, and it matters little whether the thing thrown be a fish or a baseball, because the cause of the motion is quite clearly from without. And if the fish be seen swimming in an aquarium, there is also no great difficulty in identifying this motion as naturaL That is one of the ways you go about identifying fishes and various species of living things; their characteristic motions manifest their natures, and thus have a primary claim to being termed naturaP 5 Somewhat the same thing may also be said for the motions that proceed from inorganic primary units, particularly when the motions considered are alterations and fundamental changes. For instance, it is natural fo:r radium to break down to lead by radioactive disintegration, The very fact that such a phenomenon is referred to as natural radioactivity is a tacit admission of the validity of this view. But when the problem is raised about the •• St. Thomas, ll Physic., lect. 1; Aristotle, b •• Compulsory motion is also called violent motion. Cf. IV Physic., b 88, lect. 12. •• Cf. W. H. Kane, "Comment on Dr. Foley's Paper," Proceedings of the .American Catholic Philosophical Association, XXVI (191i2), pp. 144-146. NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 167 local motion of inorganic bodies, and particularly about gravitational motion, the answer is not so obvious. Is gravitational motion a compulsory motion, something imposed on the body completely from without, or is it a natural motion that proceeds in some way from within the falling body itself? This is the basic issue at stake in the question of gravitational attraction; it must be faced squarely if an answer is to be given in terms of fundamental physical principles. The most simple way to solve the difficulty, of course, is to enumerate the various features of natural motions that are found in more obvious cases, and then to apply them to the case under consideration. If all can be verified of gravitational motion, then there is strong reason for holding that the latter is a natural motion. If, on the other hand, this motion has nothing in common with other motions that are known to be natural, then the presupposition that it is only a compulsory motion should be favored, and the search started for the compelling agent or the physical causes that properly produce the compulsion. Nat ural motion can be identified from these conditions that accompany the work of nature: it is from within/ 6 spontaneous, uniform in its action/ 7 and always directed to a definite goal or term. 28 Furthermore, the term to which it is directed is characteristic of the particular primary unit having that nature. Moreover, all these conditions are verified in gravitational motion, and thus it should be regarded as a natural motion. Gravitational motion is from within. No matter what extrinsic factors may affect the motion, the single most important cause of the motion is the characteristic of the body that makes it ponderable. We refer to this as its gravity, and measure it by the various operational procedures for determining weight or mass. But there is something within the body that we are measurmg, and this is the most fundamental source of its motion. •• Cf. II Physic., 199 b 26, lect. 14. •• Cf. VIII Physic., lect. 15. •• Cf. II Physio., 198 b 10, lect. 4, lect. 12. 2 168 W. A. WALLACE Further, because gravitational motion is from within, it is spontaneous. As soon as the props are taken out from under a heavy object, it immediately and spontaneously falls to the ground. As soon as any massive body is left to its own devices, it immediately and spontaneously seeks its proper place in the physical environment in which it happens to be. There is no sluggishness, no indifference as far as the manifestation of the tendency is concerned. All that is required is the removal of the impediments restraining the tendency, and the material body will unhesitatingly seek a physical place compatible with its nature. Again, gravitational motion is always uniform in its action. Bodies of any particular chemical element, to make the case simple, will follow exactly the same path, will .fall with exactly the same velocity in a given medium as they seek their natural place. If this were not the case, all of Newtonian physics would have to be rejected immediately. Obviously, the particular details describing the motion will vary for different chemical elements, for different chemical compositions that might characterize various bodies, but given the same type of body it will always follow a characteristic path. Nature acts uniformly unless it is impeded by an outside agent, and this is also seen to be the case in gravitational motion. Finally, gravitational motion is always directed to a definite goal or term that is characteristic of the falling body. This is not to say that every body has an absolute point in empty space to which it tends. The term referred to here is not a mathematical entity, but rather a term that is understood in a physical context. If a gas chamber contained atoms of all the elements in the periodic table, and the atoms were allowed to :reach equilibrium at a given temperature, all of them would seek definite levels of stratification characteristic of their particular natures. In fact, that would be one way of sorting out the various elements and classifying them, and has been so used by Aston in his mass spectrograph. Similarly, bodies composed of various elements would seek definite places in any physical NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 169 environment determined by the proportions of the elements of which they were composed. The term sought in any particular environment is the natural place of the body, and when it is attained, the body comes to rest. This, too, is characteristic of natural motions, for nature is the principle of motion and rest, as has been clearly asserted by Aristotle. 29 Thus gravitational motion gives all the indications of being a natural motion. It might be objected at this point that these arguments are convincing enough, but they do not prove that gravitational motion is a natural motion in the sense that they remove all doubt, nor do they completely exclude the hypothesis of another body or a corporeal medium acting outside the falling body and causing its motion. The objection is valid, but there is a twofold difficulty involved in it that needs elucidation. First of all, to say that a motion is a natural motion is not to eliminate the need for an efficient cause of that motion. Nature is a principle of motion within the body undergoing motion, but it is a principle in the order of formal or material causality, not in the order of efficient causality. Thus, even a body that is naturally in motion must have an efficient cause of that motion, it must be moved by an agent distinct from itself. This is no less true of motions that proceed from active principles within living organisms, than it is of non-living things having only a passive principle of motion within them. But the mover in the case of a natural motion has to be one that can move the body naturally, i.e., in accordance with its nature. It cannot be a violent agent that leaves no determination to the thing moved by pushing it or pulling it from without in haphazard fashion. Secondly, the identification of the efficient cause of a natural motion is a problem that is considerably more difficult than recognizing that particular motion as natural. But it does not require proof of the naturalness of a motion before it can be discussed. In fact, that any motion is natural cannot be proved in a strict sense; it can only be discovered. Nature is itself •• Ibid., 19!l b lect. 1. 170 W. A. WALLACE such a fundamental principle that there is nothing more fundamental in terms of which it can be demonstrated, and the same thing is true of natural motions. In general, however, when nature is known to be the first principle of motion that proceeds from within a body, the first question that should be asked about any motion is whether or not it can be properly explained by this principle. Hypothetical conjectures about extrinsic movers are all right in their place, but they have no place obscuring the proper order of investigation into the world of nature. That any motion is natural cannot be demonstrated, but it can be recognized, and when the available evidence is in its favor, it is quite unscientific to overlook this evidence for a hypothetical mechanical explanation that neglects the most obvious features of the motion. 811 Yet for those who remain unconvinced that gravitational motion is a natural motion, it is still possible to argue against this antinomy by questioning the physical reality of gravitational attraction, for this is something that has never been proved. One of the best indications of this is that Newton, who first used the concept, over and over again explains that it is only a mathematical device, to which he sees no reason for assigning a physical reality. If he thought that its physical existe:nce could not be proved, and repeatedly warned against accepting it as a reality, it is foolhardy for his students to urge such a " reality " against the prima via. Moreover, as far as the antinomy itself is concerned, Newton and the founders of mathematical physics would never have subscribed to it. Far from being convinced that the inversesquare law made God unnecessary, they were quite convinced that gravitational motion could only be explained by ultimate reference to God. As one Newtonian scholar has written: He (Newton) points to the necessary existence of some active principle of force which would conserve and compensate lost motion. Newton did not take very seriously the attempt to explain this conservation mechanically, as has been noted above from his 80 Ibid., 198 a !'l, lect. I. NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 171 letters to Bentley, saying that gravitation. must be caused by an agent following certain laws. He is willing to have Cotes refer to the fact that it is the Creator who by his will produces gravitational action. The same references are to be found in the words written by Newton himself, and in the writings of Newton's best defenders; also Samuel Hosley, the editor of Newton's Opera, says that.the originator and sustainer of gravity is not material but divine, and that Newton did not explain his laws of motion in terms of repulsion but in terms of immaterial causes, not perceivable to the sense, but manifested to the spirit and effect of God. 31 A confirmatory argument ii;J. the rejection of gravitational attraction, and one of particular appeal to those who favor facts over the endless multiplication of hypothetical constructions, is the fact that such an attraction has never been shielded. It is all well and good to speak of magnetic and electrical attraction, for these have physical meaning; the influence of a magnet or a charged body can be and has been shielded many times over in the laboratory. This gives indisputable evidence of the physical existence of such attraction. But the remarkable thing is that for all the advances that have been made in every field of physical research in the two and a half centuries since Newton's Principia first appeared, not the slightest evidence has been obtained of gravitation ever being shielded. This may be due to our appalling ignorance of facts concerning the physical world, it is true, but it is certainly no less likely that it is due to a fundamental misconception of gravitation itself. Further, if any additional proof be needed for those who would identify mathematical concepts with the physical reality they so accurately describe, new developments in theoretical physics also disregard the theory of gravitational attraction. For instance, " least action " concepts as developed by Hamilton can be used to give a very elegant treatment of gravitational phenomenona, with no mention of attractive forces. One of Hamilton's basic notions is that all bodies try to reach a place of least potential energy, and in so doing, seek 81 A. J. Snow, Matter and Gravity in Newton's Physical Philosophy (London: Oxford Univ. Press, pp. 162-168. 112 W. A. WALLACE the path that involves the least work. This is the principle of least action, which Bertrand Russell has named the "law of cosmic laziness." When the energy equations are written and calculations are made of the paths of falling bodies, for instance, exactly the same results are attained by Hamilton's method as by the use of Newtonian equations. 32 This again reveals the superfluous character of attraction concepts. Another development along the same line, perhaps more startling in its experimental confirmations, is Einstein's theory of General Relativity. This theory does not regard gravitational motion as something initiated by a pull extrinsic to the body itself, but rather conceives the whole motion as an " event" in the space-time continuum. A physical evaluation of this theory will not be attempted here; it suffices to note only that its mathematical formulation is made without reference to any attractive forces. And yet calculations made with Einstein's equations give results that not only approximate Newton's predictions, but in three now classical experiments give a more accurate description of phenomena."" The solution to the first antinomy should thus be clear. It is based on a false, or at best, an arbitrarily taken supposition, namely, that gravitational motion is a violent or compulsory motion caused solely by the mechanical pull of another body. A more penetrating analysis of all that is involved in this type of motion reveals that it is properly a natural motion, proceeding from an intrinsic principle within the body. And like all other natural motions, it requires physical pre-motion by the Author of Nature, either directly or at least through an intrinsically subordinated chain of moved movers, at each instant of its motion. 34 It is possible that this causality be exercised •• Cf. A. G. Van Melsen, The Philosophy of Nature (Pittsburgh: Duquesne Univ. Press, 1958), p. 161. 33 The three experimental verifications offe1:ed by Einstein were: (l) the advance of the perihelion of the planet Mercury, (2) the deflection of a beam of light passing the limb of the sun, and (3) the shift of spectral lines in the gravitational field of the sun. Cf. G. Rainich, The Mathematics of Relativity (New York: John Wiley, 1950), pp. 159-167. •• The details of this proof constitute the positive exposition of the prima via, NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 178 instrumentally through some corporeal medium, or even through surrounding physical bodies. But these can never be the adequate efficient cause of gravitational motion, any more than a baseball bat, of and by itself, can be the adequate efficient cause of the motion of a baseball. Moreover, there can be no conflict between this explanation and the methods used by Newton to derive the inverse-square law. This particular law, as a physico-mathematical relation between various measurable properties following on gravitational motion, abstracts completely from an efficient mover. 35 It does not deny the existence of such a mover, it does not reject one mover or even a system of movers. It merely states an equality that is found to obtain when the resulting motion is described mathematically. Therefore it does not follow that a mutual " attractive force " gives an adequate physical explanation of gravitational motion. The inverse-square law does not dispense with a single mover in an intrinsically subordinated chain, let alone manifest the superfluity of God, and anyone who would speak as though it did is only creating for himself an apparent difficulty. * * * * * According to Newton's first law of motion, a body in uniform rectilinear motion will continue in that motion indefinitely unless acted upon by an external force. But such a body is sufficiently moved by its own inertia and does not require an external mover. Therefore it is not true that whatever is moved must be moved by another, and thus the proof for God's existence based on this principle must be rejected. 86 SECOND ANTINOMY: which can be illustrated and understood on its own merits, quite apart from the peculiar difficulties associated with gravitational motion. Cf. Summa Theol., I, q. 2, a. 8; I Cont. Gent., c. 18; VII et VIII Physic. •• Cf. J. A. Weisheipl, 0. P., "Natural and Compulsory Movement," The New s'f:holasticiam,XXIX (1955), 80, and also the two other excellent articles by the same author: "The Concept of Nature," ibid., XXVlli (1954), 877-408, and "Space and Gravitation," ibid., XXIX (1955), 175-228. •• This is basically Whittaker's rejection of the prima via. Cf. Space and Spirit, p. 47. 174 W. A. WALLACE This antinomy is built around the concept .of inertia in much the same way as the first antinomy employed the concept of gravitational attraction. In a sense, however, it presents a more straightforward argument. The force of the objection would seem to follow directly from the principle of inertia, enunciated as the first law of motion, and not from a particular interpretation of an equation such as the inverse-square relation. Further, since no equation-is mentioned explicitly, it would appear that the distinction between physical and mathematical principles invoked in the solution of the first antinomy cannot be applied in this case. Finally, the first law of motion is simply stated by Newton at the beginning of his technical exposition of the Principia, with no detailed derivation and with no extended argumentation in its justification. Thus it would appear that he thought it sufficiently obvious and selfevident to be accepted immediately at the beginning of the tract. Therefore the arguments that were used in the solution of the first antinomy drawn from Newton's own admissions would not seem to be applicable in this case. These observations highlight the additional difficulties present in the second antinomy, and at the same time point out the main problems that have to be solved before the antinomy can be resolved. As in the preceding solution, the textual approach will serve as a good introduction to these problems, so it will be convenient to begin with a discussion of the first law of motion and the position it occupies in Newton's Principia. Newton entitled his work, as will be recalled, the Mathematical Principles of Natural Philosophy. Yet he did not write it as a modern textbook with a long list of equations functioning in each derivation. Rather he started out with a few definitions of basic concepts, then stated the three laws of motion and their corollaries, and immediately launched into the various propositions that could be deduced reasonably from these principles and their consequents. Some propositions functioned for him as theorems and lemmas, and others were introduced NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 175 merely as problems. But all propositions were stated in words; except for an occasional proportion, all his derivations are described in the expositive form of an essay without the mathematical derivations that characterize present-day treatises on mechanics. The point is of historical interest, but it also accents a significant detail. The absence of an explicit mathematical equation does not indicate the absence of a mathematical principle. Because a principle or law is stated in words does not- indicate that it is not basically mathematical, or at least founded on mathematical presuppositions. Newton stated the first law of motion, which was the very first of his "Mathematical Principles," in these words: Law 1: Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. 37 On face value, there is nothing in this statement that would seem to imply that it is a mathematical principle. It should be noted, however, that this law has been preceded in Newton's text by eight Definitions and one Scholium, though of all the terms mentioned in the law, only one is considered in the definitions, viz., " forces." Yet this may be of some significance, for Newton does state in Definition VIII: " I here design only to give a mathematical notion of those forces, without considering their physical causes and seats." 88 This may be a clue to the solution, but at best it is only a clue, for the term "forces" does not seem to enter essentially into the statement of the first law. It plays only a negative or accidental role. What the first law states is that without these forces, even mathematically considered, a body will continue in its state of rest or of uniform motion in a right line. The real problem is the first part of the principle of inertia. How is this to be conceived? Is it physico-mathematical or purely physical, and if the former, in what precise sense does mathematics enter into it? This is the key problem involved in the principle of inertia •• Mathematical Principles, p. 14.. •• Ibid., p. s. 176 W. A. WALLACE from the viewpoint of a foundational physics, and quite fundamental to the solution of the second antinomy. There can be no doubt that the principle of inertia, as we shall henceforth designate the first law of motion, is not a physico-mathematical principle in the sense that it will ever enter explicitly into an equation of mathematical physics. There is no way of writing it in the form of an equation, and it does not seem to express an equality that could be of any use in any other equation. ·At best it tells what can be left out of another equation, and this is hardly a positive contribution. As far as the positive, formal principles that bear directly on the derivation of conclusions of mathematical physics are concerned, the principle of inertia should not be included among them. Yet the principle itself has some positive content. Moreover, it states what obtains in a limiting case, and thus presupposes the use of a limit concept in its derivation. And since such limit concepts pertain more to mathematical modes of reasoning than to physical ones, the principle of inertia is more physico-mathematical than it is physical. Thus Newton was justi:tied in enumerating it first among the mathematical principles of natural philosophy. As a matter of fact, the concept of a body proceeding in a uniform motion in a straight line to infinity is mentioned by Newton in his explanation of Definition V even before he states it in the first law. In the discussion following this definition, which defines a centripetal force as that by which bodies tend towards a point as to a center, he also gives clear indication of the reasoning which led to the statement of the principle of inertia. He says in part: That force ... by which the sling continually draws back the stone towards the hand, and retains it in its orbit, because it is directed to the hand as the center of the orbit, I call the centripetal force. And the same thing is to be understood of all bodies, revolved in any orbits. They all endeavor to recede from the centers of their orbits; and were it not for the opposition of a contrary force which restrains them to, and detains them in their orbits, which I therefore NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 177 call centripetal, would fly off in right lines, with an uniform motion. A projectile, if it were not for the force of gravity, would not deviate towards the earth, but would go off from it in a right line, and that with an uniform motion, if the resistance of the air was taken away. It is by its gravity that it is drawn aside continually from its rectilinear course, and made to deviate towards the earth, more or less, according to the force of its gravity, and the velocity of its motion. The less the gravity is, or the quantity of its matter, or the greater the velocity with which it is projected, the less will it deviate from a rectilinear course, and the farther will it go.39 Before giving the rest of this citation, it will be weH to point out that the last sentence states the empirical basis for the first law, for it states something that can be observed experimentally. It also shows how this empirical basis is to be used in reaching a limit concept, insofar as the approach to the limit is stated as a proportion. The less the gravity or the greater the velocity, Newton notes, the less the deviation from rectilinearity and the farther the projectile will go. This is a true observation as far as it goes, and it sets up the conceptual framework for approaching the limit. Newton continues: If a leaden ball, projected from the top of a mountain by the force of gunpowder, with. a given velocity, and in a direction parallel to the horizon, is carried in a curved line to the distance of two miles before it falls to the ground; the same, if the resistance of the air were taken away, with. a double or decuple velocity, would fly twice or ten times as far. And by increasing the velocity, we may at pleasure increase the distance to which it might be projected, and diminish the curvature of the line which it might describe, till at last it should fall at the distance of 10, 30 or 90 degrees, or even might go quite round the whole earth before it falls; or lastly, so that it might never fall to the earth, but go forwards into the celestial spaces, and proceed in its motion ad infinitum. 40 Here he continues to apply the proportion, increases the velocity at pleasure and at the same time allows the ai:r resistance to go to zero, and thus concludes to the limiting case: the projectile will proceed in its motion in infinitum. This •• Ibid., p. 6. •• Ibid. 178 W. A. WALLACE reasoning process is not completely original with Newton; Galileo, in his "Discourses on Two New Sciences," had discussed similar situations and had shown how limit concepts could lead to interesting conclusions. 41 But Newton's genius consisted in this: he did not restrict himself to the mathematical proportion involved in approaching the limit, but rather concentrated on the limiting case itselt He stated the limiting case as a general principle for all local motion when he formulated the first law. As should be evident from this analysis, the principle of inertia is actually a conclusion, an inference drawn from a physico-mathematical approach to a limit, and for this reason is not a purely physical principle but is itself physico-mathematicaL A more rigorous statement of the approach to the limit that is actually involved would be this: the distance a projectile will travel in a resistive medium under a given impulse is an inverse function of the resistance of the medium. Similarly, the limiting case might be stated: as the resistance of the medium goes to zero, the distance travelled goes to infinity. Examining the principle of inertia in the light of this analysis, then, it can be seen that it is neither a self-evident principle nor demonstrable. The reason why it is not self-evident is simple enough. It is never found in ordinary experience that a body in uniform motion continues in such motion indefinitely. All the bodies met with in ordinary experience encounter resistive forces in their travel, and sooner or later come to rest. Nor does refined experimentation and research supply any instances where such resistive forces are absent. The best vacuums attainable in well-equipped laboratories are still quite gross, and present-day information about so-called " empty " interstellar space indicates that the :rarest matter density that can be expected there is one nuclear particle per cubic centimeter. So it would appear that resistive media are a quite universal phenomenon. "E. g., Discourses, Third Day, prob. IX, prop. Scholium. NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 179 But it might be objected that this is to overlook the second half of the principle enunciated explicity by Newton, viz., "unless it is compelled to change that state (uniform motion) by forces impressed upon it." When this is taken into account, although it might be conceded that the first part is not evident to sense experience or to laboratory measurement, the entire principle seems evident to reason, to rational analysis. Unfortunately, however, this type of self-evidence must be rejected too. Th'e second half of the statement cannot be taken as confirmatory of the first half, even when rationally considered. When the first half is considered in the light of the second half, all that is left is the statement, made notorious by Eddington, that " every particle continues in its state of rest or uniform motion in a straight line, except insofar as it doesn't." 42 Literally correct, no doubt, but hardly a first principle on which to build a mathematical physics. The principle of inertia is not self-evident, then; furthermore it cannot be demonstrated, for there is no way of proving that it is true. Another way of saying the same thing is that the principle of inertia is a dialectical principle, and this by reason of the limit concept involved in its verification. The principle, as has already been noted, is an inference from observational data by means of a limit concept. The observational data are certainly true, but the only way in which it may be maintained that the limiting case is also true would be by maintaining that what is verified in the approach to a limit is also verified at the limit itself. The latter statement, however, cannot be maintained, because it is not universally true. There are many instances in mathematics where it is known to be violated. One illustration is the approach of polygon to circle as the number of sides is increased indefinitely. All through the approach to the limit, assuming the simple case where all figures are inscribed in the limiting circle, every figure constructed that has a finite number of sides is a polygon. The •• The Nature of the Physical World (New York: 1937)' p. 1£4. The Macmillan Company, 180 W. A. WALLACE limiting case is a figure of a different species, it is no longer a polygon, but a circle. It is not true to say that a polygon is a circle; the difference is as basic and irreducible as that between the discrete and the continuous. In this case, what is verified in the approach to the limit (polygon) , is not verified at the limit itself (circle) . Now if it is not always true that what is verified during the approach is necessarily verified at the limit, and indeed there are excellent arguments to show that it can never be true/ 3 then the fact that the observational base for the principle of inertia is true cannot be used to prove, or demonstrate, that the limiting case stated in the principle is also true. Thus it remains that the first law as stated by Newton is neither self-evident nor demonstrable, and as such is not certainly verifiable of physical phenomena in the real world. 44 But this does not necessarily derogate from the utility of the principle of inertia as a physi<;!o-mathematical principle. What it does indicate is that this principle does not have the broad applicability of a generalized physical principle that would be universally verified in all real motions. Rather it gives an idealized account of local motion that abstracts from extrinsic factors present in the real world and affecting such motion. And since it abstracts from extrinsic factors acting on real bodies moving in a physical enviroment, it should not be surprising that it also abstracts from efficient causality influencing the body in its motion. In point of fact, in all observable cases in the real world, an extrinsic mover is needed in order to have a motion that is exactly uniform. The reason is obvious from what has been said above about resistance being present throughout the known universe, and therefore the need for such a mover is quite consistent with the statement of the first law. Resistance is always encountered from objects extrinsic to the thing moved, and to •• Cf. J. Lalor, 0. F. M., The Concept of Limit (unpublished doctoral dissertation; Quebec: Universite Laval, n. d.). "Cf. Weisheipl, "Natural and Compulsory Movement," loc. cit., p. 72. NEWTONIAN .ANTINOMIES AGAINST THE " PRIMA VIA ,. 181 overcome the decelerating effect of this, an extrinsic force will have to continue to be applied to the object being moved. Of course, it is possible to abstract from this resistance, and conceive of a body moving uniformly without reference to its external physical situation. But when one does this, it is very analogous to conceiving of a body at some arbitrary temperature in the real world that maintains this temperature indefinitely despite any changes of temperature occurring around it. It is all well and good to conceive of insulators that suppositionally isolate it from the real world, but all physicists know that such insulators do not exist in practice. Making the supposition eliminates the problem of a heat source to maintain the body at the given temperature, but it does this only in the mind of the physicist. The same thing goes, mutatis mutandis, for idealized local motion. If one makes a supposition that eliminates thinking about extrinsic movers, then for him they do not exist, but that does not eliminate their necessity in the real world. It might be objected that what has been said here is true enough if one wishes to be a rigorist and speak of motions that are exactly uniform. However, it would seem that Newtonian physics does not attempt to give an exact account of the physical universe, but only an approximate account. Therefore, if the motions of stars and planets are considered, or of projectiles in very rare media, they.will actually decelerate slightly, but the resistance is so small that in practice it can be neglected. Thus the motion that is in practice referred to as uniform, though in fact slightly decelerated, does not :require an extrinsic mover, but is sufficiently accounted fo:r by the inertia of the moving body. The answer to this further difficulty, like the basic answer to the difficulty of gravitational attraction, must be given in terms of a generalized science of nature such as that developed by Aristotle and Saint Thomas. In fact, there is a marked similarity between the two cases, as will become apparent in the development below. But there is also a considerable difference, and it will be well to make this clear at the outset. 182 W. A. WALLACE Inertial motion is universally taken as opposed to gravitational motion. The latter is usually referred to as "free" or natural motion, while the former is " forced " or compulsory motion. In the strict understanding of natural motion, it is called such because it proceeds from the nature of the body itself, it proceeds in some way from within the body undergoing the motion. Compulsory motion, on the other hand, is imposed from without; it is violent, it is contrary to the natural inclination of the body being moved. The reason why it is recognized as not being a natural motion is that it does not fulfill the conditions mentioned above as associated with all natural motions, viz., it is not from within, nor spontaneous, nor is it uniform in its action, nor does it always tend to the same term characteristic of the particular body. Obviously, if a motion is a composite of gravitational and inertial components, care will have to be taken to isolate what comes from nature from what is imposed from without. But assuming, in the spirit of the difficulty that has been proposed, an inertial 'or compulsory motion in which gravitational tendencies can be neglected, these conditions will also be lacking. The inertial motion does not originate from within, but rather from without. It is not spontaneous, but is initially forced and sluggish. It is not uniform in its action for any particular body, for the same projectile may be thrown fast or slow, it may be rolled or spun, it may be juggled back and forth. And it is not directed to a place determined by the particular body and its physical environment, for it may be directed now up, now down, now in any direction conceivable for a three-dimensional vector. Thus inertial motion is not natural motion. Yet there seems to be something about inertial motion that is similar to natural motion. When a projectile is thrown, it appears that an impulse is imparted to it by the thrower, and impulse further appears to be in some way the source of its motion. Again, once initiated, the motion proceeds in a uniforrn fashion for that particular impulse, and moreover, it proceeds in a very determined direction. It is true that it does not seek NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 188 a compatible place in a particular physical environment, but there does not seem to be any doubt of an inherent tendency in a particular direction. And this direction is not necessarily that intended in the mind of the thrower, but appears to be objectively realized in the thing thrown; otherwise it is extremely difficult to understand how there can be such a thing as poor marksmanship. What is objectively realized does not have the perfectly determined tendency of a nature, but it nonetheless has an inherent tendency sufficient to make the physicist realize that momentum is a vector. These reasons impel us to argue that there is associated with inertial motion an impulse that is analogous to the impulse of gravity found in natural gravitational motion. 45 In a sense, this impulse is a sort of " second nature." It is not natural as coming from within the body itself. Rather, it is more like a behavior pattern induced in animals from without, by training or by continued application of certain stimuli. Still it is different from this, because all material bodies have an immediate susceptibility for the impulse of inertial motion. And further, once it has been imparted to a body, there appears to be no reason to believe that it would not perdure endlessly, unless overcome by something extrinsic encountered in the course of its motion, which however is always the case in our experience. 46 Now, granted the existence of such an impulse associated with inertial motion, it is important to realize that even this impulse needs an extrinsic mover in order to sustain the motion efficiently. The reason is basically the same as that advanced for an extrinsic mover in natural gravitational motion. Just as •• Cf. Dominicus de Soto; Super octo libros Physicorum Quaestiones (Salamanca, 1551), Lib. VIII, q. 3, fol. 104v-105v. •• The precise entitative status of this impulse is disputed among Thomists, as is the subject of its inherence, some maintaining that it is in the medium surrounding the projectile, others that it is in the projectile itself. For a summary of opinions, cf. A. Rozwadowski, S. J., "De motus localis causa proxima secundum principia S. Thomae," Divus Thomas Piacenza, XVI (1939), 104-114; P. Hoenen, S. J., Oosmologia (4th ed., Roma: Aedes Pont. Univ. Gregorianae, 1949), pp. Father Weisheipl has a good evaluation of these opinions in "Natural and Compulsory Movement," loc. cit., pp. 3 184 W. A. WALLACE the nature itself requires an extrinsic mover, so the "second nature " which is a modification of the nature must be actuated from without. Both are principles in the order of formal or material causality, and both therefore require actuation in the order of efficient causality in order to be continually operative. 47 When abstraction is made from such an efficient agent, of course, it is possible to conceive of the impulse itself as an inertia, as some type of explanation of the compulsory motion, and it is possible to speak also of measures of this, such as momentum. Such measures will be useful in accounting for the apparent uniformity of the motion, for estimating the potentiality of the thing moved in originating other motions, etc. But neither inertia nor momentum sufficiently accounts for the entire motion any more than a body's gravity can completely account for its fall. Further, far from the principle of inertia disproving the existence of God, the more one tries to verify this principle, the more one is led to affirm the existence of an infinite Mover. If all the idealized concepts that have been discussed be granted, and the idealized case be considered as physically :real, then not only is some extrinsic mover required, but also one of infinite power, and this can only be God. The reason for this is based on the proportionality that must exist between cause and effect. If it be maintained that a finite impulse can impart a motion that will perdu:re ad infinitum, this is to hold that an infinite effect can proceed from a finite cause. 48 Since such a position is untenable, if the principle of inertia in this understanding is to be maintained, it must be held that the cause is finite from the part of the formal cause (the impulse), but infinite from the part of the efficient mover that sustains the motion. And such an infinite efficient mover would be none other than God. Thus the principle itself, taken in the most realistic sense possible, leads to the postulation of a first unmoved Mover. •• Cf. Weisheipl, "The Concept of Nature," loc. cit. •• Cf. R. Garrigou-Lagrange, 0. P., God: His Existence and His Nature (London: B. Herder, 1938), II, 447-452. NEWTONIAN ANTINOMIES AGAINST THE '" PRIMA VIA " 185 Now it may come as a surprise to the modern physicist, but this explanation that has been offered is quite consistent with what Newton himself thought about inertial motion. It is true that he does not explicitly mention an extrinsic principle for such motion in his discussions throughout the Principia, apart from what he says generally about God as the universal Mover and to which we will refer in the solution of the third antinomy. But in his animadversions on mechanics that occur at the end of the Optics, he does explicitly clear up any misunderstanding that might exist about his position on inertial motion, quite apart from his reservations on gravitational motion. He states: The vis inertiae is a passive principle by which bodies persist in their motion or rest, receive motion in proportion to the force impressing it, and resist as much as they are resisted. By this principle alone there never could be any motion in the world. Some other principle was necessary for putting bodies into motion; and now they are in motion, some other principle is necessary for conserving the motion. 49 A clearer statement could not be made about the necessity of an extrinsic mover, not only at the beginning of inertial motion, but also at every instant throughout that motion, The evidence is thus indisputable that Newton would not have rejected the fundamental principle, " whatever is moved is moved by another," on the basis of the law he was first to enunciate. The solution to the second antinomy should therefore be dear. The first law of motion and the concept of inertia that it involves state only partial truths. They are not verified of an entire physical reality, but rather abstract from efficient causality and its relation to compulsory motion. Although not explicitly mathematical, they nevertheless are based on a physico-mathematical reasoning process and invoke a limit concept in their verification. Because of the dialectical aspect of the approach to the limit, the principle of inertia cannot be proved to be true in a complete and self-sufficient sense. Nor is it •• Optics, p. 540. 186 W. A. WALLACE evident either to experiment or to reason. Consequently it cannot be invoked as a certain argument against the validity of the foundational principle: whatever is moved must be moved by another. Further, looking at the truth contained in the first law from the vantage point we have now attained, it can be seen that the former attains its full stature and most intelligent justification when understood as requiring tP.e continued application of an extrinsic mover. The latter mover's influence may not be directly measurable, but it is knowable. Although it is not known to modern physicists, moreover, it was known to Newton, the father of their science, who knew better than they the limitations of the principles he first formulated. Far from underm,ining the motor causality principle, it furnishes yet another instance of its universal verification. The principle still stands, and along with it the proof for God's existence from motion in the universe-motion both gravitational, and inertial. * * * * * To every action, there must correspond an equal and opposite reaction. But there can be no such interaction between any body and an incorporeal mover. Therefore it is impossible that motion proceed from an incorporeal mover, and any proof that would terminate with such a mover must be rejected. THIRD ANTINOMY: The third antinomy does not contain difficulties of the magnitude of those presented by the first two. It is not, like them, directed at the fundamental principles which function as the premises of the' prima via. Rather it raises a question about the term of the proof, and this in a general way. It proposes that there can be no such thing as an incorporeal mover, and thus jeopardizes the proof by maintaining that it reaches a nonsensical conclusion. 50 •• The attitude of mind underlying this objection is characteristic of logical positivism and operationalism, both of which would categorize an incorporeal mover as a "meaningless concept." NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 187 The answer to this antinomy, as to the preceding ones, is suggested by Newton's treatment of the problem in his development of the Principia. Actually, he does not state the actionreaction principle in the very broad and general way in which it is employed in the antinomy, but restricts it specifically to actions where two bodies are involved. His original statement of the third law is this: Law III: To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. 51 His explanation of the law also makes clear that he is excepting the case of incorporeal movers from its ambit, for the only illustrations he furnishes in justification of the action-reaction principle involve corporeal movers. Thus he states: Whatever draws or presses another is as much drawn or pressed by the other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone; for the distended rope, by the same endeavor to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part. 52 It is interesting to note here that of the three instances that Newton uses for exemplification of the principle, two concern cases where bodies are in physical contact, and the third is clearly an instance of an intrinsically subordinated instrumental motion, viz., the case of the horse pulling a stone by means of a rope. We shall have occasion to return to this later, but for the moment it will suffice to note that all are concerned with corporeal movers. 51 Mathematical Principles, p. 14. 52 Ibid. 188 W. A. WALLACE Now it may be maintained that Newton restricts himself to corporeal movers in this principle because he is convinced that these are the only type of movers that exist, and so it would be nonsensical to :refer to incorporeal movers in his Principia. Or the possibility suggests itself that he himself might have believed in incorporeal movers, but that he did not think they had any place in physical science, and therefore left them out of consideration. Both of these hypotheses, however, are untenable in the light of explicit citations from the great scientist. As to the existence of incorporeal and immaterial entities in the physical universe, he takes the general position that such things do exist. For instance, in discussing his meaning of attraction in one of the texts already referred to, he states: "I here use the word attraction in general for any endeavor whatever ... whether it arises from the action of the ether or of the air, or of any medium whatever, whether corporeal o:r incorporeal." 53 Again, in a letter to Bentley after the first edition of the Principia had appeared, he mentions: "Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers." 54 A person who was convinced that material movers were the only type that existed would never make the allowances explicit in these statements. Beyond this, it is further evident that Newton attributed actual dominion to the supreme Being over the workings of the physical universe, and this for him also included motion. Insofar as God was the mover and governor of the universe, He also pertained to the :realm of physical science. Newton makes these ideas explicit in the General Scholium which he wrote at the end of the third book of the Principia, where he is at pains to exclude the type of interpretation of his opus which is at the root of the antinomy now under discussion. Some citations which bear this out are the following: •• Ibid., p. 130. 54 Correspondence of Sir Isaac Newton and Professor Cotes, p. 159. NEWTONIAN ANTINOMIES AGAINST THE " PRIMA VIA " 189 It is not to be conceived that mere mechanical causes could give birth to so many regular motions .... This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. 55 It is the dominion of a spiritual being which constitutes a God .... And from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and, from his other perfections, that he is supreme, and most perfect. 56 In him (God) are all things contained and moved; yet neither affects the other: God suffers nothing from the motion of bodies; bodies find no resistance from the omnipresence of God. 57 He (God) is utterly void of all body and bodily figure, and can therefore neither be seen, nor heard, nor touched; ... We have ideas of his attributes, but what the real substance of anything is we know not . . . all our notions of God are taken from the ways of mankind by a certain similitude, which, though not perfect, has some likeness, however. And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy. 58 The very last sentence indicates the relevance of God to physical science in Newton's estimation, for his use of the term " natural philosophy " was equivalent to our understanding of physics and astronomy. And the citation stating that God moves all things, " yet neither affects the other: God suffers nothing from the motion of bodies, etc.," supplies his direct answer to the third antinomy. As should be clear now from the distinctions that have been made in the solution of the previous difficulties, the actionreaction principle is a physico-mathematical relation that holds only between quantified bodies that are already being moved by some physical agent. It merely stresses the mathematical symmetry involved in the transmission of mechanical impulses, and this is wholiy consistent with what one would expect in terms of more fundamental principles. If bodies are in contact and an impulse is being transmitted, obviously its metrical aspects are the same whether it be looked at from the viewpoint 55 Mathematical Principles, p. 369. •• Ibid., p. 370. Ibid. •• Ibid. 57 190 W. A. WALLACE of the transmitter or the receptor. And the same thing is true if a physical case is being considered where a motion is being transmitted by a series of connected instruments. Here, as can be seen on a moment's reflection, there is specifically only one motion involved. One should therefore not be surprised if its metrical aspects will be the same in each of the transmitting instruments. It is further true that the action-reaction principle, precisely as physico-mathematical, can also be extended to the twobody problem in the case of gravitational motion. For instance, if two bodies in a given physical environment approach each other in seeking their natural places in accordance with the inverse-square law, there is a certain mathematical symmetry about the phenomenon. As far as the mathematics is concerned, it makes no difference whether one is conceived at rest while the other approaches, or the second is at rest while the first approaches, or both approach each other. And if either of the first two cases are to be conceived in terms of "attractive forces," evidently the latter will manifest the same equality as the motions. Thus the action-reaction principle can be applied to "attractive forces" in gravitational motion, and it will be found to be operationally verifiable. But while this is a valid principle of mathematical physics, it is not true when the total :reality is considered, it cannot be taken as a strict physical principle of universal validity. The reason is simple enough. If there is a strict equality between agent and receptor, there can be no motion. Nothing dynamically new can proceed from strict equality. One rope, of and by itself, cannot pull another rope. That is the reason Newton, in explaining the third law as cited above, makes a slight excuse for the example of the horse drawing a stone by a rope. He says, " ... the horse (if I may so say) will be equally drawn back towards the stone .... " The reason he inserts " if I may so say " is that there is a big difference between the horse and the rope and the stone when aU three are considered physically. A rope, of and by itself, cannot pull a horse, but a horse can NEWTONIAN ANTINOMIES AGAINST THE "PRIMA VIA" 191 pull not only the rope but also something tied to it. If abstraction is to be made from this fact for the purposes of noting physico-mathematical equalities, all well and good. But the physical reality contains much more than the physicomathematical equality. The obvious answer to the third antinomy then is that it is based on a misunderstanding of the third law of motion. The physico-mathematical character of the actionreaction principle accents the fact that it abstracts from efficient movers considered in their physical totality. It neglects all movers except bodies already in local motion, and then only seeks an equality that is verified of the moving parts. It abstracts from the movers that form the subject matter of the prima via, but it does not reject them. Indeed, it presupposes them, for Newton's third law of motion, like his other two, has its only solid foundation and ultimate justification in the physical movers which lead their discoverer inexorably to the existence of God. * * * * * This completes the resolution of the three Newtonian antinomies. Apart from their utility in penetrating the prima via through a more thorough understanding of local motion, they also contain a message for the modem physicist. For it should be clear now that the scope and intent of the science Newton proposed never was clearly grasped by his successors. The many generations of physicists who now are referred to as " classical physicists " concentrated on the physico-mathematical aspects of his Principia, to the neglect of the further ordination that Newton made of the new science to discovering true physical causes. Flushed by early successes in predicting the details of many macroscopic phenomena, they saw the physicomathematical technique for the powerful tool that it was, and then forgot that it was only a tool. Not possessing the traditional foundation in which Newton himself was grounded, they read too much into the father of their science. They took his mathematical principles as the total explanation of physical reality, and were content to stop where he had begun. l9i W. A. WALLACE Needless to say, such men were not prepared for the rise of the new physics. Having slipped into the error of mathematicism, not appreciating the methodological use of mathematics in physical science, their illusions of a facile explanation for the entire gamut of physical experience were quickly dashed to the ground. Later generations of physicists seemingly profited by their mistake, and so began anew. But the pendulum did not swing to center; its momentum carried it to the other extreme. The philosophers of the new physics still failed to grasp the importance of a generalized physical science which could give true and certain knowledge of the universe; they claimed now that nothing could be certain or absolute. They were content to settle for a provisional explanation of reality; hypothetical constructions and mathematical models were the " ultimate " they were willing to concede. Their concern became manifest when the rapid multiplication of postulational systems soon involved them in contradictions, and so they turned to the problem of logical consistency. Here the logical positivists began to have their day, for a super-mathematicism has become the vogue, and this in turn is nothing more than logicism. Amid present confusions as to what is logic and what is mathematics, there are very few scientists who have intelligent notions on the basic question of what is ·physics. But the question has been raised anew, and there is hope that the present generation of physicists may start to work on the answer. Of all the attempts made so far, the foundational physics of Aristotle and St. Thomas alone gives full meaning to the term" physical," as opposed to" mathematical" and" physico-mathematical." Newton had sufficient knowledge of this to orient his new science properly at the outset. His sons would do well to return to where he began. Not only will they find there the answer to the nature of their science, but they will learn how such science can lead them to their God. w. A. WALLACE, 0. P. Dominican House of Philosophy Springfield, Kentucky EXISTENTIALISM AND THE DEGREES Of KNOWLEDGE I N an issue of THE THOMIST of some time ago, Professor Max Charlesworth has shown, in an article on The Meaning of Existentialism, how " certain principles and distinctions drawn from the thought of St. Thomas Aquinas . . . provide a perspective for the proper appreciation of the importance of Existentialism." 1 Professor Charlesworth's main conclusions, if I understand him correctly, are to the effect that "the findings of the Existentialists are of value and can ... be integrated into an authentic philosophy of man," and that "so long as the Existentialists keep to their own proper sphere . . . their conclusions are valid and valuable." 2 But what are we to understand, in that context, by " integration"? In what sense is it true, as Prof. Charlesworth affirms, that some existentialist conclusions are " valid and valuable"? Evidently, he does not mean that existentialism can be integrated with an authentic philosophy of the nature of man by way of fusion or merger; otherwise he would not warn us of the " fundamental confusion of Existentialism " between the metaphysical and the existential, and that " the error of the Existentialists consists in merging the metaphysical order into the existential order." 3 The implication, it seems, is that there is some distinction between these two orders: if so, what is this distinction and how can the two orders of knowledge be integrated? And again, evidently Prof. Charlesworth does not believe that some conclusions of existentialism are valid as they stand and as they are meant by the existentialists; 1 M. Charlesworth, " The Meaning of Existentialism," THE THOMIST, XVI (1958)' 472-496; p. 472. • Ibid., p. 494. 8 Ibid., pp. 486 and 490. 193 194 LESLIE DEW ART otherwise he would not warn us of the " absurdities " and " errors " of existentialism. The implication is, it seems, that the doctrines of existentialism must be understood only in a certain way and in a certain context before they can be considered valid and valuable: they must be understood, as he puts it, in " their own proper sphere." But precisely what is the proper sphere of existentialism? Thus, Prof. Charlesworth's "a priori" approach not only puts in relief for us the importance of existentialism and suggests that Thomists should not dismiss existentialism too airily lest they get rid of the wheat along with the chaff, but also raises further problems. It raises the problem, particularly, of how Thomism can profit, if at all, by re-adapting existentialism to itself in accordance with its own needs; that is, by incorporating or digesting, if such an " integration " is possible, whatever there may be of truth in existentialism. Therefore, the enquiry which logically follows after Prof. Charlesworth's article is to examine more closely the nature of existentialism and its relations to the various philosophical sciences in order to conclude whether, and if so, under what conditions, it may be considered valid philosophical knowledge. That is precisely the purpose of this study, namely, to present and explore the question whether existentialism has a valid place within the hierarchy of the philosophical sciences as described and explained by Thomistic philosophy. I INTRODUCTION We must note from the outset that although existentialism offers itself as a full-fledged system of philosophy, or indeed, sometimes as the only valid system of philosophy, we need not take existentialism's own conception and appraisal of itself in order to recognize its peculiar contribution, if any, to the perennial stream of philosophical knowledge itself. We are not required to take the existentialist's word at face value when he offers a substitute for metaphysics or for ethics or for EXISTENTIALISM AND THE DEGREES OF KNOWLEDGE 195 philosophy as a whole. It may well be that the real novelty and true philosophical value of existentialism, if any, do not consist in its being a new way to solve old problems, but rather in its being a new way to approach new problems and to attempt their solution from its own particular viewpoint. Very especially, the fact that existentialism deals with being-or, perhaps, even with being as being-need not mean that existentialism must be taken as a metaphysics or not at all. It is true that existentialists usually think, it seems, that any "doctrine of being," or of " being as such " is metaphysics or ontology; but to show that existentialism is not true metaphysics is not to show that existentialism is not true knowledge at all: it is to show that existentialists do not know what metaphysics is. By the same token, the erection of existentialism into a system of ethics, which seems to be a fairly common event among existentialists, should not blind us to the possibility that existentialism may have something all its own to offer, even if as ethics it is false and, perhaps, even corrupt. Of course, it is very important to demonstrate that existentialism is committing, not merely an error, but even a tragic blunder (with overtones of moral perversity) when it aspires to be metaphysics or ethics. It is even more important to show, as at least one Thomist has shown, that the metaphysical aspirations of existentialism, insofar as they are legitimate, could be realized only within the existentialist metaphysics of St. Thomas, and that, insofar as they are illegitimate, they constitute an irrational attempt to destroy the intellect itself and to substitute philosophy by the art of forcing the mind to feed on absurdity rather than on being. But once that work is done the question proposed here still comes up: is it not possible that existentialism provides us with a new and additional valid way of looking at being? Is there not a sense in which existentialist philosophy is valid and valuable knowledge? The question is important, because if the answers are in the affirmative, then existentialism-or, at least, that type of philosophical enquiry which is typical of existentialism-win have its own proper 196 LESLIE DEW ART place within the scheme of philosophy, and it will, therefore, offer its own unique contribution to philosophical knowledge: philosophy would become all the richer for it. It may be asked, however, whether it is a legitimate procedure thus to disregard existentialism's own conception of itself. In answer, let us note that a somewhat similar procedure is followed by epistemology when it studies the positive sciences. The conception of science which is common to many scientists is false; yet, Thomists agree that the positive sciences, properly understood, have a rightful place among the degrees of knowledge. To determine the nature of science and to defend its legitimacy is not necessarily to take the view that science (i.e., positive science) is the only true knowledge or the only scientific knowledge (properly so-called) which man can acquire. Nor is it to accept uncritically each and every scientific doctrine, nor to accept each and every scientific discovery without discriminating between the scientific truth itself and whatever philosophical (or pseudo-philosophical) interpretations may be offered along with it. We do not fail to recognize (at least, not lately: we have so failed in the past) the limited, but unique, knowledge-value of the sciences merely because some scientists (or however many; all, if you · wish) seem to think that they are a substitute for metaphysics and ethics and, sometimes, even for religion. By the same token, we may very well, for our present purpose, disregard existentialism's own appraisal of its nature and its value. Our problem, then, which is essentially an epistemological one, is to ascertain what is the nature of an existentialist philosophical analysis. Thereafter we shall have to fix the position of this type of analysis within philosophy, and to determine the order that obtains between it and the other philosophical disciplines. Now to achieve this end we shaH have to make use of a standard of distinction among sciences. Thomists will agree that a science is characterized, and therefore distinguished from another sicence, by its peculiar " disposition with :reference to EXISTENTIALISM AND THE DEGREES OF KNOWLEDGE 197 separation from matter " 4 or, in more recent terms, by its degree of abstraction. We may otherwise refer to it as the idiosyncracy of the conceptualization which is proper to any given science, which in turn is rooted upon the type of abstraction which is distinctive and characteristic of the exercise of the science in question. 5 Consequently, to investigate the problem of the relation of existentialism to the Thomistic scheme of the sciences we shall try to ascertain what is the way of conceiving and defining which is peculiar to existentialism. Thereafter, a comparison of that characteristic mode of understanding with those of the other degrees of philosophical knowledge will give us some indication of what their relations may be. This characterization and this comparison, in an inchoative, limited way, are what will be attempted in the remaining sections of this article. II ABSTRACTION IN EXISTENTIALISM So far it has been possible for us to speak of existentialism as a philosophical genus, but if one would attempt to express in what consists its characteristic way of conceiving it would be necessary to specify exactly which of the many varieties of existentialism one has in mind. Let us, therefore, restrict existentialism, for the present purposes, to the " phenomenological ontology" of Sartre and Heidegger. What applies simpliciter to this type of existentialism will apply secundum quid to other expressions of this movement. Now, as is well known, the term " phenomenological ontology " is Sartre's, not Heidegger's: indeed, Heidegger would probably object strongly to the application of the name, " ontology " to the doctrine of L' Etre et le N eant. However, thS:t is only a question of terminology; Heideg• St. Thomas, In Boetk. de Trin., V, 1, ed. P. Wyser, p. 26, line 21; trans. A. Maurer (Toronto, 1958), p. 7. • I am taking for granted here the doctrine of John of St. Thomas concerning the distinction and unity of the sciences. See especially his Logica, II, Q. 27, a. 1; ed. Reiser (Turin, 1980), pp. 822-828. 198 LESLIE DEW ART ger believes that beyond his doctrine of Sein und Zeit there isor there may be-an ontology properly so-called, namely, a study of being as such, to which Sein und Zeit is only propaedeutic. Sartre, on the other hand, apparently believes that the seemingly restricted and partial " doctrine of being " which can be reached through the method of phenomenology is the whole of ontology, and indeed, the whole of philosophy. The question of whether in maintaining this doctrine Sartre is more consistent with his own principles than Heidegger is with his, need not detain us at this point. The more important fact is, rather, that the ontological propaedeutic of Heidegger and the phenomenological ontology of Sartre coincide in at least this one respect: in both cases a phenomenological approach is used in order to arrive at a doctrine of the meaning of being human (or, what is the same, of being humanly or of being in a human way). It is, partly, insofar as both systems arise out of the implications of the " phenomenal field," and insofar as both philosophies reach a weltanschauung concerning human existing, that they may be grouped together under the heading of existentialism. Now, as Maritain has explained, "the central intuition at work in . . . existentialism . . . [is that] of the nihil whence we come and towards which we tend . . . [of ourselves ]-the intuition of pure nothingness (which is the sole residue discoverable in the creature once the Creative Action has been suppressed) and of the radical absurdity of an existence uprooted from God." 6 We must bear these words in mind. However, for the epistemological purposes of the present enquiry we have to attend primarily, not to the meaning of this central intuition, but rather to the way in which the mind of the philosopher must .work (i e., the way in which it must· abstract and conceptualize) in order to possess such an intuition. Let us suppose, therefore, that we share with the existentialist this intuition into the nothingness which is at the heart of created being, and that we agree with Maritain as to • J. Maritain, Existence and the Existent, (New York, 1948), p. 134. EXISTENTIALISM AND THE DEGREES OF KNOWLEDGE 199 the true meaning of that intuition: how is our mind working when it possesses such an intuition? At this point we must remember Hegel. Being and nothing negate each other; but being and nothing are not the mere contradictories of Aristotelian logic. They are, rather, related as thesis and antithesis; that is, they are real contradictories and therefore at the root of the one reality, becoming, which they (by themselves only "abstractions") constitute by their very contradiction. Consequently, the nothingness of being and the being of being are one: indeed, it is the nothingness of being which constitutes the being of being. What the existentialist is trying to do when he thinks this way is to transcend abstractive thought: he is trying, as it were, to swallow reality whole. But why? Because, having previously identified abstraction with total abstraction (abstractio totalis, in the language of Cajetan and John of St. Thomas; extensive visualization, in that of Yves Simon and Maritain) , he has become disappointed in abstraction as a means of discovery. 7 In a word, existentialists try to reject abstraction because they have seen the consequences of identifying logic and metaphysics. 8 And the metaphysician can well sympathize: after aU, no amount of logical reasoning can substitute for understanding. 9 7 G. Marcel explains the existentialist disappointment in "abstraction" in his Man Against Mass Society (Chicago, 195Z), pp. 114 ff. 8 Note that this corrupts not only metaphysics, but also logic itself. See J. Maritain, Sept Lerons sur l'Etre (Paris, 1954), pp. 43-44. Perhaps we should refer, instead, to the identification of metaphysics with a nominalistic or aprioristic logic. 9 In a well-known doctrine which is cardinal for the proper understanding of the nature of metaphysics, St. Thomas explains that metaphysics is said to proceed "according to the mode of intellect" (intellectualiter) rather than "according to the mode of reason" (rationabiliter); for it is clear that " ... rationalis consideratio ad intellectualem terminatur secundum viam resolutionis, in quantum ratio ex multis colligit unam et simplicem veritatcm. Et rursum, intellectualis consideratio est principium rationalis secundum viam compositionis vel inventionis, in quantum intellectus in uno multitudinem comprehendit. Ilia ergo consideratio, quae est terminus totius humanae ratiocinationis, maxime est intellectualis consideratio." (In Boeth. de Trin., VI, 1; ed. P. Wyser, p. 60, lines U-18). However, it should be 4 200 LESLIE DEW ART But is there any alternative to abstractive thought? As a matter of fact, says the existentialist, there is an alternative: I can transcend abstraction if I can bring myself to break away from logic, even from the logic of Hegel. Indeed, as we have just seen, the logic of Hegel has taught me this much, which I will save after discarding the systematic wrappings in which it is offered: I transcend abstraction when I realize, when I become immediately aware, when I feel in the marrow of my bones, indeed, when I directly experience and actually live the truth that nothingness is the being of being. It is by living this truth, by being this truth that I can reach being. And so, my experience of nothingness (however arrived at: through dread, consciousness, or what you will) reveals to me the mystery of being. Thus, after the logic of Hegel, (which is at the same time the last refuge of rationalism and the point of origin of irrationalism), the existentialist is literally free to think and philosophize about existing being and not merely about concepts, for he will not be restricted by contradiction nor repelled by absurdity when he has just discovered that existing itself is contradiction and absurdity. This freedom, he says, is one with his freedom from abstraction. For those of us, however, who are aware of the distinction between total abstraction and formal abstraction or intensive visualization, the existentialist way of thinking remains abstractive regardless of its avowed emancipation from logical categories. We may still speak, therefore, of existentialist abstraction and conceptualization. How, .then, does the existentialist conceive existing? How does his mind work when he possesses the intuition of existing which we have just studied? Strikingly enough, the existentialist conceives existing in much the same way as the ordinary man does (albeit the former does so habitually, and the latter only occasionally and rarely) when the latter, for example, noted that ". . . intellectualiter procedere non attribuitur scientiae divinae, quasi ipsa non ratiocinetur procedendo de principiis ad conclusiones, sed quia ejus ratiocinatio est intellectuali considerationi propinquissima, et conclusiones ejus principiis." (Ibid., p. 61, lines 7-10). EXISTENTIALISM AND THE DEGREES OF KNOWioEDGE £01 complains about " leading a difficult existence " or when he describes with deep concern (and not merely outwardly) "the vicissitudes of his existence " or how he has managed to " eke out his existence." Beyond the simple, vague, everyday meaning of being and existing, beyond that esse which everyone takes for granted and without which no thought or speech is possible, yet below the metaphysical meaning of being, the ordinary man sometimes thinks and talks in a pre-metaphysical way about his life, his existence and his being. As a matter of fact, the ordinary man talks about existence in this way precisely for basically the same reasons as the existentialist does: because he, too, sometimes finds his undisciplined, pre-scientific, merely logical way of abstracting, insufficient and radically inadequate to reach the depths of the subjectivity of being. It is at this point that the possibility of genuine metaphysical conceptualization is opened to the ordinary man: but the chasm from philosophical ignorance to metaphysical habit is often too wide to be bridged successfully when it looms up suddenly. And so, the metaphysical seed falls, if not by the wayside, among the rocks or the brambles, and his experience fructifies, if at aU, only in the idioms, the wise sayings and the popular insights which others will soon process into the flour of the truism and the insipid bread of the cliche. But the fact that this conception of existence fails to reach the heights of metaphysics does not mean that it does not rise above the level of everyday, common sense experience. A question has been asked and the intellect has been excited. And the possibility of philosophical enquiry at this level may not be apparent to many, but it does not elude the existentialist. It is unfortunate, however, that because of a complex of historical circumstances the existentialist also, in his own way, is prevented from ever realizing his true metaphysical aspirations when he finally concludes that only this type of philosophical enquiry and this level of philosophical knowledge may possibly be reached by the human intellect. And yet, felix culpa! if the metaphysical failure of the existentialist leads to LESLIE DEW ART a discovery that will enrich the treasury of human philosophical knowledge. But let us return to the question in which the ordinary man first conceives existence in an existential way: what is the meaning of "existence," what is the meaning of "life? " Note, first of all, that in this connection " life," as the synonym of being or existence, is shorn of aU Biological meaning: that is, the question is not one for Biology. If I ask, in this everyday, reflective (but pre-metaphysical) way, for the "meaning of life," no amount of biochemical or physiological information comes even near to answering my question. Similarly, an ordinary philosophical explanation of the nature of man (e. g., that he is a rational animal) , even if it were a true explanation, also fails to answer my question in the sense in which I am asking it. What I am asking about is something more simple, more personal, a great deal less learned and sophisticated, and yet, a little more important. I am enquiring about this very · curious happening which is happening to me, or which, more properly, I am doing, and which I call enduring or living or existing. Existence, in this sense, is what a mother gives to her child: it is what one does when one "brings a life into the world." It is existence in this sense, existence which is both exercised and perceived by me as mine (because I am " doing " it), which is of interest to the existentialist, for it is the origin of a number of philosophical problems. Thereafter, from the direct, lived, existential, "ontic" experience of existence, the existentialist proceeds, by means of certain techniques, to analyze that experience in order to extract, as it were, its meaning-or :rather, its meaningfulness. He goes on to codify and systematize its characteristics, to distinguish what is basic and proper to it from what is adventitious, and finally, to search for a " theme " which will thread together the aspects in which existence has been analyzed, and which will fit together the various facets cut at different times into existence by a temporalizing human intellect. In other words, he proceeds to treat existence (the EXISTENTIALISM AND THE DEGREES OF KNOWLEDGE 203 "ontic" datum), scientifically, philosophically and systematically, and thus arises "ontology." But the same way of conceptualizing existence remains throughout the philosophical and scientific systematization of the implications of ontic data or experience. In Heidegger, for example, the point of contact between the ontic and the ontological, and the reason why the ontological must be preceded by the ontic, is precisely that the ontic always provides the basic intuitions, the root experiences, the raw data which once analyzed and systematized can become philosophy. Similarly in Sartre: the elaborated doctrines and the final conclusions (i. e., the " ontology ") of L' Etre et le N eant are obtained by drawing out the implications of a number of experiences. For instance, the experience of feeling ashamed implies the possibility of my becoming an object for another, and so reveals the possibility of the alienation of the transcendence of my being. 10 The ontic, therefore, notwithstanding its non-scientific status, is what characterizes most distinctively the conceptualization of existentialism. It provides the basic intuition which is the point of departure of an existentialist analysis. An existentialist analysis is only the systematic elaboration of an ontic datum. The typical abstraction of existentialism, therefore, and its characteristic way of conceiving and defining, is what might be called, for the present, ontic abstraction. The ontic is the existential of existentialism: existentialism only adds the ism to the existential. III EXISTENTIALISM AND METAPHYSICS It is quite possible that even from the etymological point of view the term ontic is also adequate to characterize the degree of abstraction which is proper to the philosophical analyses of existentialism. We have come to associate so customarily To ov with metaphysics (i.e., with metaphysics in •• See e. g., J-P. Sartre, L'Etre et le Neant (Paris, 194ll), p. S!i/:0. 204 LESLIE DEW ART the Thomistic sense) that we seem to forget that, as some historians of philosophy tell us, the term has been in philosophical circulation since long before a metaphysics of being had been suspected. To ov is usually translated as " being " or as " the real," which does not prevent us from saying that St. Thomas was a realist and his metaphysics a metaphysics of being, but which should not lead us, if Fr. Owens is right, to read into Aristotle what is only in St. Thomas. 11 Now, existentialism also deals with being and with the real; indeed, it professes to deal with " being as such," and it may be permitted to wonder whether the existentialist usage of the term is not closer than the Thomist to the original (especially the pre-Aristotelian) Greek meaning, whence the etymological propriety of ontic abstraction. At any rate, the important point is that " the real" does not convey to the existentialist the same meaning as "that which is " conveys to the Thomist metaphysician. It would not do to identify the id quod est of the Thomist with the '' :really being " of the existentialist, because the being of existentialism is real in much the same sense as that of everyday language when we say that " this problem is real," or "this is what really matters." It is real in much the same sense as Longfellow's when he says that "Life is real, life is earnest .... " 12 The real being of existentialism is real because it is earnest, because it matters, because, resorting again to Longfellow, you must" Tell me not in mournful numbers, 'I..ife is but an empty dream.' . . ." The aptness of the name " Existentialism," therefore, is not entirely unapparent: existentialism is not a philosophy of being or of human being properly so-called; it is a philosophy of existence, especially of human existence. Indeed, perhaps it could be said that the most distinctive difference between existentialism and Thomistic metaphysics is that the latter deals with being as being, whereas the former deals 11 See J. Owens, The Doctrine of Being in the Aristotelian Metaphysics, (Toronto, 1951). 12 This verse, and those quoted shortly after, are from Longfellow's "A Psalm of Life." EXISTENTIALISM AND THE DEGREES OF KNOWLEDGE with being as existing. The being of metaphysics is being which is. The being of existentialism is being which exists. What is meant, however, by this distinction between being and existing? It is the outcome of two different ways of regarding " the reaL" To understand this let us consider two ways in which we may regard an " appearance." When we say that something " appears to be " such and such, the implication is that it may or may not truly or really be what it seems to be: the appearance may or may not be one with the real. In this sense, therefore, appearance is not identical with being: behind the appearance there is being, and what matters is not what things appear to be, but what they :really are. It is clear, moreover, that this sense of " appearance " does not entail for the Thomist (unlike, as it seems, it did for the pre-Socratics) a divorce between appearance and reality, for the mind does not grasp an appearance from which it concludes to, or posits, a reality. Rather, the intellect grasps as intelligible-or as being-the being that the senses grasp as sensible. The Thomist knows better than to hold that the senses grasp accidents and the intellect grasps substances, for although it is true that the intellect alone can apprehend an intelligible substance, the intellect also grasps as intelligible-or as being-the accidents that the senses grasp as sensible. Being, therefore, is " behind " appearance not only when the appearance is deceptive, but quite as surely when the appearance is perfectly truthful. That is why we say that the appearance may or may not be as it seems. On the other hand, when we say that so-and-so " put in an appearance," there is no question of there being anything else beyond' or besides the appearance. The appearance is a fact and a reality in itself, and, from this point of view, it is as ultimate a fact and a reality as it could possibly be. Even if so-and-so appeared as a deceiver or as an impersonator, so that I might mistake him for someone else, the reality of the appearance and the fact of his appearing are not altered in the least. From this point of view reality and appearance are identical. 206 LESLIE DEW ART Everyday experience furnishes many examples of this way of considering appearances. For instance, if a child experiences fear of ghosts, the real existence, the metaphysical reality or unreality of ghosts is quite irrelevant to the fact of his fear. In his experience ghosts do exist, because they are that of which he is afraid. From his point of view ghosts are real, because they are identical with his experience of them. And the fact is that he is afraid even though ghosts do not, as we might say, really exist, and even though so-called ghosts are only an appearance, the only reality of which may be a tricky shadow or a lively and unruly imagination. From the child's point of view, which is an existential one, the appearance of the "apparition" of its very nature produces fear, and the more "metaphysical" or ontologically-oriented considerations are completely out of order. Clinical psychologists know this very well, and that is why they will not commit the error of trying to " reason" with the child. They know that the only way he can cease to " see ghosts " is to re-structure his " phenomenological field: " he must be made not merely to conclude that ghosts do not exist, but rather to experience the same environmental stimuli with a different meaning. He must be made " to perceive in different terms," which in turn is made possible only by facilitating the re-organization of his personality. Of course, the type of conceptualization which is proper at the scientific level of existentialism is more greatly refined and probably a great deal less common than the experience of a child being afraid of ghosts. However, the \point of the preceding illustration is this: what characterizes the ontic abstraction of existentialist philosophy is the essential reference of the real to experience, and, therefore, the phenomenological identity of appearance and reality. When the metaphysician as such conceives being, he is, on the contrary, oblivious of himself and his own experience. Even if he conceives his own being, he objectifies himself, quite unlike the existentialist, who tries to subjectify, insofar as it is possible, whatever he beholds. The metaphysician sees in being a unique perfection EXISTENTIALISM AND THE DEGREES OF KNOWLEDGE or actualization which is not unlike a deserved merit or an intrinsic right possessed by that which is precisely because it is. When under the transcendental aspect of truth being speaks to the mind of the metaphysician, " what is then manifest is of the nature of an obligation attached to being. An I ought to be consubstantial with I am." 13 He may give recognition and respect to being, but that is only a consequence of the resonance that being produces on him. What characterizes his conceptualization is that he sees the perfection of being as possessed by being itself whether or not that perfection is recognized and respected by anyone. But whereas the metaphysician loses himseH and disappears before being, the existentialist finds himself and reveals himself to himself in being, because being is, for the latter, recognized being or respected being: that is why the being grasped by ontic abstraction is always being-in-experience. Consequently, for existentialism the real is identical with the really-appearing or, what is the same, with the apparently-real. If we must give it a more descriptive name, then let us say that the typical way of abstracting and conceptualizing which is proper to an existentialist analysis is not only ontic but also, and more precisely, phenomenontic. If metaphysics, whether by inherent right, prescription or common agreement, is to be granted title to the name Ontology because it deals with being, then that type of philosophical knowledge which obtains through existential analysis, and which deals with appearing-being should perhaps be given the name Phenomenontics. The use of some kind of phenomenological method, therefore, is essential to existentialist philosophical analysis, for if we abandon the description and interpretation of what-is-inexperience and attempt to get at what is beyond experience, we have thereby abandoned our distinctive way of conceiving. However, unlike the original phenomenology of Husser], where the phenomenological E'lToxl] is undertaken in order to cut the 13 J. Maritain, A Preface to Metaphysics l' Etre (Paris, 1934), p. 76. (London, 1948), p. 66; Sept Let;ons sur 208 LESLIE DEW ART Gordian knot caused by the tangle of idealism and realism, the modified phenomenology of existentialism does not grant that there is even a problem of idealism against realism within the boundaries of existentialism. Indeed, in order to grant not only a solution, but even the very position of the problem itself, it would be necessary to withdraw oneself from the existentialist coign of vantage. To ask the critical question which may be answered in terms of idealism or realism or, for that matter, in t