Stanley F. Grove - Quantum Theory And Aquina's Doctrine On Matter

THE CATHOLIC UNIVERSITY OF AMERICA

Quantum Theory and Aquinas's Doctrine on Matter

A DISSERTATION

Submitted to the Faculty of the School of Philosophy Of The Catholic University of America In Partial Fulfillment of the Requirements For the Degree Doctor of Philosophy

By Stanley F. Grove

Washington, D.C. 2008

UMI Number: 3340658

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Quantum Theory and Aquinas's Doctrine on Matter Stanley F. Grove, Ph.D. Director: William A. Wallace, O.P., Ph.D.

The Aristotelian conception of the material principle, deepened by Aquinas, is today widely misunderstood and largely alien to modern mathematical physics, despite the latter's preoccupation with matter and the spatiotemporal. The present dissertation seeks to develop a coherent understanding of matter in the Aristotelian-Thomistic sense, and to apply it to some key interpretive issues in quantum physics. I begin with a brief historical analysis of the Aristotelian, Newtonian ("classical"), and modern (quantum) approaches to physics, in order to highlight their commonality as well as their differences. Next, matter - especially prime matter - is investigated, in an Aristotelian-Thomistic perspective, under several rationes: as principle of individuation, as principle of extension or spatiality, as principle of corruptibility, as related to essence and existence, and as ground of intelligibility. An attempt is made to order these different rationes according to primordiality. A number of topics concerning the formal structure of hylomorphic being are then addressed: elementarity, virtual presence, the "dispositions of matter," entia vialia, natural minima, atomism, the nature of local motion, the plenum and instantaneous action at a distance - all with a view to their incorporation in a unified account of formed matter at or near the elementary level.

Finally I take up several interpretive problems in quantum physics which were introduced early in the dissertation, and show how the material and formal principles expounded in the central chapters can render these problems intelligible. Thus I propose that wave and particle aspects in the quantum realm are related substantially rather than accidentally, and that characteristics of substantial (prime) matter and substantial form are therefore being evidenced directly at this level - in the reversibility of the waveparticle transition, in the spatial and temporal instantaneity of quantum events, and in the probabilism encountered in such phenomena. I offer related hypotheses for Heisenberg uncertainty and for quantum nonlocality. In closing, I address some strengths and weaknesses in others' work on quantum interpretation in the light of Aristotelian principles. Three Appendices explore further aspects of matter as a cosmic principle.

This dissertation by Stanley F. Grove fulfills the dissertation requirement for the doctoral degree in Philosophy approved by William A. Wallace, Ph.D., as Director, and by Richard F. Hassing, Ph.D., and Kevin White, Ph.D., as Readers.

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Table of Contents

Chapter One - Introduction

1

A. The scandal of physics

1

B. The thesis and its development

6

Chapter Two - Three Phases in Physics

12

A. Aristotelian physics

13

B. The departure from Aristotle

15

C. What does classical physics say?

24

D. Is classical physics scientific?

28

E. Quantum physics, considered qualitatively

35

F. The background

36

G. The emergence of quantum theory

39

H. Continuous and discrete: complementarity

41

I. Complementarity or hiddenness?

45

J. Bell's theorem and nonlocality

53

K. What is quantum physics about?

54

L. Some problem areas in quantum interpretation

58

iv

Chapter Three - Matter Considered Philosophically

63

A. Introductory

63

B. Physicalists and atomists

65

C. Plato's chora

71

D. Aristotle: Physics and Metaphysics

75

E. Neoplatonic commentators

91

F. Aquinas's conception of matter

94

G. Individuation and unilocality (impenetrability)

105

H. Matter and spatiality

123

I. Principle of corruptibility

131

J. An existential principle of essence

136

K. Further metaphysical reflections

140

L. Ground of cosmic intelligibility, unintelligible to us

152

M. Three-dimensionality as primordial

160

N. Reduction of the several accounts of matter

162

Chapter Four - Formal Structure of Material Being

167

A. The Thomistic account of form

167

B. What is form?

174

C. Accidental forms and sensibility

180

D. Unicity of substantial form

182

E. Elemental virtual presence

184

F. Dispositions of matter

201

G. Entia vialia

212

H. Minima naturalia

216

I. On some characteristics of elemental particles

222

J. Atomism true and false

228

K. Motion in the physical continuum

235

L. Action at a distance

245

M. Conclusion

249

Chapter Five - The New in Light of the Old

250

A. Introductory

250

B. Wave-particle duality

252

C. Discontinuity in quantum phenomena

259

D. Probabilistic outcomes of quantum events

263

E. Uncertainty relations

266

F. (Non)locality

273

G. Matter and quantum physics

276

H. Bohm, Heisenberg and Wallace on potentiality

278

I. Wolfgang Smith's "Hidden Key"

285

J. Conclusion

299

vi

Appendix 1. The Ultimate Boundary of Matter

301

Appendix 2. On Matter's Place in a Larger Scheme of Ontological Principles

304

Appendix 3. Materiality and Temporality

309

Bibliography

312

vii

Acknowledgments In the first place I thank my parents, my first teachers, for all they have given me. I thank my director, Rev. William A. Wallace, O.P., Ph.D., who has been for nearly twenty years a source of encouragement and inspiration in my intellectual life. I hope this thesis is a not unworthy token of my regard for him and his life's work, and of gratitude for the many hours spent in his classroom and in his home, discussing the sorts of matters that are treated herein. My intellectual formation owes a considerable debt also to my friends John F. Nieto, Ph.D., Kevin White, Ph.D., and numerous other professors at Thomas Aquinas College and The Catholic University of America. I am grateful to Richard F. Hassing, Ph.D., for guidance, to many colleagues for the stimulus of philosophical conversations over the years, and especially to all who have helped me more by their prayers than by any amount of learned discourse. That in all things God may be glorified. May the Blessed Virgin Mary, Seat of Wisdom, and St. Thomas Aquinas bless all who read these pages.

viii

Chapter One Introduction

A. The scandal of physics There is something unsettling in the realization that the natural and technological science which dominates our world and our worldview today - a science which points reductively to "pure" physics as its foundation - is far from being a unified science, precisely at the deepest levels which it contemplates. The discipline we have inherited from Galileo and Newton, Maxwell and Einstein, Bohr, Heisenberg, Schrodinger and a host of collaborators over the past 400 years is, in fact, unified only by its empiricalmathematical method (and in some instances hardly even by that). It has undergone "paradigm shifts" of startling significance in the past, and today it is a house very much divided against itself. One thinks especially of the relativity-quantum theory impasse, and of the interpretive disputes within quantum theory itself. This may not seem problematic to a generation raised in the awareness that science proceeds, after all, through the clash of opposing theories and the battleground of endless experimentation, much of it destined to "failure." There is no disputing the historical march of science, the astonishing success of its theoretical and practical manifestations, the deep insight it has gained for us into the fabric of the universe past and present. Surely physical science "works." Let it continue on its present course, a course of exhilarating triumphs regardless of any anomalies!

1

2 But such an attitude runs counter to the deepest instinct of scientists themselves. The sheer number of books and articles that have been written on the interpretation of quantum physics attests to this. Science proceeds in the conviction that the universe is rational, and rationality precludes ultimately contradictory accounts. The suspicion is both real and justified, that whatever the successes of the scientific enterprise thus far, even more - perhaps far more - could be expected if lurking discrepancies were resolved once for all. There is no inconsistency in saying that physical science can be both successful and self-defeating. A philosophical theory, especially one of the metaphysical order, depends on insight into what is given, more than on the "extent" of what is given. Philosophical speculation is sometimes said, accordingly, to be "vertical," to compass depth. Physical or natural science, in contrast, is "horizontal," aiming at breadth. Physical sciences deal with phenomena which bewilder by their sheer variety and complexity. That there are innumerable causal connections among these phenomena is beyond doubt; but the connections themselves require to be inferred or discovered one by one. Inspired theorizing facilitates the process of discovery but never dispenses with it; physical science looks at the sensible, first, last, and always. And so the success of physics is due to the large number of connections which have been elucidated over time, while its more troubling aspect, which I have described as a lack of underlying unity, is due to the number of connections which have not yet been made, and especially those which seem unlikely ever to be made. It happens regularly that a physical theory has merit in view of a partial insight. It has heuristic value based upon a real cor-

3

respondence to experimental data, even though it falls short of being a "theory of everything." There is no reason for either apathy or complacency in view of this state of affairs. If the theoretical foundations of the physical edifice can be made firmer - and they always can - the structure can only benefit. There is no incoherence in nature; that ours is a cosmos, rather than chaos, is implicit in the entire scientific enterprise. In fact, the ever-increasing degree to which physical science is unified, notwithstanding the disunities to which I have alluded, echoes that of the universe itself. Three phases may be discerned in the long history of physical science. The first of these, all too often adverted to only in condescending terms nowadays, is the Aristotelian or "philosophical" phase, extending from the flowering of Greek speculation in the 4th century B.C. down to the late Renaissance. The second phase, which saw mathematical physics come into its own, is what may be called "classical" physics, emerging hesitantly from late medieval treatises and gaining sudden vigor in the work of Galileo and his contemporaries. Newton would become the great exemplar here, and it is the science which held indisputable sway down to the time of Einstein, Lorenz and Poincare in the early 20th century. Finally there is the "quantum" phase, typically presented, in dramatic contrast to what had gone before, as a "revolution" with philosophical as well as physical ramifications. At the risk of oversimplifying, we may say that the first phase was characteristically non-mathematical and concerned with a multiplicity of causes and natures; the second phase, as noted, represented the ascendancy of mathematical methodology,

4

while the third, though certainly not abandoning the mathematical as such, would raise new questions about the effectiveness of mathematics in providing a comprehensive view of nature, as unpredictability and uncertainty assumed a new prominence. Is there, then, more than one science of physics? Few would deny that quantum physics bears enough of a relation to, and continuity with, physics of the classical era to warrant being called one and the same science. But many authors facilely dismiss the earlier thought of Aristotle and his followers as being of no consequence in the modern physical perspective. They would say there is only one "real" physics, ignoring "philosophical" physics altogether and then forcing classical and quantum physics into a single mold by dint of Niels Bohr's "correspondence principle" (according to which the classical description of physical phenomena represents a "limiting case" of the quantum-theoretical description). In the present investigation I aim to show that this interpretation is faulty. Contrary to textbook implications, there is a radical distinction between physics as advanced in the age of Galileo and Newton, and physics as reconstituted by the quantum theorists. Moreover, the physics bequeathed to us by Aristotle is a real science, offering authentic insight into material being, and not just naive superficiality. I will argue that certain aspects of the natural philosophy inherited from Aristotle, and refined by Thomas Aquinas a millennium and a half later, offer the key to a unification of the insights of scientists working much more recently - that is to say, during the 400 years since Galileo made his fateful break with the earlier tradition.

5 It will be seen that, paradoxically enough, it is classical physics, rather than its Aristotelian precursor, which represents the departure from a holistic and comprehensive account of the way things are. Quantum physics, "revolutionary" only in contrast to the Newtonian paradigm which had dominated the formative centuries of modern science, points the way to a resuscitation of Aristotelian insights which are vindicated, not because the ancients had miraculous powers of anticipating the modern worldview, but because they reflected well and truly upon the fundamental given: that physics is about matter in motion. This starting point is given to the ten-year-old who observes a baseball's path, no less than to the physicist who follows the trajectories of muons in a cloud chamber. There is no essential difference, in terms of analyzing the motions involved, between Aristotle dropping a stone (granted, he doesn't seem to have done this very carefully, if at all!), Newton envisioning an endlessly falling (orbiting) moon, or Rutherford bombarding gold atoms with helium nuclei. In all cases the physicist is dealing with things in motion: with spatiotemporal relations of entities that are defined ultimately in spatiotemporal terms. The mathematical description may be more or less sophisticated, or nonexistent. But motion in and of itself remains the subject of a unitary definition and causal account. The conclusions of an Aristotle, a Galileo, and a Schrodinger can all be true while representing differences of perspective. But to unite these perspectives should be a high priority. In describing physical science as a knowledge of nature, we sometimes forget that it is not just a knowledge of nature but a knowledge of nature, conditioned by the

6 human mode of knowing. Implicit in this statement is the fact that there are only so many kinds of questions that can be asked and answered. Such questions vary in their content from age to age, but not in their form. Problems may be expected to arise, however, when scientists neglect to ask all the questions of which the inquiring mind is capable. Although scientific inquiry cannot but be affected, in any given epoch, by the Zeitgeist, and in fact may benefit from the discipline afforded by reigning prejudice, the other and darker side of the coin is that whole areas of legitimate and perhaps urgent questioning may be left unattended. The almost comically highlighted hubris of a scientific community facing endless surprises, setbacks and paradigm shifts - pick up any copy of Scientific American and you will see the evidence - has to do with the fact that nature is always more intricate and varied than we surmise. Whatever may be said about nature's own resistance to interrogation, let us not fall short in our methods as we interrogate it. Let us not arbitrarily narrow the field of genuinely scientific, which is to say causal, inquiry.

B. The thesis and its development I have alluded to the subject matter of this study in historical terms, as proffering a key to the unification of physics as pursued in different eras. The present thesis is not concerned with the historical as such, however, but with the retrieval of a broader tradition in physics, in the interest of deepening the level of current physical understanding. It aims at restoring, to the physicist's conceptual arsenal, the fourfold causal analysis of Aristotelian physics, while giving up nothing of what modern science has achieved. In

7 particular, its immediate goal is an explication of the enduring validity of material causality, of matter as understood philosophically, in a physics from which it had been effectively banished for centuries. In a word, my thesis is this: The Aristotelian conception of matter is coherent and compatible with modern mathematical physics, and in particular it promises to shed light on our understanding of quantum-level phenomena. I work toward these conclusions in four chapters. In Chapter Two is traced the theme of what physics is, or has been considered to be, about - not in the particulars of its investigations, so much as in the kinds of conclusions that have been expected of it. Here my main framework is that of the threefold division of physics already mentioned. The treatments of Aristotelian and classical physics are the most summary. Aristotle's is presented as a physics of all-embracing causality. Classical physics, traced through some of its great inaugurators, is shown to be progressively less concerned with the manifold of Aristotelian causality and more preoccupied with the quantitative as such. The question of whether physics in the classical conception can be considered scientific under Aristotelian principles is then raised and given a qualified affirmative answer. The remainder of the chapter, somewhat more than half, is then devoted to a description of quantum physics. This description is wholly nonmathematical, and part of the reason for my devoting more space to it is a perceived need to assure the reader that a subject noted for its mathematical complexity can be addressed meaningfully in qualitative terms. In this conviction I follow the precedent of many quantum theorists themselves,

8 of course, but it seems especially warranted in view of my project of bringing a "minority" philosophical interpretation to the data of quantum physics. Particular attention is given to what I take to be the essential features of the quantum physics: complementarity and the uncertainty principle, arising from the waveparticle duality with its juxtaposition of continuous and discrete aspects. My focus throughout is "physical" rather than epistemological, in the belief that the much-vexed epistemological debates over quantum interpretation will be obviated by a sound physical approach. I then recapitulate the three phases in physics, by way of suggesting that the notion of potentiality will provide the key to understanding their succession and differences. The chapter is then closed with a listing of five aporiai, drawn from the heart of quantum physics, that I will be keeping in mind as I proceed through the following chapters. Chapter Three is the longest and the main chapter. It aims at presenting the principal features of the Aristotelian-Thomistic doctrine on matter as a principle of physical (cosmic, hylomorphic) being, in their proper relation to each other as constituting an integral account. A brief history of conceptions of matter begins the chapter, and then a synopsis of Thomistic references is given. The several rationes of matter are then taken up section by section, progressing roughly from the physical to the metaphysical, in the conviction that a compelling account, even for modern readers, must exhibit the wholeness that metaphysics alone can bring to the discussion. Thus we consider the material principle as grounding all change or motion, as a co-principle with substantial form, as individuating and constituting things as spatial, as occasioning corruptibility

9 among a plurality of cosmic beings, and as the sine qua non of intelligibility even though unintelligible in itself. At the deepest metaphysical level matter is seen to be a mode of existence, synonymous with hylomorphic contingency. In Chapter Four I take up a variety of considerations bearing directly on the formal principle in hylomorphic being; these are the aspects of form that seem most pertinent to our attempt to explicitate the role of matter in physics. It will be seen, indeed, that one cannot treat adequately of either matter or form without complementary allusion to the other; our intellectual grasp of these principles reflects their intimate relation in reality. After a brief historical introduction, the doctrine of Aquinas is summarized from his De principiis naturae. I then attempt to elucidate the identity of form qua real principle and form qua principle of intelligibility. There follows a distinction between accidental and substantial form, and some remarks on the necessary unicity of the latter. Next is a rather more detailed treatment of elemental forms and their virtual presence in higher composite beings, which is then situated in relation to the conception of "dispositions of matter." The ideas of natural minimum and impossibility of void are then treated, by way of arguing for an elemental or inflma structure of the physical continuum. The "atomism" that is proper to an Aristotelian or Thomistic view of the universe is then presented, and the Aristotelian conception of motion is related to this structured plenum. The chapter closes with a discussion of the impossibility of "action at a distance" as classically understood, and a summary of the main points that have been treated.

10 Having thus gone over the traditional terrain, making what I hope will prove occasionally elucidating observations, we are in a position to return, in Chapter Five, to the aporiai of Chapter Two, prepared to offer plausible resolutions of each. Since my approach has been to focus on the concept of potentiality as understood in the philosophic! perennis, I then turn to some recent authors in order to compare my conclusions on potentiality with their own. It must be noted that this is a philosophical study, and while I think it will be clear that modern mathematical physics is heavy with philosophical implications, one cannot pretend to "do physics" with no more than philosophical insights. The historically delicate (and needlessly provocative) relationship between philosophy and modern physics will, I hope, emerge from my pages as more fruitful than not - indeed, as being a relationship urgently needing cultivation. This certainly does not imply, however, that I am in a position to "resolve" quantum dilemmas in a positive sense; I will be satisfied if I can sketch resolutions that are plausible enough to stimulate further thought and investigation. In a word, I trust I will not have forgotten that the relation between the disciplines of philosophy and mathematical science is one of subsidiarity: each benefits the other in different ways, the former contributing a broader perspective on reality as such and the latter disclosing particular aspects of one order of reality. It may well be wondered whether, in the attempt to bring many elements together in a small space, I will have failed to do justice to any of them. Every synthesis, after all, depends for its cogency upon adequate analyses. In defense I will say, first, that in so far as I am for the most part covering ground non novum sed noviter, it would

11 be tedious to treat exhaustively of what amounts to no small part of the AristotelianThomistic physics and metaphysics. Secondly, this thesis is written in the conviction that a re-establishment of Aristotelian and Thomistic principles in the sciences must begin with a convincingly architectonic portrayal. For the ancient science was rejected en bloc because of the perceived inadequacy of its several particulars; whereas that science, qua science, never really depended upon particular data, but upon far more general and certain observations of nature. The particular as such cannot constitute a science, let alone a philosophy. Any attempt to show how well the Aristotelian vision holds up, despite the collapse of however many particulars that were once associated with that vision, will be a task worth pursuing.

Chapter Two Three Phases in Physics

To the extent that modern physics is disunified, it must fall short of the explanatory character iconically associated with it. The very feature that has marked post-Galilean science and its transformation of the western world-view - mathematical intelligibility of a more or less deterministic nature - seems called into question by physics at the quantum level; and if the quantum revolution has furthered dramatically man's penetration into the workings of nature, it has done so in virtue of an unhappy truce with the classical-physics paradigm, and at severe epistemological cost. In this chapter I sketch out what distinguishes classical physics - that of Galileo, Newton, Maxwell, et al. - from quantum physics on the one hand, and from Aristotelian physics on the other. Such an approach may seem unduly broad: is not the problem before us a problem within physics, rather than a problem of defining physics as a whole? But just as physics after Galileo marked a significant epistemological departure from the Aristotelian paradigm of the preceding 1900 years, so has physics after Planck and Einstein undergone a shift that is epistemological at root (quite apart from the specific problems of the "Copenhagen interpretation"), and not simply a matter of what is studied. The very nature of physical explanation is at issue.

12

13 Focusing on a few definitive thinkers in physics, let us compare the kinds of questions that have been asked, and the kinds of answers given, during the three historical phases of physical science. It will be part of the burden of this thesis to show that physics, so far from having altered direction as a whole - not once, but twice over the past 400 years - has really only passed through an interval (the era of classical physics) in which it was unduly constricted, notwithstanding the enormous increase in mathematical sophistication. With the advent of quantum theory, physics is poised to regain an explanatory depth that had belonged to it, though never of course fully realized, during the Aristotelian ascendancy.

A. Aristotelian physics For Aristotle, physics is the science of being as mobile, i.e., of natures which have intrinsic principles of motion (change) and rest.1 The changes to which spatiotemporal beings are subject are four in number, all, however, being involved in some way with local motion.2 Substantial change is not motion in the proper sense, though it is conditioned by, and attendant on, motion properly speaking, which pertains to accidental being. There are three principles of motion, by whose elucidation Aristotle brilliantly resolved the difficulties of both the preSocratics and his master Plato: matter, form, and privation.3 Of these the first two are identified as causes properly speaking; they are in1

Physics HA (192b8-23). Physics V.l, 2 (225a34-226b9). 3 Physics l.l (190bl0-191al); 1.8, 9 (191a24-192a34).

2

14 trinsic to the thing moved. The full analysis of motion brings in two additional (extrinsic) causes, agent and end; all other "causes" are variants on one of these four.4 Matter becomes, for Aristotle, a main factor in determining the possibility and the divisions of science.5 Every science presupposes the basic abstraction from particular matter whereby intelligible forms can be received into the immaterial intellect; but since this is the only abstraction prerequisite to a science of mobile being, it is commonly linked to physics in particular. Thus physics is the science of those things which are material in re, and which also involve matter (taken universally) in their definitions. (A further abstraction, whereby things associated with matter in re are defined without reference to matter, gives us the objects of the science of mathematics; finally, the science which is able to consider even beings that are immaterial in themselves, i.e., metaphysics, is made possible by the intellectual abstraction more properly known as separation, separation The Aristotelian analysis of material being proceeds, in the first instance, from the intellect's primordial apprehension of motion as such. His is a science, in other words, which depends on no particular grasp or enumeration of material beings; it is absolutely universal. That Aristotle himself, to say nothing of generations of followers, applied these universally valid scientific principles to imperfect observational data, yielding such hybrid constructs as the earth-centered cosmos, the four elements and four humors, and so on, no more detracts from the soundness of his fundamental analysis

4 5

Physics II.3 (194bl6-195b30); II.7 (198al4-bl0). Metaphysics VI.l (1025b25-1026a20).

15 than, say, today's highly problematic classification of elementary particles can be said to detract from particle physics as such.

B. The departure from Aristotle It is a commonplace of intellectual history that a "revolution" was inaugurated in the physical sciences during the 16th and 17th centuries, sweeping away earlier modes of natural-philosophical discourse as successive triumphs of the 18th and 19th centuries prepared the way for our own scientifically sophisticated and highly technologized era. While better scholarship has done much to temper the myth of a radical break with their medieval precursors,6 scientists of the early modern period were certainly originative enough to write, self-consciously and at times pointedly, about the freshness of their approach. But we will not find the point of departure where later apologists have pretended to see it. Copernicus, often taken to have signaled a radical break with the universe of the ancients, was, as Koyre says, "not a Copernican" (in the oft-alleged sense of being a

See for instance Pierre Duhem, Le Systeme du monde: Histoire des doctrine cosmologiques de Platon a Copernic (Paris, 1913-1959); James A. Weisheipl, The Development of Physical Theory in the Middle Ages (London, 1959); William A. Wallace, Prelude to Galileo: Essays on Medieval and Sixteenth-Century Sources of Galileo's Thought (Boston, 1981) and Galileo and His Sources: The Heritage of the Collegio Romano in Galileo's Science (Princeton, 1984); David C. Lindberg and Robert S. Westman, eds., Reappraisals of the Scientific Revolution (Cambridge, 1990). Useful bibliographies will be found in, inter alia, Pierre Duhem, Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds, edited and translated by Roger Ariew (Chicago, 1985), and William A. Wallace, The Modeling of Nature: Philosophy ofScience and Philosophy of Nature in Synthesis (Washington, D.C., 1996).

16 wholly anti-Aristotelian revolutionary).7 His geometrical rearrangement of the heavens is hardly different in kind from the Ptolemaic elaboration of the ancient and Aristotelian conception; circular paths are transposed and reassigned, but the underlying physical reasons, so far as they are alluded to at all, could equally have been found in the presentation of an Aristotle. "I consider that gravity is nothing more than a certain natural desire given by divine providence of the Architect of the Universe to all parts to recover their unity and wholeness by coming together again in the form of a globe. We may believe that this tendency is shared also by the Sun, the Moon and the other wandering stars...." In this he anticipates the identification of terrestrial and celestial physics that will come to flower in the thought of Newton, but as yet the reasoning, while unAristotelian in its particular recognition of multiple centers of attraction, rather than of Earth as the unique center of the cosmos, is nonetheless "traditional" in acknowledging something other than a quantitative description as prior causal foundation for the latter. Not that Copernicus dwells at length on the physical as such; he is preoccupied with mathematics to a degree that makes some passages sound thoroughly modern.9 Kepler is the next great name on the march to modernity, his greatest claim to fame being perhaps his abandonment of the circle with its connotations of celestial perfection. (Not that "celestial perfection" wasn't to play a very large role in his own think-

7

Alexandre Koyre, The Astronomical Revolution: Copernicus, Kepler, Borelli, translated by R. E. W. Maddison (Ithaca, N. Y., 1973), p. 65. 8 Cited in Koyre, Astronomical Revolution, p. 56. 9 Koyre^s Platonism leads him to argue {Astronomical Revolution, pp. 58 and 113) that Copernicus saw geometrical forms as causative of planetary movements; but he cites, inter alia, E. Brachvogel as perceiving that for Copernicus the geometry was only a concomitant of the planetary natures. Cf. 58, n.l 13

17 ing, down to the end.) Nevertheless, his mathematical sophistication - achieved at no small cost, as he lingered in strange byways of a priori numerological considerations remained coupled with a deep reliance on a causality which is only described, not constituted, by the quantitative as such. He was stimulated in his prodigious astronomical efforts by the discrepancies in existing tables of planetary positions; yet in bringing greater accuracy to the numerical aspect of astronomy, he believed himself to have plumbed the question of causality in a newly fecund way. The very title of his New Astronomy indicates as much: Astronomia Nova AITIOLOGETOS ["Causal Explanations"] seu Physica Caelestis tradita.... He says in the preface that, while setting himself to correct the planetary tables "I came also upon Aristotle's metaphysics, or more precisely, celestial physics, and I studied the natural causes of motion. This consideration provided very clear reasons which show the Copernican doctrine to be true...." 10 That his eventual assignation of the cause in question - a quasi-magnetic force residing in the Sun - is cast in terms hardly Aristotelian, is not the point; differences of expression or conception within an intellectual tradition can be no less striking, prima facie, than differences in the traditions themselves. But Kepler evidently thought himself to be improving upon, rather than overturning, the Aristotelian view. He is pleased to have shown a posteriori, "by a rather long investigation" rather than a priori "from the particular significance of the Sun" - that since "the Sun is situated at the center of the [solar] system, it follows.. .that the source of the motive 10

Koyre,p. 167.

18 force also is situated in the Sun."11 It is "more likely that the source of motion is motionless where it is situated [as is the Sun, in Kepler's conception], than that it has motion [per both Ptolemy and Tycho]."12 At the same time, Kepler did not hesitate to assail a very distinctive Aristotelian and medieval doctrine, that of "natural place" in its geocentric formulation. My point is, not that Kepler was a crypto-Aristotelian, but that he had not made the essential break with Aristotle, which would consist in the jettisoning of causal explanations as such.13 Galileo is typically seen as constituting the watershed between pre-modern and modern ways of thinking physically. This is not at all to say that he marks a clean rupture with the developments of the late Middle Ages, nor that he remained free of what must now appear as decided archaisms. But with Galileo physicists can generally feel that they are in familiar territory; in his writings the quantitative approach to the study of mobile being becomes well established, and causes beyond the reach of mathematical analysis are barely considered, even in passing. The question of most interest to our inquiry is, not to what extent did Galileo insist upon observation and experiment (answer: very much indeed), nor to what extent did he mathematize the world under his consid-

u

Koyre,p. 191. Koyre,p. 192; cf. p. 198. 13 It is worth notice, that the much-derided doctrine of "natural place" in Aristotle, assailed with ever-increasing confidence by Copernicus, Kepler, and Galileo, and utterly alien to the Newtonian formulation of celestial physics, turns out, on deeper consideration, to have suffered only a slight transposition. Matter is attracted to matter, the more according as it is the more densely situated "in space": this broad expression is as compatible with the thought of Newton and Einstein as with that of Aristotle. It is ironic that, just as the ancient and medieval mind had rejoiced in a metaphysics and an anthropology conformable to the presumed unicity of the Earth (man's abode) as cosmic center, so have scientistic philosophers of more recent times linked their denials of human pre-eminence to the very plurality of such centers. 12

19 eration (answer: almost completely), but how did he view this experimentally determined and mathematized body of knowledge vis-a-vis causes in the real order? In 1612, approaching mid-career, he wrote that "in our speculating we either seek to penetrate the true and internal essence of natural substances or content ourselves with a knowledge of some of their properties. The former I hold to be as impossible an undertaking with regard to the closest elemental substances as with more remote celestial things."14 The "properties" which remain accessible to us - Galileo instances, in the case of the sunspots which form the subject matter of the present Letter, "their location, motion, shape, size, opacity, mutability, generation, and dissolution" - are all features susceptible of quantitative description and mathematical analysis. He continues, in a vein that would be repeated even much later in his works, "These in turn may become the means by which we shall be able to philosophize better about other and more controversial qualities of natural substances."15 Galileo's Assayer (II Saggiatore) of 1623, often called his philosophical manifesto, actually contains relatively little in the way of philosophical remarks, and those mostly upon the unreality, or rather the subjectivity, of sensible qualities in the context of an atomism that recalls Lucretius. But there is this famously succinct passage: "Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of

14 15

Cited in Stillman Drake, Galileo at Work: His Scientific Biography (Chicago, 1978), p. 199. Drake, Galileo at Work, p. 200.

20 mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it... ."16 One need not adopt an extreme Platonist reading of this passage (such that the universe is constituted of mathematical entities) in order to be impressed by the boldness of Galileo's claim. The mere reference to quantitative universality is hardly novel; scholastic philosophy, to which Galileo had been thoroughly exposed as a student, was well aware that material being is inevitably quantitative being, and medieval thinkers had returned often to the scriptural declaration that God "has disposed all things according to measure, number, and weight." But while the tripartite Aristotelian division of sciences comprised physics, mathematics and metaphysics - to which the scholastics added scientiae mediae such as astronomy and optics, embracing aspects both physical and mathematical - it was hardly an Aristotelian way of speaking, to identify the second of these with philosophy simpliciter. In the context of his other remarks about substances and their qualities it cannot be held that Galileo had rejected an underlying reality beyond the quantitative; he is employing hyperbole here, or rhetorical emphasis. As Drake says, "The concept of a science in which measurements, rather than qualities or essences, would govern physical conclusions....strongly appealed to Galileo, who conceived it not as a substitute for or a rival of philosophy, but as a basis of establishing at least some reliable knowledge that would not have to be continually revised. There would

16

Stillman Drake, Discoveries and Opinions of Galileo (New York, 1957), pp. 237-8. "But note that the passage is unclear about the precise status of this geometrical language....it lierally says that mathematics is the language, not of the universe, but of philosophy." Gary Hatfield, "Metaphysics and the New Science" in Lindberg and Westman, eds., Reappraisals of the Scientific Revolution, p. 130.

21 always be other knowledge that science could not touch, and he was content to leave that to philosophers."17 Galileo, then, seems to have been at least moderately skeptical about philosophical inquiry into underlying causes; he was dedicated, in any case, to the mathematical grasp of phenomena accessible to the senses. Restricting himself to the phenomenal and the measurable, he nowhere denies that the latter is grounded in an underlying substantial reality. But that is, for him, no longer science's concern. The same cannot be said of Descartes. A greater mathematician than Galileo, he also retained a stronger instinct for causal explanation in science. In a letter to Mersenne he writes, concerning Galileo, "I find generally that he philosophizes much better than ordinary, in that he avoids as best he can the errors of the scholastics and undertakes to examine physical matters by mathematical reasonings. In this I accord with him entirely, and I hold that there is no better way to find the truth... .But he has not examined things in order, and...without having considered the first causes of nature he has only sought the reasons of some particular effects, and thus he has built without foundation."18 What Descartes perceives as Galileo's weakness is, of course, the latter's strength, namely his refusal to let a priori constructs lead him from the path of true inquiry. Descartes, while seizing upon quantitative methods in the science of mobile being, did not sufficiently allow his mathematical facility to be tempered by a respect for 17

Cf. Galileo's remark, "Philosophy itself cannot but benefit from our disputes, for if our conceptions prove true, new achievements will be made; if false, their refutation will further confirm the original doctrines." Cited by Drake in his Galileo at Work, p. 108, from Galileo, Dialogue Concerning the Two Chief World Systems (translated by Stillman Drake, Berkeley, 1953). 18 Cited by Drake, Galileo at Work, pp. 387-8.

22 observation. Too eager to unfold the deductive consequences of a given hypothesis, Descartes failed to generate a physics of lasting value. Note that all four representative thinkers mentioned thus far were thoroughly mathematical in their modus operandi, and to that extent marked a break with the mixed (quantitative and non-quantitative) explanations sought by their predecessors. But this remark needs qualification. On the one hand, the "predecessors" were by no means strangers to mathematical considerations, with a long-established tradition of "saving the phenomena" in astronomy and the beginnings of a quantitative analysis of terrestrial motions. Nor were they, in some pursuits (such as alchemy) more than others, incapable of proceeding experimentally. On the other hand, the growing mathematical commitment represented by 16 and 17 century astronomers and physicists hardly entailed a principled disregard for underlying causality tout court, however agnostic their scientific methodology might be in that regard. Newton, more than any other physicist down to the quantum era, may be taken as paradigmatic in our survey of the evolution in scientific thinking about causality. The "philosophy of nature" which animates his works was adumbrated in his predecessors, especially Galileo and Descartes, and remained normative for two centuries. Here, preeminently, we see the essence of post-Aristotelian and pre-quantum physics. From the standpoint of the 21 st century we can say that Newtonian thought is a major fault-line, separating definitively the ancient and modern even as it constituted an upheaval in its own right; but like upheavals generally it would prove to be not altogether constructive.

23

The very title of his greatest work would have struck earlier philosophers as oxymoronic; what "mathematical principles" cannot ground is a philosophy of nature. At times Newton rejects any inquiry into the causes underlying those properties which he is confident of describing mathematically.19 But he does not altogether refrain from attempts at causal explanation in an analogical mode, as for example in the "Queries" which are appended to the "hypothetical" discussion of the nature of light in the Opticks.20 Nor have such explanatory forays stood the test of time to the extent that his other more purely mathematical contributions have. In fact, the very mathematization which constituted the Principia a work of mastery, where the Opticks remained one of exploration (however brilliant), proceeded in virtue of a certain abstention from the nature and definition of that which it described. The laws of motion and gravitation are not explanatory, in the sense of tracing causal dependencies to ever deeper levels; they are descriptive, albeit in unprecedented detail. This narrowing of scientific inquiry to the quantitative is of course what we have been tracing in Newton's predecessors as well; it happens to be particularly well exhibited in Newton because of the magnitude and overall coherence of his accomplishment. The paragon of physical theory, prior to the 20th-century revolution in physics, is often taken to be Maxwell's work in electricity and magnetism. Physics is here pushed

19

See for instance Definition 8 in Principia mathematicae philosophiae naturalis: "I use interchangeably and indiscriminately words signifying attraction, impulse, or any sort of propensity toward a center, considering these forces not from a physical, but only from a mathematical point of view." The Principia: Mathematical Principles of Natural Philosophy, translated by I. Bernard Cohen and Anne Whitman (Berkeley, 1999), p. 408. 20 See for instance Queries 8, 11-14, 17, etc.: Isaac Newton, Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours ofLight (New York, 1952), pp. 339-406 passim.

24

far beyond what Newton could have imagined; many phenomena of light and electromagnetism unknown in Newton's day, including those whose wave character seemed now beyond question, were brought together in a sophisticated treatise, nearly every page of which seems worlds removed from the comparatively primitive treatments in the Principia. But it is precisely the differences between Maxwell and Newton which underscore their radical similarity. From a philosophical (as opposed to experimental) standpoint, their work is cut from the same cloth. By the 19th century, prodigious advances in many branches of physics and chemistry had occurred against the backdrop of a prevailing insouciance with respect to substance philosophically conceived. The fourfold account of causality implied in Aristotle's doctrine of nature was methodically ignored; in the positivistic apotheosis of the late 19th century it was quite explicitly rejected. Mathematics alone prevailed. The Humean and Kantian critiques of causality and knowledge of the noumenal only provided post hoc support for a scientific attitude that had learned to find its own way.

C. What does classical physics say? Let us observe three simple instances of physical description, as proposed on the verge of the quantum era. The first is Newton's law of universal gravitation, F^GMiMj/r2. The attractive gravitational force F expresses the tendency of two masses Mi, M2, separated by distance r, to move toward one another across a distance r. This force, i.e. the

25 tendency which it names, can be meaningful (and measurable) only within a finite time interval during which the said motion could occur. This time-reference appears in the dimensioned constant G ~ 6.673 x 10"11 m3 kg-1 s"2. We have, then, an expression for a relation between the fundamental quantities distance (r, measured in meters), time (measured in seconds), and mass (Mi, M2, measured in kilograms). But mass, Newton's quantitas materiae, is, in the Newtonian context, both the quantitative measure of a body's resistance to a change in its velocity, and that which attracts or is attracted gravitationally. In other words, in Newton's theory of gravitation, mass refers to a center of physical attraction (always having spatial dimensions, though often treated pointwise mathematically), an attraction which is "greater" according as its inclination to another such center is greater in spatiotemporal terms, d/t2. Force, speaking generally, is a push or a pull - whatever effects or tends to effect a change in the velocity of a body. This is encapsulated in Newton's second law of motion, F = ma, a being the acceleration (change of velocity) of a body of mass m, subject to force F. Physicists today generally recognize four kinds of force in nature gravitational, electromagnetic, weak nuclear and strong nuclear. An expression of central importance in the Newtonian project, one which enters into the description of such infinitely varied actions as the fall of a raindrop or the collapse of a supernova, is thus seen on reflection to be nothing but a relation of distance

26 and time and mass; and even time is but the measure of spatial variation.21 Clearly, however, more than mass, time and distance are presupposed in the equation. We do not consider raindrops and supernovas to be mere relations of quantities ultimately reducible to spatial variation. Newton's law of gravitation, then, expresses a universally applicable relation among bodies, namely their tendency to move toward one another, but it neither states nor implies anything about what those bodies are, beyond their mere possession of mass and their spatiotemporality, i.e. their propensity to vary spatially. Compare this with our second exhibit, Maxwell's electromagnetic equations, which are analogously fundamental in describing a wide range of electric and magnetic field phenomena:

v

VD =p V-B = 0 x E = -as / dt

VxH

= J + dJ)/dt

Here D stands for electric displacement, B for magnetic flux density, E for the electric field strength, H for the magnetic field strength, J for electric current density and p for electric charge density. These equations describe electromagnetic phenomena, that is, various spatiotemporal relations among entities which exhibit attraction and repulsion through "forces" other than gravitational. (A generation after Maxwell it would be realized that, 21

This statement is compatible with the Aristotelian quasi-definition of time as the measure of change, inasmuch as all change either is or entails locomotion: cf. Physics VIII.7 (260a27-bl4). Substantial change is not motion and is instantaneous. As we shall see, it does not occur "through" space either.

27 unlike gravitation, a feature common to matter as such, electrical forces are associated in different ways with different constituent particles of subatomic matter, while magnetic forces result from certain motions of electrically charged particles.) Of course, restriction of the applicability of these equations to phenomena deriving from attractions and repulsions differentiated at the subatomic level is nowhere apparent in the equations; that is presupposed by them. What do the equations actually express (or imply)? They describe relations of attraction and repulsion between "charges" (spatial centers of attractive or repulsive activity) through more distended regions of attractive and repulsive influence ("fields"), whose "densities" and "strengths" (as well as quantities derivative from these) are so many specifications of the locomotive behavior of charges within them. In other words, just as in the case of gravitational force and mass, so are electromagnetic forces and charges defined ultimately in spatiotemporal terms, and this not merely as presupposing space and time but as constituting nothing other than specific determinations of spatial variation, measured temporally. The elaborate structures of Maxwellian theory shed no further light on the underlying nature of electromagnetic attractions and repulsions. We have, again, only an abstract system of spatiotemporal relations whose applicability presupposes knowledge of entities on a less abstract plane. I present one more instance of physics in the classical mode, that is, of physics conceived as a purely quantitative investigation into the sensible world. This is the central group of equations constituting Einstein's Special Theory of Relativity, and the example may seem surprising inasmuch as Relativity is considered to be distinctively

28

post-Newtonian. But whatever may be said about its alleged transformation of how space and time must enter into physics, special relativity at any rate does not depart from the paradigm already instanced by Newton and by Maxwell. The Lorentz transformation which is at its core, x' = (x-vt) / Vl-(v2/c2), y' = y,z' = z, t' = (t-vx/c2) / Vl-tf/c2), is, once again, nothing but a relating of distances (x, y, z) and time measurements (t), v and c, the speed of light, being themselves simply distance/time ratios. The dynamic implications of the "physics of the Lorentz transformation" (as special relativity has been called), leading to the celebrated mass-energy equivalence E = mc , introduce no further physical content inasmuch as m, as we have seen, is defined ultimately in terms of space and time (Newtonian definitional circularity remaining a feature of mathematical physics down to our own day), while c is an immediate space/time relation and E (energy) is simply the potential for work, i.e. for applying a force (an attractive or repulsive tendency between bodies) through a distance. There is no positive "content" in the equations of special relativity, as there was none in the equations of Maxwellian electrodynamics or Newtonian gravitation or anywhere else in the vast edifice of prequantum physics, beyond the quantifiable aspect of local motion, i.e., variation in spatial relationships.

D. Is classical physics scientific? With this sampling of paradigmatic physical statements before us, it is worth asking: if post-Galilean (which is to say, post-Aristotelian) physics is no longer about the causes

29 of nature, but is only quantitatively descriptive of changes in spatial relations, in what sense is it a science? Leibniz and others had already made the charge against Newton, and it is no less applicable to everyone from Galileo to Einstein: without a basis in definitions expressive of the nature of mobile being, is not the mathematization characteristic of modern physics radically deficient? Is it not looking only at a part rather than the whole, with the concomitant risk of mistaking the part for the whole? From an Aristotelian standpoint, modern mathematical physics is not about substantial being at all, except indirectly: concerned exclusively with, and restricted in its very methodology to, the quantitative, it is about accidents in so far as they are associated with quantity. It is a scientia media, as noted previously, physical on the material side, mathematical on the formal side.22 Now mathematics is a demonstrative science according to the canons of the Posterior Analytics; its certitudes are anchored in the fact that it proceeds deductively from principles abstracted entirely from matter. "Entirely" means, not only that material being is the sole origin of our quantitative concepts, but, in the first place, that the principles of mathematics - discrete and continuous quantities, posited in the imagination or "intelligible matter" of the mind are defined without any reference to matter and its contingency. "Three apples" is con-

22

Cf. Thomas Aquinas, In De caelo 1.3: "a natural body has sensible matter added to its mathematical extension, and therefore it is not improper for the natural scientist to use mathematical principles in his demonstrations" {corpus naturale addit materiam sensibilem supra magnitudinem mathematicam: et ideo non est inconveniens si naturalis in suis demonstrationibus utatur principiis mathematicis: non enim est omnino aliud genus, sed quodammodo sub illo continetur) - cited in William A. Wallace, "Thomistic Reflections on The Modeling ofNature: Science, Philosophy, and Theology," unpublished essay. Cf. pp. 1-2 in that essay, and other references to Aquinas therein. See also Jacques Maritain, The Degrees of Knowledge, trans. Gerald B. Phelan (New York, 1959), pp. 35-46.

30

tingent; apples come and go. But "three" simpliciter is abstracted from the materiality of the apples themselves (or oranges or anything else).23 As a universal, it is abstracted from designated matter (materia quantitate signata); as a mathematical, it is further abstracted from matter simpliciter. Matter is an indeterminate principle which escapes intelligibility precisely in so far as it is not actual but only the possibility of the actual. Herein lies the inability of mathematical physics to have achieved an all-encompassing formulation, and an embarrassment to the "final theorists" of every generation. Physics, like every natural science, proceeds in virtue of an alternation and interplay between moments of discovery and theoretical constructs. The discovery phase is always present because material being the "matter" of the physicists - is not purely actual but is radicated in a potential principle which can only be rendered intelligible to the extent that it becomes (imperfectly) actualized. A great deal of scientific observation and experimentation is directed toward unveiling new levels of actuality or actualizing further the potentialities of matter, and thereby enriching our awareness of hylomorphic being. Physicists do not make "mathematical discoveries." They learn to apply, to the ever-growing data of sense experience, a mathematics which, however stimulated in its growth by physical requirements, remains self-sufficient and independently coherent. In fact it is one measure of the inadequacy of a physical theory, that it does not provide a 23

The process of abstraction is not without mystery; the intellectus agens works in virtue of a certain connaturality between knower and known, discerning ("illuminating") in the latter a factor which is at once concrete and universal. The reality of "three" is attested continually in the mind's reversion to brute reality; were "three," as abstracted from three apples, not real in a universal sense, it could not be coherently applied to three oranges.

31 mathematically comprehensive account of the phenomena; it remains to some extent disunified, because the phenomena have not disclosed their quantitative aspects in their entirety to the investigator. The mere fact that mathematical physics deals with material being is not sufficient reason for denying to physics a properly scientific character. Aristotelian physics, dealing with being precisely as material, is understood to be a science in the strict sense. But mathematical physics is removed from the universality of Aristotelian physics; it is concerned with the particular, specifically with the particularization associated with determinate quantity as accidental to substantial being. Quantities in the abstract are grasped universally, but quantities as accidents of natural being are grasped contingently. Knowing that 5 times 12 gives 60 does not enable us to say that any 5 carbon atoms will contain a total of 60 nucleons. Other factors, which can only emerge through further observation and experiment, may supervene, varying the neutron numbers. Modern physics has a scientific character to the extent that it involves the constancy of definable natures, but is unscientific to the extent that it treats of the accidental rather than the substantial. Natural substances are determinative of their concomitant accidents, but only within certain limits. A carbon atom cannot (so far as we know) contain only one neutron, or as many as 20; its very nature as carbon - a configuration of six protons - is incompatible with these extremes. But it can have six neutrons, or seven or eight; these accidents are conformable to the substantial nature of carbon. Against all these considerations of the contingency and accidentality of physics' subject matter there seems to be the determinism so characteristic of pre-quantum phys-

32

ics. But this determinism has never been realized beyond simple cases over a restricted time interval. It is brave talk; it may even be said to have guided scientific investigation;24 but the standing reproof to every claim of physical determinism is the contingency and unpredictability, not only of physical systems as they are encountered in everyday investigation, but of the entire course of physical science over the centuries. This is not to say that there is an absolute indeterminacy in material being (as it would appear from a divine or perhaps angelic standpoint). But determinism in the classical sense - an inevitability in the historical trajectory of physical systems that is in theory accessible to scientific analysis - is incompatible with the radical indeterminacy of matter as the potential principle of cosmic being. Such indeterminacy, already long known in principle through the Aristotelian analysis of mobile being, had to await the unique circumstances of quantum-physical investigation to disclose itself to the scientific mind. Now classical physics, dealing quantitatively with the accidents of hylomorphic being, does so by tracing mathematically, through differential equations, the relationships into which those quantities enter. I have already touched on this, in regard to the three "paradigmatic instances" of physical formulation; let us develop the point further. It should provoke no little wonder that mathematics, the universal language of physics, is applied analogically rather than univocally across the entire domain of physical inquiry. The physical qualities that are investigated quantitatively are, in and of themselves, incommensurable - or so it must seem. Just as it is meaningless to speak of 24

"In practice, the belief in Determinism has rendered a great service to scientists by preserving them from sloth." Louis de Broglie, Matter and Light: The New Physics, translated by W. H. Johnston (New York, 1948), p. 238.

33

the "sound" of a painting, or the "color" of a sound (except metaphorically), so there is no ratio between the concepts of, say, "volume" and "pressure," the one referring to space and the other to the collective momenta of particles. But physics in the modern sense is not about qualities as such; it is about the quantifiable aspect of qualities. Both volume and pressure being susceptible of quantitative measurement, their measurements can enter into true ratios. Nor is this an arbitrary result of the mind's a priori constructs. It is at root due to the fact that every physical quantity, as noted previously, is reducible to spatial relation and variation. In the next chapter I identify this spatiality with the prime matter that enters into all cosmic being as such. It is because the objects of physics, disparate as they seem to be, are all manifestations, so to speak, of prime matter, that they can be known and related quantitatively. What of the equations themselves? It is one thing to speak of the analogical applicability of quantitative analysis to every aspect of hylomorphic being, and of mathematics as the means whereby we effectively relate physical quantities to one another. But just how much does the mathematical formulation tell us? The universality of a physical formula is represented by its abstractness. But in the abstract a formula does not give us a description of the concrete reality; it does so only as solved, i.e., as stated in terms of determinate quantities. The formula is, as it were, in potency to its solutions as "actualizations." The "truth" of an abstract formulation consists only in its applicability to concrete instances. But this applicability is not implicit in the formula itself; it was only a contingent basis for the formula's derivation. Given the contingent nature, the

34

materiality, of what is governed by the formula, there is always the possibility that the formula will be found inadequate, i.e. that not all its mathematically possible solutions are physically realizable. Of course the formulas of physics are derived on the basis of their physical applicability, and if the supposition is made that nature is continuously (infinitely) variable, then infinitely many solutions will have a physical as well as mathematical import. But such continuity, however implied by mathematical expressions in their own order, cannot thereby be inferred to be a physical characteristic. This would be the lesson of the quantum revolution in physics: if physical reality is not simply quantity, then the features of quantity as such will not be adequate to its description; other, nonquantitative factors may supervene. The quantitative will be only a part, and not the whole, of what is being described only quantitatively. These quantitative relations are not only made possible, but have physical significance - they disclose real relationships among material beings - because they are ultimately manifestations of the very materiality that unites cosmic being. Nevertheless, to say that physico-mathematical relationships are real is not to say that they are other than accidental, or that mathematical physics is on that account a demonstrative science, or that the qualities which modern physics investigates (and a fortiori their underlying substances) are reductively no more than quantitative.

35 E. Quantum physics, considered qualitatively Having briefly reviewed key aspects of both Aristotelian and classical physics, it remains now to introduce the third era in physical science, that of quantum theory, before giving a comparative overview. I present this part of the account in a little more detail, since it is in the heart of quantum physics that the aporiai of the present dissertation are located. The claims of some philosophers to the contrary, theoretical physicists on the whole are satisfied that their investigations are of the real world, describing the very same order of being in which airplanes fly and steaks are grilled and poets move their pens. That is a world amenable to quantitative description, which is not to say that it is a world entirely quantitative. It is, an Aristotelian would say, accidentally quantitative, its quantitative aspect inhering in a deeper stratum of being, namely substance, which is form and matter. This entails that physical being is susceptible of an analysis in terms that are non-quantitative - indeed, that the essential description, pertaining to the substance, must be non-quantitative. On the other hand, the materiality which constitutes physical being as physical or mobile is manifested, as I shall argue in the next chapter, precisely in terms of threedimensionality. The fact that mathematical explorations of the physical world can lead to working hypotheses whose physical meaning (i.e., capacity to be realized threedimensionally) currently eludes us, does not warrant the conclusion that the reality being described is inherently incapable of such visualization. If material being is essentially three-dimensional being, and if all motion is reducible to variation in the three-

36 dimensional continuum, then every physical process or configuration must be referred, ultimately, to that continuum. To be rejected, on this view, is every "multidimensional" construct in which higher dimensions are considered to be spatial yet distinct from the everyday spatial dimensions; so also, all physical entities or states or processes which are claimed to be beyond three-dimensional description (as is commonly said to be the case, for example, with electron "spin"). Although the analogical mode of scientific discourse is continually prone to misinterpretation and any number of false starts or dead ends, it remains indispensable in so far as it is anchored in a reality primordially grasped, and visualizable, as three-dimensional.25 Even the most mathematically complex theory, in so far as it corresponds to reality, must be reducible to description in terms of three-dimensional configurations and temporal variation. In this conviction I seek to present quantum physics in terms no less applicable to the world of everyday observation.

F. The background Quantum physics dawned about the turn of the 20th century, with the growing realization that the subatomic domain is governed by certain laws having no clear analogy in the classical-physics framework. All through the 19 century there had accumulated evidence, in physics and especially in chemistry, for an atomic constitution of ordinary matter. "Atoms" were understood to be the least particles of substances with irreducibly 25

"Now among the systems of geometrical entities that are called Euclidian, Riemannian, etc., spaces, only tri-dimensional Euclidian space is directly constructible in intuition." Jacques Maritain, The Degrees of Knowledge, p. 168.

37

fixed properties, the chemical elements. But atoms in turn were found to have particular components. In 1897 the electron, basic unit of negative electric charge, was recognized to be one such component.26 The location of the much more massive proton, positively charged component of the atom, within a comparatively tiny nuclear region of the atom was established in 1909.27 (Neutrons, comparable to protons in mass but electrically neutral, were discovered in 1932.) These new "elementary particles," whose numbers would be greatly augmented as the century wore on, were understood to have finite dimensions even if their activity could sometimes be described in terms of points in space. Meanwhile electromagnetic radiation had begun to reveal aspects inconsonant with the wave interpretation of Maxwell's hallowed equations. Planck suggested in 1901 that intractable theoretical difficulties could be resolved if the energy of electromagnetic waves were considered to vary across the spectrum, not continuously, but by discrete amounts, these amounts (later called quanta) being proportionate to the radiation frequencies. In 1905 Einstein carried the idea further to explain why light is observed to dislodge electrons from certain metallic atoms only if its frequency (rather than intensity) is above a certain minimum threshold (a function of the metal in question), and to impart only discrete kinetic energies to the ejected electrons. It had been known for some time that incandescent gases emit light, not in continuous spectra but at discrete frequencies; in 1885 it had been shown by Balmer that 26

J. J. Thomson; R. Millikan measured the charge in relation to electron mass, 1909 and thereafter. 27 E. Rutherford's gold-foil experiments, 1911.

38

these frequencies, in the case of the hydrogen spectrum, can be related by a simple numerical formula. The structure of the atom, in the wake of Rutherford's discovery of the nucleus, was at first assumed to be on the model of a planetary system; but theoretical difficulties involving the energy loss of orbiting electrons forced a reassessment. Bohr then posited that electrons are locked into discrete orbits, which somehow preclude radiative loss (and consequent inward spiraling).28 He showed that, for the case of hydrogen, the discrete energy levels represented by the Balmer lines corresponded well to the energy levels represented by the discrete electron orbits. The Compton effect, in which light is scattered by free electrons with a resultant change in frequency as well as direction,29 was interpreted in 1923 in terms of light quanta acting as particles with definite momentum (a directed or vector quantity); both the light quantum (photon) and the electron are affected by the interaction, with momentum being conserved such that the difference in photon energy corresponds to a difference in the kinetic energy of the electron.

Although this step is often treated as a master-stroke of scientific insight, it amounted to no more than a simple denial of the hitherto presumed electron radiation, proffered without theoretical justification. But from a purely mathematical standpoint it opened the door to a coherent account of electron quantization, as will be seen. 29 "In the quantum theory, this process must be described as the absorption of a quantum from the incident light, and the emission of a new quantum in a new direction. Insofar as energymomentum relations are concerned, however, this process can equally well be described as the scattering of a single particle...." David Bohm, Quantum Theory (Englewood Cliffs, N. J., 1951), p. 33.

39 G. The emergence of quantum theory In 1924 de Broglie suggested that, just as light exhibits wavelike and particulate aspects, so might electrons, hitherto regarded as particles, have definite wave features. The connaturality of light (electromagnetic radiation) and matter, already indicated at the macroscopic level by the obvious fact that all our knowledge of the former is had through its physical interaction with the latter, could only be further substantiated by a deepening awareness of how electrons and photons - quanta of matter and light respectively - are intimately linked in such phenomena as the photoelectric effect, the discrete spectra of the Bohr atom, and the Compton effect. De Broglie stated that the wavelength X of the electron is related to its momentum p by X = hip, where h is a constant that Planck had earlier employed in relating the frequency of a photon to its discrete energy, E = hv.30 Shortly afterward, Schrodinger made use of de Broglie's idea to give a physical foundation to the Bohr's discrete electron orbits, namely by conceiving each electron "orbit" as a sort of standing wave in three-dimensional space. Details of this theory, in which each orbit has, in accordance with its energy level, definite parameters in terms of size, shape, and orientation, still constitute a major part of modern chemistry. Thus a fundamental feature of quantum physics had been limned: discreteness rather than continuity in certain interactions of radiation and matter (understood to be

Electrons give further evidence of their wavelike character in scattering and diffraction phenomena, such as those put to everyday use in the electron microscope.

40 atomic matter), together with a wavelike structure in both.31 This duality of aspect would give rise to endless speculation about the seeming incompatibility of wave and particle. In general, the challenge was to describe the reduction of a wavelike (and to that extent relatively dispersed or "continuous") entity to a much more localized (particlelike) entity. Two mathematical formalisms were devised in quick succession to describe the interplay of variables on the quantum level: Heisenberg, with the assistance of Pauli and others, came up with a matrix algebra that very well reproduced the discrete quantities encountered in experiment; such a methodology did not imply anything whatever about the "between" states, but there was growing doubt whether reference to a physical basis made sense anyhow. Schrodinger meanwhile developed a wave equation, not unrelated to classical wave theory, though modified through the application of certain boundary conditions to yield the discrete quantum states (rather than the infinitely variable solutions of classical wave theory). The two formalisms were soon found to be mathematically equivalent: both wave mechanics and matrix mechanics gave the probability that a particlelike event would occur at a given point in space and time, given the parameters of its corresponding wave phenomena. SchrOdinger's own physical interpretation of his wave equation was that "wave packets" representing energy concentrations were in fact 31

Bohm, in Quantum Theory, p. 26, says there are "two crucial differences between the kind of physical law obtained in classical theory and the kind suggested by experience with quantum phenomena. The first difference is that whereas classical theory always deals with continuously varying quantities, quantum theory must also deal with discontinuous or indivisible processes. The second difference is that whereas classical theory completely determines the relationship between variables at an earlier time and those at a later time (i.e., it is completely [deterministically] causal), quantum laws determine only probabilities offuture events in terms of given conditions in the past."

41 what had classically been described as particles. But this interpretation was destined to falter, even though his equation remains fundamental to this day.

H. Continuous and discrete: complementarity In situation after situation it became evident that there could be no univocal comparison of continuous and discrete (of wave and particle, etc.) under either formalism. Wave characteristics (e.g., momentum) and particle characteristics (e.g., position) could be observed and described only at each other's expense; this was an empirical fact, and it showed up in the mathematics in a significant way.32 Observations, thoughtexperiments and mathematical constructs alike implied that the reduction of continuous features to more discrete features involves an element of unknowability. I will return to this shortly, only remarking for now that these situations are all dynamic in nature, i.e., having to do with transitions or, in the language of an older physics, the "mutability" of being at the quantum level. The quantization which had been invoked and mathematized to deal with such phenomena as the photoelectric effect and hydrogen emission lines had not presupposed other than a classically "deterministic" interpretive framework - that is, the discrete nature of the phenomena could still be accommodated to a physical world-view in which cause-and-effect can be described with 100% probability, event by event. But it soon became evident that, at the quantum level, when dealing not simply with particular out32

"...where matrix mechanics depends upon the properties of non-commuting matrices, wave mechanics can be derived from the properties of non-commuting [algebraic] operators." Jim Baggott, The Meaning of Quantum Theory: A Guide for Students of Chemistry and Physics (Oxford, 1992), p. 30.

42

comes (as in the two instances just cited), but with their genesis in time and space, probabilistic considerations were inescapable. The reduction of a wavelike propagation to a particlelike event involves (among other things) the physical quantities position and momentum. Momentum in turn implies a change in position over time, being defined as p = mv. Basically, that aspect of a quantum entity that is evolving over time can be seen as precluding positional precision, inasmuch as it is position that is evolving. Motion, in other words, partakes of the continuous (as does time, which is its measure), while place is more determinate. The paired physical quantities that are related as continuous and discrete at the quantum level go beyond the oft-cited and paradigmatic "momentum and position." For instance, the excitation energies of atomic orbitals stand in relation to their finite lifetimes as discrete to continuous - as do the masses of unstable particles to their halflives. In these and analogous cases it is noteworthy that no physical parameter is entirely determinate by nature. Every characteristic of a quantum system admits of a range of quantitative determinations, corresponding to a potentiality which "exceeds" any particular actualization. Thus the electron or photon can be elsewhere than where it actually is, can have an energy other than what it presently has, and so on. Since this inherent variation applies to all quantum characteristics (being, as I shall argue later, a manifestation of materiality itself), among which are those paired entities mentioned above, there is a relation of uncertainty between the conjugate parameters such that the more determinate the one, the less determinate is the other. Such linked properties are

43

most often supposed to be physically related so that the probability function governing the pair of them entails a reciprocal relation between their probabilities taken separately.33 In the limiting cases, a 100% probability of a particle's being in a given location would entail a zero probability of its having a determinable momentum, and vice versa. To return to the instances mentioned above: there is a range in the values of an electron's excitation energy for a given orbital, and in the values of its average lifetime (duration of excitation) in that state. The more precisely one of these ranges is determined, the less will be the other. Or: there is a range in the values of a pi-meson's mass, and in the values of its half-life. But the more determined the mass value, the less determined is the half-life, and vice versa. The uncertainty relation, a relation among probabilities, emerges as a quantitative expression from the mathematical formalism of both Heisenberg's matrices and Schrodinger's wave equation. It is the physical counterpart to the noncommutative operators of the former. It can be better "visualized" via Schrodinger: in his wave mechanics, a particle (which is only an extreme localization of energy) emerges as a "wave packet," or - speaking roughly - a condensation of mass-energy where waves of different frequency have coincided to constitute a semi-permanent spatiotemporal entity. But

More technically, the psi-function widths for momentum and position, or analogous pairs of conjugate variables, are Fourier transforms of each other such that AxAp > hiAn.

44 the wave packet is always of finite extent, always a little "fuzzy" and to that extent not precisely here or there.34 Bohr famously laid down as the principle of complementarity that the wave and particle aspects of physical entities are equally valid descriptions, but impossible to determine simultaneously. Since one aspect emerges under one kind of observation, and the other under a different kind of observation, we cannot observe both together; rather, whichever aspect we observe is determined by our choice of observation apparatus. The very nature of the quantum theory ... forces us to regard the space-time coordination [meaning: particle behavior] and the claim of causality [meaning: wave behavior], the union of which characterizes the classical theories, as complementary but exclusive features of the description .... 35 Bohr's philosophical predispositions, and the nuanced meaning he assigned to his physical conceptions, have been the subject of much discussion.36 Here I will only observe that one need not impute to him a raw subjectivism; that would be the dubious achievement of some later interpreters. To say that one's modus observandi dictates which aspect of reality one observes is not the same as to say that one's observations determine reality as such.

This physical interpretation or visualization of a particle is highly debatable, and far from the conception embraced by most physicists today; nevertheless it represents the way in which SchrSdinger himself, de Broglie and Einstein preferred to conceive of the quantum. 35 Niels Bohr, in Nature 121 (Supplement, 1928): 580; cited in Abraham Pais, Niels Bohr's Times, in Physics, Philosophy, and Polity (Oxford, 1991), p. 315; bracketed text by Pais. Jim Baggott (The Meaning of Quantum Theory, p. 86) summarizes neatly: "For Bohr, complementarity lay at the heart of the strange nature of the quantum world. The uncertainty principle becomes merely a mathematical statement expressing the limits imposed on our ability to make measurements based on complementary concepts of classical physics." 36 See for example Steen Brock, Niels Bohr's Philosophy of Quantum Physics in the Light of the Helmholtzian Tradition of Theoretical Physics (Berlin, 2003).

45 I. Complementarity or hiddenness? By way of introducing the great 20th-century conflict of "quantum philosophies," let us consider the celebrated two-slit effect. It is well known that light, in virtue of its wavelike nature, can form alternating light and dark interference bands after passing through narrow and closely spaced slits in an opaque screen. These bands, on analogy with what is clearly seen in the case of water waves passing through twin apertures in a barrier, have been interpreted as the result of constructive and destructive interference among light waves. When either one of the two slits is closed, the light, as would be expected, no longer forms an interference pattern. The especially intriguing thing, however, is that as long as both slits are left open the interference pattern will eventually develop, even if the light is admitted through the screen slits one photon at a time. But the very concept of the photon arose in consideration of light's discrete or particlelike aspects. How can wavelike behavior be exhibited by a particlelike entity? Feynman set the tone for much of modern reflection when he described this phenomenon as one which is "impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery."37 Now the obvious interpretation, on analogy with classical wave theory, might seem to be that light maintains its extended and wavelike nature even in its least configuration, i.e., photon by individual photon - in other words, that a single quantum does, or at least can, pass through both slits and self-interfere on its way to the recording apparatus. But note how the interference pattern is seen to develop: it is literally built up 37

The Feynman Lectures on Physics, vol. 3 (Reading, Mass., 1965), p. 1-1.

46 "particle by particle." In other words, on being recorded, light's particlelike nature is manifested, presumably in virtue of whatever quantum event was involved in the recording (e.g., chemically affecting a grain of photographic emulsion, etc.). Thus the interference pattern built up from numerous individual photon-recording events appears as a statistical accumulation of places where the photon energy has become localized (particlelike) after traveling wavelike through the slits. It may be supposed that it is the characteristics of the wave propagation that have determined the statistical distribution of wave-particle transition events; but the resulting interference pattern is not so analogous, after all, to that formed by water waves, where countless individual water particles can add and subtract. Rather, the interference pattern is discovered to be a statistical distribution of possible outcomes, each having a distinct probability, of individual photon trajectories, each of them somehow wavelike until it encounters a situation which reduces the wave to a more localized entity. There seems to be no deterministic way to describe the transition from wave to particle. Before the particle is "here" in the recording apparatus it is not "there" - since the wave aspect precludes that kind of description. Historically, de Broglie, Schrodinger, Einstein, and Bohm, inter alia, sought an interpretation whereby both particle and wave aspects could be maintained in actuality, while allowing for only one or the other to dominate a particular experimental (observational) situation. The issue was perceived to be one of causality. Einstein led the way with his conviction that a physics theory, as reflecting the way things are in the world,

47 must in principle refer to causal mechanisms.38 If an entity with obvious wave characteristics (e.g., the light passing through a slit) suddenly evidences the localized properties of a particle, it cannot be a causeless event even if the formalisms of quantum mechanics fail to identify a cause. In particular, Einstein was perturbed by the implication that an instantaneous quantum transition would exhibit acausality by violating special relativity's implication of c as a maximum velocity of transmission of causal influences. One idea, originating with de Broglie and taken up by Einstein, was that the photon (for instance) is a real particle associated with a real wave ("pilot wave," in some descriptions), which "guides" the particle on a trajectory; this dual entity could be expected to display particle and wave aspects, depending on the experimental circumstances. Since the "particle" is understood to remain unobservable until there is a particlelike interaction (at which point the wave aspect is no longer evident), this hypothesis could be regarded as the harbinger of what would later be called (in the work of Bohm and others) hidden-variables theories, characterized by the supposition that there exists an aspect of quantum reality, hidden from our observations, which determines (causally, even if unpredictably) the quantum event to one outcome and not another. But the pilotwave hypothesis encountered theoretical difficulties which prevented its wide accep-

Bohr presents a detailed account of his debate with Einstein over these matters in Paul A. Schilpp, Albert Einstein: Philosopher-Scientist (Living Philosophers, vol. 7) (La Salle, 111., 1970).

48 tance. Moreover it did not go sufficiently to the heart of the problem as Einstein conceived it. 39 The perceived acausality, and therefore incompleteness, of the quantumtheoretical description was brought into new focus in 1935 by Einstein, Podolsky and Rosen, who proposed a situation involving widely separated particles A and B having some property X, whose values for the two particles (XA, XB) must be mutually exclusive because of quantum rules governing the circumstances of the property's origin. Someone, measuring the value of XA, could thereby know, without measuring, the corresponding value ofXB. Moreover, if one decided to measure instead A's value for some conjugate property Y, again having mutually exclusive values for the two particles (YA, YB), the same situation would obtain. EPR argued that this gedankenexperiment ruled out the Copenhagen understanding of quantum reality (so called from its origins in the thought of Niels Bohr and others based in 1920s Copenhagen), whereby one determines reality through the act of measurement. If, depending on the observer's choice of measurements at A, the value of either X or Y (conjugate variables related through the uncertainty principle) could be inferred also for the unmeasured particle B - while the "choice" at A remained, in principle, uncommunicated to B, then an observer-induced "collapse of the wavefunction" (see next 39

"The hidden variable is not the pilot wave itself- that is already adequately revealed in the properties and behaviour of the wavefunction of quantum theory. It is actually the particle position that is hidden. Now we know.. .that two correlated quantum particles cannot be locally real, and so the pilot wave idea can be sustained only if we acknowledge that influences between the two particles can be communicated at speeds faster than that of light. It seems that we cannot have it both ways: either quantum theory is already complete or we must introduce non-local hidden variables which, in turn, appear to make the theory incompatible with special relativity." Baggott, The Meaning of Quantum Theory, pp. 161f.

49 section) at A, determining which one (of two) conjugate variables would be known there per the uncertainty principle, would not be applicable at B, in apparent violation of the uncertainty principle. This point can be sharpened by noting (as EPR did not) that in principle, another observer at B could decide at the same moment to measure instead the opposite property Y or X respectively, giving rise to a contradictory situation. For, on comparing notes later with the B-observer, the A-observer would be in a position to know, via inference from his own measurement of the X-value at A, particle B ' s l value, and also, through the other observer's direct measurement at B, particle B's Yvalue - in violation of the uncertainty principle without depending upon the specialrelativistic consideration. This further development of their reasoning would have strengthened the claim of EPR, that quantum mechanics' intimation of ontological indeterminacy is premature at best. Bohr's response to the EPR argument was the claim that the observer's choice of which variable to record at A precludes the possibility of recording the conjugate variable there; hence, for Bohr, the EPR objection is a non-issue because it couldn't correspond to any real experimental setup. The observation I made above, concerning the use of two observers working simultaneously, should put Bohr's own confidence on this point in a rather dim light.40

Cf. also Baggott: "I find Bohr's wording really rather vague and unconvincing. His emphasis is once again on the important role of the measuring instrument in defining the elements of reality that we can observe. Thus, setting up an apparatus to measure the position of particle A with certainty, from which we can infer the position of particle B, excludes the possibility of measuring the momentum of A and hence inferring the momentum of B. If there is no mechanical disturbance of particle B (as EPR assume), its elements of physical reality must be defined by the

50 The Copenhagen explanation of situations involving complementarity reached its apotheosis in Max Born, who rejected the physical (real) interpretation that Schrodinger had given to his own wavefunctions, relating the latter instead to the probability of finding a quantum particle in a given region. Although his idea owed something to the "pilot wave" conception of de Broglie and Einstein, Born's underlying philosophical commitment was decidedly positivist, and much of the subsequent discussion of quantum mechanics' "meaning" implicitly or explicitly entailed as much: that the formalism is no more than a description of what we can know of quantum systems the "reality" being inaccessible. The terminology of conventional quantum mechanics is laden with such notions as "superposition" (the principle by which indefinitely many realizable states, "eigenstates," are considered together, as so many probabilities constituting the wavefunction originally derived by Schrodinger), and "wavefunction collapse" (the mathematical description of the realization of one quantum state from among all the other probables, brought about - in a poorly defined manner - by the act of observation). A related and yet bizarrely different approach would be afforded by Feynman's development of quantum electrodynamics. His is a method, says Polkinghorne, identical to the traditional approach in its physical consequences, which bypasses the Schrodinger equation and proceeds directly to the calculation of probability amplitudes. It is called the path integral or sum over histories approach. To calculate ij>i [the probability amplitude or wavefunction] Feynman tells us that we should think of all the different ways in which an old-fashioned electron with classically picturable simultaneous position and momentum could nature of the measuring device we have selected for use with particle A." The Meaning of Quantum Theory, p. 101.

51 travel from the source through slit 1 and onto the specified point on the second screen. There is obviously a vast number of such possible trajectories....Feynman tells us to consider all such possibilities and to assign to each a complex probability amplitude. He is able to specify a rule for what that amplitude should be. It involves a quantity which physicists call action....[T]here is a natural number associated with any quantity of action, namely the number of h[bar] units....Feynman next gives a rule for associating a complex amplitude with this number....You then add together all the contributions from all the different paths and - hey presto! - the result is the same probability amplitude which you would have calculated by the more pedestrian procedure of solving the Schrodinger equation.... From the point of view of conventional quantum theory the electron has no trajectory; from Feynman's point of view it has every trajectory. Either way the neat classical idea of tracing a well-defined motion is lost."41 In an influential treatise on quantum theory David Bohm wrote that "we must give up the classical picture of a precisely defined spin variable associated with each atom, and replace it by our quantum concept of a potentiality, the probability of whose development is given by the wave function."42 Whatever he meant by "potentiality" in this case, he would later develop a theoretical context in which hidden variables loomed large.43 Bohm interpreted the wavefunction, as had Schrodinger, as an objectively real field, in which every real particle has a definite position and momentum; but he also introduced a "quantum potential" which governs particle motion in a way that is not dependent on distance (as is a classical potential, e.g. the gravitational field). Thus the quantum potential enters into the description of a particle's motion in a nonlocal way: "The quantum potential is the medium through which influences on distant parts of a correlated quantum system are transmitted. The measurement of some property (such as vertical polarization) of one of a pair of correlated photons instantaneously changes the quantum potential in a non-local manner, so that the other particle takes on the required properties without the need for a collapse of the wavefunction....such an instantaneous transmission cannot be exploited to send coded information, and so conflict 41

J. C. Polkinghorne, The Quantum World (Princeton, N. J., 1984), pp. 41f. Quantum Theory, p. 621. 43 In the brief account that follows my guide is Baggott, pp. 162-5. 42

52 with the postulates of special relativity might in principle be avoided....In Bohm's theory, changing the measuring device...instantaneously changes the wavefunction and hence the quantum potential: all future trajectories of quantum particles passing through the apparatus are thus predetermined. The quantum potential effectively interconnects every region of space into an inseparable whole."44 Bohm would go on to situate the "wholeness" entailed in nonlocality (i.e., instantaneous physical influence across arbitrarily large expanses of space) in a larger theory of "implicate order," the basic idea of which is that observable reality depends, for its order and causal relations, partly upon a hidden or implicate level of reality, which stands to the observable as potential to actual. Interestingly, to my knowledge Bohm did not attempt to relate this to the ancient doctrine of a potential principle common to all physical being, namely prime matter. It is worth noting how far Bohm was willing to go in his holistic ruminations, in light of what we will be saying in later chapters. Baggott summarizes: By modifying the equations of quantum field theory, he has done away with the need to invoke the existence of independent, objectively real particles. Instead, particle-like behaviour results from the convergence of waves at particular points in space. The waves repeatedly spread out and reconverge, producing 'average' particle-like properties, corresponding to the constant enfoldment and unfoldment of the wavefunction. This 'breathing' motion is governed by a super quantum potential, related to the wavefunction of the whole universe.45 If Bohm was impressed to a nearly mystical degree with the wholeness implied by hidden levels of order, Bohr and the Copenhagen theorists were no less committed to another holism, that of the observer-observed manifold. It remains to be seen whether physics can abide the danger of subjectivism attendant on either position.

Baggott, pp. 164f. Baggott, pp. 166f.

53 J. Bell's theorem and nonlocality Many physicists were more inclined to adopt the epistemologically vacant Copenhagen approach, leaving aside the question of what the wavefunction "really" signifies, than to entertain Einstein-Bohm's assumption of a hidden ontological order. In effect, there has been a greater willingness to espouse mathematical constructs which cannot be shown to correspond directly to reality, than to hypothesize real but unobservable entities.46 In furtherance of Bohm's theory, with its dependence on nonlocal physical influences, J. S. Bell developed an argument that no "local" hidden-variables theory could, in principle, give the statistical results of quantum mechanics: thus the choice becomes ineluctably one of a Copenhagen-style positivism or the rejection of locality in a "realistic" quantum physics. I will not attempt to reproduce Bell's reasoning here. Essentially, Bell's theorem states that the statistical predictions of quantum mechanics (for a given series of quantum measurements) cannot equate to the deterministic predictions of any locally-real model; this so-called Bell inequality need not obtain if and only if locality (and special relativity) are rejected.47

I find curious, as well as inconsistent, many physicists' vaunted dislike of hidden variables and ad hoc suppositions. Curious, because the value of such theoretical entities in at least pushing empirical science forward should be obvious, and inconsistent, because the "received doctrine" at any given time typically includes any number of such constructs accepted with little or no protest - one thinks, for instance, of the currently prevalent notions of "dark matter" and "dark energy" in cosmology. 47 Experiments by Alain Aspect and others, beginning in 1981, seem to verify Bell's theorem; the experiments, it should be noted, are fraught with technical difficulties. See papers by Aspect etal. in Physical Review Letters Al (1981): 460; 49 (1982): 91; 49 (1982): 1804, etc.

54 K. What is quantum physics about? Hundreds of published works will discuss its history, its benchmark experiments, its mathematical formalisms, its "deeper significance" and its titillating "weirdness," without saying just what quantum physics really is. To say that quantum theory presents the world as radically discontinuous at the most fundamental level is not definitive; there is, after all, a physics of the discrete, an atomism even, that is entirely Aristotelian, and another that is Galilean or at any rate Newtonian - nothing decisively new there. To say that quantum physics deals with probabilities (leaving aside the most extreme formulations of QED, which reify those probabilities) is not yet to distinguish it from statistical physics, though it certainly touches on an important part of the quantum-physical insight into material being. Although some see the "essence" of quantum theory in the wave-particle duality and still others in Heisenberg's uncertainty principle, it can also be said that de Broglie's was the genetic insight: light and atomic matter, and all things studied under physics, constitute a single order of being, dual in aspect and convertible, modalities analogous to raindrops and pond-ripples. From this identification the rest will be seen to follow: the complementary manifestations of continuous and discrete, according to the kind of interactions and observations being made; the probabilistic nature of our descriptions; the uncertainty relation governing the descriptions; even the correspondence between quantum-level "anomalous" behaviors and the macroscopic world with which classical physics and everyday experience is familiar.

55 But as a simple, qualitative depiction of what quantum theory is about - what distinguishes it from the physics that had gone before - 1 submit this: quantum physics is the attempt to comprehend nature at a level so basic that its potential aspect figures prominently, through changes that are substantial or quasi-substantial in character. The elements of this formulation are chosen with some care. In the last chapter I will defend it as a proper definition of the subject-matter of quantum physics; here I only briefly indicate the direction of development. Quantum physics is a physics of the very small; more precisely, the physics whose distinctive character is most prominently disclosed in the realm of the very small. Yet "smallness" as a spatial measure is not the primary criterion, though it is closely related (as a proper accident) to that which is the primary criterion of quantum phenomena as such, namely elementarity in the sense of "closeness to prime matter." At the elemental level, potentialities grounded in prime matter assume proportionately more significance than they do at higher levels of physical structure. At those higher levels, all motion or change is still "driven" by the potentiality of prime matter; but the potentiality is attenuated, so to speak - contracted or determined would be more formal terms by the "intervening" levels of structure. It will be my task to indicate why it is this prominence of the potential that gives quantum phenomena their distinctive characteristics: distinctive both in contrast to the world encountered in sensation, and in contrast to the phenomena treated in classical physics. Having glanced at all three phases of the discipline known historically by the one name, physics, it is opportune to compare them. Such a comparison can only be

56 provisional inasmuch as I have not plumbed the depths of the content and method of each phase. But at a sufficiently general level I believe we can note the following. Ancient physics was a science of motion in terms of causes inferred, at the substantial level, from the flux of accidental being. It recognized the quantitative aspects of mobile being as the subject matter of a scientia media that was properly scientific (i.e., proceeding demonstratively from true and certain principles) in its mathematical aspects, but dependent, materially speaking, on analogical (and therefore always partial) insights into natures themselves. While the scientia media was understood to have its scientific dimension in virtue of the inseparability of quantitative accidents from their underlying substances, the variability and contingency of those same accidents militated against the kind of physical certitude in quantitative analyses that was understood to obtain at the level of causal analysis strictly speaking. The rise of classical physics, on the other hand, was largely a matter of derogating from causal analysis as such (although it remained more or less implicit throughout the classical era), and of focusing on the quantitative analysis of accidental features of mobile being. Since the quantitative is only accidentally referred to substantial causes, and is indiscriminate with respect to each of them, mathematical methods could not directly reveal the causal fabric of cosmic being.48 This was a relatively minor concern as long as physics dealt with objects at higher (non-elementary) structural levels. At such

48

Thus the distinction between cause and effect is not expressed by any of the equations cited in Section C above, but only "read into" those equations; the mathematics as such describes only spatiotemporal relations. The causal ambiguity of mathematical physics is strikingly evident in the correspondence between Newtonian and Einsteinian accounts of gravitation, or, within general relativity itself, in the equivalence of gravitational and accelerative force.

57 levels the continuity afforded by subordinate "layers" of structure allowed for the discernment, if not of causes properly speaking, at least of a certain determinism evoking causality. One could describe the acceleration or specific heat or refractive index of a body with equations based on physical laws, because the body in its formal integrity was presupposed, i.e., was understood to maintain a certain coherence and permanence through space and time. The light whose velocity was measured as far back as the seventeenth century was understood to be maintaining its identity as it traveled through space, and so on. In other words, the dynamism of mobile being implied something essentially constant at a deeper level. Only this implication made any sense of mathematically expressed laws of nature. At the same time, mathematical formulas depended for their validity on having solutions which corresponded to actualizations of the mobile; there is no equation for the potential as such. Yet motion itself is an existential condition intimately bound up with potentiality and contingency. Paradoxically, then, mathematical physics is not adequate to the expression of precisely that which gives rise to its subject matter. The era of quantum physics brought scientific analysis down to the level of elemental structures where there was no longer a continuum of actual being on which to base deterministic quantitative descriptions of the changes that were occurring. The objects of physics at this level no longer exhibited trajectories in space and time that would allow for predictable behavior in accordance with mathematical formulations. Probabilities loomed large, and apparently discrete phenomena could be united only via statistical methods. Thus far the break with classical physics would seem to be deep and

58 irrevocable; but as I hope to show, what was really occurring was a confrontation, at the new levels of physical analysis, with matter's radically potential aspect - an aspect not directly amenable to quantification. Potentialities by their nature must be expressed through probabilities. But this does not imply a failure of classical physics, except in the sense that it was a partial and not a comprehensive view of nature; the very existence of the continuous, in mathematical physics, presupposed what the quantum physics would enable us to "discover": a ground of all physical dynamism, refractory to classical quantitative expression, which turns out to be none other than prime matter in the old Aristotelian sense. With the rediscovery of matter (in Aristotle's sense) we mark a return to the broader and deeper causal analysis of ancient physics, although married, so far as possible, to the mathematical understanding and technique inherited and developed from physics in the modern vein. Quantum theory, then, in so far as it is (overwhelmingly!) mathematical, partakes of the strengths and weaknesses mentioned earlier vis-a-vis the scientia media. But in so far as it acknowledges the potentiality at the heart of material being, it is poised to become more scientific in the traditional sense, rather than less so.

L. Some problem areas in quantum interpretation The present thesis is conceived as a study of matter (and, secondarily, of form) in the Aristotelian sense, with an ancillary view to showing its applicability to some topics in quantum physics. If the complete resolution of any of the quantum enigmas is a rather too ambitious undertaking, at least I hope to show that the conceptual apparatus of the

59 older philosophical approach is eminently conformable to modern physical discourse, and indeed provides an unexcelled basis for attacking those very enigmas. Having reviewed some key ideas of quantum theory, I now list five concerns as deserving special attention if my project is to show any promise: [1] wave-particle duality [2] discontinuity in quantum phenomena [3] probabilistic outcomes of quantum events [4] the uncertainty relation [5] nonlocality Of course there is a great deal more to quantum physics than is contained under these headings, but they are paradigmatic, as well as being among the major issues discussed historically. The first of them pertains especially to the substantial or quasi-substantial nature of entities at the quantum level, or to the relation between different modes of those elemental entities; the second to the formal causality underlying changes at the quantum level; and the third to the material causality underlying those changes. The fourth and fifth topics are perhaps more complex, in that they entail epistemological as well as ontological considerations; but I will suggest that they are closely related to the first. There is, of course, some overlap in the principles that must be brought to bear on each of these areas of investigation. With this in mind, I select the following aporiai for particular consideration. [1] The wave-particle duality. Gone is the classical dichotomy whereby some physical entities are reducible to waves, others to particles. Instead, entities which are evidently, or at least presumably, one in nature are found to exhibit both characteristics - and this goes for both matter and "radiant energy." Historically, this discovery began

60 with Planck's suggestion (1901) of the particulate or quantized nature of electromagnetic radiation (of course, corpuscular theories of light had been around long before this, but apparently had been laid to rest via Maxwell's electromagnetic theory), and in the 1920s found a complement in de Broglie's hypothesis about the wave nature of electrons. The wave-particle duality would become more intriguing as it was perceived that entities are only wavelike or particlelike, never both at once, and especially problematic with the growing realization that entities reveal wavelike or particlelike characteristics depending on how the observations are conducted. The aporia facing us, then, is: How can a physical being exhibit properties that are so incompatible as those of wave and particle? And, as a corollary: How can the act of observation itself determine which kind of properties are to be exhibited? [2] Discontinuity. Gone is the classical understanding that events in space and time are connected by continuous trajectories. Instead, states yield instantaneously to other states with no "in between." As a photon is released from an atom, one electron energy level with its well defined spatial characteristics yields instantaneously to another with rather different spatial characteristics, and so on. The temporal instantaneity of the transition, though not insignificant, is perhaps not as dramatic as the spatial instantaneity: one "shaped volume" is succeeded by a different one, without any process of shrinking or swelling. Nothing like this ever seems to be observed macroscopically. The aporia for us: How can there be temporal transition from one spatial condition to another, without any spatiotemporalpassage between them?

61 [3, 4] Probabilism and uncertainty. Gone is the classical worldview in which deterministic trajectories in space and time yield certitude, at least in principle, about when, where, how and what physical events will occur. There are now only probabilities about such occurrences, even if these probabilities are closely defined in a statistical sense. Moreover, it appears that events in the quantum realm are such that in so far as we determine one property - in any of those paired properties related as conjugate variables - some other property becomes less determinate (and therefore less knowable), and vice versa. Nature will not yield the entirety of itself to our probing, but only a certain maximum of information governed by the uncertainty relation. The aporiai here: How can individual physical states be realized in seemingly random fashion, given the causal influences which seem to be implied in the statistical laws by which those realizations are described? And: Why must a greater determinacy in one conjugate property render the other property less determinate? [5] Nonlocality. Gone, apparently, is the classical (Maxwell-Einstein) understanding of instantaneous action at a distance - namely, that "it cannot occur." Quantum phenomena give evidence of being correlated in ways that imply either a bizarre effect of the very act of observation upon the outcome, or instantaneous communication between parts of the quantum system itself- in a word, action at a distance or "nonlocal" action. The aporia would appear to be: How can either of these options comport with an everyday scientific realism? These problems and their like arise from the heart of quantum physics. As noted earlier, the avenues by which physicists have approached such problems vary consid-

62 erably, even if the great majority have chosen one main avenue, that of Bohr-BornFeynman et al., rather than others. We shall adopt the realistic path of an AristotelianThomistic physics, metaphysics and epistemology. In doing so we can make no room for Copenhagen-inspired reflections on quantum acausality, observer-induced realities, and entitative indeterminacy; these should be seen as rather desperate notions that evaporate in the light of a coherent philosophy of potentiality and form in nature. In the next two chapters I will present the doctrine of matter and its correlative, material form, respectively, with a view to showing its synthetic cogency. I will not explicitly address our quantum-physical topics until the final chapter, when it will be my task to apply some of the conclusions of Chapters Three and Four to the preceding aporiai. In so doing I will hope not only to point the way to a consistent understanding of "quantum reality," but also to make plausible a doctrine which, more venerable than mathematical physics as such, would be abandoned by the latter only at the cost of preparing the way for a 20th-century revolution in physics.

Chapter Three Matter Considered Philosophically

A. Introductory In the preceding chapter I traced three main conceptions of physics, highlighting their differences as I established some aporiai for the present study. But the commonality among them, in virtue of which all can lay claim to the name of "physics" despite their differences, was also evident in the comparisons; and that commonality may fairly be summed up in the phrase "science of mobile being" - which indeed is Aristotle's understanding of physics. Mobile being is that which undergoes change both accidentally and substantially, in interaction with other beings; it is what is spatiotemporal, extended, sensible. These notae are grounded in its being material - and in fact physics is often characterized, if somewhat redundantly (since everything material is dynamic), as the science of "matter in motion." But what is matter? In taking up this deceptively simple question, or the closely related one, How is material being constituted?, we are at the heart of man's coming to terms with the cosmos and with his own existence. Philosophy, historically speaking, may even be portrayed without much exaggeration as the attempt to think through matter and its implications. At its inception, the Ionian physicalists are attempting to explain all things through some unitary principle which is a "stuff," a that-from-which, that either corresponds roughly to "matter" as later formulated, or is distinguished by its very opposition to the same. 63

64 Parmenides startles us to this day with a "grand unified theory" that ignores the pressing demands of material being on our senses. For Democritus, all is matter and its negation, void; Plato, wedded to his Forms, can only introduce them as explanatory principles of cosmic being through a sort of bastardization, an imaging by way of the chora or receptacle which has so many of the characterizations that Aristotle would assign to hyle, matter properly speaking. With Aristotle and his successors over two millennia, a theory of matter as a principle that is intrinsic even while transcending the visible order takes its place at the foundations of philosophical thought - as implied in the very division of the sciences. Modern science, all but dominating the intellectual scene in the last few centuries, makes a certain conception of matter central to all else; and philosophers of the same era do not always resist the temptation to erect materialistic monisms in lieu of an authentic metaphysics. What we call matter is so fundamental that, while everyone "knows" what it is, definition proves elusive, and indeed an entire philosophical apparatus is likely to be entailed in any attempt to account for it adequately. In the post-Newtonian world mass is perhaps more meaningful than matter. Modern physics has a definition, a primordial one, for mass, but a concept of matter scarcely more refined than that of the common man. And for the physicist, mass is - in Newtonian terms - simply quantitas materiae, best regarded as a measure of resistance to acceleration, which is a feature of motion, which is a feature of bodies, which are characterized by having mass.

65 In opposition to those who, in positivist or reductionist mode, acknowledge only material being in their worldview, we must note that matter is also, and especially, apprehended in contrast to that which is its opposite. If there is no kind of being other than the material, why speak of matter at all? Why is it not synonymous with being? Yet the common experience of mankind discerns a level of being that is contraposed to matter: an order of being that is not sensible, measurable, quantifiable, spatial or even temporal - what is designated as the immaterial, or spiritual. With realities falling under this latter head my inquiry is not concerned; but they do constitute a backdrop to that inquiry In starting an investigation as deep as that into the nature of matter, we can do no better than to trace, however briefly, the historical path of the philosophers - indeed we would be suspect of hubris, of inattentiveness to the real, were we to attempt otherwise. It is not an a priori concept of matter that we seek, but that which validates the common experience of man, as confronted in and disclosed through the senses. Reflection upon the sense datum issued, eventually, in a concept of matter that, for all its elusiveness, must stand at the foundation of our thinking.

B. Physicalists and atomists The physical impulse that arose with the Ionian thinkers and continued down to the time of Aristotle is more remarkable for unity of purpose than for the diversity of its manifestations. Always the underlying concern is to explain the world of experience in terms of first principles. To explain: things are not self-proclaiming, but point inevitably beyond themselves, refusing to stand alone in our awareness. The world of experience: it

66 is that which falls within the realm of the sensible that first and always demands explanation, even if thinkers commonly discern a supra-sensible order of being, lurking behind what is seen, as well. In terms of first principles: each explanation leads to a new level of questioning, and a deeper level of explanation; the philosopher is drawn toward ever more prior principles of explanation, seeking greater unity through paucity of principle until he reaches the ne plus ultra. Aristotle, more than his master Plato, was wont to trace with care the opinions of his predecessors, as in the dialectical first books of his Physics and Metaphysics: these references now constitute a main source for the physical opinions of the earliest Greek thinkers. Aquinas also considers it worthwhile to give a summary of the history of thought concerning matter, in the very place where he is tracing the order of material causality back to God.1

1

Summa theologiae la, 44.2: "dicendum quod antiqui philosophi paulatim, et quasi pedetentim, intraverunt in cognitionem veritatis. A principio enim, quasi grossiores existentes, non existimabant esse entia nisi corpora sensibilia. Quorum qui ponebant in eis motum, non considerabant motum nisi secundum aliqua accidentia, ut puta secundum raritatem et densitatem, congregationem et segregationem. Et supponentes ipsam substantiam corporum increatam, assignabant aliquas causas huiusmodi accidentalium transmutationum, ut puta amicitiam, litem, intellectum, aut aliquid huiusmodi. Ulterius vero procedentes, distinxerunt per intellectum inter formam substantialem et materiam, quam ponebant increatam; et perceperunt transmutationem fieri in corporibus secundum formas essentiales. Quarum transmutationum quasdam causas universaliores ponebant, ut obliquum circulum, secundum Aristotelem, vel ideas, secundum Platonem. Sed considerandum est quod materia per formam contrahitur ad determinatam speciem; sicut substantia alicuius speciei per accidens ei adveniens contrahitur ad determinatum modum essendi, ut homo contrahitur per album. Utrique igitur consideraverunt ens particulari quadam consideratione, vel inquantum est hoc ens, vel inquantum est tale ens. Et sic rebus causas agentes particulares assignaverunt. Et ulterius aliqui erexerunt se ad considerandum ens inquantum est ens, et consideraverunt causam rerum, non solum secundum quod sunt haec vel talia, sed secundum quod sunt entia. Hoc igitur quod est causa rerum inquantum sunt entia, oportet esse causam rerum, non solum secundum quod sunt talia per formas accidentales, nee secundum quod sunt haec per formas substantiales, sed etiam secundum omne illud quod pertinet ad esse

67 It is noteworthy that the principles of unifying explanation invoked by the physicalists more often than not answered to a truly philosophical spirit of inquiry. Too many histories of science fail to credit the ancients with penetrating vision: but when Thales, for example, says that "all is water" he is not offering a mere story, but has reflected deeply on the constitution of things and concluded that those features of being which are most manifest in water are the principles needed to account for water, and all else. Aristotle notes that Thales made water primordial, "getting the notion perhaps from seeing that the nutriment of all things is moist." Nevertheless the earliest philosophers of nature are marked by a peculiar limitation, one signaling the difficulty of completing the transition from a sensible to an intellectual grasp of reality: their first principles tend to be either very close to the sensible order, or very far removed from it. These extremes are paradoxically related, for both, as I see it, reflect taking an "easy way out" - to see, either in certain features of sensible reality or in its simple negation, the explanans one is driven to find. To be hesitant in moving beyond the sensible, at this very threshold of philosophy, is understandable enough. But once there exists a realization that that move is called for, an outright negaillorum quocumque modo. Et sic oportet ponere etiam materiam primam creatam ab universali causa entium." Leonine edition, vol. 4, pages 457-8 (hereafter thus: Leon. 4.457-8). 2 Aristotle, Metaphysics 1.3 (983b20-24). All translations of Aristotle will be from Richard McKeon's The Basic Works of Aristotle, translated by various authors (New York: Random House, 1941). Cf. Heraclitus Homericus, Homeric Questions 22: "For moist natural substance, since it is easily formed into each different thing, is accustomed to undergo very various changes....Therefore Thales declared that water, of the four elements, was the most active, as it were, as a cause." Cited in G. S. Kirk, J. E. Raven and M. Schofield, The Presocratic Philosophers: A Critical History with a Selection of Texts, 2nd ed. (Cambridge, 1983) (hereafter KRS), p. 92. Thales may have also posited an immaterial principle, soul, based on the attractive properties of magnetic stones (cf. Aristotle, De anima, 405al9), but this has more the aspect of efficient cause.

68 tion of the sensible order will occur more readily than nuanced distinctions, as it is prior to the latter in the order of discovery. The basic element, which for Thales was "water," would be designated by Anaximenes, and again somewhat later by Diogenes of Apollonia, as "air" - infinite, eternal, and in some way divine.3 Anaximenes' contemporary Anaximander was no less monistic, if more subtle, as he said "that the principle and element is the Indefinite (apeiron), not distinguishing air or water or anything else."4 This apeiron was by no means immaterial, but simply a stuff which of itself had no specification.5 Xenophanes took up a popular idea when he reduced all mutable being to earth and water.6 Empedocles would apparently be the first to identify four "roots," presented as gods, but already understood by his contemporaries to be earth, water, air and fire.7 The impulse toward recognizing a plurality of elements is easily understood; unity of itself cannot give rise to plurality. For Anaxagoras there will be no warrant for either a single element or any finite number of them: every kind of cosmic being is represented in kind at the elemental level, the elemental particles themselves being so fine as to be indiscernible on their own, but constituting the various kinds of being when they come together in sufficient

3

KRS, p. 598. *KRS,p. 100. 5 KRS, p. 110. 6 KRS, p. 176; cf. Iliad 7.99. 7 KRS, p. 286.

69 numbers, being more or less "sifted" from those of unlike kind: all things have a portion of everything.8 In the atomism of Leucippus and Democritus, the elementary particles are no longer distinguished as to kind, but quantitatively: they are infinitely varied in shape and size, as well as in arrangement and position.9 In contrast to the material preoccupations mentioned thus far were the emphases placed upon form or structure by some thinkers. Heraclitus, though recognizing three elements (fire, water or "sea," and earth - with fire clearly being given a primal role), is above all attentive to the logos or formal arrangement of things.10 The composition and decomposition that is characteristic of everything in the cosmos is an arrangement and re-arrangement of opposing principles, made possible only by the divinely unifying logos. Pythagoras and his followers seem to have displaced material considerations even more completely in their mystagogic focus upon number and harmony in all things. Parmenides likewise will have no use for a "stuff in any material sense. Like Pythagoras, he offers no natural philosophy to speak of; he wrests the observed world of change to an intellectual standstill by insisting on the unity of all being, and a consequent skepticism as to the evidence of the senses: "light" and "dark," though introduced as cosmic elements, are but inventions to save the appearances; they belong only to the realm of mortal opinion.11

8 9

KRS, p. 358. £itf,pp.414f.

10 n

KRS, pp. 198f. KRS, pp. 255-1.

70 An important development, perhaps first introduced by Melissus, and made central in the thought of Leucippus and Democritus, is that of void. As a non-entitative principle, void not only seemed to resolve a problem concerning the possibility of movement in a plenum, but constituted, at the metaphysical level, a principle of plurality in being that would not be liable to the charge of infinite regress (if being A specifies or individuates being B, what specifies or individuates being AT), and allowed for maintaining the fundamental unity of being as such.12 In this brief survey of physical principles before Plato we should mention also the varied roles occasionally played by an agent principle. Implicitly or explicitly associated with divine activity in several of these early thinkers, the role would be expressly assigned to principles of "condensation and rarefaction" by Anaximenes, "strife" by Heraclitus, "love and strife" by Empedocles. In Democritus the principle of activity is scarcely distinguished from the subject particles themselves, being reduced to properties (weight, shape) which of themselves engender perpetual motion. In summary, pre-Socratic thinkers tried to identify one or more material principles, in relatively few instances supported by more formal considerations, and but seldom juxtaposed with a principle of motion distinct from the material principle itself. When such a motive principle is intrinsic, it is not distinguished from the actuality of the material component as such. The unifying principles sought by the physicalists tended to be material in the sense that they constituted simply the "stuff of the uni12

Although this reification of nonbeing, assigning to "nothing" distinct features such as spatiality and dimension, would not withstand the critique of Aristotle, it would remain very much a part of the thought of so great a physicist as Newton.

71 verse, in no further need of formal principles distinct from the stuff itself. "Of the first philosophers, then, most thought the principles which were of the nature of matter were the only principles of all things....and therefore they think nothing is either generated or destroyed, since this sort of entity is always conserved.... Yet they do not all agree as to the number and the nature of these principles."13 The being of the elements is always conceived, though not of course articulated, only as actual, even if indeterminately so.

C. Plato's chora With Socrates and Plato the emphasis of philosophy shifts to the ethical and political, and natural philosophy recedes well into the background. But Plato, in Timaeus, does devote considerable speculation to the principle of cosmic being, even if it is distinctly metaphysical in tone (as well as being couched in the mythical language that Plato reserves for the most difficult and obscure areas of philosophic inquiry). I submit that his analysis of mobile being anticipates Aristotle's to a greater extent than is often granted.14 Everything that comes to be is a copy of its maker's own goodness and perfection: this is "the supremely valid principle of becoming and of the order of the world" (29E). This work of Reason, of intelligibility - the burden of the first main part of Timaeus' discourse, 29D-47E - is characterized by goodness, which entails generosity (freedom from jealousy) and therefore freedom. 13

Aristotle, Metaphysics 1.3, 983b6-20. Of course, it may make more sense to say that Aristotle drew more upon his own master's thought in this regard than is commonly recognized - or than was even acknowledged by Aristotle himself. 14

72 The second main part (47E-69A) deals with the contrasting principle of Necessity, which is opposed to freedom (and hence, it would seem, to goodness). As J. Sallis has observed, the "new beginning" in which Timaeus ventures to discourse upon a second kind of things, those which involve necessity, is heralded by the term chalepon "severe, difficult, troublesome, even dangerous."15 This difficulty is indicated variously in the almost faltering pages that ensue: in the wide range of metaphors that are used to circumlocute the chora, the principle of necessity, itself; in the designation of the kind of discourse as illegitimate, "bastard"; and in the remarkable hesitation over entering upon the discourse itself (48A-E). At first one might suppose Necessity, that which is juxtaposed with Reason, to be "that which cannot be other than it is," but it soon becomes clear that the opposite is somehow the case: necessity is what can only be other than it is, nothing at all in its own right, an entity in flux, or rather a manifestation, and as such wholly subordinate and passive in relation to what is manifested. The necessity is one of complete nondetermination, contraposed, in other words, to the freedom whereby the Good communicates or participates itself as it wishes. What is first introduced in terms of necessity is also denoted, from the beginning of this new phase of the discourse (48 A), as the Errant Cause. I believe this means simply that what is clearly a "cause," in the sense of being a sine qua non of cosmogenesis, is at the same time infinitely malleable, determinable: involving in some sense the possibility of Form-manifestation, it is nonetheless devoid of any influence upon the suc15

John Sallis, Chorology: On Beginning in Plato's Timaeus (Bloomington, Ind., 1999), p. 12.

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cession of Forms in themselves. Inquiring more deeply into this mysterious passivity, Plato begins with a series of metaphors which depict "a form difficult and obscure," which "more than anything else...is the Receptacle (hypodoche) - as it were, the Nurse - of all Becoming" (49A). The "elements" as cognized by his predecessors cannot comprise the deepest principles of cosmic being. They cannot be identified with any sensible substances, every single one of which is manifestly in constant flux; rather, the socalled elements appear to be but qualities of a substratum. "Receptacle" suggests, of course, the passivity which we have already assigned to the order of things-becoming, and this is corroborated by a number of the images that will follow. But "nurse" may seem anomalous. Why would Plato resort to an image that hardly seems primordial enough to do duty as a metaphysical arche, even in metaphor? I hypothesize that the image of the nurse - and specifically of the wet-nurse, with its connotations of nourishing (and so enabling) life while not actually bringing it forth (the prerogative of the mother) - is well suited to depicting a principle which, although a sine qua non of formmanifestation, remains powerless to bestow the formal likeness in question. Plato then likens the substrate successively to gold, fashionable into infinitely varied shapes; to a mother, whose reception of the paternal likeness gives rise to his offspring; to the neutral base used by parfumiers; and to the shapeless wax which receives all shapes (50B-51A). Finally, having reiterated that "we shall not be deceived if we call it a nature invisible and characterless, all-receiving, partaking in some very puzzling way of the intelligible and very hard to apprehend" (5 IB), Plato introduces the notion of the chora, a word which can be variously translated but for which "space" is a good

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first approximation. The chora is everlasting, not admitting of destruction, providing a situation for all things that come into being, itself apprehended without the senses by a sort of bastard reasoning, scarcely an object even of opinion (51E-52B). It is further likened to what we behold in a dream, where place is not really place - not a thing, nor yet nothing. What precisely is this choral Some commentators would equate it with the space of everyday experience, or that in which mathematical entities are posited; but this is too facile. Would such a space really tax Timaeus's powers of understanding and articulation to the utmost? Would it call forth such repeated warnings of difficulty, not to mention his metaphor of beholding-in-a-dream? Plato wants to employ the image of space for what it is worth, but it remains only an image. Chora designates primarily not just space, but space as that in which something occurs, or is brought about. There must be a principle of that impermanence that distinguishes cosmic being from the eternal Forms. But what distinguishes the impermanent from the permanent is simply the negation of the permanent's permanence. The Receptacle, it seems to me, is posited as the principle of negation of the permanence of the Forms - the negation, not of the permanence of the Forms of course, but of the permanence of the Forms-asmanifest. Since Plato evidently considers three to be a sufficient enumeration of primordial ontological principles, this principle of negation must be none other than the principle of manifestation itself. It is precisely in the manifesting of the Forms that the aspect of impermanence enters ineluctably: it is precisely the being-received, the "receivedness," of the Forms that constitutes their likenesses or appearances in the sensible order.

75 If we look for a common meaning in all of Timaeus's metaphors for the Receptacle, it is not hard to identify this as mutability. Mutability or impermanence is characteristic of a recipient, inasmuch as what is merely passive cannot "hold on" to any determination, but is "errant," subject to the activity of whatever is received. We can discern, in the hypodoche of Timaeus, a differentiating principle that is indeed relative nonbeing - having no positive explanation in terms of our discourse, which is immersed in the order of being-becoming. To say that the not-formness of the Forms, or the impermanence of the permanent, is what constitutes the "third kind" in Timaeus's cosmology, is to say that we are at the limit of intelligible discourse altogether. It is not merely because Plato's Timaeus has brought us to the threshold of intelligibility that the discussion of the chora is fraught with elusive and metaphorical language. That threshold is the meeting-point of a certain kind of being and non-being. Underneath all appearances - in some way constitutive o/all appearances - is a negation of that which appears.

D. Aristotle: Physics and Metaphysics As noted above, the pre-Socratic physical thinkers, while animated by a search for unity of underlying principle, generally failed to make a crucial distinction within that realm of being that they sought to explain: their principles, however concrete or abstract in concept, were in every case either actual (i.e., no less actual than that to which they stood as principles), or an absolute negation of that actuality (cf. the void of the atomists). Opposed to these variants on the physicalist theme were the "escape routes" of the metaphysicians: Parmenides especially, and - more subtly - Plato himself. I include

76 Plato here in so far as his emphasis on the reality of the supra-sensible order, and even his resorting to myth in such works as the Timaeus, impede his analysis of nature properly speaking. Nevertheless, as we have seen, his presentation of the obscure, unintelligible yet (almost) intrinsic nature of the chora places him well beyond the earlier thinkers. In a word, Plato offers a distinction between levels or grades of reality that marks a crucial new sophistication on the way to Aristotle. It is Aristotle whose relentless analysis, first of changes in being and then of being itself, will result in a fully articulated understanding of matter as a principle of the real, rather than a being in its own right. Yet this principle is located solidly in the heart of being, as truly constitutive of it: matter enters into a real ontological composition, rather than occasioning a mere imaging or manifestation of the real. The notion of matter which enters Aristotle's philosophy by the twofold route of physics and metaphysics (thereafter to permeate much of his thinking in one analogical guise or another) serves to distinguish the three great realms of scientific thought (episteme) according to their objects and the way in which those objects are known: physics, mathematics, and metaphysics. He could not have so confidently distinguished among these domains, in a way that his predecessors never did, without discerning the role of matter in its radical primacy, as constituting the difference between the human intellect, with its ordering to being as such, and cosmic flux, the appearing and disappearing of being, in which our corporeal nature also shares. Despite, or rather because of, the very fundamental role played by the Aristotelian doctrine of matter, authentic expression of that doctrine has been controverted al-

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most from the beginning. Perhaps no feature of Aristotle's physics and metaphysics is more revolutionary with respect to his own intellectual antecedents, or more charged with implications for the rest of philosophy. In identifying matter as an ultimate substrate, beyond the threshold of being itself so to speak, Aristotle brings us to the limit of intelligibility. Devoid of nearly all the positive characteristics that its analogues had enjoyed in the thought of his predecessors (Plato's chora being the notable exception), matter as conceived by Aristotle would nonetheless enter deeply into his metaphysical fabric - to say nothing of its role in the posterior sciences, which treat of material being specifically. I now summarize the presentation of matter in two of Aristotle's works, the Physics and Metaphysics. (His further treatment of this topic in On generation and corruption and On heaven and earth is occasionally more lucid, but adds nothing substantially different.) In Book I of the Physics, Aristotle, reviewing the cosmic principles postulated by his predecessors, rejects them one by one on his way to the dialectical conclusion that the principles of mobile (changing) being must be plural but not infinite (Chapters 3, 4), must be contraries (Chapter 5), and need not be more than three in number (Chapter 6). His reasoning, in a nutshell, is that a mere pairing of principles, one acting on the other, would seem to yield nothing more than an opposition from which no new thing could issue. But to invoke more than three principles, on the other hand, is to multiply

78 principles needlessly, and indeed to multiply contrarieties in a manner inconsonant with the unicity of the genus of substance.16 He argues, then, that a thing which changes or "becomes something else" is commonly understood in one sense to perdure through the change, and in another sense not.17 In the case of an accidental change it is apparent that the substance remains while one accident succeeds another.18 But even substantial changes require, by analogical inference, a substrate.19 This is a crucial point whose proof is left to the Metaphysics,20 but which is indicated in the Physics by reference to the instance of plants and animals coming from "seed." (What Aristotle has in mind here, apparently, is seed as being substantially different from the developed organism: perhaps in the sense of "sperm" rather than "embryo.") Paramount in Aristotle's analysis is the distinction between primary and secondary matter: these are only analogically related, the latter being informed matter and to that extent radically distinct from primary matter, which is utterly formless. The inference to prime matter is what sets Aristotle firmly in opposition to his forbears who, although preoccupied - we may even say to excess - with what Aristotle will call the material cause, nevertheless do not proceed beyond what, for Aristotle, must remain secondary in so far as it is already possessed of formal characteristics.

Physics 189b 16-26. 190a9-13. 190a31ff. 190M-5. Book VII (see 1029al0-25).

79 What appears to be the impulse behind Aristotle's analogical reasoning, though nowhere made explicit, is a refusal to countenance substantial change as no more than successive moments of creation and annihilation (entailing no substrate). Although we might speculate as to his motivation, in the context of an apparent conviction of both the eternity of the world and the analogical continuity of all cosmic being, speculation it must remain. It is at least curious that he is so reticent on the point. Aristotle acknowledges that earlier thinkers were right in denying that anything can come from sheer nonbeing. But where the physicalists and atomists only conceive of "being" under one or another aspect, however elementary (an aspect always actual, though of course they do not denote it thus) - such that every cosmic being is understood to arise only from pre-existent being - Aristotle posited a qualified nonbeing, and this in two key senses, matter and privation.21 First there is a purely potential principle of being which is matter - a ground devoid of actuality, incapable of existence in its own right, yet a factor in existent being, and necessary as a principle of continuity (that is, if change is not to be conceived as a process ex nihild). Having posited matter as the substrate or ground of continuity in change, Aristotle notes that this is not one of the "contraries" demanded by his earlier analysis: these are, rather, form and privation (Chapter 7). Form is the principle of specificity and intelligibility, the "whatness" of an existent. It is the principle which terminates every process of change, but is immutable in and of itself (Aristotle shares Plato's deep conviction 21

Physics 192a2-34.

80

that cosmic becoming is refractory to intelligibility). Along with matter, form is a positive principle of motion since its real presence in the mobile is a per se cause of mobility. But matter cannot be one of the contrary principles required by motion, because it perdures. The principle which stands as contrary to form, the terminus ad quern of motion considered precisely as not present in the mobile, is of the formal order though not actualized, and is called privation?2 Privation is specified non-being, the specification of matter's potentiality, arising in virtue of a. present form, but in the matter. It is the absence of a certain form which, as all our experience of change testifies, "directs" change in one course rather than another. (In the acorn is a negation of everything except acornness; but a privation only of oakness.) Aware that his introduction of both matter (as a principle of receptivity to form) and privation (as a specific principle of the nonexistence of form) marks a decisive break with his precursors, Aristotle is at pains to distinguish the two (Chapter 9). Whereas privation is by definition non-being (with respect to a particular form), matter is by definition a receptivity to form.23 These principles, it is worth noting, are paradoxically similar and dissimilar. Neither can be identified v/ith form as a present actuality; but while privation differs from form in being not present, matter differs from form in being not actual. How, then, can Aristotle go on to say that matter, but not privation, is a positive principle, and even in a sense the substance?24

190b23. 192a2-6. 192a5.

81 Matter, although opposed to actuality, is nevertheless a constituent of actual or existent being, while privation is not. To say that matter is not actual is not to deprive it of all hold on reality: it is a real lack of a certain actuality, which is to say a potentiality, in the concrete existent, nor as such is it incompatible with form as the present actuality. Actuality as such does not preclude receptivity to further actuality, and such receptivity as constituent principle is what Aristotle means by matter. Although privation shares with the form the note of formality, of being a "what," it is one in subject with matter.25 The material principle is, in its own right, a receptivity; but its receptivity is with respect to a form - more particularly, the form referred to under the aspect of privation. It is not form which has the inclination to be replaced by other form; nothing in form's intelligibility implies this; rather, it is matter which "desires the form".26 Hence privation is "in" a subject which is identified as matter. The Aristotelian analysis of change in terms of matter and privation, act and potency, is presented in the context of resolving the impasse into which physical speculation had hitherto been led; all the quandaries of earlier thinkers concerning the roles of being and nonbeing in change or coming-to-be are dispensed with, through Aristotle's recognition of qualified nonbeing. "It was through failure to make this distinction [between absolute and relative non-being] that those thinkers gave the matter up, and

190b23ff. 192al7-24.

82 through this error that they went so much farther astray as to suppose that nothing else comes to be or exists apart from Being itself, thus doing away with all becoming."27 Since matter is the ultimate substrate, it cannot have come into being, nor can it pass out of being, since its nature is precisely to be ultimate, i.e., to presuppose no further subject in which to inhere. But without a subject (here we again note Aristotle's non-consideration of the creation / annihilation alternative), there is no coming-to-be.28 In Book II of the Physics Aristotle identifies matter as one of the four causes two intrinsic (material and formal cause) and two extrinsic (efficient and final cause). Further, having shown that all motion, even that occurring "by chance," is for an end, he shows that there is a necessity in the mobile but this necessity is not that of the end; rather, the principle of necessity is identified with matter itself.29 This may seem strange for a principle of indeterminate receptivity, but the necessity Aristotle refers to is only a conditional or hypothetical necessity: given such and such an end, then such and such will be necessitated with respect to the matter. (The bell need not come into being, but if it is coming to be, then bronze is indispensable.) Broadly stated: matter is necessary for any change whatever, but the nature of the change is not determined by the matter, but by other causes, primarily the final cause. The discussion of necessity in reference to matter is evocative of the necessitarianism of several earlier philosophers, as well as that necessity associated by Plato with

191M0-13. 192a25-34. 200al5.

83

the chora. The relation of necessity to matter's ratio as substrate will be evident: if no substrate, then no motion or change. In Book III Aristotle defines motion as "the act of the potential as potential."30 He acknowledges the difficulty of this formulation, a difficulty that arises from its primordiality - it is concerned with what is barely actual. Motion clearly involves both actuality and potentiality; it is neither potentiality alone, which is prior to motion (as terminus a quo), nor actuality alone, which is posterior to motion (as terminus ad quern). To speak only of "the act of the potential" - except, as Aristotle occasionally uses it, as a shorthand expression for "act of the potential as potential" - would be inadequate. For, in the cosmic order, every act presupposes a potentiality, and every potentiality is so with respect to some act: so that every hylomorphic being is "the act of a potential." Thus far only stasis is indicated, but we want to express the dynamism of motion. Bearing in mind that motion is from one state of being to another, i.e., from one form/matter composite to another (whether this transition be at the substantial or the accidental level), we discern in mobile being both a potentiality (in virtue of its material principle) and an actuality (in virtue of its formal principle). It is the dynamism which such a being possesses with respect to further information that Aristotle seeks to convey by "potential as potential." There is certainly ambiguity, especially in the English. A fuller expression of his meaning would be "actuality of the potential to be what is po-

201al0; Hardie and Gaye's "fulfilment of what exists potentially, in so far as it exists potentially" (McKeon ed., p. 254) reads too much into the Aristotelian text. Cf. 202a7.

84 tential," taking "potential" in the first usage with a purely existential connotation, and in the second usage as entitative.31 Language is being strained, to be sure, but we should expect no less. What is actual in motion is the ability-to-be of what is not (yet). What the definition seeks to convey is a state midway between potency and act, using only "potency" and "act" as suitably prior elements of the definition. What characterizes motion is that it is neither merely potential, nor fully actual, in terms of that to which it tends. Eliminate either aspect, and one no longer has motion. One of the difficulties in grasping the definition is that the notion of end, which is altogether extrinsic to the mobile (considered hie et nunc), is indispensable to the definition: it is implied in the notion of "potential" (as that term first appears in the definition). It is only with respect to an end, a "toward which," that potentiality can be understood. Aristotle seems to express this role of the final cause in a word of his own coinage, entelecheia, which is used synonymously with energeia to connote what we are calling "actuality." The roots of the word indicate "holding the end," which I take to mean "existing with respect to the end." What is the role of matter with respect to motion? Matter is the intrinsic source of the mobile's potentiality, but is not itself a per se moving cause. As Aristotle shows immediately after presenting the definition of motion (Chapter 3), motion does not occur except through the agency of an extrinsic mover (efficient cause). This agency in

31

In an "existential" formulation there is less ambiguity: "existence of the existibility of the existible." Or again, "the be-ing of the can be of what can be."

85 turn is only in virtue of an end; so all four causes must be brought in, in a full account of motion. There is a correlation between the agent and material causes: the cause of motion can only operate in virtue of a receptivity to its operation. Is material being necessarily mobile, in Aristotle's conception? Considering matter alone - despite the nature of matter as potency - it would seem not. This is due to the need of an actuating or efficient cause in motion. Of course the analysis of mobile being in the Physics is just that, an investigation into being as mobile, so we would not expect it to address being in a way not involving motion. We do not find, nor is it meaningful to conceptualize, any "material being" within the physical realm that has no extrinsic cause, actuating matter's potency.32 It will remain for metaphysics to address matter as a principle of being, rather than becoming. In Metaphysics Book III, Aristotle places matter squarely among those things whose investigation belongs to a science of being as such.33 All the theories of the preSocratics, down to that of his own teacher Plato, are here put in question: are cosmic existents composite, or not? Is there an order of causality beyond that of brute matter (in the sense of the element, or elements)? Aristotle will situate his discussion of matter in the context of discerning the fourfold causal fabric of the universe, a fabric considerably more intricate than hitherto supposed. In Book V, the Lexicon, he presents the notions of matter as cause (Chapter

See further remarks on this topic in Appendix 3. 995b4-996a4.

86 2), as natural principle (Chapter 4), as substance (Chapter 8), as potency (Chapter 12),34 and as "that from which" (Chapter 24). Although, in Metaphysics Book VII, he is commencing an inquiry into being as such - having already, in the last book of the Physics, concluded to the existence of an order of being transcending matter and mobility - Aristotle nonetheless anchors even his metaphysical investigation in the data that are best known to us, i.e. in the realm of material substances.35 The sensible substances all contain matter.36 A consideration of "substance" indicates that of four (or more) senses in which the term is applied, "substrate" (hypokeimenon) is prior to the others (ousia, kath' auto, genos); but substrate in turn can be resolved into substrate proper (hyle), form (morphe), and the combination of these two.37 A straightforward analysis of how we commonly understand, and therefore speak of, beings discloses the primordiality of hyle: "When all else is stripped off evidently nothing but matter remains.. ..By matter I mean that which in itself is neither a particular thing nor of a certain quantity nor assigned to any of the other categories by which being is determined. For there is something of which each of these is predicated, whose

34

See 1019al 5-20. Thus it is bodies to which substance "is thought to belong most obviously" (1028b8-9); "Some of the sensible substances are generally admitted to be substances, so that we must look first among these....For learning proceeds for all in this way - through that which is less knowable by nature to that which is more knowable" (1029a35-b 5). 36 1042a25-27. 37 1029a3-4. 35

87

being is different from that of each of the predicates (for the predicates other than substance are predicated of substance, while substance is predicated of matter)."38 Where the analysis of mobile being as mobile had pointed, by way of analogy, to a material substrate as preserving the observed continuity in cosmic change, against an (unintelligible) creation/annihilation, it is now the consideration of mobile being as being which entails, by the way of predication, a material substrate as ne plus ultra of our understanding. (Note that the two approaches are related: predication supposes a knowledge of cosmic being which is gained, ultimately, through abstraction from the conditions of mobility, as the mind moves from the level of sensation to properly intellectual knowing.) Matter, having appeared in an ultimate role in the deepening search for what is first, turns out not to be the "ultimate substance" since it lacks, by virtue of its sheer indeterminacy, the "separability and 'thisness' [which] are thought to belong especially to substance."39 Analysis per viam predicationis has taken us too far, in view of Aristotle's express aim in Book Z. "[A]ll things produced either by nature or by art have matter; for each of them is capable both of being and of not being, and this capacity is the matter in each."40 Again, "by matter I mean that which, not being a 'this' actually, is potentially a 'this'." 41 These

38

1029al3-14, 20-24. Aristotle, here as elsewhere, is not indulging in an "analytical" exercise in the modern sense, beyond what is entailed in the recognition that all our knowledge of the world is our knowledge. The universal apprehensions of mankind are indispensable in attaining to a properly human and communicable episteme. 39 1029a27-28. 40 1032a20-22. 41 1042a27-28.

88 are key texts in any understanding of Aristotle's doctrine of matter. Not only is matter that which perdures through change, securing continuity; it is the very possibility of change, the potency to newness-in-being. This note of potency emerges directly neither from the analysis of change, nor from the analysis of predication. How is matter's character as existential potency inferred? It is through a complete analysis of mobile being as involving extrinsic no less than intrinsic causes. Nothing moves itself, whence there must be efficient or agent causality; and no agent cause acts but for an end, as evidenced in the directedness of every change. End-directedness in mobile being (which is so universal as not to be absent even in "chance" events) is due primarily to extrinsic factors, but entails an intrinsic coprinciple as well: the activity of the agent implies the passivity, the ability to be acted upon, of a patient. Now Aristotle explicitly denies that the potentiality of matter, dynamis, can be unity: "of the things that are thought to be substances, most are only potencies [dynameis] - both the parts of animals (for none of them exists separately; and when they are separated, then too they exist, all of them, merely as matter), and earth and fire and air."42 He notes also that since "'unity' is used like the term 'being', and the substance of that which is one is one, and things whose substance is numerically one are numerically one, evidently neither unity nor being can be the substance of things."43 But - and here is Aristotle's key insight - where logical circularity forbids that the principle of

1040b5-8. 1040b16-19.

89 substantial unity should itself be a unity, dynamis is not being but a potency to being, and precisely as such not a unity but a potency to unity. What Aristotle discerns, through mobile being, is that a "can be" coexists with what "is." Privation of form alone is not a cause of change, since a non-existent form cannot be a source of activity. This is why Aristotle calls privation a principle only per accidens, and not a cause. But matter, "the possibility to be and not to be," is a dynamic tendency toward otherness in the existing being. Privation is a specification of that otherness, hence of the formal order; matter is the possibility of privation's realization. And while matter is completely indeterminate in itself, it is always conjoined with form, whereby its potentiality is specified to this or that privative form. In making "another fresh start" on the problem of what is meant by "substance" (ousia), Aristotle says that "clearly the question is why the matter is some definite thing."44 Why does he frame the question in this way, taking matter for granted, as it were? The approach by way of removing predicates left him with a principle described as "nothing . . . unless there is something bounded [by quantities alone],"45 as substance-candidate. But if matter cannot be substance properly speaking, as noted above, Aristotle's analysis of physical substance in Metaphysics VII.7-9, echoing in many respects the treatment in Physics II, makes it clear that matter is the existential possibility of form, and whatever realizes this mere potency of the substrate will be substance in

1041b5-6; cf. 1041a28-33. 1029al8.

90 the primary sense. "Thus what we are seeking is the cause [i.e., the form] in virtue of which the matter is a definite thing; and this is the substance of the thing."46 A "definite thing": this implies unity, the unity of "separability and individuality," and Aristotle will at once begin to speak of "that which is compounded...so that the whole is one, not like a heap but like a syllable."47 Moving beyond the quantitativeconfiguration accounts of substance which his Eleatic predecessors had offered (and which the atomistic reductionism of our own era too often embraces), but which proved incapable of explaining the true unity of composite being, Aristotle uses the analogy of something better known to us, the constitution of a syllable out of its letters. The point is, of course, that a syllable as such transcends its material elements (letters) to constitute a unity defined by a particular telos (intelligible communication). That the combination of multiple letters and more besides (a formal principle) should add up to a unity does violence to a naive conception. Only the relative nonbeing of material parts considered as dynameis saves Aristotle from contradiction, and saves natural philosophy from the contradictions and inadequacies that had burdened it thus far. None of this is to suggest that form and matter are entities somehow melded together. Form has been adduced by Aristotle as the very unifying of the matter,48 a matter whose actual (formal) multiplicity at a lower of level of being serves as a mere potency to higher actual unity. The insight which Plato and the materialist reductionists had failed to arrive at is this: with respect to being X, the constituent parts, metaphysi46 1041b8-9. 47 1041M2-13. 48

1041M-12.

91 cally speaking, are only in potency thereto. Actual unity is composed of a plurality of principles having no actuality in their own right.49 Relative non-being must be recognized in order that the unity of being itself be preserved; the alternatives, expressed all too clearly by Heraclitus, Parmenides, and even Plato, only replace a difficult concept with an impossible one.

E. Neoplatonic commentators Between the epoch of Aristotle and that of his rediscovery in thirteenth-century Europe, the main developments in the consideration of matter were at the hands of the Neoplatonists, especially Simplicius and John Philoponus, whose views I will here take as representative.50 Inasmuch as Neoplatonic thought is characterized by a conflation of Aristotelian and Platonic perspectives, it will not be surprising that, in their commentaries on Aristotle's treatment of prime matter, Simplicius and Philoponus are largely occupied with ideas of extension and spatiality, the latter being a chief connotation of the Platonic chora. But how much foundation is there in the Aristotelian corpus for assigning such notes to matter? Almost none, except the rather obscure passage in Metaphysics VII (Z), concerned with the mind's attainment of prime matter through the removal

This applies to form no less than matter, though the point is often overlooked. Apart from its materiation, form has no existence a la Plato; form, though it can be apprehended apart from matter, may be thought of metaphysically (not physically) as a potency to existence. This will be made clearer in the thought of Aquinas. 50 A good overview and analysis, and my guide in what follows, is Richard Sorabji, Matter, Space and Motion: Theories in Antiquity and their Sequel (London, 1988).

92 of predicates: "when length and breadth and depth are taken away we see nothing left unless there is something bounded by these."51 Notwithstanding the paucity of references in Aristotle, Simplicius developed, in his Commentary on the Physics, a theory of prime matter as indefinite extension (diastema aoristori).52 As we have seen, Aristotle observed in Physics IV.2, when discussing the nature of place, that if place were identified with the extension of a thing's magnitude (rather than with the magnitude itself, as a delimitation), then place would be matter. "Matter or the indeterminate is of this nature; when the boundary and attributes of a sphere are taken away, nothing but the matter is left."53 Aristotle is on his way here to the conclusion that place cannot be matter (or form); the context clearly suggests that Aristotle is only referring to a conceptual removal of attributes, not ascribing an ontological priority to matter. (As Sorabji notes, Aristotle may not even be going this far, if the phrase here translated "of this nature" denotes only a likeness.)54 Where prime matter is understood by some other Neoplatonists to be without magnitude (magnitude being an accident rather than pertaining to a subject), and therefore without extension,55 Simplicius says prime matter can be construed as extension without definite magnitude - rather than as a substrate underlying extension itself. We will see that Aquinas's own account of matter as ground of dimensive quantity is midway between these conceptions. 51

1029al6-18. cf. Sorabji, Matter, Space and Motion, p. 21. 53 209b9-10. 54 Sorabji, Matter, Space and Motion, p. 9. 55 Cf. Sorabji, p. 10. 52

93 It is perhaps startling that Simplicius should think to erect an interpretation so little justified by Aristotle's numerous other references to matter, upon a text in which Aristotle is manifestly describing a view not his own. "In so far as place is thought [i.e., by some thinkers other than Aristotle himself!] to be the extension of a magnitude, it is matter. For the extension is distinct from [i.e., prior to] the magnitude; it is embraced and made definite by form, for example by a surface and a perimeter. And that is what matter and indefinite things are like. For when . . . nothing is left except matter."56 Even if "are like" denotes "of the same nature" unequivocally, the natural reading of the passage is to understand "matter" as referring to the intelligible matter of mathematicals, which for Aristotle is only posited in the mind. Substantial form, it is abundantly clear elsewhere in Aristotle, is much more than what extension "is embraced and made definite by." As Sorabji points out, Simplicius's commentary on the Metaphysics is lost, and what we have of his writing on matter as extension is based (tenuously) on Physics IV. 2. In Philoponus, on the other hand, we have a Neoplatonic attempt to construe Aristotle as equating extension and matter in Metaphysics VII. 3. His views developed considerably over his lifetime; early on, he held that quantity, constituted by the three dimensions, is the first thing to inhere in prime matter (making extended matter a "second subject," the recipient of all further accidents).57 Later, however, Philoponus, still apparently basing himself on that text in the Metaphysics, regards prime matter (the "first

Cited in Sorabji, pp. 9f. Sorabji, p. 24.

94 subject") as already three-dimensional - albeit indefinitely so, thus coming into substantial agreement with Simplicius.58 To expressly bring the idea of dimensionality or extension into juxtaposition with the primal notion of matter's potency was a significant step on the part of these thinkers, and constitutes, may we say, a tribute to the insight of Plato himself - an insight which, albeit transformed, will not disappear altogether from the Thomistic doctrine of matter in relation to quantity.

F. Aquinas's conception of matter A cursory examination (with the help of Busa's Index Thomisticus) of the more than 300 references to materia prima (prima materia) in Aquinas's writings turns up a wide array of conceptions, attributes, nuances. On the one hand this should not be surprising: if substantial or prime matter, as we have seen, is indeed a first principle of all cosmic being, why should we not expect to find it being alluded to under a variety ofrationesl On the other hand, its very status as primordial, as standing at the threshold of transcendence, implies that we should be able to predicate nothing of it in direct fashion. Thus we find considerable diversity in the Thomistic discourse on prime matter, a diversity grounded in matter's cosmic primacy - such that all aspects of physical being can be referred ultimately to the primal material principle. At the same time, all discourse on prime matter proceeds by way of analogy and negation, indirectly, in terms of matter's co-principle, form. 58

See Sorabji, pp. 29f.

95 The diversity of allusions to prime matter in Aquinas poses a challenge to the philosopher, for whom unity must ever be a sign of understanding and of truth. Until these diverse references can be brought together under a unified conception, ordered in an intelligible sequence, we cannot yet claim to have invested "prime matter" with a sufficiently fundamental meaning. It will be part of my task to collate the different rationes of prime matter in Aquinas and to show their relationship in terms of priority and posteriority - in other words, to outline a coherent Thomistic doctrine of matter as a first principle of physical and sensible being. I begin with a condensed survey of Thomistic references, to indicate the scope of his thought. For Aquinas (the remarkable consistency of whose doctrine, across the 18-year of span of his writing, is well established), prime matter is what must underlie generation and mutation;59 found only in physical substances,60 it is the first material principle,61 receptive of, or in potency to, natural forms62 (all of them63) in a certain order64 -

Scriptum super Sententiis Liber II, d. 1, q. 1, a. 4 ("materia prima, quae generationi substat" Mandonnet ed., vol. 2, p. 25); Summa theologiae la q. 16, a. 8 ("id quod remanet post omnem mutationem, est immutabile: sicut prima materia est ingenita et incorruptibilis, quia remanet post omnem generationem et corruptionem" - Leon. 4.216); In libros De generatione et corruptione lib. 1, lect. 10 ("hyle, sive materia prima, est maxime proprium subiectum susceptibile generationis et corruptionis" - Leon. 3.301); In libros Physicorum I, lect. 13 ("natura quae primo subiicitur mutationi, idest materia prima" - Leon. 2.46). 60 De substantiis separatis c. 7 ("non potest esse prima materia spiritualis et intellectualis substantiae" - Leon. 40.D52:70-72). 61 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 4 ("materia prima dicitur dupliciter: vel ita quod primum importet ordinem naturae; vel ita quod importet ordinem temporis. Secundum quod importat ordinem naturae, materia prima est illud in quo ultimo stat resolutio corporum naturalium" - Mandonnet ed., vol. 2, p. 313); De principiis naturae c. 2 ("Ipsa autem materia que intelligitur sine qualibet forma et priuatione, sed subiecta forme et priuationi, dicitur materia prima, propter hoc quod ante ipsam non est alia materia" - Leon. 43.41:74-78); Sententia libri Metaphysicae VIII, lect. 4.

96 _ „ 4 u _ _ i L - _ : » i „ i i _ _ A . . _ i 66 sensible forms, 65 rather than intellectual. It may be said, in another vocabulary, to con-

tain the "seminal reasons" of things. 67 It receives but one form at a time, 68 this form rather than form understood universally; 69 as subject of privation, 70 as the common sub-

62

Summa contra gentiles II, c. 76 ("formae naturales recipiuntur in materia prima" - Leon. 13.480:3la-32a); III, c. 22 ("materia prima est in potentia primo ad formam elementi" - Leon. 14.53:9b-llb). 63 Scriptum super Sententiis Liber II, d. 1, q. 1, a. 4 ("omnes formae sunt in potentia in materia prima" - Mandonnet ed., vol. 2, p. 27); d. 12, q. 1, a. 1 ("materia prima secundum se considerata sit in potentia ad omnes formas naturales" - Mandonnet ed., vol. 2, p. 302); Scriptum super Sententiis Liber III, d. 31, q. 2, a. 4 ("se habet intellectus ejus possibilis ad omnia intelligibilia, sicut se habet materia prima ad omnes formas sensibiles" - Moos ed., vol. 3, p. 996); Summa contra gentiles IV c. 89 ("potentia quae est in prima materia ad omnem formam" - Leon. 15.279:26b-27b); Quaestiones disputatae de malo q. 6 ("materia prima que est in potentia ad diuersas formas" - Leon. 23.152:657-658). 64 Sententia libri Metaphysicae XII, lect. 2 ("materia prima sit in potentia ad omnes formas, tamen quodam ordine suscipit eas. Per prius enim est in potentia" - Marietti ed., §2438, p. 572). 65 Summa theologiae Iallae q. 50, a. 6 ("Intellectus enim humanus, cum sit infimus in ordine intellectuum, est in potentia respectu omnium intelligibilium, sicut materia prima respectu omnium formarum sensibilium" - Leon. 6.323); Quaestio disputata de veritate q. 10, a. 8 ("materia prima est in potentia ad omnes formas sensibiles" - Leon. 22.2.322:262-263); Quaestio disputata de anima q. 2 ("materia prima non habet aliquam formam sensibilem actu" - Leon. 24.1.14:117-118). 66 Quaestiones disputatae de anima q. 2 ("forme intelligibiles non possunt recipi a materia prima" - Leon. 24.1.15:147-148); Summa theologiae la q. 75, a. 5 ("materia prima recipit formas individuales, intellectus autem recipit formas absolutas" - Leon. 5.202). 67 Quaestio disputata de veritate q. 2, a. 9 ("rationes seminales rerum sunt in prima materia sed rationes causales sunt in deo" - Leon. 22.1.72:91-93); q. 5, a. 9 ("rationes seminales inchoationes formarum quae sunt in materia prima secundum quod est in potentia ad omnes formas"-Leon. 22.1.166:414-416). 68 Quaestiones disputatae de anima q. 18 ("materia prima simul et semel non informatur nisi una forma" - Leon. 24.1.159:414-416). 69 Scriptum super Sententiis Liber II, d. 3, q. 1, a. 1 ("materia enim prima recipit formam, non prout est forma simpliciter, sed prout est hoc, unde per materiam individuate" - Mandonnet ed., vol. 2, pp. 88-89). 70 In libros De generatione et corruptione lib. 1, lect. 10 ("privationis, cuius subiectum est prima materia" - Leon. 3.301); In libros Physicorum V, lect. 9 ("privatio formae substantialis est in materia prima" - Leon. 2.261).

97 strate of mobile being, 71 it underlies multiple forms always 72 . It is indifferent to forms in a way that allows it to be described as infinitely receptive. Prime matter is in potency to substantial act, i.e. to substantial form,74 as well as 7S

to privation of form,

Hfs

i.e. to those forms which are educed by nature.

*

Not being m act

itself77 - in other words, having neither form nor privation of form in its own right 78 - it

71

In libros De generatione et corruptione lib. 1, lect. 14 ("commune omnium generabilium et corruptibilium, scilicet materia prima" - Leon. 3.311); Sententia libri Metaphysicae VIII, lect. 4 ("prima materia est una omnium generabilium et corruptibilium; sed propriae materiae sunt diversae diversarum" - Marietti ed., §1730, p. 414). 72 Summa theologiae la q. 66, a. 1 ("materia prima neque ruit creata omnino sine forma, neque sub forma una communi, sed sub formis distinctis" - Leon. 5.154). 73 Scriptum super Sententiis Liber I, d. 43, q. 1, a. 1 ("materia prima, quae de se est indifferens ad omnes formas, unde et infinita dicitur" - Mandonnet ed., vol. 1, p. 1003); Summa contra gentiles I, c. 43 ("materia prima sit infinita in sua potentialitate" - Leon. 13.124:16b-17b); III, c. 23 ("Corpus autem celeste, secundum suam substantiam consideratum, invenitur ut in potentia indifferenter se habens ad quodlibet ubi, sicut materia prima ad quamlibet formam" - Leon. 14.58:13a-16a); Quaes-tiones disputatae de veritate q. 2, a. 9 ("in materia prima sunt inflnitae formae in potentia" - Leon. 22.1.72:93-94). 74 Quaestiones disputatae de anima q.12 ("materia prima est in potentia ad actum substantialem qui est forma" - Leon. 24.1.111:306-308); Sententia libri Metaphysicae VII, lect. 13 ("materia prima 'subiicitur actui,' idest formae substantiali de se nullam habens formam" - Marietti ed., §1568, p. 378). 75 Sentencia libri secundi De anima, cap.14 ("materia prima est ut potencia respectu forme et priuationis" - Leon. 45.1.125:119-120). 6 Scriptum super Sententiis Liber HI, d. 14, q. 1, a. 3 ("materia prima est in naturali potentia tantum ad illas formas quae per agens naturale produci possunt" - Moos ed., vol. 3, §134, p. 457). 77 Quaestiones disputatae de potentia q. 1, a. 1 ("prima materia secundum essentiam suam considerata, est denudata ab omni actu" - Marietti ed., p. 8); De principiis naturae c. 2 ("quicquid est actu, non potest dici materia prima"). 8 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 4 ("materia prima sic accepta, non habeat aliquam formam partem essentiae suae, nunquam tamen dividitur ab omni forma" - Mandonnet ed., vol. 2, p. 313); Sententia libri Metaphysicae VIII, lect. 4 ("omnia sint ex eodem primo materiali principio, quod est materia prima de se nullam habens formam" - Marietti ed., §1729, p. 414).

98 is always conjoined with form 79 and the privation of form. 80 Nor did it pre-exist form even at the beginning, 81 but is concreated: 82 its being is always in alio. Entirely passive in its own right, 83 it is rightly described as a pure potency, 84 as "being" (or "good," etc.) only in potency, 85 as containing all potency, 86 even (in a sense)

79

Quaestio disputata de spiritualibus creaturis a. 1 ("semper in materia prima est aliqua forma" -Leon. 24.2.12:11). 80 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 1 ("materia prima quae est in inferioribus, nunquam separatur a privatione formae" - Mandonnet ed., vol. 2, p. 302); In libros Physicorum V, lect. 2 ("ens in potentia tantum, scilicet materia prima, quae in principio generationis est sub privatione, in fine autem sub forma" [this said with respect to any particular generation] - Leon. 2.233). 81 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 4 ("materia prima sic accepta, non potuit esse duratione ante corpora ex ea formata" - Mandonnet ed., vol. 2, p. 313); Summa contra gentiles IV, c. 63 ("prima materia sine forma esse non possit" - Leon. 15.201:32a-33a); Quaestiones disputatae de veritate q. 3, a. 5 ("materia prima nee est per se separata existens neque esse potest"-Leon. 22.1.111:13-14). 2 Summa theologiae la q. 84, a. 3 ("materia prima est creata a deo sub formis ad quas est in potentia" - Leon. 5.317); Quaestiones disputatae de potentia q. 3, a. 5 ("materia prima per se non creatur; sed ex hoc non sequitur quod non creetur sub forma; sic enim habet esse in actu" Marietti ed., p. 49). 83 Scriptum super Sententiis Liber III, d. 14, q. 1, a. 4 ("materia prima in qua non est activa potentia" - Moos ed., vol. 3, §174, p. 464). 84 Scriptum super Sententiis Liber I, d. 2, q. 1, a. 1 ("prima materia, quae est pura potentia" Mandonnet ed., vol. 1, p. 59); Scriptum super Sententiis Liber II, d. 3, q. 1, a. 1 ("potentia pura, quia sic non differret a materia prima" - Mandonnet ed., vol. 2, p. 85); Summa contra gentiles I c. 43 ("In rebus invenitur aliquid quod est potentia tantum, ut materia prima" - Leon. 13.124:10b-lib); Quaestiones disputatae de potentia q. 1, a. 1 ("sicut materia prima est pura potentia, ita deus est purus actus" - Marietti ed., p. 8). 85 Scriptum super Sententiis Liber I, d. 39, q. 2, a. 2 ("quod est tantum in potentia sicut materia prima" - Mandonnet ed., vol. 1, p. 934); Scriptum super Sententiis Liber II, d. 34, q. 1, a. 4 ("subjectum cujus est in potentia tantum, scilicet materia prima, quae sicut est ens incompletum et in potentia" - Mandonnet ed., vol. 2, p. 884); Quaestiones disputatae de veritate q. 21, a. 2 ("sicut materia prima est ens in potentia et non in actu, ita est perfecta in potentia et non in actu, bona in potentia et non in actu" - Leon. 22.3.597:117-120); Quaestiones disputatae de malo q. 1, a. 2 ("materia prima non dicitur ens nisi in potentia et esse sinpliciter habet per formam" Leon. 23.11:164-165). 86 Scriptum super Sententiis Liber I, d. 36, q. 2, a. 1 ("sicut omnes formae sunt in potentia in prima materia, ita sunt in actu in primo motore" - Mandonnet ed., vol. 1, p. 839).

99 as "its own potency."87 It is the first potency88 or recipient,89 that which first receives the substantial forms90 - notably those of the elements.91 As "being in potency" is not nonbeing absolutely, but rather a propensity toward further being (which is not-yet), it can be variously characterized: it is simple,92 indeterminate,93 lacking all diversity in itself,94 one,95 and uniform.96 It is immobile, incorruptible, ungenerated,97 and is not an element.98

87

Scriptum super Sententiis Liber I, d. 3, q. 4, a. 2 ("materia est ipsa sua potentia"; "material est sua potentia passiva, sicut et Deus sua potentia activa" - both Mandonnet ed., vol. 1, p. 117); Summa theologiae la q. 77, a. 1 ("potentia materiae non est aliud quam eius essentia" - Leon. 5.237); Quaestiones disputatae de anima q. 12 ("materia prima est sua potentia" - Leon. 24.1.107:76-78). 88 Summa theologiae la q. 75, a. 5 ("prima potentia est materia prima" - Leon. 5.201). 89 Scriptum super Sententiis Liber I, d. 3, q. 4, a. 2 ("materia prima, quae est primum recipiens" - Mandonnet ed., vol.1, p. 117); Summa theologiae la q. 44, a. 2 ("primum principium passivum est materia" - Leon. 4.457). 90 Quaestio disputata de spiritualibus creaturis a. 1 ("materia prima, que omnino sine forma consideratur, primo recipit formam substantiae" - Leon. 24.2.17:552-554). 91 Summa contra gentiles III c. 22 ("materia prima est in potentia primo ad formam elementi" Leon. 14.53:9b-l lb). 92 Quaestiones disputatae de veritate q. 5, a. 9 ("earum simplicitas est propter earum imperfectionem, sicut et materia prima est simplex" - Leon. 22.1.166:419-421). 93 Scriptum super Sententiis Liber III, d. 23, q. 1, a. 1 ("intellectus possibilis qui de se indeterminatus, sicut materia prima" - Moos ed., vol. 3, §23, p. 699). 94 Scriptum super Sententiis Liber I, d. 8, q. 5, a. 2 ("materia prima, prout consideratur nuda ab omni forma, non habet aliquam diversitatem" - Mandonnet ed., vol. 1, p. 228); Scriptum super Sententiis Liber II, d. 3, q. 1, a. 1 ("in materia prima non sit ulla diversitas" - Mandonnet ed., vol. 2, p. 87). 95 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 4 ("ilia materia prima quae una numero est in omnibus elementis ut pars essentiae eorum, est omnino informis in sua essentia considerata" Mandonnet ed., vol. 2, p. 315); Quaestiones disputatae de anima q. 2 ("materia prima est una respectu omnium formarum sensibilium" - Leon. 24.1.21:497-498); De principiis naturae c. 2 ("materia prima dicitur una numero in omnibus" - Leon. 43.41:98-99). 96 Summa theologiae la q. 23, a. 5 ("prima materia tota sit in se uniformis" - Leon. 4.278). 97 Summa contra gentiles II, c. 55 ("in substantiis corruptibilibus materia prima est incorruptibilis" - Leon. 13.394:3a-4a); Summa theologiae la q. 16, a. 8 ("prima materia est ingenita et incorruptibilis, quia remanet post omnem generationem et corruptionem" - Leon. 4.216); q. 76, a. 4 ("materia prima non potest moveri" - Leon. 5.223); q. 103, a. 1 ("in omnibus rebus creatis est aliquid stabile, ad minus prima materia" - Leon. 5.453); De principiis naturae c. 2 ("materia prima, et etiam forma, non generatur neque corrumpitur" - Leon. 43.41:90-91); In libros Physi-

100 Prime matter is in every b o d y " and is everywhere 100 - though this last is said only per accidens.101 It is divisible in potency or per accidens,102 having no quantity in itself103 but being in potency to quantity (in conjunction with substantial form); 104 that is, to quantity considered as determinate. 105 Contracting form to an individual esse,106 it is the principle of singularity. 107

corum I, lect. 15 ("si materia prima corrumpatur, erit corrupta antequam corrumpatur, quod est impossibile" - Leon. 2.54). 98 Sententia libri Metaphysicae V, lect. 4 ("differt elementum a materia prima, qua nullam speciem habet" - Marietti ed., §798, p. 218). Scriptum super Sententiis Liber I, d. 37, q. 2, a. 2 ("materia prima, quae est in omni corpore, quo omnis locus impletur" - Mandonnet ed., vol. 1, p. 864); Summa contra gentiles II, c. 44 ("materia prima, quae est omnibus corporibus communis sed sub una tantum forma" - Leon. 13.370:4a-6a). 100 Summa theologiae la q. 8, a. 4 ("universale et materia prima sunt quidem ubique, sed non secundum idem esse" - Leon. 4.89). 101 Scriptum super Sententiis Liber I, d. 37, q. 3, a. 1 ("omnino absolutum est a situ et dimensione, non debetur locus nisi per accidens, sicut patet de materia prima" - Mandonnet ed., vol. l,p. 869). Scriptum super Sententiis Liber I, d. 8, q. 5, a. 1 ("aliquid quod non est compositum...deficit a simplicitate primi...vel quia est divisibile in potentia vel per accidens, sicut materia prima" Mandonnet ed., vol. 1, p. 227). 103 Scriptum super Sententiis Liber II, d. 30, q. 2, a. 1 ("prima materia, prout in se consideratur, nullam quantitatem habeat" - Mandonnet ed., vol. 2, p. 781); In libros De generatione et corruptione lib. 1, lect. 14 ("materia prima, sit separatum ab omni quantitate corporali" - Leon. 3.311). 104 Scriptum super Sententiis Liber II, d. 30, q. 2, a. 1 ("oportet quod materia prima ad nullam quantitatem sit in potentia, nisi quae competat formae naturali" - Mandonnet ed., vol. 2, p. 781); Sententia libri Metaphysicae VII, lect. 2 ("quantitates et qualitates, quorum subiectum proprium non est materia prima, sed substantia composita quae est substantia in actu" - Marietti ed., §1284, p. 322). 105 In libros Physicorum III, lect. 12 ("non enim est in materia prima potentia nisi ad determinatum quantitatem" - Leon. 2.140). 106 Quaestio disputata de spiritualibus creaturis a. 1 ("materia prima recipit formam contrahendo ipsam ad esse individuale" - Leon. 24.2.13:343-344). 107 Super librum De causis lect. 9 ("materia prima in rebus corporalibus quae est principium singularitatis" - Marietti ed., §235, p. 63).

101 Proper to corruptible substances, those of an inferior order,108 it is the principle of corruptibility,109 in potency to natural, i.e. mobile, being.110 It is spoken of as an "incomplete being,"111 "in act" only through its correlative principle of substantial form;112 again, it "acts" or "is perfected" only through form,113 and it is said to have substantial esse,114 albeit an "incomplete" or "least" esse.115 To say that it cannot be entirely actualized116 is more a statement about its composition with form than about matter in and of itself; "actualized matter," strictly speaking an oxymoron, is a description of matter conjoined with form. It is not improper to speak of prime matter as not being.117 Nevertheless in some sense it comes from God;118 it has some likeness to

108

Quaestiones disputatae de veritate q. 5, a. 9 ("in his inferioribus id quod est eis commune, scilicet materia prima" - Leon. 22.2.164:276-277); Super Ioannem c. 5, lect. 5 ("in istis inferioribus materia prima existens accipit formam, et subiectum subiicitur accidenti" - Marietti ed., §782, p. 148). 109 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 1 ("material prima quae est in inferioribus, nunquam separatur a privatione formae...privatio autem adjuncta materiae, inducit corruptibilitatem" - Mandonnet ed., vol. 2, p. 302). 110 Summa theologiae la q. 14, a. 2 ("Intellectus autem noster possibilis se habet in ordine intelligibilium, sicut materia prima in ordine rerum naturalium: eo quod est in potentia ad intelligibilia, sicut materia prima ad naturalia" - Leon. 4.169). 111 Scriptum super Sententiis Liber II, 34, q. 1, a. 4 ("materia prima, quae sicut est ens incompletum et in potentia" - Mandonnet ed., vol. 2, p. 884). 112 Summa contra gentiles II, c. 98 ("materia prima fit actu in esse sensibili per formam naturalem"-Leon. 13.580:14a-15a). 113 Summa contra gentiles II, c. 76 ("materia prima perficitur per formas naturales" - Leon. 13.480:28a-29a); Quaestiones disputatae de veritate q. 8, a. 6 ("materia prima non potest agere aliquam actionem nisi perficiatur per formam" - Leon. 22.2.238:162-163). 114 Summa theologiae la q. 84, a. 3 ("materia prima habet esse substantiale per formam" - Leon. 5.318). 115 Scriptum super Sententiis Liber I, d. 8, q. 3, a. 2 ("materia prima et universale non habent in se esse completum" - Mandonnet ed., vol. 1, p. 215); Quaestiones disputatae de veritate q. 2, a. 5 ("materia prima habet minimum de esse" - Leon. 22.1.60:23-24). 116 Summa contra gentiles III, c. 39 ("Aliquid vero cuius potentia tota non potest simul in actum reduci, sicut patet de materia prima" - Leon. 14.96:24b-26b). 117 Super De divinis nominibus c. 4, lect. 13 ("id quod non-est, scilicet materia prima" - Marietti ed., §463, p. 161).

102 less in some sense it comes from God;118 it has some likeness to God119 and corresponds to an idea in God,120 though it is not merely different, but diverse from Him.121 To the extent that it is "being," so can it be said to desire or to participate the good and other transcendentals.122 Prime matter, understood absolutely rather than secundum quid, is not intelligible in itself,123 but is known through analogy124 via its association with form. Although described as "first" in the order of effects,125 i.e. in the order of nature or time,126 this is

118

Summa theologiae la q. 44, a. 4 ("cum Deus sit causa efficiens, exemplaris et finalis omnium rerum, et materia prima sit ab ipso, sequitur quod primum principium omnium rerum sit unum tantum secundum rem" - Leon. 4.462). 119 Quaestiones disputatae depotentia q. 3, a. 1 ("materia prima habet similitudinem cum deo in quantum participat de ente....ita materia prima habet similitudinem cum Deo in quantum ens, non in quantum est ens actu" - Marietti ed., p. 41); Super De divinis nominibus c. 4, lect. 2 ("materia prima, inquantum desiderat formam quae est similitudo divini esse" - Marietti ed., §298, p. 97). 120 Scriptum super Sententiis Liber I, d. 36, q. 2, a. 3 ("cum materia prima a deo sit, oportet ideam ejus aliqualiter in Deo esse" - Mandonnet ed., vol. 1, p. 844); Quaestiones disputatae de veritate q. 3, a. 5 ("si proprie de idea loquamur, non potest poni quod materia prima habeat per se ideam in Deo distinctam ab idea formae vel compositi" - Leon. 22.1.112:40-43). Summa theologiae la q. 3, a. 8 ("materia prima et Deus non differunt, sed sunt diversa seipsis" - Leon. 4.48). 122 Summa theologiae la q. 5, a. 2 ("Nam materia prima participat bonum, cum appetat ipsum (nihil autem appetit nisi simile sibi)" - Leon. 4.58); Super De divinis nominibus c. 4, lect. 2 ("Omne autem causatum convertitur in suam causam per desiderium, unde materia prima desiderat bonum" - Marietti ed., §296, p. 96); lect. 5 ("non-existens, idest materia prima participat pulchro et bono" - Marietti ed., §355, p. 115). 123 De principiis naturae c. 2 ("materia prima per se non potest cognosci uel difiniri sed per comparationem" - Leon. 43.41:80-81); In libros Physicorum I, lect. 13 ("natura quae primo subiicitur mutationi, idest materia prima, non potest sciri per ipsam" - Leon. 2.46). 124 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 4 ("quia omnis cognitio est per formam, haec materia prima est scibilis, ut dicit Philosophus in I Physic, text. 69, secundum analogiam tantum" - Mandonnet ed., vol. 2, p. 313); In libros Physicorum I, lect. 15 ("materia prima scibilis est secundum proportionem" - Leon. 2.54). 125 Super De divinis nominibus c. 4, lect. 2 ("id quod est primum subiectum in effectibus, idest materia prima" - Marietti ed., §296, p. 96). 126 Scriptum super Sententiis Liber II, d. 12, q. 1, a. 4 ("materia prima dicitur dupliciter: vel ita quod 'primum' importet ordinem naturae, vel ita quod importet ordinem temporis" - Mandonnet ed., vol. 2, p. 313).

103 to consider it from the standpoint of existential priority. It is denoted as "last" in the sensible and corporeal order,

or "least"

inasmuch as it is the terminus ad quern of

intellectual discovery (resolution). It is in the genus of substance, but only potentially rather than as a species.129 Aquinas's most sustained discussion of matter, apart from his Aristotelian commentaries, appears in the De principiis naturae; the order of exposition in that work largely follows that of Aristotle in the Physics. Now the main aspects under which prime matter is apprehended in the philosophy of Aquinas may be considered as follows. (1) Prime matter is the subject of natural form and the principle of continuity in every generation and corruption. As such, it is in potency not only to substantial forms but to privations as well. (2) It is a principle constitutive of substance, "existing" only through substantial form, of which it is the potency. These first two headings comprise material in which Aquinas's account is essentially Aristotle's. As I have surveyed Aristotle's account above, in Section D, I will not go over the ground again. But in the remainder of this chapter I will take up considerations not so explicitly treated in Quaestiones disputatae de anima q. 7 ("animam humanam, que in eis [immaterial substances] tenet ultimum gradum, sicut materia prima in genere rerum sensibilium" - Leon. 24.1.60:308-311); Scriptum super Sententiis Liber II, d. 3, q. 1, a. 3 ("intellectus humanus, qui, secundum Commentatorem, est ultimus in ordine naturarum intellectualium, sicut materia prima in ordine corporalium" - Mandonnet ed., vol. 2, p. 94); a. 6 ("anima rationalis ab angelis differt, quia ultimum gradum in substantiis spiritualibus tenet, sicut materia prima in rebus sensibilibus" - idem, p. 104); Quaestiones disputatae de veritate q. 10, a. 8 ("Anima enim nostra in genere intellectualium tenet ultimum locum, sicut materia prima in genere sensibilium" - Leon. 22.2.322:258-260). 128 Summa contra gentiles II, c. 96 ("materia prima est infimum in ordine rerum sensibilium" Leon. 13.572:10a-lla). 129 Quaestio disputata de spiritualibus creaturis a. 1 ("id communiter materia prima nominatur quod est in genere substantie, ut potentia quedam" - Leon. 24.2.11:292-294); Scriptum super Sententiis Liber II, d. 3, q. 1, a. 6 ("materia prima et formae materiales non sunt in genere substantiae sicut species, sed solum sicut principia" - Mandonnet ed., vol. 2, p. 103).

104 Aristotle. (3) Matter is a principle of individuation and the ground of extension or spatiality, i.e. of dimensive quantity. (See below, sections G, H, and M.) (4) It is a principle of corruptibility - i.e., not only the principle of continuity in change, but in some way a cause of change. (Section I.) (5) It is, at the deepest metaphysical level, a modality of esse itself. (Sections J, K.) (6) Unintelligible in itself, it is the ground and sine qua non of cosmic intelligibility. (Section L.) Throughout this dissertation I generally assume and imply parity between the Aristotelian and Thomistic doctrines concerning the attributes of matter. In fact I will use the terms "Aristotelian" and "Thomistic" interchangeably at times, in lieu of the more awkward "Aristotelian-Thomistic," where there is no reason to suppose an essential difference in their doctrine. Aquinas does, however, go significantly beyond Aristotle in his account of individuation; and our later attempts to construe matter along Thomistic metaphysical lines would be harder to press into a pure Aristotelian mold. But the emphasis of this dissertation is not on shades of meaning between Aristotle and Aquinas, so much as upon the applicability of their doctrine, taken in its generality, to a physics that long postdates either of them. Again, having indicated in this section something of the richness of Aquinas's allusion to matter, I may disappoint the reader by not sticking to a rigidly textual development in the sequel. My thought is guided by, and I trust not inconsonant with, that of Aquinas, but textual exegesis is not my aim. Rather, thinking apud Thomam, I wish to present an account that emphasizes synthesis more than analysis, for reasons noted in Chapter One; which does not mean, of course, that certain points will not appropriately be dealt with rather more closely as we proceed - beginning with a topic

105 be dealt with rather more closely as we proceed - beginning with a topic where the differences between Aquinas and Aristotle are especially pronounced.

G. Individuation and unilocality (impenetrability) The question of individuation is one of the pre-eminent questions of philosophy, being one expression of the problem of one versus many which characterizes philosophy from its inception. In the question of what constitutes an individual we see at work the deepest impulse of man as an intellectual being to apprehend being itself. Individuality constitutes an immediate and primordial opposition to intelligibility, even though, as is commonly acknowledged within the Thomist tradition, it is precisely individuated being which the mind seeks to know in the first place. The notion of individuation has been variously construed by philosophers,130 but the factor common to most formulations is, not too surprisingly, what is most prior in the context of a consideration of unity-amid-plurality. For Aquinas, an individual is what is indivisum in se et divisum ab alio: a single being, not confused with other beings either intrinsically or extrinsically.131

See Jorge J. E. Gracia, "Introduction: The Problem of Individuation" in Individuation in Scholasticism: The Later Middle Ages and the Counter-Reformation, 1150-1650, ed. Jorge J. E. Gracia (New York, 1994). 131 "...de ratione indiuidui est quod sit in se indiuisum et ab aliis ultima diuisione diuisum," Super Boetium De Trinitate q. 4, a. 2 ad 3 (Leon. 50.125:258-260). Cf. Scriptum super Sententiis Liber IV, d. 12. q. 1, a. 1: "de ratione individui duo sunt: scilicet quod sit ens actu vel in se vel in alio; et quod sit divisum ab aliis quae sunt vel possunt esse in eadem specie, in se indivisum existens. Et ideo primum individuationis principium est materia, qua acquiritur esse in actu cuilibet tali formae sive substantiali sive accidentali. Et secundarium principium individuationis est dimensio, quia ex ipsa habet materia quod dividatur" (Moos ed., vol. 4, §49, p. 503).

106 Individuation arises as a philosophical issue after the intellect has discerned unity amid plurality, first as substantial unity underlying accidental plurality, and then, by a further abstraction, as specific unity inhering in substantial plurality - "substantial" in each case being taken in Aristotle's primary sense of "a this." Considering concrete existents in the light of their specific unity, the mind can then frame the question, what makes conspecifics - beings with identical intelligibility - distinct from one another?132 If the question of distinction, divisum ab alio, is perhaps the first to be explicitly formulated (because we apprehend intellectually the plurality of things before we apprehend plurality in things), the question already implies another, namely: what constitutes an individual as a this rather than a these, a unity indivisum in sel By this is meant, not what differentiates a given being from its constituent parts, as for example "dog" from "tail, paws, etc.," but what constitutes a being one with respect to other beings of its kind-e.g.,

what makes a dog one dog. The distinction of "this being" from others of

its intelligibility - whether extrinsic or intrinsic to it - can only occur simultaneously, as it were. Divisum ab alio and indivisum in se are complementary in that each implies the other: a being which is existentially distinct from those of its kind is a being precisely through being essentially distinct from any plurality of parts constitutive of it (and therefore intrinsic to it).133

Notwithstanding that the question arises in a cosmic context of multiplied beings, none of which appears to be the sole representative of its species, nothing prevents the mind from later recognizing the possibility of species consisting of a single being. 133 Among several notae associated with individuation by different philosophers, that of "identity through accidental changes" is not primordial but a corollary of a thing's definitional integrity, i.e. of being undivided in itself. Similarly, the note of "noninstantiability" (whereby this

107 The distinction of existential and essential considerations is crucial to a Thomist understanding of individuation. It is not the distinctness and indivisibility of forms, ideas or concepts that is at issue, but of concrete hylomorphic existents. What is contained in the mind singly and universally (say, "tree") is seen to be multiplied, outside the mind, in a way that does not involve its intelligibility (this tree, and this tree, and this tree). The species which is a unity essentially speaking is divided existentially.134 At the same time, that which is existentially multiplied is, in each of its instantiations, a single being existentially ("tree" is one), though its parts must be distinguished on the essential side ("leaf," "stem," etc. have different definitions than "tree").135 The paucity of references to individuation in Aristotle is perhaps surprising. Of course, he is referring to individuals as such whenever he uses the term "a this" - from the Categories onward - but he hardly touches on the cause of individuation. Nevertheless, when he does, there is nothing tentative about it: his brevity cloaks his conviction, leaving us to wonder if he simply considered the question of the individuating cause to warrant no more attention than is already implied in his carefully enunciated doctrine of the formation of universals in mente. For to have resolved one issue is to have resolved the other: they are complementary. Universals, in being abstracted from material existence, are abstracted from the multiplicity of individuals, while individuals, though instantiations of universals, are unintelligible in their very individuality. being is not replicable) is but a corollary of the thing's existential unicity, or being distinct from other beings. 134 The "division of species" which is yet another note considered as definitive of individuation is thus seen to be but a corollary of the existential aspect of individuation. 135 It is because the individual is division ab alio existentially that it is "impredicable," to cite yet another note sometimes employed in defining individuation.

108 The most direct textual evidence, then, for Aristotle on the individuation of cosmic being is a mention almost en passant: "But all things which are many in number have matter; for many individuals have one and the same [intelligible content], for example, man, whereas Socrates is one...." 136 The idea is that multiple instantiations cannot be due to form, since form is wholly present in each existent and therefore does not include in its intelligibility, in itself, "thisness." Therefore the multiplication of conspecific substances must be due to matter. In Aquinas the Aristotelian teaching will reach much fuller development. Aquinas's is still characterized as a doctrine of "individuation through matter," but it acquires refinements that not only resolve the shortcomings of Aristotle's simple invocation of "matter" alone, but also allow it to dovetail better into a complementary doctrine of the individuation of immaterial (angelic) substances.137 The problem for Aquinas and other mediaeval Aristotelians is this: individuation of hylomorphic substances cannot be due to the form, for reasons I gave above; nor can it be due to matter, since matter is indeterminate in itself and cannot be a cause of determination; nor can it be due to anything accidental, since the individual substance per-

136

Metaphysics XII.8 (1074a33ff.). Similarly Book VII.8 (1034a7ff): "And when the whole is such and such a form in this flesh and these bones, this is Callias or Socrates; and they differ in their matter (for the matter of each is different) but are the same in form, because form is indivisible." Cf. X.9. 137 On individuation in Aquinas see, inter alia, Joseph Bobik, "Dimensions in the individuation of bodily substances," Philosophical Studies 4 (1954): 60-79; Joseph Owens, "Thomas Aquinas: dimensive quantity as individuating principle," Mediaeval Studies 50 (1988): 279-310; Jean R. Rosenberg, The Principle of Individuation: A Comparative Study of St. Thomas, Scotus, and Suarez (Ph.D. diss.: Washington, D. C, 1950); Kevin White, "Individuation in Aquinas's Super Boetium De Trinitate, Q. 4," American Catholic Philosophical Quarterly 69 (1995): 543-56.

109 dures through accidental change.138 We have, then, a trilemma; let us see how Aquinas looks at each part of it. Form is the intelligible principle of a being: that aspect which, residing in (and constitutive of) the existent as the form of'the existent's matter, can also be taken immaterially into the mind. Conceived first as intelligibility, form is seen nonetheless to be a real ontological principle, rather than a congeries of accidents, through its persistence in time (amid the flux of the accidental) and its commonality in multiple existents. If form were an individuating principle, then it obviously would not be common to more than one individual; part of a thing's very intelligibility would be "to be this and not other." The question of hylomorphic individuation arises precisely as a paradox of one in many, i.e. in a context in which form, the knowable, is understood to be communicable. More puzzling is the question of matter. There is no question that individuation pertains to existents, i.e., to beings in which form is conjoined with matter; moreover, bearing in mind that prime matter has only analogous similarity to secondary matter, we certainly see matter at the second level to be incommunicable. If "dog" is common to Fido and to Rover, the matter of the one is clearly not the matter of the other. Yet as Aquinas notes, there is a deep problem here: "Therefore matter is not the principle of diversity in number, and neither is form . . . ." What is indeterminate cannot be, in and 138

"Praeterea. In indiuiduo nichil inuenitur nisi forma et materia et accidentia. Set diuersitas forme non facit diversitatem secundum numerum set secundum speciem Set materia invenitur communis in diversis secundum speciem; quia eadem materia formis contrariis subditur, alias habentia contrarias formas non transmutarentur invicem; ergo materia non est principium diversitatis secundum numerum" {Super Boetium De Trinitate q. 4, a. 2, set contra 2 et 3 - Leon. 50.123:51-54, 65-70); "dimensiones cum sint accidentia, per se non possunt esse principium unitatis indiuidue substantia; set materia prout talibus dimensionibus subest intelligitur esse principium talis unitatis et multitudinis" {ibid., ad 2 - Leon. 50.125:253-257).

110 of itself, a determining principle. In so far as matter is a pure potency, receptive of all forms, it does not possess any feature whereby it would contract form to this existent rather than that one. Aquinas pushes on. "Form is rendered individual through being received in matter. [We can't ignore the evidence of our senses.] But because matter in itself lacks all differentiation, it can individuate the received form only in so far as it bears some distinguishable mark. So form is individuated by being received in matter, but only as it is received in this particular matter, determined to this place and time."139 Here we seem to have a contradiction. Matter is described as "lacking all differentiation," yet as being "this particular matter." How can matter be particularized if its ratio is to be utterly indeterminate? As Aquinas goes on to say, in the passage just cited, "Matter, however, is divisible only through quantity [i.e., dimensions]" - but since "dimensions are accidents, they cannot by themselves be the source of the unity of an individual substance."140 The accidental is posterior to the substantial, and cannot constitute the existential unity of the latter. Whence the trilemma I have alluded to: neither form, nor matter, nor accidents seem to answer to the requirement of a principle of individuality in substances.

"...forma fit hec per hoc quod recipitur in materia. Set cum materia in se sit indistincta, non potest esse quod formam receptam indiuiduet nisi secundum quod est distinguibilis: non enim forma indiuiduatur per hoc quod recipitur in materia nisi quatenus recipitur in hac materia distincta et determinata ad hie et nunc." Super Boetium De Trinitate q. 4, a. 2 (Leon. 50.125:202208). 140 Ibid., ad 2: "dimensiones, cum sint accidentia, per se non possunt esse principium unitatis individuae substantie" (Leon. 50.125:253-258).

Ill The Thomistic solution, hinted at in the text just cited, avoids taking any of these principles singly, instead invoking all three of them, albeit in a certain ontological order. Aquinas treats of individuation in hylomorphic substances in numerous works throughout his career.141 And while some authors142 have discerned a marked evolution in his thought - alleging that he invokes an Avicennian forma corporeitatis in the Sentences, an Averroistic "indeterminate dimensionality" in the Commentary on Boethius's De trinitate, and finally determinate dimensions alone in his last writing on the subject - it is also possible to read all of his texts on individuation as expressing but one main insight: that individuation occurs always through determinate dimensions, which are grounded in the material substantial principle. I will focus on Aquinas's treatment of this topic in the De trinitate Commentary, as being one of the most explicit. Matter, however, is divisible only through quantity . . . . Accordingly matter is made to be "this" and designated owing to the fact that it is subject to dimensions. Now dimensions can be understood in two ways. In one way inasmuch as they are determinate, and by this I mean that they have a definite measurement and shape. In this sense, as complete beings, they are located in the genus of quantity. Now when dimensions are understood in this way they cannot be the principle of individuation, because there is often a variation in such determination of dimensions in the same individual, and thus it would follow that the individual would not always remain the same in number. In another way dimensions can be taken as indeterminate, simply as having the nature of dimensions, though they can never exist without some determination, any more than the nature of color can exist without being definitely white or black. Taken in this way dimensions are located in the genus of quantity as something incomplete. It is through these indeterminate dimensions that matter is made to be "this designated matter, " thus rendering the form individual . . . . Because E.g., De ente et essentia (c. 1256), Scriptum super libros Sententiarum /Scriptum super Sententiis (c. 1256), Quaestiones disputatae de veritate (c. 1259), Super Boetium De Trinitate (c. 1261), Summa contra gentiles (c. 1263), Quaestio disputata de anima (1267), and Summa theologiae (c. 1272). 142 E.g., J. Rosenberg, The Principle ofIndividuation.

112 these dimensions belong to the genus of accidents, diversity in number is sometimes reduced to the diversity of matter and sometimes to the diversity of accidents.143 Aquinas, then, recognizes that quantitative being alone - "determinate dimensions" cannot be the individuating principle, for two reasons: the first, cited earlier, is the posteriority of accidents to substance, and the second, given in the passage just quoted, is that the individual unity of a substance would depend on its being under just one set of determinate dimensions, with the result that new and distinct individual substance would be entailed by any change in those dimensions. But how can Aquinas appeal to "dimensions . . . taken as indeterminate, simply as having the nature of dimensions"? Is he not reverting to the indeterminate as a principle of determination? No more than to say that color as such is necessary for vision, though it never exists save as this color or that. Just as "color" as such (not "green" or "yellow" as such) is what underlies vision,144 so is dimensionality as such (not suchand-such dimensions) what grounds individuation. Only the actual being, the existent, is

Super Boetium De Trinitate q. 4, a. 2: "Materia autem non est diuisibilis nisi per quantitatem....et ideo materia efficitur hec et signata secundum quod subest dimensionibus. Dimensiones autem istae possunt dupliciter considerari. Uno modo secundum earum terminationem; et dico eas terminari secundum determinatam mensuram et figuram, et sic ut entia perfecta collocantur in genere quantitatis - ; et sic non possunt esse principium indiuiduationis, quia cum talis terminatio dimensionum uarieturfrequentercirca indiuiduum, sequeretur quod indiuiduum non remaneret semper idem numero. Alio modo possunt considerari sine ista determinatione, in natura dimensionis tantum, quamuis numquam sine aliqua determinatione esse possint, sicut nee natura coloris sine determinatione albi et nigri; et sic collocantur in genere quantitatis ut imperfectum, et ex his dimensionibus interminatis materia efficitur hec materia signata, et sic indiuiduat formam....Et ideo, cum hee dimensiones sint de genere accidentium, quandoque diuersitas secundum numerum reducitur in diuersitatem materie, quandoque in diuersitatem accidentis, et hoc ratione dimensionum predictarum" (Leon. 50.125:209-210, 212-230, 238-242). Translation from the Maurer edition, pp. 97-98. 144 We see a green thing, not because it is green, but because it has color: otherwise we would not see a yellow thing, since it is not green.

113 individuated. And it is always accompanied, in its substantial integrity, by certain accidents, of which the first, ontologically, are dimensions, located in the category of quantity. But quantity is radicated in matter. In other words, it is intrinsic to the potency of matter to be in potency to dimensions.145 Matter has no dimensions in its own right, but it is a potency to dimensioned existence. As indeterminate, matter's potency is receptive of various dimensions even for a given substantial form: a horse may be smaller or larger, while retaining its individual identity. But the horse cannot be dimensionless, and its dimensionality results, not from its horseness, but from its materiality, albeit in a way consonant with its ratio as a horse. Yet Aquinas was quite explicit when affirming, a few years previously, that [T]he matter which is the principle of individuation is not just any matter, but only designated matter {materia signata). By designated matter I mean that which is considered under determined dimensions.146 Has he reversed himself completely? While allowing for the possibility that his thought was clarified over time, I believe it is easy enough to see the same basic idea throughout. His earlier concern was with the cause of individuation in actu, which obviously cannot be a mere potentiality, while in the earlier text he was thinking of the deeper ground of that cause of individuation. Evidence for this is that in different places in one and the same work he will say, first that "indefinite" and later that "definite" dimen145

"...dimensiones praeintelliguntur in materia non in actu completo ante formas naturales sed in actu incompleto, et ideo sunt prius in via materiae et generationis; sed forma est prior in via complementi" Quaestiones disputatae de veritate q. 5, a. 9 ad 6 (Leon. 22.1.165:357-362). 146 De ente et essentia, 2: "materia non quolibet modo accepta est individuationis principium, sed solum materia signata. Et dico materiam signatam, quae sub determinatis dimensionibus consideratur" (Leon. 43.371:73-77). Cf. Scriptum super Sententiis Liber III, d. 1, q. 2, a. 5 ad 1: "principium individuationis sit materia aliquo modo sub dimensionibus terminatis considerata" (Moos ed., vol. 3, §145, p. 45).

114 sions are the cause of individuation.

And in yet another place in the same Commen-

tary he expressly cites two principles: And therefore the first principle of individuation is matter, by which being in actuality accrues to every such form, whether substantial form or accidental form. And the secondary principle of individuation is dimension, because from it matter has the capacity to be divided.148 So it is "through these indeterminate dimensions [i.e., the potency to dimensionality] that matter [when informed] is made to be 'this designated [i.e., specifically dimensive] matter,' thus rendering the form individual [in its concrete existence] . . . ." Due to our manner of conceptualizing and speaking, it is not unacceptable to designate the whole by a part: matter can be called the principle of individuation inasmuch as it is the ontological ground of dimensions themselves,149 while determinate dimensions (i.e., quantitative extension) can be called the principle of individuation inasmuch as the individuated existent is inevitably delimited and measured by certain dimensions, even though these vary (up to a point) over time. Just as he refers to indeterminate and determinate dimensions, so does Aquinas speak of unsigned and signed (undesignated and designated) matter: "What we must realize is that the matter which is the principle of individuation is not just any matter, but only designated matter. By designated matter I mean that which is considered under

Scriptum super Sententiis Liber II, d. 30, q. 2, a. 1, solutio; Scriptum super Sententiis Liber III,d. l,q.2,a. 5 a d l . 148 Scriptum super Sententiis Liber IV, d. 12, q. 1, a. 3: "primum individuationis principium est materia, qua acquiritur esse in actu cuilibet tali formae sive substantiali sive accidentali. Et secundarium principium individuationis est dimensio, quia ex ipsa habet materia quod dividatur." Moos ed., vol. 4, §49, p. 503. 149 Besides texts already cited, see Scriptum super Sententiis Liber I, d. 2, q. 1, a. 1; Scriptum super Sententiis Liber II, d. 3, q. 1, a. 1 ad 3.

115 determined dimensions."150 "I call matter designated if it is considered together with the determination of its dimensions, that is, with these or those dimensions. I call it not designated, however, if it is considered without the determination of its dimensions. In this connection, it must be noted that designated matter is the principle of individuation."151 To speak of matter as "unsigned" is to consider it as an ens rationis, as a principle prior to the existence of that to which it stands as matter. To speak of matter as "signed", on the other hand, is to consider it as it actually enters into the existent. Numerous texts in Aquinas affirm the role of matter and of dimensions in individuation.152 But a survey of these texts points up more than one apparent inconsistency. I have already observed that the whole may be referred to under the ratio of now one part, now another - when the individuating factor is described as simply "matter" (in terms of its ontological ground) or as "determinate dimensions" (in terms of the ac-

De ente et essentia, c. 2: "materia non quolibet modo accepta est individuationis principium, sed solum materia signata; et dico materiam signatam que sub determinatis dimensionibus considerate." Leon. 43.371:73-77. 151 Quaestiones disputatae de veritate q. 2, a. 6 ad 1: "dico signatam secundum quod considerate cum determinatione dimensionum harum scilicet vel illarum, non signatam autem quae sine determinatione dimensionum considerate. Secundum hoc igitur sciendum est quod materia signata est individuationis principium" (Leon. 22.1.66:103-109). 152 Scriptum super Sententiis Liber II, d. 3. q.l; d. 30, q. 2; Scriptum super Sententiis Liber III, d. 1, q. 2; Scriptum super Sententiis Liber IV, d. 12, q.l, a. 1; Super Boetium De Trinitate q. 4, a. 2 ad 3; Summa contra gentiles II, c. 50, c. 93; IV, c. 65; Quaestio disputata de anima a. 9; Summa theologiae la q. 7, a. 3; q. 50, a. 2, etc. Form also plays a role in individuation, since "through form, which actualizes matter, matter becomes an actual thing and this particular thing" (per formam enim, quae est actus materie, materia efficitur ens actu et hoc aliquid). (De ente et essentia, c. 2; Leon. 43.370:31-32.) Note the analogical flexibility whereby Aquinas, in treating of the complementary principles of unitary being, can say both this and "form is rendered individual through being received in matter" (forma fit hec per hoc quod recipitur in materia). Super Boetium De Trinitate q. 4, a. 2 (Leon. 50.125:202-203).

116 tualized principle), respectively.

Also to be reckoned with are passages in which

Aquinas refers the individuating principle either to "designated" or to "undesignated" matter, and again certain texts in which he invokes a formal principle, rather than a material or even accidental one. Although Aquinas is quite emphatic in singling out materia signata and determinate dimensions as the individuating factor, he is also capable of saying that "division takes place in matter only in so far as it is considered under dimensions, at least indeterminate ones,"154 and, more directly, "the matter which is the principle of individuation is not just any matter, but only designated matter."155 But I say that this need not represent a wavering conviction on his part. Rather, in his occasional allusion to the role of "indeterminate" dimension he is simply harking back to the primal role of matter as the seat of determinate dimensions. From the standpoint of the mind's consideration, indeterminate quantity, as a concomitant of matter's potency, is the prior principle. That actualization (through the union of matter and form) introduces a difference between undesignated and designated matter, effectuating the latter, is clearly what Aquinas

The "material" and "quantitative" (dimensive) accounts are brought together in several places (e.g., Scriptum super Sententiis Liber IV, d. 12, q. 1, a. 1; Super Boetium De Trinitate q. 4, a. 2). Always the underlying thought is the same: only dimensions have the requisite characteristic - parts outside of parts - through which individuation can be accomplished; but dimensions can only inhere in matter. 154 "Divisio autem non accidit materiae, nisi secundum quod consideratur sub dimensionibus saltern interminatis: quia remota quantitate, ut in 1 Physic, text. 15, dicitur, substantia erit indivisibile." Scriptum super Sententiis Liber II, 30.2 (Mandonnet ed., vol. 2, p. 781). 155 ".. .materia non quolibet modo accepta est individuationis principium, sed solum materia signata." De ente et essentia, c. 2 (Leon. 43.371:73-75).

117 means in saying "before the advent of natural forms, dimensions are presupposed as existing in matter in a state of incomplete act, not of complete a c t . . . ."156 As a summary of much that has been said thus far I cite the following extract: By definition the individual is undivided in itself and divided from other things by the last of all divisions. Now among accidents quantity alone has of itself the special characteristic of division. So dimensions of themselves have a certain character of being individual with reference to a definite position, position being a quantitative difference . . . . So it rightly belongs to matter to individuate all other forms because it is the subject of that form which of itself has the trait of being individual. Indeed even determinate dimensions themselves, which are grounded in an already completed subject, are in a sense individuated by matter that has been rendered individual by the indeterminate dimensions that we conceive beforehand in matter.i57 Another instance of Aquinas describing a single reality from different standpoints is found in Summa theologiae: "Every natural body has some determined substantial form. Since therefore the accidents follow upon the substantial form, it is necessary that determinate accidents should follow upon a determinate form, and among these accidents is quantity."158 Again, quantity is grounded in the matter, but is only actualized through

"...dimensiones praeintelliguntur in materia, non in actu completo ante formas naturales, sed in actu incompleto," Quaestiones disputatae de veritate q. 5 a. 9 ad 6 (Leon. 22.1.165:357-360). See also Scriptum super Sententiis Liber I, d. 2, q. 1, a. 1: "quidquid est ejusdem speciei, non dividitur secundum numerum, nisi secundum divisionem materiae vel alicujus potentialitatis," where division of the potential is an actuation thereof. Mandonnet ed., vol. 1, p. 60. Super Boetium De Trinitate q. 4, a. 2 ad 3 (Maurer trans., p. 99). "Ad tertium dicendum, quod de ratione indiuidui est quod sit in se indiuisum et ab aliis ultima diuisione diuisum. Nullum autem accidens habet ex se propriam rationem diuisionis nisi quantitas; unde dimensiones ex se ipsis habent quandam rationem indiuiduationis secundum determinatum situm, prout situs est differentia quantitatis....Et ideo recte materie conuenit indiuiduare omnes alias formas, ex hoc quod subditur illi forme que ex se ipsa habet indiuiduationis rationem, ita quod etiam ipse dimensiones terminate, que fundantur in subiecto iam completo, indiuiduantur quodammodo ex materia individuata per dimensiones interminatas preintellectas in materia." Leon. 50.125:258265, 270-277. 158 Summa theologiae la, q. 7, a. 3: "omne corpus naturale aliquam formam substantialem habet determinatam, cum igitur ad formam substantialem consequantur accidentia, necesse est quod ad determinatam formam consequantur determinata accidentia; inter quae est quantitas." Leon. 4.75.

118 the form. Other accidents, likewise actualized through form, are also grounded in the form. Thus it is because of matter that form actualizes dimensionality, but because of form that the actualized being is black, or white, etc. Early in his career Aquinas made use of the Avicennian notion of forma corporeitatis.159 But there is no pressing need to suppose that he regarded this as a form distinct from either the substantial form (the unicity of which Aquinas always maintained vigorously) or the accidental form of quantity. Granted, that Aquinas abandoned his early use of Avicenna's term. But it may be that a trace of what Avicenna had meant - and perhaps all that Aquinas had ever meant in using Avicenna's terminology - remained as Aquinas would refer, even in the comparatively late Quaestio disputata de anima, to "that form which of itself has the trait of being individual," i.e., quantity. For Aquinas to say that "matter does not have division in virtue of the quiddity of substance, but in virtue of the corporeity upon which the dimensions of quantity follow in actuality,"160 may be nothing less than to affirm, albeit less directly than he will do later, that quantitative extension is a consequence of the determinate dimensions which follow upon matter. Let us now turn to a key text from the Quaestiones disputatae de anima, q. 9: From the fact that matter is known to have a certain substantial mode of existing, matter can be understood to receive accidents by which it is disposed to a higher perfection, so far as it is fittingly disposed to receive that higher perfection. Moreover dispositions of this kind are understood to exist in matter prior to the form, inasmuch as they are given existence in matter by an agent, al159

"Sed prima forma quae recipitur in materia, est corporeitas, a qua nunquam denudatur," Scriptum super Sententiis Liber I, d. 8, q. 5, a. 2. Mandonnet ed., vol. 1, p. 229. 160 "...ex quidditate substantiae materia non habet divisionem, sed ex corporeitate, quam consequuntur dimensiones quantitatis in actu," ibid.

119 though there are some improper accidents of the form that are caused in the matter only by the form itself. Hence such accidents are not understood to exist as dispositions in matter prior to the form; rather is the form understood to be prior to the proper accidents as a cause is to its effects.161 At first it may seem that Aquinas is allowing for certain "dispositions" (i.e., inclinations to receive this form rather than that one) to inhere in matter prior to its information. But this would not comport with the indeterminacy of matter vis-a-vis all forms. (The only "determinacy" we can ascribe to matter, that is consonant with Aquinas's usage, is its disposition of whatever form is received to a dimensive existence: materiality amounts to extendedness.) It is true that Aquinas is distinguishing between dispositions which pertain to matter as such, and other dispositions which are consequent only upon this form or that. But even the former do not pre-exist form; rather, they "are understood to exist [in potency] in matter prior to the form," such that they cannot but come into being when "they are given existence in [formed] matter by an agent." While Aquinas, as already noted, brings in two notes as characteristic of individuation, it is not clear, from the several texts we have considered, whether one or both of these notae is involved in his fully developed account. Does designated matter - i.e., determinate dimensions grounded in matter - bring about the divisum ab alio, the indivisum in se, or both? I submit that materia signata certainly gives rise to divisum ab alio. For what constitutes the hylomorphic existent as distinct from other such existents 161

"Et ulterius, ex quo materia intelligitur constituta in esse quodam substantiali, intelligi potest ut susceptiua accidentium quibus disponitur ad ulteriorem perfectionem, secundum quam materia fit propria ad alteriorem perfectionem suscipiendam. Huiusmodi autem dispositiones preintelliguntur forme ut inducte ab agente in materiam, licet sint quedam accidentia ita propria forme quod non nisi ex ipsa forma causentur in materia. Unde non preintelliguntur in materia forme quasi dispositiones, sed magis forma preintelligitur eis, sicut causa effectui" (Leon. 24.1.81:217-229).

120 is its "having" a matter that they do not have. (I am not supposing matter as such to have extension; rather, as the ground of extendedness it bestows on each existent a dimensionality which other existents by definition cannot share, since it is of the nature of extension to have parts outside of parts.) But what about indivisum in sel Here matter, signed or otherwise, would appear to be insufficient. In fact, given the function of matter to ground the actuality of "parts outside of parts," the hylomorphic being's unity would seem to be compromised so far as its material principle is concerned. For such a being is made up of parts, beginning with the elements, which are distinct from one another through their diversity of place and position. (One manifestation of the corruption of a substance is the tendency of its parts to break down into new wholes.) Yet what holds together the diversity of parts in a substantial unity is the form, which in turn implies unity of function toward an end (entelechy). Hence indivisum in se seems to be due to the formal principle, leaving only divisum ab alio to be referred directly to determinate matter. Form and matter are complementary in such a way that each one's ratio is involved, to some extent, in the other's. And just as indivisum in se and divisum ab alio imply each other, so with respect to form and matter: it is because matter is a principle of extension that form provides unity, and because form is indefinitely realizable that matter exercises its limiting role. The question of individuation arises at the level of sensible being. Our awareness of individuality is, in the first instance, based on what is seen and felt; it is spatial. Things are perceived as distinct to the extent that they are perceived to have different

121 places, i.e. to occupy different parts of the extended order of being. Intellect then determines formal unities transcending the severality of the parts in extenso. We have seen that Aquinas invokes the quantitative potency of prime matter, the actualizing disposition of the substantial form, and the determinate accidents of extensive quantity in his account of so-called "individuation by matter." Matter as the root principle is in fact the ground of extendedness, such that hylomorphic being may be described as extended being. Matter is not extension; this is an oversimplification, embraced by Descartes and, long before him, by various pre-Socratic and Neoplatonic thinkers. Matter's pure and substantial potency must not be overlooked. Matter is a potency to form's existence, and that existence, in virtue of materiality itself, is in an extended mode. (The same form can exist immaterially, without extension, in the intellect. Were it not the same form, knowledge of essences would not be possible.) Hence, at the appropriate level of abstraction, we can say that materiality is dimensionality - which is not to confuse materiality with dimension or quantity, since "dimensionality" is here understood to mean "that whereby a thing can have dimensions" - more precisely, "the mode of existence in which a thing can have dimensions." I am using the term "dimensionality," in relation to actual dimensions, somewhat analogously to the use of term "mass" in relation to weight. Mass is not at all synonymous with weight: a massive body can be weightless. But in a gravitational field the massive body, in virtue of its mass, albeit not without the gravitational "actualization," will possess weight - a weight which can vary infinitely for that body depending on the gravitational field's strength. In analogous fashion the "dimensionality" connoted by

122 materiality can, upon actualization by substantial form, give rise to dimensions - which vary depending upon the forms, substantial and accidental, which actualize them. Expressed more concretely, then, matter is that existential principle by which a thing is extended. But is this not to say that matter is extension? Again no. Matter entails extension, but is not extension - it is the principle of extension. Only in conjunction with form does extension become actuated, and even then its precise determination falls under the accidental mode of quantity, variable within limits set by the substantial formal principle. If the divisibility implied in extendedness is what enables determinate dimensions to be the principle of divisum ab alio, then we need look no further for the radical explanation of unilocality162 - the impossibility of more than one material being occupying a given place. For one place - "the innermost immobile boundary of the surrounding body," for Aristotle and Aquinas - is distinguished from another abstractly by the non-coincidence of their parts, and concretely by the nonidentity of the beings which occupy them. Substantial being is prior in the real order to quantity, an accident, so the reason why two bodies cannot occupy the same place is that their respective acts of being are distinct. Therefore the extensive or dimensive attributes of those acts are distinct, and to be distinct with respect to extension is none other than for one to be outside the other. The question occasionally entertained by philosophically-minded scientists: "Can two bodies occupy the same place?" is thus seen to be oxymoronic in its very 162

A neologism for which I should make apologies, but there seems to be no terser expression.

123 formulation: it amounts to "Can those things which must occupy two distinct places occupy one place?" So fundamental is this approach that we can use it as a basis on which to answer, a priori, a seemingly empirical question - "Does not light, in passing through glass, occupy the same place as the glass?" - in the negative. For if light is a physical being, as evidenced by its sensibility, its local motion, its transformability into more obviously corporeal forms of being, then it cannot, per the definition and essence of physical being, be occupying the same place as the glass.163 The heart of the preceding argument may be summed up thus: No spatially individuated things are collocated (this from the definition of individuation); but all material beings are spatially individuated (this from Aquinas's argument for the role of matter as individuant); therefore no material beings are collocated.

H. Matter and spatiality The terms "place" and "space" are sometimes confused or used interchangeably, and Aristotle notes the kinship between the concepts, at least in common usage.164 But a close analysis of place ends in its being attributed only to a body in terms of other body, while space is seen to have, as its nominal definition, place with no body in it.165 The Aristotelian - and, by extension, the Thomistic - treatment of place is much more de-

163

Allowance must be made, initial appearances notwithstanding, either for some sort of adjacent coexistence (as water in a sponge), or for a transient unitary existence (light "becoming" glass or vice versa, analogous to water freezing into hail and then reverting to liquid water as it passes through different strata of the atmosphere), rather than a true collocation of distinct entities. 164 Physics IV. 6. 165 72>zVUV.7,214a5-18.

124 tailed than the treatment of space. This is largely due to the fact that space is, for these thinkers, only ens rationis, its real existence an impossibility. Place, on the other hand, is a real mode of being, conceptualized directly from the sense data prior to any mathematization and subsequent abstract consideration. Several Greek terms are nearly synonymous: what is perhaps closest to our English "space" is chora,166 which we have seen variously explicated in Plato's Timaeus, while "void," kenon, is less likely to carry the note of extension in addition to "emptiness."

"Extension" itself, diastema, is also used occasionally in contexts where Aris-

totle is addressing the topic. Proceeding, as usual, from the more known to the less, Aristotle first defines place (IV. 1-4) before attacking the possibility of subsistent dimension or void space (IV. 6-9). Nevertheless the definition of place implies the impossibility of void; what is prior in order of discovery is posterior in order of causality and explanation. The analysis of place, then, proceeds by way of an elimination of dialectically considered candidates. It cannot be either matter or form, as these are principles intrinsic to a thing which is in place;168 when a body moves to or from a place, the least we must affirm is that the body has not taken its place with it. There remain two possibilities extrinsic to the mobile body. The first of these is dimensionality or space, i.e. "the extension [diastema] between the extremities [of the

208b32,209a8,209bl2-18. 213a33,213b26ff., 214a5-18; 214M8. IV. 2, 209b21-34.

125 emplaced body]."169 Aristotle's arguments against identifying place with (what amounts to) merely the space it occupies are difficult,170 nor is Aquinas's extended commentary much easier to follow.171 The final possibility, on which Aristotle will settle as the appropriate definition of place, is "the limit of the containing body" - further specified, in view of considerations of relative and absolute place, as "the innermost motionless boundary of what contains."172 Without going into the particularities of Aristotle's cosmic scheme, which make untenable some of his conclusions about absolute and relative place and the role they play in natural motion,173 we can note that place, the basis of Aristotle's allimportant definition of motion, is defined strictly as a relation of bodies - extended beings - within the order that characterizes them precisely as bodies. For extendedness, which might seem prima facie to be a very tenuous or abstract analogue for body (given the latter's connotations of solidity), will be seen in its ontological fullness to be the proper ground of that impenetrability or "unilocality" of bodies which defines them as such, and is what solidity itself amounts to. The science of physics is concerned with mobile being: this is what first confronts us as sensible in virtue of its extendedness (and resulting connaturality with our

169

211bl4. 211bl8-29. 171 211M4-29; In libros Physicorum IV, lect. 6 (§461-3). 172 212a20. 173 But I will caution against a too facile conclusion that Aristotle's doctrine of natural place was "naive"; differing only in terminology and "location," but not in essence (since force remained only a quantifiable inclination), would be Newton's idea that bodies are accelerated toward a gravitational center, or Einstein's idea that they tend along a spacetime geodesic, in accordance with their mass. 170

126 sense organs), and is then determined to be material. What does it mean, then, to affirm that physical substances are spatiotemporal? Is this merely a statement of the brute fact, reaffirmed upon analysis, or is it a conclusion of properly physical investigation? It is both; what is first apprehended via external and internal senses as temporal (i.e. mobile) is seen, on analysis, to be extended and temporal in virtue of its material principle, i.e. through its very nature and definition. This is an instance of the demonstrative regressus: the intellectual process of discovery or resolution brings us to prime matter, which is then understood to be a principle of deductive inference in the return to sensible being, the original explanandum. At this point we can affirm that material being is per essentiam spatiotemporal, and, given our starting-point in the regressus (which was not this extended mobile being or that, but extended mobile being as such), we have convertibility. Spatiotemporal being is none other than material being, and vice versa. In turning to a direct refutation of the possibility of existent void, Aristotle first brings forward arguments from motion, and then from the definition of void itself. The main argument from motion is this: there could be no motion in a void space because such space is undifferentiated and thus cannot intelligibly ground the locomotion of any body within it.174 There would be no reason for a body to move in one direction rather than another, or to move at all. (Nor, we might add, can sufficient reason be found in the mobile as such, because at any moment it exists only in the present; past and future, which define the mobile's trajectory, are not actual qua past and future. Even appeal to 174

214bl2-215al4.

127 an extrinsic motor cause, with its implication of finality, does not circumvent the unintelligibility of a body "moving toward nothingness," which must be the condition of a mobile at each point on its trajectory through void space.) Even if the void were extension, existing per impossibile without a subject, there could be nothing in the nature of its quantitative differentiation that would influence a mobile body on one course through the void rather than another, since in respect of such a body considered precisely as mobile all quantitative determinations must be ontologically equivalent.175 The argument against void based on motion is a properly physical argument, and as such seems to lack adequate universality to rule out the possibility of void altogether. It concludes to an impossibility of motion, and, by extension, of mobile being, in a void, and this is sufficient in a cosmos comprised only of mobile being. But Aristotle goes on176 to base a metaphysical argument against void on the very concept of void. Since it is the nature only of body to be displaceable by another body, then placement of a body in void space would not displace the void; instead the latter [in its dimensionality] would "penetrate" the emplaced body. Hence there must be, in the volume occupied by the body, two identical magnitudes - that of the body itself and that of the void occupied by the body. But to have two identical magnitudes in

I mean that it would make no difference to a thing's ontological constitution whether it be moving in direction x ovy, at speed p or q, in the abstract; but given that these factors are inevitably linked to the presence of other bodies - "pure" inertial motion remaining only an abstraction - then even today we know only of motion that includes body or bodies (other than that of the mobile) in its definition. 176 Physics IV.8, 9.

128 one place is absurd.177 "How then will the body of the cube [which Aristotle is using as an example of a displacing body] differ from the void or place that is equal to it?"178 The argument is not trivial. Were nothing more meant by "body" than something which can be measured through spatial coincidence, it might seem a trivial thing to object that a body should be considered to have the same dimensions as the place in which it is located (rather like objecting that a line should be one foot long and also twelve inches long). But as we noted in treating of individuation, the impenetrability of bodies - in virtue of which they displace one another - is due precisely to their dimensive quantity which, consisting in essence of "parts outside of parts," is radicated in prime matter. In other words, quantity does not exist except in virtue of matter, and it is the nature of quantity so existing (real extension, as opposed to its abstract analogue in the mind) to be exclusive in all its parts. Extension, grounded in matter, is what individuates physical being. Hence by whatever means a body were understood to coincide with the dimensionality of void space, two bodies - or indefinitely many - could also coincide, which is absurd. The argument just presented is reminiscent of the one Aristotle had advanced in rejecting void space as a candidate for "place." In the earlier case he had reduced the hypothesis to the absurdity of having infinite places in one place, while here it is reduced, in effect, to the absurdity of individuals not being individuated.

216a26-216bl2.

129 The persistence through history of the concept of void space, not to mention its wholehearted embrace by a thinker of the stature of Newton, is a curious testimony to the power of intellectual abstraction and the risk we run of mistaking the conceptual for the real. At a pre-philosophical level it should already be obvious that nothingness cannot be; if there is dimensionality, then there is something, not nothingness; and to reify that extension - to attribute to it a positive influence on concrete being, either as that in virtue of which inertial motion can be determined (Newton) or as that in virtue of which every motion occurs (Einstein) - is simply to indulge the myopia of mistaking the part for the whole, in the manner of the proverbial blind men severally declaring the elephant to be a wall, a tree, or a rope, depending on whatever part of the beast each one had encountered. There is, then, no actual void, no possibility of dimensionality existing on its own, no ontological allowance for a "nothing" which is nonetheless "something." Whatever is extended in re, is material being; and spatiality is its very extendedness in abstracto. Or, if we insist on regarding space as anything beyond an ens rationis, we might, by stretching common usage a bit, consider it "the extendedness of material being," or better still, material being under the aspect of its extendedness. Informed matter - the only matter that constitutes existents - can thus be said to constitute space, in the only sense in which space is real. But it seems one could also say, correctly, that prime matter is space, taking advantage of Aristotle's recognition of potency as Plato (and Descartes, for that matter) did not. For if "space" cannot exist as such, it is akin to matter in precisely this regard, i.e., not existing as such, but only as

130 informed. I do not mean to say that matter and space are convertible, for space denotes only one aspect of matter; but it does seem to be synonymous with that aspect. Because "space" denotes something which can only stand as a potency to actual dimensiveness, Aristotle rightly criticized Plato for any suggestion of reifying the chora on its own. And Descartes is seen to have perpetrated a similar (and rather more explicit) error, in identifying material substance with extension. No room is allowed, in Descartes' account, for properly distinguishing the potential and formal principles of substance; but only through such a distinction can extension avoid being confused with form. As the instant is to duration in the temporal order, so is place to space in the spatial order. Only the now, and only place, entail actual existence with reference to real beings. Duration, apprehended by us as past and future - an "extension" of the moment - and space, apprehended by us as a manifold of all places, are not present to our intellect except as abstractions from the real. The subject of Euclidian versus non-Euclidian "space" is, in any physical context, likewise chimerical - a question of geometries rather than of space as such. Spatiality is mere extendedness, the condition of having parts outside of parts, and irreducibly three-dimensional; the properties of points, lines, surfaces and other geometrical entities are abstracted from bodies (spatial beings) and posited in the mathematical imagination. It is because they are defined, mathematically, without reference to their material origins that they can take on a "life of their own," submitting to manipulations which are simply not possible at the primordial level of abstraction. But it is well worth

131 noting that such manipulations, in so far as they remain logically connected (at however great a remove) to their point of origin, cannot represent a complete departure from the natural foundation whence their progenitors, so to speak, were drawn. So long as there is no break in the logical succession of abstractions (such that each is defined, positively or negatively, in terms of what precedes it), it can hardly be said that later abstractions represent other than an evolution of what was implicit from the beginning. There is no concept in non-Euclidian geometry, for example, that cannot be defined in terms that are ultimately Euclidian. The limitless variety of mathematical formalisms, not a few of them now having proved their worth upon retrospective application to the physical world, follows from the continuity and indeterminacy of the extended order as such. No mathematics will ever prove uniquely adequate to the possibilities inherent in the material or cosmic order.

I. Principle of corruptibility Perhaps no aspect of matter has drawn philosophers' attention more than its role in the corruption of substance that accompanies every generation. Whatever is material is transient, whether its existence be measured in milliseconds, millennia, or time scales comparable to that of the universe itself. It is precisely the corruptibility of material being that throws into relief the immutability of essences. The formal principle, that which primarily characterizes the essence, cannot be a cause of its own demise. Nothing in what constitutes form as form entails or indicates cessation of existence. On the con-

132 trary; the activity by which form manifests itself is in every case a perfective and preservative activity, even though really distinctfromthe act of existence itself. Do we then attribute the corruptibility of substance only to extrinsic causes, agent and end? This will not suffice either - not if we are interrogating the world philosophically, in the antecedent conviction that it is inherently intelligible. If extrinsic causality alone were responsible for the flux of cosmic being, there would be no sufficient reason (that we could discern) for things to change in a certain way rather than in another, or in any orderly fashion. The world would present itself as no more than an occasion for the play of divine free will, and our explanations would still be at the level of myth. The compelling reason for recognizing an intrinsic intelligibility in mobile being is, however, not to be found in mobile being itself. (Here, as in so many other arenas of philosophic inquiry, we find that some version of "Godel's theorem" is apropos: a given order of intelligibles cannot yield the principles of intelligibility.) This is a topic requiring further exploration than we can pursue here, but we may say briefly that when Aristotle, and still more explicitly Aquinas, traces each of the four causes to a First, he need not assume that the order of causation in question is intelligible through itself. The ground of intelligibility does not enter into consideration at this point; only the fact of intelligibility (in one causal mode or another), and its implications. But once each line of causation is traced to a First, and those "Firsts" are seen to be one, and are identified with the creative Origin of the universe, then we discern an epistemic basis for the intelligibility of each causal influence. There is reason not to

133 posit absolute unintelligibility of anything issuing from the creative Intellect. For Aquinas, it is part of the created perfection of the universe that the rationality of its Origin and End be reflected throughout its fabric. We become philosophically certain of what was known pre-philosophically: that cosmic being in itself, and not only through its extrinsic causes, is intelligible. And so I return to corruptibility, and the search for its intrinsic cause(s). Must it not be matter? This is not to suggest that we should see, in matter, a causality "displayed" for our full comprehension; matter, as pure potency, remains unintelligible to us. (My implication, in the preceding paragraph, of matter's inherent intelligibility, did not entail intelligibility with respect to the human knower, nor of the quidditative order.) Yet perhaps we could at least see in matter the source of a thing's instability in existence, however indeterminate that may be. But such an hypothesis falters on more than one count. First, since matter is indeterminately receptive of form, there would be no sufficient reason for it, considered in its own right, to be receptive of one form rather than another - in other words, no reason for it to engender any corruption at all. Secondly, as a constitutive principle of unitary being, matter cannot be implicated, any more than form, as a positive factor in its own destruction. The principles that give rise to materiated being cannot also be the principles that are destructive of it. The solution to our problem - what is the intrinsic cause of corruption? - must be drawn, not from any one of the causes, but from all four mutatis mutandis. Due to the consideration just mentioned, intrinsic factors will not suffice, but we must look to ex-

134 trinsic ones. Yet to avoid intrinsic unintelligibility we will also invoke matter and form, in roles that are not self-destructive. Let us look at form first. Form is an active principle of corruption - but of beings other than the one of which it is constitutive. A being's formal principle certainly does not act against its own existential integrity; but it can, in virtue of secondary activity through its accidental modifications, impugn the existence of other hylomorphic being. This is occasioned and occurs via spatial contiguity. (As cause of corruption in other beings, form of course operates under the aspect of agent cause.) But how does one formal principle act to "eliminate" another from existence? There is, to be sure, a cosmic mystery here: somehow, in ways we designate quantitatively with terms like "force" and "energy," there is a prioritization or hierarchy of existents, so that some of them succumb to others, rather than the other way around, as the cosmic dynamism plays itself out. A formal principle that is "dominant" amid one constellation of accidents (its own and others') will not be so in another. But to the activity of one formal principle there must correspond the "passivity" of another. I put the word in quotes, because this is only a relative characterization; every form is properly an active principle. What is it, then, that causes mobile being to undergo the substantial change called corruption, under the agent and teleological influences of other mobile beings? It is the passivity or potentiality of matter that enables the "other" formal principle to act on the composite undergoing corruption. This matter is just as receptive of a new form as it is of the form that currently inheres in it - more properly, by the acci-

135 dents grounded in that form. We say that prime matter's receptivity is absolute and undifferentiated - but that is to speak of it in the abstract. In the concrete existent, matter's potentiality is limited, conditioned, predisposed, by the form which inheres in it. Here is where we find the only role of form in its self-destruction, so to speak - not as a cause, but as a dispositive factor.179 A hylomorphic being is inclined to corruption, to the separation of its matter and form, only so far as its material principle is receptive of forms indiscriminately. (That is what matter is: a receptivity or inclination to the existence of other forms.) But the same being will, under the influence of extrinsic causes, corrupt only in certain ways and not others, thanks to the directive influence (or dispositio materiae) constituted by the accidents of the formed matter. Thus the substance known as table salt, while not inclined to ^e^-destruct, will, under sufficiently strong extrinsic influence (e.g., a powerful electric current), corrupt - not into nitrogen or argon, however, but only into sodium and chlorine. While form's positive role in the corruption of hylomorphic being is only dispositive, there is another sense in which form can be spoken of as a more direct principle of corruption. But this is a negative role, not a positive one. Hence we cannot call it a cause under this aspect. I mean, of course, the privation identified by Aristotle as one of the three intrinsic principles of change. Privation is the absence of a form , not just any form, but a form toward which the present form is disposed. Hylomorphic being, then, undergoes substantial change in so far as it is acted upon by other being. Its matter renders it susceptible to corruption, not directly but indi179

See next chapter, section G.

136 rectly inasmuch as matter is indifferently receptive to all forms. Its present form constitutes, in virtue of accidents associated therewith, only a dispositive or directive principle in any corruption that does occur. The object of this disposition - the absent or future form to which the present form is said to be disposed - is called the "form" simply, as terminus of the change. But the absence of that form, considered as "present" in the mobile being, is called the privation. Because form as such is not inclined toward nonexistence (its very ratio is that of existential specification), the present form of an existent X is not included by Aristotle or Aquinas among the intrinsic principles of change. When we frame our investigation in terms of the most radical metaphysical principle, we find it natural to express the relation between matter and privation thus: as esse is to form, so is matter to privation. Matter is the not-yet of existential act, a certain dynamism of esse, while privation is the not-yet of form or intelligibility, a certain inclination to other form. To the consideration of matter and esse I now turn.

J. An existential principle of essence Every meaningful philosophical analysis presupposes a metaphysical foundation, even when that foundation does not come into explicit consideration during the analysis. Our project, in this dissertation, of considering physical phenomena in terms of naturalphilosophical principles would remain incomplete if we did not indicate the metaphysical radication of those principles. The doctrine of matter, as taken over by Aquinas from Aristotle's natural philosophy, could not but be adapted in accordance with Aquinas's clarification of the Ar-

137 istotelian approach. This modification, perhaps the greatest single advance in the history of philosophy, is a recognition of the distinct roles of essence and the act of essence in the metaphysical analysis. What was relatively obscure in Aristotle would become quite clear in the thought of Avicenna, and central in the philosophy of Aquinas: that every finite ens is composite, with the existential act or esse being the ground, in the composite, of different aspects of being than the essentia. A further explicitation of the Thomistic doctrine of the real distinction between essence and esse (N.B. that "real" does not connote that these principles are real in and of themselves, but that their composition gives rise to ens reale) is the notion, largely a product of the lO^-century revival in Thomism, that esse has primacy to the extent that even essence must be reduced in some way to esse. In so far as all finite being flows in its entirety from God who is pure act, ipsum esse subsistens, there can be nothing in finite being which is not derived from divine esse. Now that which limits this participated esse, and which we know as essence, cannot itself be esse, nor can it be "something else." In the first case, that which limits esse would itself be esse, existence limiting existence, the unlimited limiting the unlimited both meaningless conclusions. In the second case, the "something" would either lack esse, so that the nonexistent would constitute a limitation upon existence, or it would "have" esse, which would involve circularity. Hence what limits esse in the order of real being is neither esse itself nor anything else which has esse; the limiting principle is not of the existential order at all, except in so far as it is a limitation of existence. It is, in a real sense, "nothing." Any other conclusion, ascribing to essence even the slightest enti-

138 tative or existential character in its own right, fails to do justice to the primacy of the actualitas omnium actuum, existence considered as what sets off beings from their mere possibilities. Indeed, the way in which we are compelled to think about esse can easily mislead us into treating it as a quasi-essence, when it is simply the existential principle. The only thing (ens rationis) which can delimit esse is non-esse, and this is what essence must be: none other than the limitation of esse. Contrary to the fears of some Thomists, that an existentialist account of essence must impugn the doctrine of the "real distinction" of essence and esse, there is in fact no contradiction in maintaining such a real distinction even though the principles so distinguished are existence and its delimitation. (Analogously, there is a real distinction between every spatial being and its spatial boundary, though that boundary is not a separate entity, but simply "where the being ends." We cannot predicate of the boundary what we predicate of the being, and vice versa. Yet the being cannot exist without its boundary, and vice versa.) It is noteworthy that, while Aquinas doubtless holds for the real distinction which in later times would become so closely identified with his metaphysics, he is not given to using the term perhaps because he prefers to avoid any implication that the principles really distinguished are themselves independently real. Now the essence comprises, in hylomorphic being, both formal and material principles. If essence is a limitation upon existence, such that every finite existent, an essence-e^e composite, is a limited participation in esse, then both form and matter as co-principles of essence must be referred to esse as its limitation. Form, for both sepa-

139 rated and hylomorphic substances, is a primary principle of limitation, and as such the principle of intelligibility for finite intellects.180 The question, then, is how matter can be explicitated as a principle of existential limitation while remaining distinct from the primary limiting principle within the essence. We have seen that matter enters into the essence inasmuch as material beings must be defined with reference to matter; that it is the ground of individuation, and of extension; that it is the substantial principle which enables corruption. All of these notae can readily be grasped under an existential aspect. The material essence is precisely one whose existence is contingent through corruptibility. Extension or spatiality is the mode of existence whereby individuals are at once distinct and interactive (corrupting and corruptible). And complementary to the corruptibility of individuals is the continued existibility of the species, since the individual existent does not exhaust the existibility of its essence. Hylomorphic forms exist only as materiated; it is by "composing form and matter" that the agent cause brings them into the order of existence. In other words: certain kinds of form are only able to exist contingently. Clearly matter exercises a causality which is existential rather than essential, in so far as it is not directly intelligible. Its role in the essence is that of conditio sine qua non - just as form is a kind of limitation of existential act simply speaking, so is matter a kind of limitation of the limitation, a secondary limitation that emerges from the dynamism of hylomorphic esse. Hence matter is included, in a division of the four causes, with the agent as an existential-order 180 Angelic being remains incomprehensible to us because, firstly, it exceeds the capacity of our lower intellects and, secondly, it is not conjoined with matter - abstraction from which being the only human mode of knowing in statu viae.

140 is included, in a division of the four causes, with the agent as an existential-order cause, rather than with form and end as essential-order causes.181 Form is a limitation constitutive of the essence; matter is a limitation within the essence. Form, in limiting esse, brings about intelligibility, while matter re-introduces unintelligibility to the extent that it "opposes" form's hold on existence.182 The unintelligibility of esse is tantamount to the unreplicability, by the human knower, of the creative act in which esse is imparted; the unintelligibility of matter is that of the dynamism or contingency of that imparting. Both esse and materia evoke the Creator's power.

K. Further metaphysical reflections Among those who have tried to express a neo-Thomist understanding of matter in terms of esse was William Carlo, whose contributions in this regard exhibited both the boldness and the weaknesses of a pioneer's effort. Carlo's overriding thesis is indicated by the title of his full-length study, The Ultimate Reducibility of Essence to Existence in Thomistic Metaphysics. In his approach to treating essence as simply the limitation of existential act, he alleged certain texts in Aquinas which admit of apparently contradictory interpretations. Among these, he said, are passages which treat of esse now as primatial, now as accidental to essentia; those which speak of essence as something

181

See Appendix 2. It may be speculated that, were matter a principle only of individuation through unilocality, it need not be an impediment to intelligibility; but since its role is also that of substratum of change, entailing a passive potency to new informations (corresponding to the active potency in the agent cause of those informations), all material being is dynamic and mutant. In abstracting from matter the intellect is abstracting from both matter as mode of existence and matter as indeterminate. 182

141 receptive of esse, yet as nonbeing; and those which portray matter also as nonbeing, which nonetheless is a similitude of divine Being. Carlo summarized Thomistic prime matter as pure potentiality, stripped of all determination, deprived of all form but nonetheless combined with form, exerting a real causal efficiency in order to limit it. This principle is in the genus of substance but it does not exist except under form. It is so completely bare of intelligibility that even God does not know matter: He does not have a divine idea of matter except in the composite, under form....It is non-being or nihil. But in other texts it has a form of its own. It is without qualification but it is a similitudo and has a being of a sort, a weak esse and an incomplete esse. It is almost nothing, yet it is a being. These apparently contradictory texts are the same kind which we find in the doctrine of the possible essence.183 The hypothesis whereby such contradictions can be resolved at the metaphysical level is presented in negative terms: "any attempt to explain the ontological location of prime matter without reducing it to a mode of esse is ultimately fruitless and eventually ends in the kind of discussion that consists in repeating over and over again the simple elements of the definition of prime matter"184 - i.e., such an attempt does not move beyond the physical to a properly metaphysical ground. Again, "since matter is a mode of being we should be able to explain the doctrine of matter with all its application without using the term matter itself, but substituting a metaphysical language of esse plus some adjective or group of modifiers in lieu of a definition."185 He rightly observes that the "test case problems of the doctrine of matter ... would include historically: the substratum

William E. Carlo, The Ultimate Reducibility of Essence to Existence in Thomistic Metaphysics (Leiden, 1966), pp. 119f. 184 Carlo, Ultimate Reducibility, p. 121. 185 Op. cit, p. 122.

142 underlying change, individuation, indetermination and pure potency, abstraction, extension and so on."186 Why is it that when we attempt to extend metaphysical principles to cover all of the reality to which they properly apply, we always stop short at change? As soon as it is a question of explaining change we prescind from the principles of being and fall back upon the Aristotelian theory of matter and form. But Thomas Aquinas was not aware of such limitations on the doctrine of being. He speaks of change as the movement from esse ad non-esse. He actually defines motion as actus existentis imperfecti in potentia. Why do we almost invariably ignore the large number of texts in which Thomas Aquinas seems to be attempting to explain change in terms of ewe?187 It seems to me that Carlo's own endeavor, while animated by a sound instinct, was at times only minimally philosophical. Trying to formulate a thesis that has not hitherto been widely excogitated, Carlo wrote in a far from linear fashion and was much given to vague and repetitive assertion, with a tendency to intimate abundant textual corroborations of his thesis though never adducing many texts. "When Aristotle arrived at the idea of prime matter by a progressive process of abstracting all positive determinations from the substratum underlying change, is it possible that, as he peeled away form after form, he arrived at a reality that was, but was not conceptualizable?"188 This prescinding from the intelligible altogether can reasonably be assigned to a "deprivation rooted in esse.... And just as essence and existence are not reciprocal causes but essence is reducible to existence, so matter is the limitation of form, the place where form stops, in what is basically an immaterial universe."189 l

*"Op.cit., p. 123. Op. cit., p. 124. 188 Ibid. 189 Op. cit., pp. 124f. The last qualification is extreme; we are certainly not doing away with matter when interpreting it as a modality of esse; but perhaps Carlo had in mind "immaterial" with reference to a quasi-formal, essentialist conception of matter. 187

143 Acknowledging the significance of the principle forma dat esse materiae, Carlo asks: what does it mean? If it cannot entail, absurdly, that matter somehow preexists form, "does it simply mean that form as the concrete existent is that in which matter has existence as a privation of some sort?"191 By privation he means, not the principle of generation identified by Aristotle (that principle is of the formal order, albeit per accidens), but a lack or receptiveness in the existential order, what we may call an existential analogue to privation in the essential order. Privation of form, in virtue of which substantial change occurs, finds a corresponding principle (in virtue of the universal complementarity of potential and actual principles) in the privation of esse. But the privation of form is apprehended only through distinction of forms, through successive formal intelligibilities, while privation in the existential order is apprehended (broadly speaking, since it is not intelligible as such) through the sheer dynamism of hylomorphic being - not what it changes into, but its changeableness, the existential succession of forms. "Esse thus provides an ontological status for matter outside of form but still within being as the phenomenon of the 'elasticity of ewe.'" 192 Again, each hylomorphic existent shares in "the causal efficacy of Ipsum Esse Subsistens. The whole universe of

190

Cf. De ente et essentia, c. 4: "illud quod habet rationem causae potest habere esse sine altero, sed non conuertitur. Talis autem inuenitur habitudo materie et forme quod forma dat esse materie, et ideo impossibile est esse materiam sine aliqua forma" (Leon. 43.376:43-48); Deprincipiis naturae c. 1: "Sed materia habet esse ex eo quod ei aduenit, quia de se habet esse incompletum. Unde, simpliciter loquendo, forma dat esse materiae" (Leon. 43.39:30-32); Quaestiones disputatae de anima, q. 10 ad 2: "cum materia sit propter formam, hoc modo forma dat esse et speciem materie" (Leon. 24.1.92:286-288), etc. 191 Ultimate Reducibility, p. 125. 192 Op. cit, p. 126.

144 esse is an elastic thing, each component acting on the other, the constituents sharing their basic acts of existence. Each thing desires esse....The movement of the material being to add to its esse has a very illuminating parallel for St. Thomas with the amplitude of the intellectual being"193 - since the soul "is the least in the order of intellectual substances, as prime matter is least in the order of sensibles."194 "Matter is not esse itself, nor the determination or limit of esse, nor the absence of esse purely and simply, but 'the esse itself as somehow deficient,' but deficient precisely in what is not owed to it by its nature ... but in what it could receive from secondary causes."195 It is "not simply mode or limitation but it is a secondary mode or limitation."196 This is perhaps the heart of Carlo's attempt to understand prime matter in terms of esse. "Essences are the primal stages of esse, and make things to be the kind of things they are. But within this primal stage there is a secondary stage which enables a thing to be more or less what it is, to increase in being without becoming other than what it is." In this last, and some other related remarks, Carlo seems to have had in view only accidental change. But, as he elsewhere makes clear, the same understanding of

Iy3

Op. cit, p. 127. St. Thomas, Quaestiones disputatae De anima, cap. 8: "[anima] sit infima in ordine intellectualium substantiarum, sicut materia prima est infima in ordine rerum sensibilium" (Leon. 24.1.66:185-187). 195 Carlo, p. 128. Another instance of Carlo's lapsing from rigorous terminology is his saying, when describing matter as ens in potentia, that it is "an existent which is capable of perfecting itself or being perfected by the reception of esse to the aggrandizement and completion of its original esse, precisely because it lacks esse" {ibid.) - the problem here being denoting matter as an "existent" (it is only & principle of the existent). Of course, Carlo is following Aquinas's lead, and the constraints of ordinary language, in referring to matter's "reception" of esse. 196 Carlo, p. 135. 197 Ibid. If I may suggest a simpler way of putting it: form is a delimitation of esse; matter is variability in the esse thus delimited; the form-matter composite is "esse delimited variably." 194

145 matter applies to substantial change. Not only does the esse of a hylomorphic being admit of accidental variation, but it entails the existential vulnerability of the entire substance. To say that form is the actuating principle of a hylomorphic being is to say that form is a determination of participated esse of such a nature as can be supplanted in existence by another formal determination thereof, through the cosmic interaction proceeding through formal principles but made possible by materiality. The esse debile of hylomorphic beings entails their mutual susceptibility and dependence - a dependence, as we have seen, manifested at the physical level in their spatiality, unilocality, and mutual interaction.198 The existence of all finite being is contingent on the agent cause; the contingency of hylomorphic being, unlike that of separate substances, is mediated, even at the substantial level, by other hylomorphic beings. Matter's "potency to form" (the very phrase an artifact, I make bold to say, of a somewhat essentialist terminology) is really a potency to the existence of form, to beinginformed, whether at the accidental or the substantial level. Now matter thus considered emerges first from an analysis of mobile being: it is, in other words, a properly physical principle. But once we have situated it in its metaphysical context as the modality under which spatiotemporal beings have their esse, we are in position to examine further this ratio of potency. I now address the following questions: (1) What does it mean to describe prime matter as pure potency? (2) What does it mean to speak of prime matter as esse or as having esse? (3) What does it mean, 198

Carlo was given to using the phrase esse debile to denote matter, but Aquinas in fact never does so; the closest he comes is in Quaestiones disputatae de veritate q. 3, a. 5 ad 1: "quamvis materia prima sit informis, tamen inest ei imitatio primae formae: quantumcumque enim debile esse habeat, illud tamen est imitatio primi entis." Leon. 22.1.112:56-60.

146 to speak of prime matter as "receiving" esse from form? (4) How is prime matter to be understood vis-a-vis the ipsum esse subsistens or pure act? (1) When matter is apprehended under the aspect of potency, two distinct considerations arise: [a] the ground or subject of this potency, and [b] its term or object. The two taken together give us the ratio we are seeking. As to the first consideration, clearly it cannot be the form, as though the hylomorphic form were in its essence ordained to self-destruction. Nor can "matter" coherently be said to be the subject of its own potency. Its subject must rather be the composite being as such: we predicate potency, not of matter simply (except convertibly), nor of form, but of the hylomorphic ens as a whole. And the object, or that to which the potency is ordered, is the existence of further formal perfection. In the next chapter we will examine the role of form in disposing every hylomorphic composite to receive certain forms and not others. But with respect to matter considered in itself, there is no specification: prime matter as such is potency to any and all form. Prime matter is called potentia pura because it involves no actuality whatever in its own right; it is a principle of potentiality, of incompleteness, in that which is actual. As pure potentiality, matter must be susceptible of every information. Any limitation of its potency could only come about through a principle of actual limitation, namely its correlative principle, form. Of course we speak of matter's boundless potency only within a context of spatiotemporal cosmic substances; matter, Aquinas was at pains to emphasize, is in no sense a potency to angelic existence.

147 (2) Now esse is act, the actualitas omnium actuum, and as such is immediately contrasted with the potentiality of matter. It would seem that there could be no admission of esse with respect to matter; and whatever is distinguished from esse is non-esse. Is matter, then, nonbeing? Have we defined it out of existence? And if so, how can it have a ratio, or any bearing on reality? It is this phantom character of the material principle which, when it has been rightly grasped at all by philosophers, has led to skepticism concerning its validity in the scheme of cosmic being. Let it be recalled that we prescind to matter, on both the physical and metaphysical levels, by a sort of via negativa: inferring an unintelligible substrate of change in the one case, an unintelligible basis of substantial predication in the other. These methodologies reflect something mysterious about matter itself - as in the concept of essence more broadly considered: that it is a "not" at the heart of the "what." We are back to the realization of matter as limit, as "where form stops." The notion is by no means confined to the primordial principles of being. Even at the sensible level we are constrained to apprehend any limit or boundary, considered precisely as such, in terms of negation: the boundary of a plane figure is the very negation of the figure, it is where the figure terminates or "is no more" - standing, in regard to the figure, not as part but as principle. (Thus circles and squares are areas, but they are determined by lines which have no area. The lines which define them do not have the properties of circles and squares as such.) The existentialist grasp of reality, far from losing coherence through paucity of principle, is inexhaustibly rich through its referral of all to the ultimate ontological principle, (participated) esse. All else - essence, form, matter, substance, acci-

148 dents - is constituted of, or in relation to, existential act through a variety of principles of limitation. Hence none of the principles of Thomistic metaphysics save esse alone has "independent" positive content, yet all are ineluctably real in that they are determinations of existential act. So matter, as a certain kind of existential limitation, must be inseparable from esse in its very ratio. And because the intellect, mirror of reality, apprehends all in terms of esse, its approach to matter cannot but be in those terms. We cannot abrogate all reference to esse in our discourse on matter; that were to abrogate knowledge and discourse altogether. "Prime matter" is an ens rationis, inasmuch as it does not enter into the fabric of reality on its own but only as an existential condition of form; but that cannot prevent us from assigning to it a spurious "positive" content, even as we negate all positivity in our deepest analysis. The analogical flexibility whereby we treat of matter as a sort of esse, or as having esse, even while knowing that it is not and has not, is not alien to Aquinas's modus dicendi: he is known to speak even of God, ipsum esse subsistens, as supra existentia.199 This does not mean that matter, rightly conceived, is other than a lack of esse. But it is a lack that presupposes that which it lacks. It will be recalled that matter is not identified with a simple negation of esse, nor with the privation of that first determination of esse which constitutes the essence. It is, rather, the negation or privation of an esse beyond what the form currently possesses.

"Deus non est existens, sed supra existentia, ut dicit Dionysius." Summa theologiae la q. 12, a. 1, obj. 3 (Leon. 4.114). Cf. numerous references to this theme in In De divinis nominibus.

149 (3) Similarly, if matter itself must occasionally be referred to in positive terms, and hence as in some way as being or having esse, it will also be the case that prime matter is spoken of, context permitting, as "receiving" esse through form or from form. Clearly Aquinas is employing a figure of speech and cannot mean literally that form "has" esse to "give." And Thomistic analysis of hylomorphic being never construes the matter as "having" an esse distinct from that of the form; but if matter's esse is in some way that of the form, how can matter and form be distinct principles? What we must avoid at all costs is an excessive ontologizing of either the material or the formal principle: both are aspects of esse, while neither is esse as such. But since our notion of matter is first derived from secondary matter, which is really formed matter and hence only analogous to prime matter, it is natural to continue our philosophizing with respect to prime matter in the terms which were first appropriated through our reflection on secondary matter. What does it mean, then, to say forma dot esse materiael Bearing in mind that esse here can only refer to the existence of the fully constituted being, no an actuality proper to matter in its own right - we must understand that form is that whereby matter enters into the order of existents. Yet it is no less true that matter is that whereby form enters into existence. The two are coexistent and concreated. The esse of the hylomorphic composite, Aquinas says in a key passage,200 consists in the joining of form and

"...esse substantie composite non est tantum forme neque tantum materie, sed ipsius compositi." De ente et essentia c. 2 (Leon. 43.371:51-53).

150 matter. Why do we not find in Aquinas an expression of this correlative principle, "materia dat esse formae"? Given matter's status as the (existential) indeterminacy of the (essential) determination of creatural esse, it would not be Aquinas's way, I submit, to assign matter any active role such as is connoted by the verb "give." In the constituted being it is form that is the principle of all activity (even though all activity is a consequence, ultimately, of the existential act of which form constitutes the specification, and even though such activity occurs only in virtue of the material constitution, the "materiation," of the form). In other words, it is due primarily to the form, rather than the matter, that any activity occurs. Since our denomination of the roles of matter and form is from what is posterior and more known to us, it is appropriate that we should say forma dat esse materiae rather than materia dat esse, even making allowance for the faltering nature of language at the limits of intelligibility. (4) We come finally to the question of matter and God. Aquinas is careful always to distance the two as much as possible, yet he does so with varying emphasis depending on context. It is easy to pit the two as being at opposite poles, through the radical contrast between act and potency: God is pure act, and matter pure potency, so how more opposed could two principles be? Although this is true, it must also be remembered that potency is not absolute nonbeing, but a privative aspect of being, and hence cannot be opposed to God as absolutely as "pure nonbeing" could be. Within the vast range of being, God and prime matter are as opposed as opposed can be; but mat-

151 ter, whatever it is, is o/God, though the "least aspect," so to speak, of that which is of God - being merely a tendency to otherness within one realm of created being. As coming from God, matter is intelligible to Him in a way that completely escapes us. Matter is unintelligible to us because our intellects, proportioned to finite being within a certain order, fail before the indeterminacy of matter, which is correlative to the freedom of the divine agent cause (active potency). Such indeterminacy does not connote unintelligibility in the divine intellect, however. Although it must be said that God Himself does not know matter except in relation to form (since that pertains to the ratio of matter, as three sides pertain to the ratio of a triangle), the divine knowledge and providence, from the standpoint of the eternal now, compasses all possibilities with respect to that relation. Is there, then, a divine Idea corresponding to matter? Aquinas answers yes, and notes that the Idea of matter in God is not other than that of matter as it enters into real existents, namely as co-principle with form. In bringing the analysis of material being back to God as first principle, Aquinas employs his usual caution. As he traces each of the four causes back to God, only the material cause is not predicated of Him.201 Unlike the extrinsic lines of causality, agent and end, which can terminate in God "within" their own order, the intrinsic causes (because they are intrinsic in ratio), in being traced to a First, require to be "supplemented" by considerations outside their own order: thus Aquinas's Third and Fourth Ways,

Summa theologiae la q. 44, aa.1-4.

152 based (as I have argued elsewhere)202 on material and formal causality respectively, must advert to agent causality in order to complete their arguments for God.

L. Ground of cosmic intelligibility, unintelligible to us It is through matter that we confront one of the most mysterious aspects of our own being, the complementarity of the transient and the transcendent, of contingency and permanence. Such a confrontation is, of course, an intellectual activity, already the sign of a certain "detachment" from the cosmic milieu. It is the pre-eminent activity of human beings, and of philosophers especially, to work out the implications of our materialized existence. Knowledge begins in sensation. What Aristotle described in terms of "reception of sensible species" is none other than what modern science describes in terms of molecular interactions, light absorption, electrical impulses and so on: a brute contact between matter and matter - the matter of what is sensed (as it emits or reflects light, imparts vibrations to a medium, releases molecules, presses against us physically), and the matter that is first involved in the sensing (biological structures, tissues, cells). At a certain point in the ensuing process, as raw sense stimuli are submitted to the internal activities of imagination, memory and intellection, the purely material nature of the original data is transcended and the intellect forms, through abstraction from matter, what is proper to its own nature as immaterial. The concept is born. And it is intellect, actualized thus, which returns our attention to the material world from which 202

"Five Ways through Four Causes," M.A. thesis, The Catholic University of America, 2001.

153 sensation began, and conceives a paradox. For the content of what the intellect had engendered is at once like and unlike the reality that is presented to sense. The being which "entered" into the order of thought lost, in the process, its materiality, though not all recognizability. Why is the thought, the concept, not the same as that which gave rise to it? With this question emerges the sense of wonder - intellect, having been set in motion so to speak, now perpetuates the cycle. No sooner does the mind conceive "dog" as an intelligible, than the next real dog encountered provokes interrogation: what, in the nature that I have apprehended as "dog," is the place of this or that feature, aspect, behavior of the dog I now behold? For the mind compares the intelligible content which it has already abstracted, with the thing from which it abstracted that content, and finds the thing itself ever richer, ontologically, than what has yet been conceived with respect to it. In some mysterious way, in "taking" that thing into itself suo modo, i.e., without matter, the intellect has left behind something of precisely what it was seeking to know. The mind knows, then, through immaterial concepts, but it does not know those concepts - the Kantian attempt to maintain otherwise is a tragedy now two centuries running - rather, by means of the immaterial concept the mind seeks to "become" the material thing. The proper object of the human intellect is the material existent, and there is set in motion a kind of oscillation: from concrete existent, tantalizing in its partial knowability, to the universal intelligibility thereof, and back again. (This is of course only the barest sketch of human knowing: the fact that knowledge and truth are ordered in the first place to materiated sensible being does not ex-

154 elude the intellect's ascent, through subsequent analogy and negation, to a consideration of being which is altogether beyond matter. But even in regard to a metaphysical and theological subject-matter, truth is always had via explicit or implicit reversion to the sensible order.) Why, then, does the mind seek to possess precisely that which somehow eludes possession? Why is matter at once the sine qua non of human knowing, and the cosmic unknowable? We find the answer by considering matter's very unintelligibility. Already in its first attainment, per viam analogiae, to matter as substrate of substantial change, the mind found itself with a concept unintelligible. It is one thing to know that something is, and another to know what it is, to grasp it as a definable essence. Not only does physical analysis fail to yield a definition of that to whose underlying presence, amid the flux of cosmic becoming, it inexorably concludes; but it is only by withdrawing from flux or motion at all that the mind can even discern essences. Perhaps no one has ever been more deeply affected by the realization man Plato, but it is an Aristotelian and Thomistic realization as well: that essences are atemporal, and grasped only in disjunction from the mobility of mobile being. In concluding to matter as a substantial principle - through the predicateremoving analysis of what we know of material being - the intellect came no closer to an intelligible concept. "Matter" remained precisely as the ultimate predicate, of which nothing could in turn be predicated. Once again, just as in its role as physical substrate, matter proves to be a mysterious "accompaniment," elusively necessary but otherwise inscrutable, at the heart of substantial being. Further consideration of matter's relation

155 to form - which is that of potency to act - sheds a further light on its unintelligibility: for only what is actual is knowable, and the potential as such is beyond the intellect's grasp. In consequence of matter's ratio as principle of quantitative extension and individuation, we see that material being precisely as particular, as individual, is unintelligible: the mind, knowing things immaterially, knows them universally, that is to say in precisely that mode whereby the one concept is applicable to many instances without alteration or diminution. The mind, then, in abstracting from what is given it through sensation and other faculties, conceives that which is disjunct from matter as principle of change, from matter as merely potential correlative of form, from matter as that which is opposed to universality. Let us, in continuing to follow this trajectory, press on to the metaphysical level of analysis where unification of these rationes is achieved. Recall that, in the wake of Aquinas's development of the essence-esse distinction, it is seen that essence, the intelligible principle, is intelligible precisely as a limitation of participated (created) esse. This is to say that existential act is not what our mind grasps or possesses; rather, it is only the limitedness of that act. Again, we must beware of a spurious "reifying" of the essence. The essence without its act of existence is nothing; we say that it is "that which can exist," quod quid erat esse; but if the "that" which can exist is itself utterly without existence in its own right, then what does it "bring" to the act of existence save non-existence?

156 Now essence, or the limitation of esse, "where esse stops," is primarily the form - such that, in angelic being, essence is only form (for which reason we cannot know such being abstractively, but only through analogy and negation). But the essence of hylomorphic being also includes matter; and as we have seen, this is constituted, in terms of esse, as an existential limitation upon form. In other words, just as form entails intelligibility through the limitation of existential act,203 so matter - as the condition of form's limiting activity, the mode of existence of form - asserts the dynamism of esse over and against such limitation. Matter, as a mode of that very esse whose limitation constitutes form, shares in the unintelligibility of esse as such. Any illustrative analogy is bound to be severely deficient, so primordial are the notions we seek to illustrate thereby. But we might offer, as the merest suggestion, the following. Let a blank expanse of paper, of indefinite dimension, represent created esse; then figures which are drawn on that expanse - circles, triangles, and so on - can represent so many essences, formal limitations (infinitely replicable) upon inherently unlimited esse. Now, if we imagine any of these figures as being variable in size, or shape, then the array of different sizes and shapes which results from this variation can represent sequences of new forms (accidental or substantial, as we will). But the variability of the area within those diverse figures - not their area, but the variability of their area, as concomitant of the variation in figures themselves - is what represents matter. And

Part of the resistance to "existential" Thomism may be due to the long continuance of an essentialist vocabulary: merely to call esse the act o/form is to prioritize, in our consciousness, that (form) which is really posterior.

157 precisely as a "variable," a dynamism, a certain "unlimiting" of esse, is matter once again seen to be unintelligible. For esse is unintelligible to us: how could it be otherwise? Esse is the be-ing, the very act of the Agent Cause present in that which it causes. It is, in a word, the beingcreated of the thing, or even its "createdness." It is senseless to suppose a thing's esse as other than in the thing, instantiating the thing, constituting it as "not non-being." The intellect, in apprehending things immaterially, is apprehending them without that which most radically constitutes them as beings, their actus essendi, and this includes the material mode of that actus which is proper to hylomorphic or cosmic being. Hence, in a metaphysics of esse, we see that the unintelligibility of matter is allied to the unintelligibility of esse itself; that the mind, by taking in form, takes in nothing of what pertains to that form's existence or the modality thereof; that what constitutes the existent as just that, as a particular instantiation of being, a creature, is inalienable and certainly not granted "admission" to the knowing intellect. Individuals as such are unintelligible because it is precisely as existents that they are individuated: matter, the ground of quantitative individuation, is again seen in this role to be an existential principle within essence. Mobiles as such are unintelligible, because mobility is an existential condition, flowing from matter as mode of esse. If esse, in its material mode, is what constitutes the difference between a being and our knowledge of that being; while that same esse is indeed "the thing" in its positivity, its not-nothingness, so that it is true (and most profoundly so!) to say that created being participates through its esse in God, but through its essence only in some manifes-

158 tation of not-Godness, then it is small wonder that the mind of man, having begun (through sensation) with things in their ontological plenitude, is driven ceaselessly to return to that source, dimly aware that its knowledge is not yet a knowledge of what is most intimately constituent of things - their esse, unintelligible (to us) simpliciter and in its material mode. Matter's unintelligibility as an "unlimitation" of formal limitation should also be viewed in light of its relation to its correlative extrinsic (non-causal) principle, active potency in the agent cause. As esse is the intrinsic correlate to agent cause - the act of the agent in the patient - so is matter, the dynamism of esse so to speak, the intrinsic correlate to active potency. Or to put it slightly differently, as agent causality is that whereby esse is imparted, so is agent potency that whereby "further" esse can be imparted. But where the unintelligibility of esse is that of an incommunicable principle, the unintelligibility of matter is that of a principle "tied" to the inscrutability of the originative Intellect. The potential is unknowable to us because we are constrained in time and place. There remain a couple of considerations of the unknowability of material being, as only quoad nos, which will prove of significance in the course of our physical investigation. Aristotle was the first to reduce the apparent acausality of chance events to a rational account in terms of intersecting lines of causality. The random or unpredictable nature of chance occurrences is due, not to a failure of causality but to a defect of our knowledge. This defect is traced to the indeterminate character of materialized being, i.e., of the material factor as such. Because matter is indeterminately receptive of form,

159 all material being is "open" to endlessly varied mutation depending on circumstances of time and place. In Aristotelian-Thomistic physics there is a universal determinism in the sense that all events are caused and therefore in principle knowable; but it is not a "strict" determinism because the number of possibilities and variables stemming from the potential aspect of hylomorphic being far exceeds our capability of knowing. Such an obstacle to knowing does not, of course, exist with respect to an infinite Intellect, a fortiori the Intellect which is the creative origin of all material being in its very materiality. From the standpoint of divine ultimate causality all is foreseen, determined, caused.204 Indeed, "chance" becomes, for an all-knowing and provident God, the instrument of a supremely determinate causality: there is no more "chaos" in a universe whose causality, partly hidden from us, appears largely as chance, than in the most deterministic scenario conceived by agenda-driven philosophers. As for the reason why the Author of the universe would build chance into its fabric, I refer the reader to Appendix 3, on cosmic becoming as the condition for the exercise of human free will. Surely an analogous situation obtains in the present regard as well: the "hiddenness" of nature, a partial obscuration of underlying causality due to the correlative potencies of matter and the divine agency, is the appropriate context in which human will assumes its self-determining role. In a strictly deterministic universe there would be no scope for properly human acts; man need be no more than a passive participant amid cosmic flux, at no point asserting moral causality on his own part.

204

Human free will constitutes a supervening factor on "brute nature," and a source of further unpredictability, but does not on that account escape the universal causality of the First Cause.

160 The consideration of the radical intelligibility of all being, even if it is not an intelligibility quoad nos, leads to a second observation: the causality which cannot but be operative at levels beyond our direct access, can and does manifest itself even in circumstances where there is (to us) only a partial intelligibility. Thus, to cite an example which I have mentioned before, the radioactivity of unstable atoms exhibits utter unpredictability on an individual-atomic level, but follows strikingly precise quantitative laws in the aggregate. Such statistically coherent behavior cannot but be due to causalities that remain hidden to us, and only the most benighted positivism will pretend otherwise.

M. Three-dimensionality as primordial I return, briefly, to the datum from which we began as knowers, the realm of sensible being - extended, individuated, spatial. This spatiality is grounded in, and the very manifestation of, materiality; and materiality, as a modality of existence itself, is most intimately constitutive of cosmic being. It is not too much to say that a being's spatiality is the way in which it participates in the very being of God (since esse is precisely that participation, and matter is the hylomorphic "way" of esse). Small wonder that matter entails mystery: and I invite the reader to ponder, in the awareness of that mystery, the irreducible three-dimensionality of the physical. What is a dimension? As the name indicates, it is a measurable. And to measure is to compare - to hold two things in the mind together, so their similarities and dissimilarities are seen modo universale. Hence dimension is an ens rationis, like "equality" or "duration," yet, like these and many other concepts, rooted in the extramental reality.

161 That dimensionality is radicated in beings themselves, despite its formal existence only in mente, is indicated, inter alia, by their invariable three-dimensionality. Were dimension something of our invention, we could apprehend one being as three-dimensional, another as two-dimensional, and so on; but such is not the case. Why three dimensions? To science and philosophy there can be, I suspect, no answer. Spatiality is primordial; matter, of which spatiality is the "manifestation," is beyond predication, beyond direct intelligibility: it is the brute fact, the absolute given. At most we can say, perhaps, that - given the very nature of extension as "parts outside of parts" - no fewer than three dimensions are required to answer to the notion of "parts," while more than three cannot be conceived without implying rationes other than that of "part" simpliciter. Here the restless impulse of man as interrogator of the universe seems to be thwarted. At this last threshold, which was also the first beginning, of intelligibility, we are confronted with an inexplicable but undeniable feature: that the very extendedness of a certain kind of being, which proves to be the ground of our knowing anything at all, cannot be adequately grasped except as "three," even while it is one. Nothing distinguishes one dimension from another, except their distinctness. None can "exist" without the others except in artificial mathematical abstraction; no physical being can exist without them. A mystery, yes - and well worth pondering for that reason.

Note that I am not considering the question of "Euclidian" versus "Non-Euclidian" spaces here. Any geometry which limits itself to just the spatial, as abstracted from physical reality, can be reduced to a Euclidian (flat) space, even if this is not the most efficient way mathematically speaking.

162 N. Reduction of the several accounts of matter Having in mind the various notae of matter as elucidated by Aristotle and Aquinas, we are now in position to relate them and offer a summary account. [1] Prime matter's ratio as substrate of substantial change is discerned, analogically, through analysis of accidental change, as the rational alternative to an intrinsically causeless process in which creation and annihilation would occur unintelligibly. This is the properly physical apprehension of prime matter. [2] Its ratio as substantial co-principle with form is discerned, quite apart from its role as principle of continuity in change, through analysis of our intellectual apprehension of sensible being, which occurs through conceptualization and judgment (predication). The intelligibility of that being which is first intelligible to us is grounded, so to speak, in matter as the ne plus ultra. Matter as substrate of change [1] and as an ultimate substantial principle [2] is understood to be one and the same principle, there being no reason to posit a difference: the substantial form apprehended metaphysice is that which is initially inferred physice, but whereas form is only considered in abstraction (abstractio formae) from matter (as the preliminary to any science at all) in physics, it is considered in separation (separatio) from matter in metaphysics, such that formal and material principles can be considered under the latter perspective without reference to their role in change. [3] As a cause of individuation, matter is first apprehended metaphysically, being understood as a potency to dimensive quantity (the first of accidents) such that by virtue of materialization a form is associated with determinate dimensions precluding

163 penetrability (collocality). The full analysis as presented by Aquinas takes into account matter, form, and the accident of quantity as factors in individuation. The metaphysical account of individuation is complementary to a physics in which material existents are both agents and patients of motion through formal principles acting via spatial contiguity afforded by matter. Through motions at the accidental level (all such motions or changes involving, directly or indirectly, local motion206), substantial changes are also educed. The material order consists of extended being and, void being an impossibility, is synonymous with what is abstractly denoted "space." The spatial continuum, constituted by hylomorphic being through its materiality, is, by virtue of the individuation arising from materia quantitate signata, contiguously filled with existents. That which serves as the principle of divisum ab alio also entails contiguity (adjacency) among the alia, in virtue of which formal principles can exercise reciprocal activity. [4] Corruptibility is due to matter, not directly (since then a being would be composed of contrary principles, one seeking to maintain its unity and one seeking to destroy it), but indirectly, inasmuch as matter is a principle of potency to other forms' existence. Every corruption is, sub alio aspectu, a generation, and form is the principle of the action involved. Materiality is the existential precondition, necessary but not sufficient, of hylomorphic forms acting upon one another.207

206

Physics VIII.7, 260a27-bl4. Were there, per impossibile, but one hylomorphic being comprising the universe, it would be incorruptible since there would be no other contiguous being, in virtue of whose material principle either being might undergo mutation. 207

164 [5] At the deepest level of metaphysical analysis, matter is just that modality of esse which constitutes a being as contingent, not absolutely (this is due to the essenceesse composition per prius), but secundum quid, namely through the action of other composite beings. Hylomorphic being is dependent, in both its accidental and its substantial being, on the intermediacy of other (hylomorphic) existents.208 (This existential dependence is radicated in matter itself, prior to the reception of any accidents; the extracosmic possibility seems to remain, that hylomorphic being, existing without certain accidents that condition and induce substantial change, could be spatial without being mobile - i.e., its substantial and causal relationships, as entailed by materiality, having an atemporal mode.) Matter is to the existential aspect of hylomorphic being what privation is to the formal aspect: privation is the not-yet of form, matter the not-yet of existence - privation the what and matter the can be of "what can be." As one form can yield existence to another, so does one act of esse {esse proprium, actus essendi) yield to another, and matter is precisely this impermanence of existence. [6] Spatiality (three-dimensionality), first condition of our sensing and thereby knowing hylomorphic being, is a primordial given. It is the manifestation to us of materiality, of mutual substantial dependence and contingency in being. In so far as being is sensible, spatial, particular, materialized, it is unintelligible. As the unintelligibility of esse itself arises from not being limited by form, so does the unintelligibility of matter itself arise from not being limited by form; both indeterminacies are existential in nature, but the one is absolute and the other relative. Esse and matter are both potentially 208

Separated substance is dependent on other finite existents only in its accidental being.

165 infinite, but the one transcends an order (that of cosmic being) within which the other is circumscribed. The unintelligibility of the individuated material existent as such grounds the possibility of intelligibility through abstraction from the sensible order; hence there is no circularity or infinite regress in grounding intelligibility upon intelligibles.209 At the end of a long and, I fear, sometimes rambling discussion of matter - it is always matter as such, "pure" or prime matter, that we have had chiefly in view - can we reduce the whole to a single affirmation, in which all else is somehow implied? That would be too ambitious; the relation of subordination among the sciences requires that distinct principles be enunciated for each. But I submit that, having tried to follow in the footsteps of Aristotle and Aquinas (ad mentem when not ad litteram), we are in a position to state that, physically speaking, matter is that intrinsic aspect of substances whereby they can act on each other both accidentally and substantially, while in metaphysical perspective matter is that intrinsic aspect of substances whereby existence is contingent. Matter is a certain kind of potentiality in a certain kind of being, that constituting the spatiotemporal world to which our senses are directed. And so we leave our consideration of pure matter to take up, in Chapter Four, several topics with respect to informed or secondary matter. In particular, with a view to resolving our physical aporiai, we shall examine form in so far as it is the basis of structure in the extended cosmic order of being. The material aspects of "formed matter" will 209

This obtains with respect to the abstractive mode of human knowing in statu viae. A very different mode of knowing obtains for disembodied intellects, and for man in the beatific vision, etc. Moreover, our knowledge of immaterial being - angels and God - occurs not through abstraction and conceptualization alone but through analogy and negation as well.

166 never be outside our purview, but the analogy between prime matter and informed matter will always be as important for what it leaves out, as for what it contributes toward our understanding of hylomorphic being.

Chapter Four Formal Structure of Material Being

A. The Thomistic account of form For Aquinas, as for Aristotle, form as a constitutive principle of cosmic being is discerned as a stability-amid-flux, a unity persisting through the multiplicity and succession which present themselves to us through the senses. This occurs on different levels. To begin with, change as such (implied in every act of sensation) can only be apprehended in virtue of the mind's "holding," as so many points of comparison, concepts which, having been abstracted from experience, are adverted to as "here," "at that time," "green," and so on. These first conceptualizations are of accidental forms. At a deeper level, the mind grasps a unity that underlies various constellations of accidental change; the accidents, for one thing, change only within certain limits, and moreover they evidence a functional coherence or unity, which gives rise to the inference of substance. (Accident and substance are apprehended formally in virtue of one another, as complementary aspects of being. The accidents, though first to be grasped and conceptualized, cannot be apprehended qua accidental except through the concurrent apprehension of substance.) Analysis of substance, in turn, indicates a stable and actualizing principle distinct from the principle of instability or potentiality. Thus does the mind arrive at substantial form.

167

168 The mind's inherent activity moves it, then, from "accidents" to "substance," and thence to "form" as the actualizing principle thereof; but this is not to say that substantial forms are easily defined. Since they are always and only inferred through an imperfectly perceived accidental order of being, we are as uncertain about accurately defining (most) natural substances as we are certain about their reality.1 The objective reality of form, especially substantial form, is questioned or denied by those who are uneasy in moving beyond the certitude proper to the order of sense knowing. Traditionally, the realist's attempt to address such skepticism has begun with reflection on what we know best - ourselves and other higher organisms, in which the form or soul seems most evidently greater than the sum of the material parts. But such attempts, while inherently most suitable to the task, suffer when pitted against ingrained prejudice in favor of mechanistic and atomistic reductionism. Perhaps we do well to tackle the issue where it would seem most germane to the modern mind: at the primordial physical level. In De principiis naturae Aquinas notes that form, whether accidental or substantial as the case may be, is that which "makes a thing to be in act" (forma facit esse in actu),2 and is the end-result of every generation, or process of change (generatio est mo-

The inevitable tension in this situation has led to oversimplifications on the part of both scientists who deny the existence or relevance of substance as such, and others who rebuke scientists for an exclusive preoccupation with sensible reality. 2 De principiis naturae, c. 3. The language is interesting: there is no direct object serving as subject of the infinitive ("form makes Xto be in act"), but esse more plausibly serves as the direct object ("form brings about esse in act"), without undue strain on St. Thomas's Latin. Either way, form cannot be understood here as an efficient cause of esse, which would be nonsensical, but simply as the formal sine qua non of finite being's realization.

169 tus adformam).3 One of the three principles of every generation,4 form (along with matter) is properly denoted as (intrinsic) cause,5 one which can coincide in re though not, of course, in ratio with either the efficient or the final cause,6 and its own incorruptibility/ingenerability must be posited on pain of rendering unintelligible (through infinite regress of explanatory principles) the process of generation and corruption itself.7 Against Plato, Aquinas like Aristotle is insistent on the intrinsicity of form. Matter as such is only potentiality; hence form is not "in" an already-formed substrate, but is the form " o f that substrate.8 Matter and form are correlative and existentially inseparable. Neither can pre-exist the other; neither is a being, but only a principle of being.9 Although esse is the ultimate ground of all activity, form is understood to be the actualizing principle, first in its juxtaposition to matter, which is a passive and potential principle within the essence; secondly, as the determination of existential act whereby this kind and not that is realized; and thirdly, as the determinant of a thing's operations or secondary acts. When Aristotle or Aquinas identify nature as an intrinsic principle of motion and rest they single out form as being nature "most of all."

3

Deprincipiis naturae, c. 4. Ibid., c. 6. 5 Ibid., c. 17. 6 Ibid., c. 25. 1 Ibid., c. 12. 8 Ibid., c. 22; cf. Aristotle's fifth sense of "in," Physics IV.3 (210al4-24). 9 Ibid., c. 23. On the separability (because of incorruptibility) of the human form see Summa theologiae la, q. 75, a. 7. 4

170 Aquinas, especially, is most insistent upon the unicity of substantial form as entailed by a thing's ontological unity.10 Plurality of accidental forms does not compromise this essential ontological unity; an accident is by its very nature not a distinct being, having no esse of its own, but is a modification of the substantial esse. Thus accidents contribute to an entity formally but not essentially; through them a substance becomes different, but not a new being. The form-matter composite, which alone constitutes a being in the cosmic or physical order, is dependent, both in fieri and in esse, on an extrinsic agent cause, which in turn acts toward an end (final cause). In what does the esse of the composite consist? Aquinas' answer to this question is that neither form nor matter alone can have esse; the esse of the composite, rather, arises through the union of form and matter.11 We might say that "for form and matter to be united is for each to come into existence." Nor does such an understanding conflict with the existential interpretation of matter defended in the preceding chapter. Form exists precisely through the act whereby it "receives" esse from an agent cause;12 and matter exists precisely in so far as it is the modality of the

He faced a much more vigorous debate on the topic than Aristotle could have, with Averroes and Avicenna being two major protagonists. John F. Wippel has a thorough summary of Aquinas's arguments on this point in The Metaphysical Thought of Thomas Aquinas (Washington, D. C., 2000), pp. 327-351. 11 De ente et essentia c. 2: "Huic etiam ratio concordat, quia esse substantie composite non est tantum forme neque tantum materie, sed ipsius compositi; essentia autem est secundum quam res esse dicitur: unde oportet ut essentia qua res denominatur ens non tantum sit forma, neque tantum materia, sed utrumque, quamuis huiusmodi esse suo modo sola forma sit causa" (Leon. 43.371:50-57). Cf. Summa theologiae la, q. 50, a. 5: "Esse autem secundum se competit formae: unumquodque enim est ens actu secundum quod habet formam. Materia vero est ens actu per formam." Leon. 5.12. Cf. Summa contra gentiles II, c. 71.

171 esse which form has received. It is meaningless to suppose form as in any way "existing" without existence, esse or the actus essendi. Yet the language of Thomistic philosophy is notable for such locutions as forma dat esse materiae: how is this to be construed? We name according to what we know first or best. Matter as such is unintelligible, requiring form for understanding no less than for real existence. Form, on the other hand, can exist without matter (though not in hylomorphic substances); it has a priority over matter in that it connotes a determination of esse without regard to mode, while matter as one mode of esse presupposes a certain kind of form. Secondary matter, then, is given esse (in the sense of "is taken up into the existence of a new being") when it is newly informed; when the form brings about a new act, in some cases literally "a new life." It is only a step from this to the limiting case of prime matter (granted, that language is always stretched in such descriptions): form "gives existence" to matter in so far as matter does not enter into the order of existents except as conjoined with form. Does it then make sense to say that matter gives existence to form? Although Aquinas does not use this phrase, I do not see why it cannot be employed, save that it is more awkward in reference to the first-encountered case of secondary matter. We might not say "the wood made the chair's form an existent chair" quite as readily as "the chair's form made the wood an existent chair" - but no inherent impossibility impedes us even at this level, and a fortiori at the level of prime matter and substantial form. A further objection, however, is this: how can form "give" esse to that which, on our existential reading of Aquinas, is itself a modality of esse, i.e. esse under a certain

172 aspect of variability? Again, forma dat esse materiae means, both in the absolute case and analogously with respect to accidental being, that a contingent existent comes to be with a given form. Form is the "kind" of the existent which the agent cause effects in material mode; it is the sine qua non, the condition, of any imparting of esse; without form, no esse. Thus forma dat esse materiae can be understood to mean that the material existent presupposes form as a co-principle in its very existence and in the very materiality of its existence.13 Central to the Aristotelian and Thomistic account of knowledge is the role of form as principle of intelligibility. The psychology of human knowing begins with the reception of sense data from material existents; what is "abstracted" from the sensible form or species is called the intelligible form (species) and is understood to be none other than that form which determines the being in re. This account, besides maintaining knowledge as a knowledge of the real {contra the circumventions of idealists) locates, in the very immateriality ("ex-materiality") of the known qua known, its universal character. And so the eternality of form, and the possibility of an unchanging truth, are associated with the doctrine of abstraction. (In a profound analysis that goes well beyond Aristotle, Aquinas would show that this process of abstraction, under the illuminative activity of the agent intellect, is ultimately due to the activity of God more specifically, of Christ the Teacher - in the soul.)

Quaestiones disputatae De veritate q. 28, a. 7 ("materia est causa formae aliquo modo in quantum sustinet formam, et forma est aliquo modo causa materiae in quantum dat materiae esse actu"). Leon. 22.3.840:147-150.

173 Abstraction occurs at two levels or moments. The first, "abstraction of the universal" {abstractio universalis a particular?) is as just described, and the basis of all intellective thought. The second, "abstraction of the form" properly so called (abstractio formae a materia sensibili)14, is a further act whereby the mind focuses only on the quantitative forms of things, disregarding their physical matter.15 When a third intellectual distinction, that whereby a thing's relation to esse itself (as opposed to matter, a particular mode of esse) is discerned - this process goes by the technical name of separatio - we have the Thomistic basis for the complete Aristotelian division of the sciences: physics is the science of material being as material, mathematics is the science of material being without reference to its materiality as such but considering only the quantitative in abstraction, and metaphysics is the science of being without any regard, even originatively, for materiality or the lack thereof.16

Super Boetium De Trinitate q. 5, a. 3: "Sic ergo in operatione intellectus triplex distinctio inuenitur: una secundum operationem intellectus components et diuidentis, que separatio dicitur proprie, et hec competit scientie diuine siue metaphysice; alia secundum operationem qua formantur quiditates rerum, que est abstractio formae a materia sensibili, et haec competit mathematice; tertia, secundum eandem operationem, uniuersalis a particulari, et hec competit etiam phisice et est communis omnibus scientiis, quia in omni scientia pretermittitur quod per accidens est et accipitur quod per se est." (Leon. 50.149:275-286.) 5 These forms must nonetheless inhere in some intellectual quasi-matter, since it is not in their nature to exist altogether immaterially; Aquinas follows Aristotle in positing an "intelligible matter" as that which receives the abstract mathematical forms. Summa theologiae la, q. 85, a. 1 ad 2: "Species autem mathematicae possunt abstrahi per intellectum a materia sensibili non solum individuali, sed etiam communi; non tamen a materia intelligibili communi, sed solum individuali. Materia enim sensibilis dicitur materia corporalis secundum quod subiacet qualitatibus sensibilibus, scilicet calido et frigido, duro et molli, et huiusmodi. Materia vero intelligibilis dicitur substantia secundum quod subiacet quantitati." Leon. 5.331. 16 On the notion of scientia media see supra, Chapter 2, n. 22.

174 B. What is form? It seems that the notion of form - despite 2300 years' gestation in the tradition of the philosophia perennis - remains as obscure today as it has ever been. In the interest of providing a suitably primordial account of the cosmic role of matter, it will be desirable to be as clear as possible on the role of form as well. For one thing, it is impossible to treat adequately of the one principle without continual reference to the other. Moreover, a truly metaphysical account of matter, taking it back to the primal principle of esse, will stand or fall according as the complementary account of form stands or falls thereby. A philosophy which acknowledges the objective reality of things independent of the knowing subject is not on that account committed to a denial of the intellect's role in determining the knowability of objects. In other words, one need not (and, for Aristotle and Aquinas, must not) maintain an "absolute" objectivity of the thing known, as if "the thing known" were in no way the thing as known. This would in fact undermine any coherent account of knowledge as access to a mind-independent reality. To know is, in some mysterious way, to assimilate to oneself what is known. The known becomes the knower, albeit without undergoing essential modification in its own right. Unlike the case of corporeal assimilation, in which the assimilated loses its own substance in being assimilated into the substance of the assimilator, that which is known enters into the being of the knower, i.e. the intellect, without substantial alteration. Clearly this is an immaterial activity, yet it cannot be any the less real on this account. We must explain knowledge in such a way as to secure both the immateriality and the reality of the act.

175 We say "immaterial" because it is obvious that knowledge does not involve a physical communion. Matter does not enter into the intellect; matter, as noted in the preceding chapter, is unintelligible. Unintelligibility must also be ascribed, for a different reason, to esse proprium or actus essendi. But that which is known is identified, in the Aristotelian tradition, as the form - the same form which constitutes the actualizing principle of the essence. How do we account for the intelligibility of form? How can that which is the determinative principle of the thing itself come to inhere in the intellect? It would be senseless to say that knower and known become wholly identified through the act of knowing. Yet something - not the object's being as such, but a real aspect or principle of that being - must be truly and univocally common to object and subject. Anything less than a univocal explanation would destroy the correspondence of knowledge to reality. If the form in mente is even slightly other than, or less real than, the same form in re, then the mens has not truly assimilated the res. Moreover, we must look first to the intellect, to whatever characteristics intelligible content as such displays to reflective inquiry. This may seem un-Aristotelian, to the extent that one begins with intellect rather than thing; but such is not the case. It is not to embrace a Kantian or skeptical approach, which would discern in knowledge nothing more than a certain modification of intellect pursuant to its own nature. It is to recognize, rather, that while knowledge is knowledge of a thing, of the f/zmg-as-knowable, it is nevertheless, complementarily, knowledge of a thing, of the Hang-as-knowable.

176 But are there suitably prior categories, in terms of which so fundamental an inquiry can proceed? Can the mind experience being in a way which serves to ground an apodictic account of "form" as the "intelligible content" of being? In order for knowledge to be true and certain, the knower must know that he knows, must have metascientific access to the reality he would grasp scientifically. An adequate account of form as the principle of intelligibility must be able to show that the intelligible content is indeed one with the actuality of what is known. Otherwise we are faced with the subjective fallacy and the radical circularity of the claim that truth, a correspondence between mind and thing, is known through the mind's correspondence to the thing. We must somehow get outside the mind, then - understanding by "mind" the faculty of conceptualization through the apprehension of form. This apprehension is denoted, in the philosophical tradition, as the first operation of the intellect, the grasping of universal content in the act of understanding sensu strictu. This act involves the illumination by agent intellect of the "sensible species" and the consequent derivation of the "intelligible species" as expressed in the concept (traditionally called an "indivisible" as it is prior to composition through the copula). This "getting outside" occurs via the mind's second operation, the judgment, through which an existential affirmation or denial is made. This seems to me a crucial step in the validation of knowledge as well as of the Aristotelian-Thomistic account of form's role in knowledge. Only through judgment does the intellect compare its apprehension of the thing to the thing itself and verify its apprehension. A full defense of this

177 thesis would take me far afield from the present study; let the following summary suffice. Knowledge begins with the senses, but the psychology of human knowing, beginning with external sensation and proceeding with the "illumination" of intelligible content in the sensible species as mentioned above, involves no less a return to the sensible by way of "completing" the cognitive act. This does not mean that every act of the intellect is void of truth-content unless referred directly to sensible reality. But such referral is always entailed at least indirectly, by terminating explicitly in the phantasm, implicitly in that from which the phantasm is drawn. Only in referring one's concept - the universal, intelligible content, i.e. form as abstracted and apprehended in the first operation - to the concrete existent in its materiality and particularity, via the second operation, does one proceed to satisfy the primordial urge to know things in their existential integrity. The esse of the thing, in its material mode, eludes us in so far as it is not commensurable with the human intellect. But that esse is experienced through the commensurability of material sensible object and material sense-organ, the genetic relation between sensible and intelligible species, and the judgmental act whereby intellect reverts, so to speak, to its original datum. The act of judgment presupposes that the mind apprehend thing-as-known as other than thing-in-itself. Since thing-as-known is neither the esse of the thing (that would mean, inter alia, that the thing now subsists, by its intrinsic act of being, in the mind, which is patently false), nor its matter (matter being the existential condition of the thing and, as discussed in the previous chapter, that which constitutes its spatiality

178 and unilocality, as well as its contingency, etc.), it can only be the form. And form, of course, is considered synonymous with essence and nature, which in turn are expressed by the definition. But it is one thing to say that what is known conceptually is form rather than some other ontological principle; it remains, after our epistemological detour, to state just what form is, that could allow of the dual role which belongs to it as principle of both thing and concept. What is the role of form vis-a-vis the esse and the matter of the real entity on the one hand, and vis-a-vis the intellectual entity on the other? What precisely is the knowing faculty "taking in"? What is being "illumined" by the agent intellect? It will be that which, if given its own esse, would be none other than the thing itself. It will be everything except the esse and, in the case of hylomorphic being, the indeterminacy thereof (i.e., matter). We have considered already how essence serves to determine the act of existence; it is the limiting of esse to this rather than that creatural expression of a divine exemplar; and as the Aristotelian-Thomistic tradition consistently recognizes, form is the primary principle of the essence - the only substantial principle, in the case of separated substances. Indeed it is only because essence is the limitation of esse that it is at all intelligible quoad nos, esse as such being unlimited. Form, then, to repeat, is the limitation of existential act, while matter is the condition of existential act whereby a certain form can be iterated, constituting multiple interactive instantiations of the essence, multiple centers of activity falling under the one definition.

179 Form is grasped precisely as the otherness, through delimitation, of one essence with respect to others. There is no other prior principle whereby we can apprehend essence; every definition is in fact a comparison and a contrast, a compounding of "same" and "different" referring to other essential determinations, other definables or delimitations of esse. Every positive affirmation of formal content is seen, on analysis, to be negative (in the sense of delimiting) as well. But if form is the "limitation of esse" in re, what does it delimit in mentel The delimiting as such must be taken univocally, for reasons set forth above. Only in what is delimited can diversity be admitted. But what can be diverse from esse itself? The answer, of course, is "nothing," if esse be taken in its broadest acceptation as esse commune (I abstract altogether, in these considerations, from uncreated ipsum esse subsistens). But esse is, after all, an analogical term no less than are its many essential determinations. The esse proprium of the material existent is not univocal with the esse of the intellect itself. It is true that the intellect, in so far as it comes to know, i.e., be informed by, things through their formal principles, is modified existentially. But this can only be through the acquisition of accidental modifications grounded in the intellect's own esse. Somehow, that which determines esse in the order of existents, thereby constituting real beings, also determines esse intellectus, thereby constituting things-known. But the form is substantially determinative of its own esse in the one case, and of another's esse, accidentally, in the other. This is all rather abstract and may seem to afford little foothold for a discussion of beings as well-defined as the entities of physics - photons, molecules, galaxies. What

180 are the implications, for our study of material being, of the notion of form here put forward? A proper conception of form seems a necessary adjunct to our consideration of matter and its potentiality at every level of analysis. Without a suitably metaphysical foundation, the physical concept of form (and matter) cannot regain the position of central importance that it formerly (and appropriately) held among philosophers. It may seem paradoxical that I appeal to the metaphysical, in an age which traduces metaphysics, in order to validate a physical doctrine. But as I shall argue in the final chapter, there is abundant evidence for the conclusion that physics itself has lately gone astray, precisely because it has forgotten its metaphysical foundation.

C. Accidental forms and sensibility The complex array of changing sensible forms before us is seen, on reflection, to be ordered according to "centers" of activity, first in terms of persistent spatial congruity and continuity (these "brown furry barking wagging" forms are clearly united, here and there, now and then), and secondly in terms of unified functions revealing themselves as goal-directed (the aforesaid group of forms moves together, sustains itself, chases balls and buries bones, all as a unity). So decisively does this underlying unity impress itself upon us that we continue to advert to it even when a good many (though never all) of the sensible forms are removed or modified. And thus we apprehend the difference between accidents and substance. Having in view the distinction between essence and the act thereof {esse proprium, actus essendi) as co-principles of being (ens), and appropriately leaving esse out

181 of the definition,

Aquinas offers, as a quasi-definition, that substance is "a thing

whose nature is to be not in another," and accident "a thing whose nature it is to be in another."18 Precisely as that which is inferred through or "beyond" the congeries of accidents-in-flux, substance is supra-sensible; it is attained only through the intellect's illumination of the totality of sensibilia presented to it. Accidental being is not accidental because sensible (it is not absurd to conceive of a universe in which substances would be directly sensed), but sensible because accidental. More properly, it is because certain accidental modes of being - quantity and those qualities which are grounded in quantity, i.e., extendedness - are connatural with our sense organs, that they partake of the sensible.19 This does not imply that every such accident must fall within the range of our sense powers; some are accessible only through instrumental assistance, others not at all, owing to natural limits set by the material nature of the sense organs.

Esse taken modo universale is common to all that is, and therefore not a principle of definition; taken modo particulare it is absolutely proper to each existent, and as such not available for definition, or even intelligible in the sense that essences are. 18 Quodlibet IX, q. 3, ad 2: "hec non est uera diffinitio substancie: 'Substancia est quod per se est', uel : 'Accidens est quod est in alio', set est circumlocutio uerae descriptionis, quae talis intelligitur: 'Substancia est res cuius nature debetur esse non in alio'; 'Accidens uero est res cuius nature debetur esse in alio'." (Leon. 25.1.99:84-90.) 19 A detailed study remains to be written, on how the modern scientific account of light, sound, molecular theory, and human physiology fits perfectly with the Aristotelian analysis of sensation. Essentially, the physical continuum represented by the sensed object, medium of transmission (light, sound waves, etc.), sense organ and its biochemical modifications under stimulus all now described in great detail by the sciences of physics, chemistry and biology - serves to anchor our knowledge in the act of sensation and even to validate Aristotle's insight that senseknowledge is inerrant in its own order.

182 D. Unicity of substantial form Against various contemporaries and predecessors, Aquinas was at pains to defend the absolute unicity of the substantial form in any existent. Not only must a being be determined by a single substantial form, but even its accidents, each constituted by an accidental form, are but modifications or aspects of the one substance.20 The basis for this position is his understanding that substance is the most prior category of being, that substantial form therefore gives esse to matter, and that there can be only one act of existence in a single being.21 Among the several arguments for unicity of substantial form which Aquinas employs at various points in his works, I single out the one based on predication.

Our

grasp of being allows us to predicate one formality of another either per accidens ox per se, the former when the forms are not intrinsically ordered to each other, the latter when they are so ordered. But per se predication occurs in two modes. The first mode, when a predicate is included in the definition of the subject (as when we say "The dog is an animal"), necessarily involves predicating a sameness on the side of form - only the ratio differs between the two terms. But in the second mode, when a subject is included in the definition of the predicate (as when we say "The animal is a dog"), there is a diversity such that the predicate is not implied by the subject. (Aquinas observes that such 20

"Surely no other name in thirteenth-century philosophy is more closely associated with this theory than that of Aquinas." John F. Wippel, The Metaphysical Thought of Thomas Aquinas, p. 333. 21 Cf. De principiis naturae, c. 1: "quod vero est in potentia ad esse substantiate dicitur proprie materia....Unde simpliciter loquendo forma dat esse materiae" (Leon. 43.39:21-23, 32-33). See also Scriptum super Sententiis Liber I, d. 23, q. 1, a. 1, etc. 22 Summa theologiae la, q. 76, a. 3, second argument in corp.; cf. also Expositio libri Posterioruml, 10.

183 predication is based on material causality; the subject stands to the predicate as specifiable to specifying, as matter to form. In the real order, of course, this kind of predication can only refer to an existential situation in which the individuating role of matter is present.) This being the case, what if different substantial predicates are attributed to a subject (e.g., "dog" and "animal")? If each of these predicates were based on a distinct form, then they (the predicates) would be related to each other only per accidens, which is inadmissible (a dog is essentially, not accidentally, an animal), or per se through the second mode, which is likewise inadmissible (since the formality of "dog" includes that of animal). Hence, the argument concludes, the substantial predicates must be based on one and the same form. With Aquinas, unicity of substantial form is nearly always being discussed in the context of the human form or soul, and the idea has crucial implications for various theological doctrines concerning man's relation to God. But his arguments are couched in universal terms, and he clearly displays the strongest commitment to this unicity as a metaphysical, rather than anthropological or theological, principle. It emerges from a deep awareness of the form as that which "gives" esse to the composite, and as that which, consequently, is the principle of unified activity (operatio sequitur esse). And it leads him to develop a distinctive and fruitful doctrine concerning the multiform composition of physical substances.

184 E. Elemental virtual presence There arises a formidable difficulty, vis-a-vis the unicity of being, when we consider the obvious plurality of parts in any material entity. Clearly these parts are in some way definable; in many cases they existed before, or can exist independently of, the substantial being of which they are now form parts. How can the unicity of being through substantial form be maintained in the face of this obvious multiplicity of parts? To simply affirm that parts are to the whole as accidents to substance would beg the question. The very reality of the accidental as such - that is, of an order of being distinct from, and posterior to, substance, may be considered to be in question. To begin with, we will want to distinguish those parts of a composite being which never have existence outside the composite (for instance the organs of a living body) from parts that are known to exist independently (as for instance atoms and their constituent particles). It is worth observing that a hand, for example, is not found except in association with certain kinds of organisms; we might call a severed hand a "hand," but only derivatively; we are in no doubt that it is quite incapable of functioning as a hand. Its activity, its existential mode, is no longer that of "hand," which is really to say that it is no longer that of the organism to which the hand belonged. A severed hand's activity is that of its constituent atoms and molecules; it is now a soros,"heap," neither caught up into a higher substantial unity nor serving as a real principle of unity for its components. Of an organic part such as a hand, therefore, it must be said that it has no independent formal unity; and lacking this, it is perhaps not difficult to see how it may be

185 subsumed into another formal unity, that of the organism. But a rather different situation arises with respect to parts that do exist independently. Let us consider molecules and atoms. It is a bedrock tenet of modern physics and chemistry that all matter is particulate in structure; a vast body of experimental proof puts this tenet beyond serious challenge. Protons, electrons and neutrons form atoms; atoms enter into molecules (or ionic compounds); these in turn comprise more complex structures - in the case of living matter, the ascending ladder of organization includes molecular "fabrics" (membranes, etc.), organelles, cells, tissues, organ systems, organisms. And yet let us ask a seemingly anachronistic question: has any scientist ever isolated atoms or molecules within a living system - an organism - precisely as living? It is trivial to extract some part of an organism and identify in that part a particular molecular structure. Nor would it be realistic to deny that the organism's structure and function require certain chemical inputs, even as they yield certain chemical outputs; or that certain parts of a living body may be chemically analyzed in situ with no apparent alteration in their formal constitution (hair, nails, teeth, etc.). But are these parts living, or rather nonliving adjuncts to a living body? As for the manifestly living parts, i.e., those which function differently than they would in segregation from the organism - let us take, for instance, a muscle-tissue cell - it should strike us as remarkable that no experiment resolving the cell to its component parts has done so while preserving the character of those parts as living, i.e., as partaking of the life imparted to them by the cell.

186 Passing down into the inorganic realm we confront a no less startling observation. In a million different experimental situations, no component of a well-defined substantial unity has ever been observed to exhibit the very same properties qua component that it exhibits independently. Thus the properties of sodium chloride are clearly the result of a union of sodium and chlorine, and in some quantitative sense they are but the sum of the properties of the latter taken severally (the formula weight of NaCl is the sum of the atomic weights of Na and CI); and yet the properties of the compound are also so qualitatively new as to suggest that a new substance has been generated in the compound, rather than a mere mixture of prior substances. What is the significance of this state of affairs, replicated across the entire physical realm? Why is it that the law of composition, whereby lesser entities coalesce into greater, is not a law of simple addition or the "heaping" of parts, but of the transformative union of those parts into something that is at once themselves and something other? The answer to this physical question will be the same as the answer to the metaphysical dilemma posed above - how can entitative (substantial) unity be maintained in the face of a plurality of composing parts? An answer which signally fails to do justice to the facts, notwithstanding its dogmatic preponderance in recent centuries, is that posed by materialistic reductionism. This account, ignoring the form-matter composition of physical beings (a composition which eludes the method of modern physical investigation), reduces every composition in nature to a simple addition of actual parts (e.g. of elementary particles, in the case of

187 atoms; atoms, in the case of molecules; organelles, in the case of living cells; cells, in the case of multicellular organisms) to form higher or more complex actualities. Now there is a class of sense observations which suggest that each entity is simply the sum of its parts. We may view an "equation" such as 2Eb + O2 -* 2H2O as "complete"; we tend to regard the oxygen nucleus as "consisting o f just 8 protons and some neutrons; and so on. But while such "constitutive compositions" are valid on one level - the conservation laws in physics are a fundamental manifestation of this - they are not complete since they do not express the entirety of the synthesis represented by each such composition. The combination of hydrogen and oxygen to form water is not merely a matter of atomic adherence and the addition of masses; it is not even merely a matter of interatomic bonds resulting in new spatial configurations and hence in the constellation of new properties associated with water (together with the abolition of properties specific to hydrogen and oxygen as such). What is not described by an equation like that instanced is precisely the unification of the parts, the fact that they have given up something of their former individuality in the very act of entering into a new and composite unity. This is a subtle point, but a crucial one. Are the hydrogen and oxygen atoms, once they have combined into the water molecule, no different except in regard to their conjoining? To 19th century atomists this was the case, but quantum chemistry places before us a very different picture. If the atoms remain distinguishable after their combination, it is now as parts rather than as conjoined wholes, and this takes the form of their being qualitatively different (in size, shape, charge distribution, etc.) than they were prior to combination. The atoms have entered into the molecule

188 "genetically" rather than "constitutively," contributing something of their actuality to the product, but undergoing change in so doing. We seem to have, then, two kinds of composition involving actualities in the natural order: one in which the component parts (as organs in an organism) do not possess their intrinsic "natures" outside the composite, and another in which the component parts (as atoms in a molecule) do not retain their intrinsic natures within the composite. It turns out on further analysis that these two "kinds" are reducible to one. Recall that an organ as such does not pre-exist its organism; what, then, is the prior form of what, in the composite, will become an organ? It is, as we noted, multiple - the forms of the component "elements" down to the molecular or even atomic level. In general, then, we find that elements, on entering into a composite unity, lose some but not all of their former identity, and this regardless of whether the composite in question involves those elements mediately (by way of "organs" or something analogous to them) or immediately. Before turning to Aquinas's solution of the problem of the unicity of substantial form in composite beings - which is also the answer to my question about transformative union - we must consider his understanding of "element." It is evident that there are hierarchical levels of structure and composition in nature. We have already alluded to the "levels of organization" represented by subatomic particles, atoms, molecules,

189 and so on. The question arises, is there a least kind of structure in the natural order, or is hylomorphic composition extended indefinitely downward? Here we are concerned, not with the so-called "natural minimum" or atomos as it applies within any given species (such that any given individual of a given kind entails, in its actuality, certain limits with respect to its dimensions, parts and proportions). Such a minimum is established physically through the requirement of the mutual aptitude of matter and form (any form, implying as it does a finite range of properties and operations within the spatiotemporal order, must be conjoined with matter - the principle of extendedness - under a likewise finite range of dimensions).24 Rather, is there a nature which is the irreducible minimum qua nature - which is an extreme of formal simplicity, implying no prior composition? (There must always be a composition of principles - matter and form, essence and esse - but the notion of "physical nature" does not entail, of necessity, a composition of prior actualities such as we have been discussing.)

One trained in physical thinking today may find it odd, and anachronistic, that we (following Aristotle and Aquinas) extend this hierarchical scheme from the inorganic into the living realm (after molecules would come organic fabrics, organelles, cells, etc., in ascending order). It is "odd" only from a reductionist standpoint that regards living systems as no different in kind than non-living. A realist application of the principles of hylomorphism, on the other hand, must discern in the various levels of living matter a continuation of the ascending formal order. 24 It is well established in biology (see, for a famous treatment, D'Arcy Thompson, On Growth and Form [1917]) that organisms of a given kind - whether bacteria or bactrian camels - cannot function and do not exist below a certain threshold size determined by anatomical and metabolic requirements of the species. At deeper (inorganic) levels, the structural constraints are even more rigid: there is no reason to suppose that the accidents of molecules, atoms and their components are not narrowly determined in accordance with their relatively simple ontological status.

190 Certainly Aristotle, in considering the enumeration of causes, rules out an infinite regress in material causality no less than in the other kinds.25 From the finite number of natural kinds it follows that there is a "cosmic minimum," i.e. a simplest level of hylomorphic being, and such a being, irreducibly simple in composition, is what Aristotle and Aquinas (following, of course, numerous predecessors) identify as an element. Few doctrines of ancient and medieval physics are treated more condescendingly today than that of the "four elements" (earth, water, air and fire - celestial matter being accounted a special "quintessence"), but it will be imperative for us to distinguish between the theory of elements as such, and a particular empirical enumeration of them. The four elements of the ancients are long gone, but the Thomistic elucidation of "element" is so insightful as to have survived not only the ancient tetrad, but also the 1 ^-century preoccupation with chemical elements, and to have found corroboration in our era of particle physics. In De principiis naturae, where we earlier found his most comprehensive analysis of matter, Aquinas says that "Element is said properly only of those causes out of which the composition of a thing arises, and which are properly material. And not just of any material causes, but those out of which the thing's primary [i.e., irreducible] composition arises." In the ensuing discussion, based on Aristotle's well-known definition of element as that "from which a thing is primarily composed, which is immanent

25

Metaphysics II.2 (994al-6). De principiis naturae, §3 ("Elementum uero non dicitur proprie nisi de causis ex quibus est compositio rei, que proprie sunt materials; et iterum non de qualibet causa materiali, sed de ilia ex qua est prima compositio"). Leon. 43.43:86-89.

26

191 in the thing, and which is indivisible according to form,"27 Aquinas shows that this definition of element sets it off from principles which contribute to a thing's being but lose their own form entirely (i.e. are entirely corrupted) in so doing: "Elements must remain in some way, since they are not entirely corrupted, as is said in [Aristotle's] book On generation."1* It is noteworthy that, in commenting on the third part of Aristotle's definition, "indivisible according to form," Aquinas says this need not imply a quantitative indivisibility; in other words, he leaves open here the question concerning atoms or minima naturalia. Note also, that "element" is distinct from matter as such, i.e. the potential principle in physical being. An element is already formed matter, secondary matter, albeit that whose formality subsumes no other.29 Now it is one thing to admit, philosophically, the necessity of element(s) so defined - and another to identify which is or are the elements in reality. Clearly "element" in the absolute sense will not be applicable to the 100+ elements of classical chemistry (these are elements only relatively speaking, i.e. with reference to the processes studied in chemistry), and not even to all the particle types "immediately" comprising the chemical elements (protons and neutrons, for in-

11

Metaphysics V.3 (1014a26-27). De principiis naturae, c. 3 ("elementa oportet aliquo modo manere, cum non corrumpantur, ut dicitur in libra De generatione"). Leon. 43.43:107-109. 29 "The material component of an element must be absolutely formless, i.e., must be prime matter. And its formal component, therefore, must be a form which is proportioned to absolutely formless matter, i.e., a substantial form...." Joseph Bobik, Aquinas on Matter and Form and the Elements: A Translation and Interpretation of the De Principiis Naturae and the De Mixtione Elementorum of St. Thomas Aquinas (Notre Dame, Ind., 1998), p. 54. This latter consideration will prove important in the sequel, especially Chapter 5. 28

192 stance, are known to be composed of lesser entities, the quarks). In current theory, certain particles have a stronger claim to "elementarity": quarks and leptons, for example. It will be one of my main objectives in the closing chapter to suggest that the quantum phenomena involving these particles do imply a true elementarity. But a word of caution may as well be inserted here: prima facie it seems difficult, if not impossible, to achieve apodictic certainty with respect to an identification of the element(s), since one could only know empirically (i.e., in the mode of modern physical science) that one were dealing with elemental beings through a complete exclusion of other possibilities implying a perspective transcending that of empirical science itself. And from a systematic standpoint, one would have to be able to conclude that the putative element(s) manifested all those, and only those, properties of "element" precisely as such, in order to confirm the identification. Let us then turn to Aquinas's teaching, in De mixtione elementorum, on what may be called a transformative union (not his term) as maintaining the unicity of substantial form. This is his doctrine of virtual presence - really Aristotle's doctrine - and it is remarkably fecund, even in the context of modern physical theory. No arbitrary or ad hoc considerations give rise to the doctrine, but only the logical inescapability of having to resolve two opposing data: the substantial unity of the composite, manifested in its proper functionality (finality) and distinctive properties, all qualitatively different from those of the components; and the remanent evidence, discerned through those same properties of the composite, of its having been composed from prior entities. For the properties of the component elements do not disappear en-

193 tirely; they remain, says Aquinas, in a "mean" form, as black and white "remain" in shades of gray. Moreover (Aquinas doesn't address this explicitly in the text we are about to examine, but does so elsewhere), the composite cannot have "lost" its elemental components so completely that there does not remain a tendency for the composite to revert, on corruption, to just those elemental forms. Neither a mere aggregation of components nor a complete fusion of them will answer to the data. Aquinas begins by ruling out two kinds of explanation offered by previous thinkers. One, that the substantial forms of the elements remain in the composite while their qualitative accidents are altered somehow into a mean, with respect to the elements' accidents taken in themselves, is scarcely distinguishable from what a much later chemist or physicist would have expressed, had he resorted to the medieval terminology, in explicitating the views of his own day. The argument for this view, which is basically that of Avicenna, is that unless the substantial forms of the elements remain in the composite, the elements themselves would seem to have corrupted rather than blended together, and indeed to have lost their character of element altogether (particularly with respect to "remaining in" the composite). This last point is important (an objector might argue) because elemental composition, unlike composition from secondary components, entails the possibility of reversion to the originative forms.30 Aquinas's rebuttal to this first position is that multiple forms - and, a fortiori, forms which are contraries - cannot inhere in one and the same substantial matter; and if received by di30

Thus water, on decomposition, unfailingly reverts to oxygen and hydrogen (or to oxygen and the hydroxyl ion), whereas an organism does not revert, upon decomposition, to self-constituted organs and tissues.

194 verse parts of matter, the result would be multiple individuals rather than one - in other words, what a chemist today would call a mixture rather than a compound. The second position reviewed and rejected by Aquinas is that the elemental forms, being somehow inferior to other substantial forms because of their proximity to prime matter, do not possess the mutual exclusivity proper to substantial forms as such, and accordingly admit of a kind of mean, as do accidental forms. The response to this second position (which is that of Averroes) is, inter alia, that it opposes the principle of contradiction inasmuch as a thing can only be, by definition, accident or substance that which is in a subject or not in a subject, respectively. (Three other arguments, which depend on [1] the non-relation between things not in the same genus, [2] the noncontinuity of substantial change, and [3] the correspondence between substantial form and specific unity, will not be summarized here.) Aquinas then proffers his resolution, essentially this: the elemental components are understood to have undergone substantial change, such that the substantial form of each element exists no more, but a new substantial principle informs the composite whole, while the accidents of that new substance are none other than the means into which the preceding accidents have been resolved. The accidents are proper to the new substance, since every distinct substance has its own proper accidents, but the elements are such as to leave their "signatures" even when caught up into a higher form. Here we have unity and indeed radical newness of substance, coupled with an accidental succession in which there is distinctness with relation. (A not unhelpful analogy would be that afforded by the genotype and phenotype

195 in Mendelian genetics: every trait in the offspring is determined by the contributions of the two parents, and strong similarities between child and parent are often phenotypically noted; but no trait - no phenotypic element - is absolutely identical to that expressed in the parent, even on the dominant side.) This continuity- with-modification is located in the continuity of prime matter itself, together with the (related) succession of qualities through their quantitative commonalities. I offer the following diagram as an iconic model:

time —> Let the rectangles represent groups of qualities associated with three substances, "black," "white," and "gray," the first two combining, as we move from left to right, to form the third. (The paper itself can represent the prime matter which is continuous throughout.) Although there is a discrete change in the accidents associated with the substantial change (black and white become gray), simultaneous with the substantial change itself, something of both the black and the white remain, without interruption, in the gray as "mean." Now Aquinas speaks of "a certain mean quality" as being constituted out of the contrary qualities of the elements.31 This mean is the "proper quality of a mixed body [i.e., of what today's chemist would call a compound, rather than a mixture], a quality 31

"Sic igitur remissis excellentis qualitatum elementarium, constituitur ex hiis quedam qualitas media que est propria qualitas corporis mixti, differens tamen in diuersis secundum diuersum mixtionis proportionem; et hec quidem qualitas est propria dispositio ad formam corporis mixti, sicut qualitas simplex ad formam corporis simplicis." De mixtione elementorum (Leon. 43.156:130-136).

196 which differs . . . in diverse mixed bodies in accord with diverse proportions of mixing. And this mean quality is the proper disposition to the form of a mixed body.. ,."32 I will return to the important notion of dispositio shortly. It should be noted, meanwhile, that, for Aquinas as for Aristotle, the simultaneous presence of contrary qualities would be inadmissible in one and the same substance sub eodem aspectu; the mean here referred to is not a blend, but a new single entity arising from the contraries. Next comes what is the crux, but also perhaps the most difficult part, of the doctrine of De mixtione elementorum: Though the quality of a simple body is indeed other than its substantial form, it acts nonetheless in the power of the substantial form. Otherwise, all that heat would do is make things hot, and a substantial form would not be brought to a state of actuality by its action, since nothing acts beyond the limits of its species. It is in this way, therefore, that the powers of the substantial forms of simple bodies are preserved in mixed bodies. The forms of the elements, therefore, are in mixed bodies; not indeed actually, but virtually (by their power).33 It would not be enough to say that the qualities of a compound substance are derived, with modification, from those of the composing elements. This would be an accurate description, but would not express the causal ground. Aquinas's contention is stronger. The elemental qualities that enter into the mean acted, in doing so, in virtue of their underlying substances (since an accident as such is not a center of activity), and in the corruption of those former substances to yield a single composite substance the qualities

Bobik translation, p. 121. "Qualitas autem simplicis corporis est quidem aliud a forma substantial! ipsius, agit tamen in uirtute forme substantial; alioquin calor calefaceret tantum, non autem per eius actionem forma substantialis educeretur in actum, cum nichil agat ultra suam speciem. Sic igitur uirtutes formarum substantialium simplicium corporum in corporibus mixtis saluantur. Sunt igitur forme elementorum in corporibus mixtis, non quidem act used uirtute." De mixtione elementorum (Leon. 43.156:140-149); translation from Bobik edition, p. 122. 33

197 were necessarily implicated. (A hylomorphic substance, elemental or otherwise, acts only through its accidents, in virtue of extension and contiguity.) In other words, the elements themselves could not have come together to form the composite, had their qualities not remained present as the media through which they acted.34 "Otherwise, all that heat [a quality or "power," i.e., an operational capacity, of the element Fire] would do is make things hot, and a substantial form [i.e., of some higher composite into which the element Fire enters] would not be brought to a state of actuality by its [heat's] action [on the prior substance(s)], since nothing acts beyond the limit of its species [thus no accident as such can effect substantial change, but only as that whereby its underlying substance acts]." As the elemental substances act in bringing about the composite, they cannot disappear "without a trace," that is to say, in both their substantial and their accidental reality. In the instant that elements X and Y cease to exist substantially, substance Z taking their place - a "reversible instant," we might add, since every physical substance can corrupt into its elements - there cannot be absolute discontinuity in the accidents themselves, or there would be no continuity at all between the prior and posterior actualities, contrary to what is always observed. Of course, it was in order to avoid radical discontinuity and the implication of annihilation/creation that Aristotle posited prime matter. This discussion in De mixtione, 34

Let me use a mathematical analogy. In adding 7 and 3 to get 10, we have the analogue of a substantial change: for "7" and "3" as such have now disappeared, resulting in the new "10." And the properties of the new "substance" are different than those of its components; 3 and 7 are odd and prime, while 10 is neither. Nevertheless, the properties of 10 are clearly based on those of 3 and 7; were 3 or 7 other than they are, 10 would necessarily also be other than it is.

198 it seems to me, is "echoing" the physical argument for prime matter. Recall that prime matter itself is the seat of dimensionality, and the incorruptibility of prime matter entails the incorruptibility, so to speak, of dimensionality - and, by extension, of the qualities involved with extension. Thus there is a certain qualitative continuity even as the mean is educed; there is a quantitative continuity as determinate dimensions succumb to new determinations - since quantity and quality alike do not disappear so radically as do their underlying substances, but remain under modification. Aquinas's all too brief text is of central importance in any realist account of the structure and composition of material being. Driven by the metaphysical imperative of preserving substantial unity, he accounts, in the only logically possible way, for the observed fact that material beings above the level of the elements not only retain something of the qualities of the component elements, but also a potency for reverting to those elements on corruption. Clearly the distinction between substance and accidents is prominent in his account; the whole point is to give a philosophically valid description of the former while not explaining away the data of observation in regard to the latter. How scientifically germane is the doctrine of virtual presence? Physicists today, obviously, do not discuss qualities and contraries and powers, let alone substances, in any metaphysical sense. But I submit that the indications of modern physics and chemistry are such as to bolster, rather than undermine, the doctrine. The modus operandi of physical science is, as we have noted, mathematical; that is to say, that the quantitative aspects of mobile being are related through formulas which are considered as expressing natural laws. These formulations express different qualitative aspects of formed

199 matter, but always do so quantitatively - which, as I have noted, is possible because of the inevitable connection between the accidents of quality and quantity. (So intimate is this connection that it is not possible for us to grasp the quantitative except through the qualitative; abstract quantity is just that, abstracted from the sensible.) Thus physics does not formulate "yellow" or "hot" as such; it works with frequencies and wavelengths, with degrees of molecular kinetic activity and of infrared energy as the quantitative expression of these qualities. Physics today has acquainted us with mathematical expressions corresponding to every qualitative change - let us say, from "yellow" to "red," or from "hot" to "hotter." An object changes color because something has changed in its molecular structure to reflect or refract the impinging light waves differently. The relation between absorbed and reflected frequencies undergoes an alteration, since the electronic "surface" presented to the incoming light is now such as to interact differently with those photons. Photon energies that were formerly ejected from the surface molecules may now be absorbed, or vice versa. Again, this is not to deny the reality of the qualitative forms "yellow" and "red" as unitive principles at the accidental level; but we are focusing on the quantitative expressions of those qualities. Notice, and this is a crucial point, that

between the

quantitative

atomic/molecular arrangement that reflects "yellow" and that which reflects "red" there is a certain continuity. Some of the preceding molecular structure is still present as an apple turns from yellow to red. It is still a "sea of electrons" that, surrounding each atom or molecule, reflects or absorbs the incident light. But the electrons present a spatially

200 different configuration, in the transition from "yellow reflecting" to "red reflecting," which is due to the different molecular compositions of the surfaces so reflecting. It is perhaps easier to "visualize" the continuity between prior and posterior quantitative states than between their corresponding qualitative manifestations. Every sequence of spatial configurations must have something in common, must be somewhat continuous, by virtue of their very spatiality. And it can hardly be denied, whatever one's prejudice against an Aristotelian treatment of "qualitative means," that between any two quantitative states there cannot but be a mean, whether broadly or narrowly defined: this follows from the very nature of quantity. Not only the material substrate, materia prima (the very ground of extendedness in hylomorphic being), but extendedness itself- not a particular dimensionality, but dimensionality as such - is preserved, without interruption, during substantial change and corruption. No matter how radical the substantial change in question, be it that of a whale in all its majesty instantly reverting to individual atoms in a Pacific thermonuclear test, the formal component(s), before and after, are always ontologically located under determinate dimensions, dimensions which are moreover to some extent conspatial. The successive constellations of qualities (whale-qualities, element-qualities) are in turn related, i.e., continuous, through this shared, i.e., successive, dimensionality. In summary, then: when, in virtue of a substantial change, simpler beings are caught up into a higher unity - when elements form composite beings - the previous forms no longer subsist, but the accidents associated with those forms remain, in a mean configuration, in the new substance. That they constitute a new "mean" signalizes that

201 they are proper to the composite rather than to the elements; that the "mean" is only constituted as such from its precursors, and is resolvable to them alone, establishes continuity with the (accidents of the) elemental forms.

F. Dispositions of matter Prime matter's first aptitude is for elemental form; there can be no information ontologically prior to that of the elements. And as each higher substantial information occurs, the "powers" (and qualities) of the lower forms are preserved in a sort of modification, even though the lower forms themselves cannot remain and the higher substance is truly radicated at the primal-material level. Thus, while each substantial change is reduced to prime matter (accidental changes, in contrast, are radicated in the existing subject, an ens rather than aprincipium entis), it does not on that account have an absolutely indeterminate character; prime matter, it is true, is a pure potency, but substance or formed matter is disposed, in virtue of its form (and, more particularly, of the accidental forms grounded in it) toward certain changes (perhaps highly specific) and not others. This is known as the disposition of matter (dispositio materiae), but the term is used properly only of secondary matter, because even though disposition (to the reception of a certain form and not others) is referred to matter - matter being, of course, the principle that "receives" form - it belongs to matter only in virtue of that matter's prior conjunction with a form. In most general terms we say that matter is not receptive of form at all, except in so far as it is already a component of some ens; which is to say,

202

that matter does not pre-exist real being, and it is meaningless to speak of matter except as an aspect of the existent. The whole range of cosmic being is structured in accordance with the dispositiones. So-called elementary particles only enter, in virtue of their properties, into certain configurations and not others; one thinks, for example, of the specific nuclear and electronic arrangements comprising atomic matter. Atoms, in turn, only enter into so many well-defined molecular and other compounds; they do not combine randomly. And so on all the way up the scale of being. In the living realm, nothing is more obvious than the highly specific inclinations each cell, tissue, and organ displays in the course of its development. The DNA of every cell in an organism is understood to be essentially the same, yet very early in an organism's history, when the cells are less differentiated, their developmental potencies are quite differently circumscribed than at subsequent stages of development.35 As to the "mechanism" of this disposition: I have treated of it already, and will only briefly iterate here, that every hylomorphic substance acts through its accidents. These accidents, qualities inhering in the form but inseparable from the extendedness radicated in prime matter, are the expression of materiality itself and the mutual substantial influence characteristic of material being. Hence substances act on one another through their accidents, and in virtue of the spatial contiguity which those accidents, because of materiality, possess. These accidental qualities, which modern physics

Appropriation of the concept of dispositio materiae would go a long way toward obviating concerns with the role of "blind chance" in evolutionary biology.

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knows reductively as forces, at once effect physical change and predetermine it to some extent. The marvelous tapestry of particles, forces and fields that is the stuff of today's physics offers dramatic corroboration of the ancient picture of cosmic beings interacting in virtue of dispositiones, nowadays measured as so many fundamental properties. It is because molecules, on having been formed from their atomic components, have their own attractive-repulsive properties (due to redistribution of electrical charge according to quantum principles - London forces, etc. - based in turn on the previous charge distributions within the atoms), that they can and do interact with other molecules in such and such ways to form more complex structures right up through the biochemical domain. Since every hylomorphic substance acts through its accidents, it is clear that elements enter into composite beings through spatiotemporal interaction; they are "disposed" toward such and such higher informations, either mediately or immediately. (Oxygen is "immediately" disposed to enter into water, H2O; it is "mediately" disposed to enter into the manifold structures of a living organism). But the disposition works in "reverse" as well. Since the accidents of a higher substance are constituted as the mean vis-a-vis the accidents of the elements, the higher substance, inasmuch as it is material and corruptible, is "disposed" to revert to just those elements which pre-existed it: as if to say that gray can be resolved into black and white again, or pink into white and red. Moreover, such dispositions are so precisely constituted as to find expression, in mathematical physics, as the law of conservation of massenergy: at the level of the chemical elements, compounds are invariably resolvable (in

204 principle) into the same constituents from which they were formed.

Thus (even though

this particular formulation represents a considerable simplification of the processes involved): 6C + 12H + 60 ** C 6 Hi 2 0 6 , so that in principle a molecule of glucose is resolvable, on decomposition, into 6 carbon atoms, 12 of hydrogen, and 6 of oxygen, no more and no less. (At a level deeper than that of the structure that constitutes chemical compounds, an analogous resolvability obtains: thus atoms broken down in nuclear fission reactions can be reconstituted in fusion reactions, and at a still deeper level, 2 "up" quarks plus 1 "down" quark are understood to comprise the proton, while today's highly consistent theory construes those quarks as having had - or, conversely, being able to have again - independent existence at energies of the order of 1 GeV [corresponding to 10"2 sec, in the early universe].) Since a hylomorphic substance acts (including self-preservatively) only through its accidents, they must be proportioned to it, within certain limits, and once the accidents are altered beyond a certain threshold corresponding to those limits (through being acted upon by another substance, through its accidents), the underlying substance

There is some dispute as to whether the constituents (atoms, in terms of contemporary discourse) can be numerically the same; Aristotle's view, expressed in On Generation and Corruption II.7, would seem to be negative: "it is evident that those things whose 'substance' - that which is undergoing the process - is imperishable, will be numerically, as well as specifically, the same in their recurrence: for the character of the process is determined by the character of that which undergoes it. Those things, on the other hand, whose 'substance' is perishable (not imperishable) must 'return upon themselves' in the sense that what recurs, though specifically the same, is not the same numerically" (338M3-18; McKeon ed., p. 531). But a closer study of this question would entail, not only a resolution of the "reality of atoms" issue, but also a material definition of just what specifies an atom: is it finally just the proton number, or must neutrons and/or electrons be considered as well?

205 will fail of existence and its "place" in the material continuum be taken by another substance, or substances, to which the previous substance's matter, in virtue of its form, was disposed. The dispositions of a hylomorphic substance must be referred to prime matter, i.e. to a being's openness to substantial change, since it is precisely the latter to which they are dispositive; an accidental being considered merely as such could not be a cause of substantial change. Nor could we say that the other substantial principle, form, is absolutely dispositive toward any kind of substantial change, since form is an immutable and constant principle. Form, as the ad quern of substantial change, is precisely that which terminates change as such. Aquinas speaks regularly of both dispositio materiae and dispositio ad formam, but never of "dispositio formae" (genitivfe). Concluding that dispositions toward substantial change are radicated in matter, there are two other errors to be avoided. First, as was discussed in our chapter on matter, it cannot be maintained that the material principle is a principle of selfcorruption, i.e. of the dissolution of the substance in which it currently serves as constituent, since this would make substance inherently self-destructive. Rather, matter is a principle of corruption only in so far as it is receptive of other forms which, through a kind of "superiority" of activity, can supplant that form with which matter is at any

37

See, e.g., Summa theologiae Iallae, q. 112, a. 3 ad 3 ("in rebus naturalibus dispositio materiae non ex necessitate consequitur formam, nisi per virtutem agentis qui dispositionem causat" Leon. 7.325); Ilia, q. 77, a. 2 ("prima dispositio materiae est quantitas dimensiva" - Leon. 12.196); la, q. 76, a. 4 ad 4 ("Manent enim qualitates propriae elementorum, licet remissae, in quibus est virtus formarum elementarium. Et huiusmodi qualitas mixtionis est propria dispositio ad formam substantialem corporis mixti, puta formam lapidis, vel animae cuiuscumque" Leon. 5.224).

206 moment conjoined. Secondly, since matter as such is indeterminate, its dispositive role (which implies always some determination) must occur in virtue of its information. Matter, we might say, is a "source" of receptivity to forms other than that to which it is at a given moment conjoined; but the specificity of this receptivity is due to its present form. Thus when dispositiones materiae are referred to, it is with matter's primal potency in view; but when dispositiones adformam are under consideration, it is really the same dispositions, but under the ratio of their specificity. One of Aquinas's most probing treatments of the dispositions of matter is found in Question Nine of his Quaestiones disputatae de anima. I will summarize the body of his response and give particular attention to a couple of difficult points.38 It is the substantial form which, as that which gives existence absolutely speaking, first comes to prime matter and is in it most intimately.

Nor can there be more

than one substantial form. Hence even in higher grades of natural things, where there are more perfections than in the lower grades, all of the perfections (as corporeality and life and rationality, in the case of man) are due to one and the same substantial form. A more perfect form, then, in so far as it constitutes with matter a composite of lower perfection, is material with respect to greater perfection.40 And so a given form, qua consti-

38

1 am guided here also by William A. Wallace, "Thomistic Reflections on The Modeling of Nature: Science, Philosophy, and Theology" (unpublished paper [1997], 49 pp.), pp. 5ff. 39 "Est autem hoc proprium formae substantial quod det materiae esse simpliciter," Quaestiones disputatae de anima q. 9 (Leon. 24.1.79:145-80.146). 40 Ibid.: "...forma perfectior, secundum quod constituit materiam in perfectione inferioris gradus, simul cum materia composita intelligatur ut materiale respectu ulterioris perfectionis, et sic ulterius procedendo" (Leon. 24.1.80:191-195).

207

tutive of a lower grade of being, is in some sense a mean between matter itself and the same form qua constitutive of a higher grade of being.41 Let us pause at this subtle passage. Aquinas is certainly not saying that one and the same form can have different manifestations - now as a being of lower grade, now as a higher one - in any genetic or successive sense. Rather, since a form, in constituting a higher being, also constitutes, as aspects of that being, what would be complete formalities at a lower level of being, one may think of those aspects (coexisting with and in the substance) as a sort of mean - as dependent existents - between the sheer potentiality of matter and the independent existence given by the substantial form in question. If I may again attempt a visual model:

A

Bi

B2

Let the equal bases of each figure represent prime matter, common to each successive information, and the shapes of the figures represent the forms, with substantial form A yielding to substantial form B. The form which is entirely constitutive of A must enter accidentally into the higher substance informed by B. Hence Bi does not represent as well as B2 the actual composite.

Ibid.: "Et sic quodammodo una et eadem forma, secundum quod constituit materiam in actu inferioris gradus, est media inter materiam et se ipsam, secundum quod constituit earn in actu superioris gradus" (Leon. 24.1.81:201-205).

208

Returning to our paraphrase of the text: prime matter, entering into a being of a lower grade, is the subject of proper accidents and of dimensions, whereby it is divisible into parts receptive of accidental forms. Such accidents include those whereby the matter is disposed and made suited to further perfection. The dispositions due to these accidents are thought of before the form itself, as having been induced into the matter (by the agent cause), even though they are in fact so proper to the form as never to exist in matter except through that form.42 (In other words, the dispositions cannot pre-exist the form with which they are uniquely associated, but inasmuch as the form depends, in its own continued existence, on the presence of those dispositions, they may be thought of, in a way, as prior to the form.) The form of a higher being, then, did not exist in the previously formed being as a disposition; it can exist only in its proper, fully constituted role, but in that role is causative of the dispositions in question. Unicity of substantial form is thus maintained at all times, with higher informations incorporating the perfections of the lower. And it is appropriate to think of the prime matter together with its lower perfections as dispositive toward its substantial perfection. Since Aquinas is treating of the human soul, he uses this as concrete example: although it is the rational soul which, as man's unique substantial form, gives to man

lb id.: "Huiusmodi autem dispositiones preintelliguntur forme ut inducte ab agente in materiam, licet sint quedam accidentia ita propria forme, quod non nisi ex ipsa forma causentur in materia." Leon. 24.1.81:222-226. Cf. Summa theologiae la, q. 16, a. 6 ad 1: "Sicut ergo materia praeintelligitur perfecta secundum esse ante intellectum corporeitatis, et sic de aliis; ita praeintelliguntur accidentia quae sunt propria entis, ante corporeitatem. Et sic praeintelliguntur dispositiones in materia ante formam, non quantum ad omnem eius effectum, sed quantum ad posteriorem."

209 sensation and nutritive powers and corporeality, still it is reasonable to speak of these lower perfections as dispositive to rationality itself. It is a virtual presence of the parts in the whole that Aquinas is discussing in Question Nine, though he does not use the term here. What holds of the parts as such, he continues, holds no less of their operations: activities that were primarily characteristic of lower forms remain, even in higher grades of being (and, we may assume, in a modified or "mean" mode), as secondarily characteristic. (And so, we can say, a living organism manifests, albeit in a somewhat modified way, the activities proper to, say, water or even hydrogen.) An important distinction is introduced here, one which we have already had occasion to consider, namely that between least parts or elements, and complex parts or organs. With respect to the former, diversity of activity requires no more than a diversity of accidents - i.e., those characteristic of the elements as such; but with respect to the latter there are levels of complexity of operation beyond the merely elemental. Since the complexity of the organ is not self-constituted, but arises only through the unifying substantial form of that to which the organ belongs, corruption of the substance must result, not in the organ's acquiring its own substantial existence, but in a reduction all the way back to the elements. Finally, the fact that the substantial form gives existence immediately to all parts of the composite whole does not entail that the operations of those parts proceed likewise. On the contrary, there is, among the operations of the parts of a composite being, an ordering such that one is caused by another, and that by still another, etc. It will be

210 seen that matter, so far from being an "inert" principle of receptivity, is intimately involved in the dynamism of change. Put simply, without matter there is neither corruption nor generation; form, the principle of activity properly speaking, acts only in virtue o/its being enmattered - and this, not merely in the sense that matter is the conditio sine qua non of form's activity (as proximity is the condition of seeing or hearing anything), but in the deeper sense that form is the act of matter, the "expression" or determination of a principle which is, in its own right though inchoately, dunamis.43 I now return to a theme sounded before: the relation between qualitative and quantitative, as one key to a rapprochement between the Aristotelian physics and the modern. Aquinas and others in the Aristotelian tradition did not excogitate the doctrine of dispositiones materiae on the basis of any quantitative analysis, nor would it have occurred to them to do so (their concern in science was with substances more than with accidents). But the results of their analysis - bringing into a single coherent account the unity of being, the diversity of its parts, and the patterns of succession in a changing world - are so compatible with the quantitative considerations of today's physics as to seem even more suited to the latter. For if it is not often evident (as noted in regard to the virtual presence of elements) that such and such qualities stand as "contraries" vis-a-vis the "mean" qualities of a new substance, still less is it evident that they are dispositive to this or that new substance - for example, that the metallicity of sodium or the gaseous state, yellowgreen color and corrosive odor of chlorine are dispositive to common table salt. We can 43

See, e.g., Metaphysics IX. 1 (1046al9-25).

211 conclude, modo philosophico, to the dispositions in question because at the universal level (where science, in Aristotle's sense, occurs) we cannot conclude otherwise, given the elemental or substantial natures of sodium, chlorine, and sodium chloride, the distinction between substances and their accidents, and the necessary role of the latter in effecting substantial change. But mathematical physics and chemistry provide a different insight: a more imaginable, if no more certain, grasp of relationships between the quantities that ground every qualitative disposition and transformation. As noted earlier, my premise here is that there is an unambiguous spatial continuity between successive configurations of elemental and substantial accidents - not an identity of "space occupied," but a commonality or "overlap." The volumes, shapes and spatial orientations of sodium and chlorine atoms (for example) can be directly related to the volume, shape and orientation of sodium chloride molecules (empirical units). And while some sensible qualities seem to remain beyond our analysis - the taste or smell of salt, for instance - other qualities, such as its crystal shape, density, solubility and color, find a very straightforward explanation in terms of quantitative alterations occurring to sodium and chlorine atoms as they merge into a new unity. (At this level the alterations are discerned in terms of electron configurations and charge distribution, entailing new spatial relations between the atomic nuclei themselves and new modes of interaction with incident photons, etc.) Again, there cannot but be some commonality in the "space occupied" by reactants and their products, even at the level of the least particles.

212 I have used a chemical example, but the same kind of reasoning applies at the subatomic level. A pair of deuterium nuclei does not have the same quantitative characteristics as a helium nucleus - that is why deuterium is deuterium, and helium helium yet there is enough commonality between them - i.e., between (2H+)2 and 4He - to serve as a basis for understanding similarities as well as differences in their respective qualitative features. (With respect to both atomic and subatomic configurations, some of the quantitative relationships will occur at the level of energetics - we take into account not only the "apparent" differences of particle arrangement, but also the energies implied in their specific heat, binding energies, and so on.) In closing this section I iterate caution against taking the quantitative analysis for a holistic view. No purely quantitative relating between the prior and posterior states of a physical system will explain the formal unities implied in those states.

G. Entia vialia I have reviewed, and noted the metaphysical foundations for, the basic structure of physical being in terms of its potential and actual principles, giving attention also to the relation between its substantial and accidental aspects, and to the ordering between more and less complex beings (through virtual presence and the dispositions of matter). Throughout we have seen the role of form as the determining factor, exercising its specificity amid the flux and variety that are radicated in matter. In an initial grasp of all this we can abstract from close consideration of form's permanence; it suffices to discern in form the basis of relative permanence, in contrast

213 to the radical dynamism afforded by the material principle. But the question of permanence entails, not only temporal comparisons but an examination of the relatedness among forms understood to be essentially distinct. For however atemporal form may seem in juxtaposition to the dynamism of matter, the fact is that forms ceaselessly yield existence to other forms, and in a completely ordered (which is not to say deterministic) way. It does not void our concept of nature to regard the seedling-form as ordered essentially toward the mature plant-form. But what about the ordering of one organism's form toward another's, further along the evolutionary sequence? And, in the present moment, should we regard the form of sodium as "ordered toward" sodium chloride, or photons and electrons as "ordered toward" each other in the phenomena of light absorption and emission? Is the distinctness between formal principles in all such instances univocal - or are some distinctions more definitive than others? In theorizing about the transience of some formal instantiations as contrasted with others, thinkers in the scholastic tradition have enunciated the notion of ens in via {ens viale), or "transient being."44 A question most germane in this regard is: on what basis should certain natures be classified as "transient"? If the notion of ens in via is to 44

"Now, among the great discoveries of modern science is its uncovering an astounding number of transient entities in the physical universe. I refer to the world of elementary particles, most of which have a transitory existence....A realist philosopher of science thinks of these as more than entia rationis, as having some mode of existence outside the mind. Do they also have natures? On the basis of my model for inorganic natures I would tend to answer in the affirmative....but I would not regard them as having stable natures, like those of elements and compounds. Rather they are transient forms that emerge from the potency of protomatter under more or less violent conditions and then recede back into that potency, only to be replaced by other emergent forms." William A. Wallace, "Thomistic Reflections," pp. 7f. Wallace's discussion of transient natures is a main inspiration behind the following reflections.

214 have ontological validity it must exclude two reductionisms: on the one hand, that whereby all natures are considered as substantially and genetically independent, and only accidentally susceptible of mutual transformation; and on the other hand, that whereby all natures are equally "dependent" in the sense of being ordered toward other natures - in other words, the extremes of apotheosizing being and becoming respectively. It is obvious that some natures (i.e., beings considered as intrinsic principles of being and activity) have a more tenacious hold on existence than others. Nor is this primarily a matter of temporal duration, even though shorter durations are often associated with what we are calling the transient natures. Rather, it is a matter of whether a certain fullness or perfection of being is attained by the nature in question. Some simple invertebrates have lifespans measured in days, some bacteria lifespans measured in hours or even minutes. Yet these organisms seem to have reached a certain completeness, including reproducibility, in their allotted spans.45 On the other hand, whatever form is possessed by (say) a mammalian embryo, or even by the egg and sperm before fertilization, may be retained, to all appearances, on timescales considerably longer than the entire lifespans alluded to above; yet it would hardly occur to anyone to posit "completeness" of such natures prior to their maturation outside the placental environment.

The succession of forms over evolutionary timescales, and its implications for an Aristotelian philosophy of stable natures, is an important and closely related topic, beyond the scope of this thesis. I only observe in passing that the teleological approach which alone makes biological evolution meaningful - a thought worth pondering by evolutionists and anti-evolutionists alike - implies in its very notion a terminus ad quern, such that even in a thoroughly evolutionary universe not everything can be in transition.

215 At the level of physical and chemical analysis, and particularly with reference to particle physics, the difficulties only increase. Convention may assign "stability" to certain particles and not others, based on measured lifetimes. But nothing is exempt from the law of decay; so where is the line to be drawn? Is the proton to be considered a "nature" in the full sense because, in the current cosmic environment, it appears capable of existing on the order of at least 1032 years, while neutral Jt-mesons are better regarded as transient because of their evanescent half-lives on the order of 10"16 seconds? Or, to take some instances from the radioactive decay series for uranium-238: is there a difference in nature between lead-214 (half-life: 27 minutes), lead-210 (half-life: 22 years) and lead-206 (no known decay)? Because the criterion of temporal duration, notwithstanding the dramatic differences, seems arbitrary, given the considerable overlap between "lifetimes" that are definable, on other grounds, as "complete," it appears that a more philosophical criterion would be that based on the "direction" of actualization: there is a clear distinction, in the natural world, between developmental processes that are reversible and those that are not. Thus an embryo is only ordered toward becoming a mature organism, and not the other way around - whereas the "ordering" of sodium and chlorine toward sodium chloride may, with appropriate inputs of energy, be exactly reversed. Hence the embryonic nature is transient ("unidirectional" in the order of actualization) in a way that sodium and chlorine are not. As for the case of radioactive decay products, it seems that a determination of whether any such are "transient" or "stable" might have to take into account the possibility of some sort of reversibility, at least in principle - and so, mutatis

216 mutandis, for the case of "elementary" particles which are to all appearances stable, but are theorized not to have been so at an earlier stage of cosmogenesis, and again of particles, such as quarks, which today seem to exist only virtually, but are presumed to have had independent existence at an earlier epoch. Perhaps the distinction between transient and stable natures is of only secondary importance, in view of the overriding consideration that they are in any case natures, serving as specifying principles regardless of their relative duration.46 Whatever the ontological status of entia vialia, they give positive evidence, however fleetingly, of acting in virtue of intrinsic principles of functional unity, i.e., of forms, which govern the mere potentiality assignable to their material constituents.

H. Minima naturalia Aquinas devotes little attention to the question of natural limits (spatiotemporal minima and maxima), but he clearly acknowledges their existence and necessity. The topic would be addressed more intently by late medieval thinkers.47 Here I wish to bring together two main considerations: the reality of natural minima or least dimensions, and the impossibility of an actual infinite in the order of cosmic being. These considerations

46

See Wallace, "Thomistic Reflections," p. 8. See John E. Murdoch, "The Medieval and Late Renaissance Tradition of Minima Naturalia", pp. 91-131 in Late Medieval and Early Modern Corpuscular Matter Theories, ed. C. Liithy, J. E. Murdoch and W. R. Newman (Leiden, 2001), which includes a survey of recent historiography on the subject, and the fine collection of Duhem's writings in English translation, Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds, ed. Roger Ariew (Chicago, 1985), esp. Chapter 1.

47

217

will enable us to acknowledge, in the next section, that the physical continuum has a radically atomic structure that is most explicit at the deepest level of physical analysis. "The ultimate source for the conception of minima naturalia is a text in the fourth chapter of the first book of Aristotle's Physics"

where he is refuting Anax-

agoras's theory of an infinite multitude of constituent physical principles, each indefinitely small (indivisible). 48 Aquinas, commenting on this passage, says If the parts of a whole do not have a determinate quantity, either great or small, but can be any size, either great or small, it is not necessary that the whole have a determinate greatness or smallness. This is so because the quantity of the whole comes from the parts. (But this must be understood of the parts existing in act in the whole, as flesh and nerve and bone exist in an animal. Hence he says, " . . . by parts I mean components into which a whole can be divided and which are actually present in it." And by this he excludes the parts of a continuous whole which are in the whole in potency. But it is impossible that an animal or a plant or some such thing be related indeterminately to any size, whether great or small, For there is some quantity so large that no animal exceeds it in size. So also there is some quantity so small that no animal is found to be smaller. And the same must be said of plants. Therefore by denying the consequent it follows that the parts are not of indeterminate quantity. For what is true of the whole is true of the parts. But flesh and bone and things of this sort are parts of an animal, and fruits are parts of plants. Therefore it is impossible that flesh and bone and such things should have an indeterminate quantity, either greater or smaller. Therefore it is not possible that there should be certain parts of flesh or bone which are nonsensible because of smallness.49 48

Murdoch, p. 91; cf. Physics 187M3-21: "if the parts of a whole may be of any size in the direction either of greatness or of smallness (by 'parts' I mean components into which a whole can be divided and which are actually present in it), it is necessary that the whole thing itself may be of any size. Clearly, therefore, since it is impossible for an animal or plant to be indefinitely big or small, neither can its parts be such" (McKeon ed., p. 225). 49 In libros Physicorum I, lect. 9: "Si alicuius totius partes non habent aliquam determinatam quantitatem, sive magnitudinem vel parvitatem, sed contingit eas quantascumque esse vel secundum magnitudinem vel secundum parvitatem; necesse est quod totum non habeat determinatam magnitudinem vel parvitatem, sed contingat totum esse cuiuscumque magnitudinis vel parvitatis: et hoc ideo, quia quantitas totius consurgit ex partibus. (Sed hoc intelligendum est de partibus existentibus actu in toto, sicut caro, nervus et os existunt in animali: et hoc est quod dicit, dico autem talium aliquam partium, in quam cum insit, scilicet actu, dividitur aliquod totum: et per hoc excluduntur partes totius continui, quae sunt potentia in ipso). Sed impossibile est quod animal vel planta vel aliquod huiusmodi habeat se indeterminate ad quantamcumque

218

The argument is this: actual parts comprising a whole are either determinate or indeterminate in size. If indeterminate, then the whole cannot be likewise. But a natural thing (whole) cannot be of indeterminate size, because there is some quantity so large that no natural thing exceeds it, and again some quantity so small that no natural thing is smaller. (Implied here is that there cannot be an infinite number of natural things. If the implied premise were that natures must exist within certain size limits, the argument would fail by petitio principii.) Therefore, modus tollens, the actual parts of a natural thing must be of determinate size. The last part of Aquinas's conclusion, "it is not possible that there should be certain parts of flesh or bone which are non-sensible because of smallness," must be understood in the context of the Anaxagoran doctrine to which Aristotle was responding: "[The physicists thought] that things come into being out of existent things, i.e., out of things already present, but imperceptible to our senses because of the smallness of their bulk."50 What is being rejected, it seems, is a particle size so vanishingly small as to be insensible even en masse. I do not think Aquinas meant something so obviously untenable as a denial of the possibility of particles that are beneath the threshold of sensibility

magnitudinem vel parvitatem: est enim aliqua quantitas ita magna, ultra quam nullum animal extenditur, et aliqua ita parva, infra quam nullum animal invenitur; et similiter dicendum est de planta. Ergo sequitur ad destructionem consequentis, quod neque aliqua partium sit indeterminatae quantitatis, quia simile est de toto et de partibus. Sed caro et os et huiusmodi sunt partes animalis, et fructus sunt partes plantarum: impossibile est igitur quod caro et os et huiusmodi habeant indeterminatam quantitatem vel secundum maius vel secundum minus. Non ergo est possibile quod sint aliquae partes carnis aut ossis quae sint insensibiles propter parvitatem." Leon. 2.29; English translation from Commentary on Aristotle's Physics, translated by Richard J. Blackwell, Richard J. Spath, and W. Edmund Thirlkel (Notre Dame, Ind., 1999), pp. 36f. 50 187a35-187bl.

219 considered individually.

Nothing in the context warrants reading anything more into

Aquinas's statement. Aquinas raises and resolves an objection concerning divisibility: It seems, however, that what is said here is contrary to the statement that a continuum is divisible to infinity. For if the continuous is divisible to infinity, and flesh is, indeed, a kind of continuum, it seems that flesh is indivisible to infinity. Therefore, some part of flesh, according to a division to infinity, goes beyond every determinate smallness. But it must be pointed out that although a body, considered mathematically, is divisible to infinity, the natural body is not divisible to infinity. For in a mathematical body nothing but quantity is considered. And in this there is nothing repugnant to division to infinity. But in a natural body the form also is considered, which form requires a determinate quantity and also other accidents. Whence it is not possible for quantity to be found in the species offleshexcept as determined within some termini.52 This argument based on the determinateness of quantity inhering in any finite substance is found elsewhere.53 Interestingly, Aquinas, having just argued for natural minima (de-

51

Cf. Aquinas, Sentencia De sensu tract. 1, cap. 18, where he distinguishes two kinds of indivisibility, that according to the nature of a thing itself, and that according to its sensibility: "set aliquando indiuisibile, uidet autem non indiuisibile. Quod potest intelligi dupliciter. Uno modo secundum quod indiuisibile dicitur aliquod corpus naturale minimum, quod non potest diuidi ulterius quin corrumpatur et tunc resoluitur in corpus continens; et tunc sensus erit, quod corpus indiuisibile est quidem in se ipso sensibile, set tamen huiusmodi indiuisibile sensus uidere non potest. Alio modo potest intelligi indiuisibile quod non est actu diuisum, sicut pars continui; et huiusmodi indiuisibile non uidet sensus in actu." Leon. 45.95:197-208. This passage, incidentally, is the only one in St. Thomas that I have found (using R. Busa's Index thomisticus) where the term naturale minimum appears. 52 In libros Physicorum I, lect. 9: "Videtur autem quod hie dicitur, contrarium esse divisioni continui in infinitum. Si enim continuum in infinitum divisibile est, caro autem continuum quoddam est; videtur quod sit in infinitum divisibilis. Omnem igitur parvitatem determinatam transcendet pars carnis secundum divisionem infinitam. Sed dicendum quod licet corpus, mathematice acceptum, sit divisibile in infinitum, corpus tamen naturale non est divisibile in infinitum. In corpore enim mathematico non consideratur nisi quantitas, in qua nihil invenitur divisioni in infinitum repugnans; sed in corpore naturali consideratur forma naturalis, quae requirit determinatam quantitatem sicut et alia accidentia. Unde non potest inveniri quantitas in specie carnis nisi infra aliquos terminos determinata." Leon. 2.29; Eng. trans., op. cit. p. 37. 5 See Summa theologiae la q. 7, a. 3, where the reasoning is more explicit: "de corpore quidem naturali, quod non possit esse infinitum in actu, manifestum est. Nam omne corpus naturale aliquam formam substantialem habet determinatam, cum igitur ad formam substantialem consequantur accidentia, necesse est quod ad determinatam formam consequantur determinata accidentia; inter quae est quantitas. Unde omne corpus naturale habet determinatam quantitatem

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terminate least dimensions) on the presupposition (as I read it) of the finite number of natural existents, now responds to an objection by arguing for natural minima on the presupposition (as I read it) of the finite nature of substantial form. The arguments are distinct, each standing on its own, and it seems the latter could as well have been made a primary argument in the rebuttal of Anaxagoras. But of course Aristotle did not do this, although Aquinas for his part elsewhere relies on the argument from form alone.54 I have alluded to the impossibility of an actual infinite in the order of hylomorphic being; this important Aristotelian and Thomistic doctrine is established, inter alia, in Physics I. 4. Aristotle there first gives an argument against infinite body, based on the perception of bodies as terminated by surfaces, and then an argument against infinite multitude, based on innumerability.55 These are only dialectical arguments, but they are followed by arguments proper to natural philosophy, though even the first of these is premised upon the existence of a finite number of elements.56 "After the Philosopher has shown, upon the supposition that the elements are finite, that there is no infinite sensible body, he here57 shows the same thing without qualification and without any supposition."58 Following Aquinas's commentary (lectio 9) on this part of the Physics, I offer this summary.

et in maius et in minus. Unde impossibile est aliquod corpus naturale infinitum esse." Leon. 4.75. 54 See preceding note. 55 204b4-10; cf. Aquinas's Commentary, Book III, lect. 8 (Eng. trans., op. cit. pp. 175ff.). 56 204bl0-205a7. 57 At 205a9ff. 58 Commentary, op. cit. p. 180.

221 (205a9-205b24) First argument: by reduction, to the effect that an infinite body must be either immovable, or always in motion, or only accidentally in motion - none of which is admissible; or again, that an infinite body would have to be comprised of either finite parts, or infinite kinds of parts, neither of which is admissible. (The argument, even in Aquinas' s explication, is dense and I make no attempt to replicate it here.) (205b24-31) Second argument: if there were an infinite body no part could be distinguished from any other part, and hence natures would not tend toward one attractor rather than another. (This is a modernized interpretation on my part, to eliminate the distracting, but by no means essential, references to natural place that are the burden of ancient and medieval cosmologies. The argument holds no less with respect to any particular determination of a place ad quern, e.g. the centers of gravitating masses, etc.)59 (205b31-35) Third argument: In our three-dimensional world there are six orientations (above/below, before/behind, right/left), and every natural motion is referred to these; but such would be meaningless in an infinite world. This argument is related to the preceding; but where that one dealt with the natural significance of place, this one deals with its quantitative aspect. (205b35-206a7) Fourth argument: An infinite body would require an infinite place, which is impossible because the very notion of place entails limit. Throughout the discussion, as is typical in Aristotelian and scholastic thought, the infinite is taken very seriously as the now-finite, as that which is beyond quantity, 59

Interestingly, this argument can be said to adumbrate modern formulations of Olbers' paradox, in both its "light" and "gravitation" expressions. See Stanley L. Jaki, The Paradox of Olbers ' Paradox (New York, 1969).

222 immeasurable, innumerable. Anything that is measured or numbered is by definition finite, however indefinitely large or small; the confusion between uncounted and uncountable, or unmeasured and immeasurable, is a characteristically modern artifact of the post-Humean dependence on sense rather than intellective knowing. That there cannot be an infinite "body" (or a universe of contiguous bodies, which amounts to the same thing and is what Aquinas means)60 is, as I mentioned, already implicit in the Aristotelian argument against infinite divisibility of natures. Now if we take the argument against infinite divisibility of bodies (based on the finitude of substantial form) in conjunction with the disproof of an infinite number of bodies just surveyed, we conclude that, in the cosmic range of being, there is no process ad infinitum in smallness of bodies; there is, in a word, a least (atomic) level of hylomorphic structure.

I. On some characteristics of elemental particles I now wish to summarize some reflections presented in an article published by Edward MacKinnon61 which seem to me particularly relevant to our concerns in the present thesis. Much of what MacKinnon discussed had to do with elementarity as such (i.e., the characteristics of being at the infima level of natures), rather than the indivisibility or

In libros Physicorum III, lect. 9: "in toto universo determinate sursum et deorsum secundum motum gravium et levium: secundum autem motum caeli determinatur dextrum oriens, sinistrum occidens; ante vero hemisphaerium superius, retro vero hemisphaerium inferius; sursum vero meridies, deorsum vero septentrio. Haec autem non possunt determinari in corpore infinito: impossibile est ergo totum universum esse infinitum." Leon. 2.130. 61 "Thomism and Atomism," The Modern Schoolman 38 (1961): 121-141.

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minimality implied by the "atomism" of his title, through of course the two are closely associated. MacKinnon sought to relate the physical and philosophical perspectives on elemental reality, by considering certain theses derived qualitatively from modern physics, in the light of basic metaphysical analyses. These positiones (so called in reference to their status as physical principles, imported, without the physical formalism in which they possess their full intelligibility, into the arena of metaphysical investigation) are the following: (1) Fundamental particles exist. (2) They have systematic interactions. (3) They can form more stable complex units. (4) Knowledge of ultimate physical reality must remain somewhat indeterminate. (5) There is no completely isolated physical system. Commencing with some epistemological observations, MacKinnon noted that the apparent blurring of the distinction between subject and object in quantum-physical observations does not warrant a lapse into sheer equivocity or operational definitions; critical realism can offer a solution through the appropriate application of analogous concepts.62 This is not to say that there is no difficulty in deriving and applying the analogies in question; on the contrary, even when physical and metaphysical propositions are materially the same, formal relatability is possible only if they are framed with enough generality (though not, of course, at the expense of verity) to allow of epistemic 62

Op. cit., pp. 125-7. The second part of his paper, synopsized below, essays just such an application. A much more wide-ranging and comprehensive approach to the analogical harmonization of science and philosophy, though focusing more on natural philosophy than on metaphysics, would be William A. Wallace, The Modeling of Nature: Philosophy of Science and Philosophy of Nature in Synthesis (Washington, D.C.: CUA Press, 1997).

224 overlap. Thus, metaphysics could not be expected to interpret a technical proposition couched in the mathematical language of physics - not only is the mathematical language itself proper to the subordinate science, but it also cloaks an epistemological divide between statements concerning the external world and those which concern only the mind's constructs (a divide which perennially bedevils attempts to understand the world mathematically). On the other hand, since metaphysical principles "are validly developed from an analysis of the objects more immediately known and of the knowing subject" theory can be expected to apply to "physical" statements of sufficient generality - of which MacKinnon offers as examples the positiones noted above. Turning then to properly metaphysical themes, MacKinnon follows the Thomistic potency-act analysis in three stages: essence-existence, matter-form, and substanceaccident. "What we hope to obtain from our experiment are some philosophical conclusions concerning elements which may be compared with the scientific positiones concerning fundamental particles."63 MacKinnon's conclusions are as follows. (1) Aquinas bases the notion of perfection in being on a thing's relation to its first Cause, which is ipsum esse subsistens. "Things are perfect according to the mode in which they exist," i.e., to the degree to which they enjoy actuality rather than potentiality.64 Thus, says MacKinnon, with his eye on elemental existents, "[t]he least being has the least self-identity [or ontological unity, which is convertible with being TTOsJis" an apt especially in Chapter 5. 64 "Omnium autem perfectiones pertinent ad perfectionem essendi, secundum hoc enim aliqua perfecta sunt, quod aliquo modo esse habent." Summa theologiae la q. 4, a. 2 (Leon. 4.52); cf. Summa contra gentiles II, c. 90. The "degree of actuality" implies, of course, the determinative role of essence, itself considered as a potency with respect to existential act.

225 hence with actuality] . . . . It should be so merged with its environment [the extended physical continuum] t h a t . . . it is difficult to determine where it starts and ends, though it is something distinct from its background."65 (2) At the level of the matter-form complementarity, MacKinnon again has foremost in view Aquinas's prioritization of act over potency. Elemental being "is the one closest to prime matter; that is, most in potency and least in act. It is reasonable to expect that such an element is highly mutable and easily transformed."66 Moreover, given that a thing only acts according to the actuality which it possesses,

an element

should manifest the "least perfect action" - however that should be defined. MacKinnon proposes that the criterion of perfection in actions is the degree of immanence. "God is pure immanence . . . . we would expect elements to be characterized by actions which have the least degree of immanence. More concretely, we might surmise that the proper activities of elements would be so strongly dependent upon environmental influences that any distinction between the activities of the particle and those of the associated fields (the environmental influences) would be somewhat arbitrary."68 This comparative lack of immanence in elemental operations (MacKinnon singles out, for consideration in this regard, efficient causality) implies a correlative dependence upon extrinsic influences: "the weak causal efficacy of an individual element must be supplemented by the causal determination given by other agents. More concretely, while A acts on B, it in turn is acted on by a concatenation of causes of the same 65

MacKinnon, "Thomism and Atomism," pp. 132f. MacKinnon, p. 133. 67 Cf. Summa contra gentiles III, c. 69; Summa theologiae la q. 14, a. 8 and q. 77, a. 1 ad 4. 68 MacKinnon, pp. 134f. 66

226 order and relative degree of efficiency."69 This leads to a concept - interestingly enough, also introduced from a different perspective by such non-Thomistic thinkers as Reichenbach and Bohm - of mutual causation or a "causal mesh" in which, to a much greater degree than occurs higher on the ontological scale, every action entails a related "reaction": "When A acts on B, its very activity must be strongly influenced by the reaction ofB."70 MacKinnon is careful to note that none of these considerations vitiates the principle of causality; nothing (I will interpolate) is ever cause and effect sub eodem aspectu; but there is an indeterminacy in individual causal activity that (I take it) places it at the opposite pole from the supremely determinate causality of the Creator, which gives being itself ex nihilo. MacKinnon closes his remarks on matter and form with the observation that the simplest composites would be expected to evidence "properties not too different from those which we have ascribed to the elements."71 Although he does not mention virtual presence, this seems to be what he refers to when, following Hoenen, he continues: "Two elements combine by acting upon each other and so altering each other's disposition that a new third body arises which combines the qualities of its two progenitors in a unified way."72 (3) "A substance is that which exists through i t s e l f . . . . If this participation in existence is minimal the substance must be minimal in some sense of the word. Since substance acts as potency with respect to accidents and an element is close to pure po69

MacKinnon, p. 135. Ibid. 71 MacKinnon, p. 136. 72 MacKinnon, p. 137. He cites P. Hoenen, Cosmologia (4th ed.: Rome, 1949), p. 349. 70

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tency, we would expect an element to have such little substantial unity that it would almost seem to be a bundle of accidents."73 MacKinnon distinguishes, with Aquinas, proper accidents (those which flow "from the essence of a being inasmuch as the being is in act") and common accidents, which are "determined by an extrinsic efficient cause."74 "The being least in act, an element, should have the fewest and least determined proper accidents. For example, we might expect that an element's size and shape [i.e., that of the naturale minimum] would be determined in a general way by the nature of the element.... However, the precise determination of this size and shape would be a common accident and thus dependent upon the causes acting upon it."75 Acts of measurement, MacKinnon notes, "would supply just such an extrinsic cause" - and with this, I will interject, a great deal of the vaunted "quantum weirdness," which historically engendered the "Copenhagen interpretation" and ever more bizarre offshoots, suddenly seems poised to evanesce: "Since the knowledge of fundamental particles is based on the measurements performed it should be difficult to separate, even conceptually, the properties and characteristics 'proper' to the particle itself from those determined by the causal mesh, including the measurement process."76 MacKinnon concluded his fruitful reflections with a reminder that the positivist/operationalist reductionism is an over-reaction to the previously reigning mechanistic reductionism. A metaphysically respectable approach to the science of elementary particles, on the other hand - one anchored in awareness of the ordering of the entire 73

MacKinnon, ibid. MacKinnon, p. 138. 75 MacKinnon, ibid. 76 MacKinnon, p. 139. 74

228 cosmos to its Creator - can make meaningful statements about the elements (whatever these should turn out to be), while acknowledging inherent limitations to our knowledge of them, due to their primitive place in the scale of being and actuality. I have presented MacKinnon's "philosophical conclusions" in order to add grist to the mill of my own attempt to understand quantum phenomena philosophically. From the foregoing, here are some principles to keep in mind as we return to quantum physics in Chapter Five: Elementary being, it is to be expected, will be the most indeterminate vis-a-vis its hylomorphic environment; it will be most mutable, most reciprocal (dependent on external agencies) in its on activity, and most subject to accidental variations. All of this, I think, we will find evidence at the quantum level.

J. Atomism, true and false In the Aristotelian and Thomistic understanding, the cosmos is atomic in structure. Every hylomorphic nature is extended and has quantitative limits. Since every nature is either elemental or composite, and the composite ones are virtually (and therefore reductively, upon decomposition) elemental, it may be concluded that the elemental entities, whatever they are, are the atoms of Aristotle and Aquinas. These are naturally indivisible, in the sense that they cannot be divided without destroying their nature and (at the very least) becoming something else - but this transformation cannot occur ad

229 infinitum.17 As elements, they are indeed the least actualities, the most prior entities, in the universe. Thus the Democritean insight, that matter consists of irreducible particles, was in fact embraced by the greatest of those who are generally represented as being antiatomists. Of course, Aristotelian "atomism" is in key respects far from Democritus's conception. In the first place, as we have noted, there can be no question of "atoms and the void," void being a metaphysical impossibility. Rather, the atoms of Aristotelian realism must form a plenum, a "contiguum." Secondly, the elemental atoms are, like every other hylomorphic composite, mutable: not however in the sense of being able to decompose into prior entities, since they are in essence irreducible, but in the sense of being able to yield their substantial forms to one another, or to higher forms in composites, while "persisting," virtualiter, through the modified accidents of the higher form. The reductionistic atomism of Democritus and Lucretius, of Dalton and Newton and most modern physicists, recognizes no such transformation: atoms (meaning not just the entities conventionally called atoms today, but any "elementary particles" in physics) are held to be always present, as actual constituents, in higher composites. And in keeping with this, such reductionisms can admit no higher principles of unity, no succession of forms but only a "heaping" of pre-existing forms, notwithstanding abundant evidence to the contrary from both everyday and laboratory perspectives.

On the impossibility of infinite regress in constitutive material principles, see Metaphysics II.2(994a3-19).

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Thomistic atomism is a holistic atomism: every physical composite, while reducible through corruption to atomic components, is nevertheless, prior to its corruption, substantially non-atomic, informed by a unifying principle at a level higher than the elemental or atomic. The inexorable conclusion, from the Thomistic synthesis of substantial unicity, virtual presence and elemental atomicity, is that the cosmic beings of our everyday experience are not composed of "heaps" of atoms - that the substantial natures of the atoms are not actually present precisely in so far as they compose (i.e., have entered into the composition of) the beings in question. The objections, not to mention ridicule, in response to such a conclusion are predictable enough, from those who take the methodology of modern physics for a philosophy. As I said earlier, a million different experimental situations are supposed to have confirmed the reality of atoms as universally and actually present constituents; no medieval head-games should disabuse us of that fact. But again I note, leaving it for farsighted physicists to demonstrate mathematically, that no atom has ever been observed, directly or indirectly, precisely qua component of any higher actuality; every conceivable "observation" upon elemental units has been carried out in a setting in which the entity in question is isolated from whatever composite it may otherwise have belonged to virtually. Philosophical analysis discloses the essential characteristics of elements as atomic units; but philosophy cannot identify them. An interesting question is whether science, as a mathematically-informed discernment of spatiotemporal relations, can identify them? There seems to be no reason a priori why the methods of physical analy-

231 sis cannot reach the very deepest level of a finitely structured actuality; but how would science know if it had penetrated thus far? Godel's theorem, mentioned earlier in these pages, serves to remind us that such knowledge is beyond reach. Science would have to compass every last aspect of the universe, past and present, and know moreover that it had achieved just this comprehension, in order to identify "the elements" positively. It is too much to ask. Modern theories of elementarity in physics distinguish among different energy regimes, and therefore, in a cosmological context, among different epochs in the putative history of the universe (at least where the "standard model" of big-bang cosmogenesis is concerned). In a word, the "permanence" of the elements may well turn out to be as much in need of qualification as the "fixity" of biological forms in an evolutionary context. But this is not a Heraclitean situation; we have learned to discern, amid the universal evolutionary flux, natures which are specifying even if only dubiously "stable" - and, in their specificity, the very principles of instability (every change being a change adformam) as well as of cosmic intelligibility. The "atomistic plenum" of the Aristotelian universe points us to a further consideration of the nature of the physical continuum. Aristotle's detailed analyses, in Physics VI and elsewhere, have long been foundational to an understanding of local motion and its causes, but he must be read with care. Among other subtleties, he makes explicit reference to, and bases some of his conclusions on, the physical continuum understood as infinitely divisible, i.e., as a continuum strictly speaking. But infinite divisibility in the abstract, in virtue of its quantitative nature, is by no means the sole

232 consideration in an analysis of the cosmic plenum. Thus Aquinas, in his Commentary on the Physics, writes: It must be noted that Aristotle has proven in Book VI that in motion there is no first either in respect to the mobile object or in respect to the time or in respect to that in which the motion occurs, especially in increase and in local motion. This is so because he was then speaking about motion in general and about mobile objects in so far as they are continuous, not yet applying his remarks to de•

79

terminate natures. Motion can be discussed in abstracto as entailing continuities susceptible of infinite divisibility: this applies to spatial distance, body, motion itself, and time. But motion in concreto, as opposed to the abstract magnitudes of mathematics, involves natures which imply determinate dimensions (minima naturalia); their motions cannot be comprehended except in virtue of formal principles which are motive only above some infima spatial level. To divide the continuum beyond a certain point is to destroy the possibility of existence of any nature which presupposes an extension greater than what remains from the division.80 Although I do not find Aristotle's argument altogether clear in this On what follows see Richard F. Hassing, "Thomas Aquinas on Phys. VII. 1 and the Aristotelian Science of the Physical Continuum," pp. 109-156 in Nature and Scientific Method, ed. Daniel O. Dahlstrom (Studies in Philosophy and the History of Philosophy, vol. 22, ed. Jude Dougherty), (Washington, DC, 1991). Hassing singles out (p. 114), among recent commentators on Physics VII. 1, William A. Wallace (his mentor and mine): "Cosmological Arguments and Scientific Concepts" in Wallace's From a Realist Point of View (Washington, D.C., 1979), pp. 313-327. 79 In libros Physicorum VIII, lect. 11: "Ubi considerandum est quod Aristoteles prius in sexto probavit quod in motu non est aliquid primum, neque ex parte mobilis neque ex parte temporis neque ex parte rei in qua est motus, praecipue in augmento et motu locali: et hoc ideo, quia tunc loquebatur de motu in communi, et de mobili secundum quod est quoddam continuum, nondum applicando ad determinatas naturas." Leon. 2.406; Eng. trans., op, cit. p. 565. 8 "Sed tamen possibile est quod aliquod continuum, sive sit movens sive motum, habeat talem naturam, ut non possit actu dividi, sicut patet de corpore solis. Et si contingat quod aliquod continuum dividatur, non retinebit eandem potentiam ad hoc quod moveat vel moveatur, quam prius habebat; quia huiusmodi potentia sequitur aliquam formam; forma autem naturalis requirit quantitatem determinatam." In libros Physicorum VIII, lect. 11 (Leon. 2.406).

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regard, the distinction between the physical continuum considered only in its quantitative aspect, and the continuum - really a "contiguum," as will be explained shortly considered as structured by natural forms, each with minimal quantitative requirements, alone brings coherence to Aristotle's difficult and subtle account of the first intrinsic motor principle. A lucid account of the difference between a "merely" physical continuum, or the three-dimensionality radicated in the material principle, and the "natural" continuum or "contiguum" to which I have referred, is given by P. A. Pearson.81 Like Hassing, Pearson finds the crucial distinction which Aristotle "presupposes, but does not explicitly state" to be more developed in Aquinas's Commentary; but where Hassing speaks of "three kinds of magnitude: (1) mathematical continuum, (2) physical continuum, and (3) magnitude of a body of determinate nature,"82 in the context of concluding to natural form as a principle of motion, Pearson is content with following Aquinas's analysis of the difference between the first two. I now summarize Pearson's synopsis of Aquinas's commentary. Things are said to be continuous, broadly speaking, if their boundaries are one. (Boundaries - ultima - axe understood to be indivisible limits of magnitudes, as points on a line or surfaces on a body.) But "one" can be understood in different ways. Thus the unity of boundaries which are both in the same position (a boundary cannot be in a "place" since it is not a body) is different from the unity of boundaries which are nu81

"St. Thomas on the Continuum: The Nature of Points in Physics and Geometry," Aquinas 35/3 (1992), pp. 673-683. 82 Hassing, op. cit. p. 125, n. 45.

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merically one, i.e., identical (and two only in notion).83 In mathematics, which deals only with the abstract order of pure quantity, there is no "nature" other than continuous and discrete quantities themselves; and since what distinguishes continuous quantities is none other than position, two points (or lines, or surfaces) which coincide positionally can only be identical. They are, at most, notionally different. If a point C is located along line segment AB, the segments AC and CB are continuous, C being "really" one and the same; the line AB is not "really" divided, but only in our consideration thereof. "The fact that a point, considered geometrically, is identifiable with its position is the foundation of St. Thomas' argument, at the beginning of Book 6, that a line cannot be composed of points, for between any two positions, there exists always another position."84 Unlike mathematical entities, which exist per se in the mind, the boundaries of physical objects are quantitative accidents of their underlying natures. But an accident is distinguished from another accident of the same kind, a numerical distinction, only in relation to the subject in which the accident inheres. An accident which is numerically one can exist in one and only one subject. Once it is granted that ultima have an accidental reality in nature, it follows necessarily that one point can function as the ultimum or terminus of one and only one thing, for it belongs to that thing according to the manner of an accident belonging to a subject.85 Hence wherever two hylomorphic beings are in contact, their boundaries must remain numerically two even though sharing one and the same position. This constitutes contiguity, rather than continuity properly speaking.

83

Cf. In libros Physicorum V, lect. 5. Pearson, "St. Thomas on the Continuum," p. 678; cf. In libros Physicorum VI, lect. 1. 85 Pearson, pp. 678-9. 84

235 K. Motion in the physical continuum A cosmic plenum, in which there is no void space but only extended, contiguous, noninterpenetrating beings, presents us with post-Newtonian, post-Einsteinian challenges in the Aristotelian explanation of local motion. Aristotle's definition of motion, taken over unreservedly by Aquinas, is among the most fundamental, most difficult, and most neglected features of his natural philosophy. Every mobile being or "nature" is understood to have, as intrinsic principles of its mobility (and rest), form, matter, and privation. But motion itself, the effect, so to speak, of these as well as of extrinsic causal principles, remains intellectively elusive because it is actus imperfectus, an imperfect existence. Motion is defined, then, as "the act of the potential as potential" - a formulation broad enough to include all of its species, and vague enough to reflect, perhaps, Aristotle's relatively inchoate distinction of essence and existence. For as he observes after concluding to this definition, motion "cannot be classed simply as a potentiality or an actuality....the potential whose actuality it is is incomplete. This is why it is hard to grasp what motion is. It is necessary to class it with privation or with potentiality or with sheer actuality, yet none of these seems possible."86 There is neither contradiction nor redundancy in Aristotle's expression, when the three terms are rightly grasped. Granted that the deflniendum is so fundamental that its deflnientes can only be primordial ontological terms - representing principles of being, rather than entities themselves - there remains the difficulty of sorting out what

Physics III.2 (201b27-202al); McKeon ed., p. 255.

236 sense is being accorded to each of these terms. For there is a twofold possibility of ontological reference at this level: the existential and the essential. A mobile being is a "between" being, on the way from one definable state to another, and the process is, to all appearances, a continuous one (we are not considering substantial change, but only motion properly speaking). The question to address is: what is in flux in a mobile being - essence, existence, or both? We are describing hylomorphic being, within whose essence the actual principle is form, and the potential principle is matter. It is important to note, however, that act and potency are broader in meaning: for form is understood as the potential principle in reference to existence or esse, and, completing the symmetry, matter is what I shall call quasi-actual, denoting a "kind" or mode, in reference to existence. (Contingency "specifies" or contracts the kind of existence a hylomorphic being enjoys.) So to speak merely of "the act" or "the potential" involves some ambiguity. But we can be more precise. One way is to begin with the apparent redundancy "potential as potential." Aristotle is much too careful to be indulging in redundancy for mere emphasis' sake here; loquens formaliter, we will rather expect one referent to be, as noted above, existential and the other essential. This leaves us with two options: "potential as potential" will mean either "the ability to be, as what is able to be" (existential + essential referents, respectively), or "what is able to be, as able to be" (essential + existential referents). The former makes no sense. Shifting our focus now to the first part of Aristotle's formulation, "act" in the abstract could mean either "existence" or "form" (when taken existentially or essentially, respectively). Motion clearly being a way of

237 being, rather than a kind of being - an existential mode, rather than an essential one we complete our analysis in the recognition that "act of the potential," in order to avoid contradiction, must also involve two different orders of reference - bringing us, again, to the conclusion that "act" is existential and "of the potential" is of the essential order. Aristotle's definition then becomes luminous: motion is "the act [understood existentially] of the potential [understood essentially] precisely as potential [i.e., as understood existentially]." In slightly less abstract terms, motion is "the existence of the existibility of what can exist." To be in motion is to be existing-toward, existing only as "can be" - not as the "can be" of matter, understood as an ordering to form (in other words, privation: this marble block can be a statue), but the "can be" which is the ordering itself (marble simply speaking is not statue-becoming; but marble under the sculptor's chiseling is existentially, and not just essentially, ordered toward the statue). It is in virtue of matter's presence, as potency to form or "the ability to be this" (again, I am limiting discussion to the intrinsic principles of change), that motion, "the ability to be this," can be realized. What is in motion exists, not as the terminus a quo or terminus ad quern, but as neither: as transition, albeit transition determined by both a quo and ad quern. To be material is in fact to be mobile, since mobility is the very raison d'etre of matter; motion is the actuating of some material potency, under the extrinsic influence of the agent cause (and all else that is thereby implied). Now this recognition of motion as existential potentiality (validating, though only as a partial insight and not as the comprehensive one that he intended it to be, Heraclitus's assertion that "all is flux"), presents us with a subtle problem in accounting

238

for the reality of motion. Precisely this reality is under attack in the paradoxes of Zeno. Recognizing that the mobile must traverse a magnitude that is infinitely divisible, he presented scenarios in which the "impossibility" of local motion arises from the sheer infinity of spatial intervals (those lying between infinitely many pairs of points) that must be traversed, requiring an impossibly infinite time. Zeno's error was to confuse the divisibility of a continuum with actual dividedness, or infinity by division with infinity by addition. Aristotle's and Aquinas's analyses of the continuum advanced an understanding of motion, and of the magnitude traversed therein (as well as of time, the mind's measure of the traversal), as being potentially infinite but never actually so. Thus, while the mind could divide ad infinitum the continua associated with local motion, such motion does in fact proceed to its terminus, inasmuch as (and here is the startlingly bold feature of the Aristotelian analysis) there is no question of the real traversal of an actual infinite. Rather, the nature of motion as actus imperfectus is such that the mobile never exists "in" a place while en route, but only "through" each place. Precisely in that regard in which the mobile is mobile, its existence is, as we noted, only "toward" a not-yet. Imagination trips us up here: we see a ball flying through the air and want to insist that the ball at every moment exists there, there, there. But no: while the ball certainly exists - and this we rightly apprehend, through intellectual abstraction from the flux presented to the senses - we cannot by the same token affirm that "the ball there" (or there or there) exists. Did it exist in any one place, the mobile would in an instant be immobile, its "ability to be" no longer actual, but only its be-ing instead.

239 It is not an actual infinite that the mobile traverses; its motion is not an actual infinite; the duration of that motion, the time required for its accomplishment, is not an actual infinite. These are, with respect to the mind's apprehension of them, only potentially infinite; and potential infinities afford no existential impossibility. Nevertheless, does not "potential existence" or the actus imperfectus of existingtoward amount to a spurious construct, a "bastard being" reminiscent of Plato's description of the choral Has Aristotle escaped the Parmenidean and Heraclitean extremes only by dissolving reality itself? It would be one thing if his solution reduced the mobile in its entirety to a shadowy "inclination to being," but such is not the case. Every mobile being is being as well as mobile; its substance maintains a certain constancy even as the accidents mutate. The projectile body which cannot be said to be actually "in" any place along its path is a body nonetheless, with characteristics as determinate as its place is indeterminate. Does the Aristotelian and Thomistic insistence on the continuity of motion (and hence its imperfect existential status) preclude any kind of discrete momenta in the course of the movement? At first it may seem so; the discrete, after all, is definitionally opposed to the continuous. Yet here again the distinction between essence and existence (at the accidental level) may enable us to resolve what would otherwise amount to a contradiction. Natural motions must involve, as termini ad quo and ad quern, moments of rest in which the accidental formalities of being are realized: only such end-points bring intelligibility to the Aristotelian analysis in its completeness. Motion is nothing if not

240 teleological. If there were not at least these fleetingly discernible "constants" amid the accidental flux, it is difficult to say how we could be other than Heracliteans after all. (Yet one must acknowledge profound difficulties: for example, we abstract pure quantities from the material world, and posit such relations as equality or straightness among them: but where is absolute dimensive equality or straightness to be found in re? In answer to this I point the reader to earlier remarks on what the intellect is doing in discerning natures at all: it is penetrating "beyond" matter altogether to apprehend an Idea through its imperfect, because material, realization.)87 What is the relation of a mobile body to the medium within which it moves? How exactly is "within" to be understood? Let us accept that the physical universe is, pace Newton and Einstein, a plenum whose parts are quantitatively continuous and physically contiguous. Now in order for motion to occur through such a continuum, we can invoke several possibilities: (1) The mobile displaces other entities informing the continuum; as it moves, they move also. (2) The mobile occupies places simultaneously occupied by other entities informing the continuum. (3) The mobile transforms other entities of the continuum, such that they "become" the mobile as it passes through. These are the only logical possibilities that accord with observation (i.e., with the evidence that a mobile body comes to be, in some real sense, in a location that was previously occupied by other bodies). But the second one must be ruled out as inconsonant with the very nature of material being.

See section B in the present chapter.

241 Motion strictly speaking involves only the accidents of physical bodies. But we need to distinguish the motion of a. body from motion in a body; and to do this, it will be helpful to remember that a body is a material being considered as extended. The extension of a substance is radicated in matter, as we have often noted; matter is even "extendedness," though never without determination as "this dimension" (i.e., never in the absence of form, which determines). A body can change location as a whole, in which case the substance itself, through its constellation of accidents, becomes differently situated in terms of its ability to interact with other hylomorphic substances. Alternatively, a body can remain at rest vis-a-vis adjacent bodies (i.e., those with which it can interact), while undergoing some change in itself (granted, that every kind of accidental change is reductively local). And since bodies - more properly, hylomorphic substances - influence each other through their accidents and by contiguity, a physical influence can propagate "through" the continuum either with its associated body, as the latter itself moves, orfrombody to body as they each remain in place. As illustrations of the two kinds of movement we may compare convective and conductive heat transfer. In the former case molecules move from one place to another, carrying thermal (vibrational) energy with them; and this is restricted to fluids. In the latter case molecules vibrate more or less in place, each one by vibrating causing its neighbors to vibrate, with thermal energy thereby being transmitted from molecule to molecule; and this is restricted to liquids and solids, the molecules of a gas not being sufficiently in contact for it to occur. In either case we say that there is heating - a transfer of thermal energy.

242

Is each mode of transfer univocally named local motion? Under consideration here are our first and third logical possibilities listed above. But a further precision must be introduced, which renders my question all the more pointed. For it would seem, at least in the abstract, that the "becoming" which is involved in local motion according to our third logical possibility could be of two kinds: [a] that whereby the units comprising the continuum are changed only accidentally (as would seem to be the case in my example of conductive heat transfer), as a physical influence is being propagated from unit to unit; or, more radically, that whereby the units comprising the physical continuum enter into a new substantial configuration, that of the mobile body, as the mobile encounters and, so to speak, "engulfs" them - so that the units under consideration, whether actually or virtually present in the informed continuum beforehand, are now virtually present, at least fleetingly, in the substance of the mobile. I think of either variant - [a] or [b] - as a "marquee theory" because it is analogous to what is seen on a marquee sign, in which the words are "moving" in virtue of different light bulbs (the "units of the medium") successively being illuminated, "entering into" the "formal unity" of the word. It is important to note that such a theory of corporeal motion through the physical continuum, like its marquee analogue (where the "actuality" is that of the illuminated words), is an account, however foreign to everyday experience, of real motion. The substantial and corporeal form is really being conjoined with a succession of matters (which, in itself, is hardly repugnant to hylomorphic theory), such that the composite being truly moves from place to place. One feature of this mode of motion, however,

243

is that it could only occur by discrete steps, rather than continuously. More precisely, such a motion must be divisible into component motions, in which accidental (or even substantial) corruptions and accidental generations have occurred, even if these moments are embedded, so to speak, in a continuum of space and time. How far may that which, at the level of the senses, is taken to be "one motion," be resolved into a series of motions and rests, a sort of "stepped motion" whose composite character falls below the threshold of sensibility? Weaning ourselves from excessive dependence on sensation, imagination and the prejudices of everyday experience, we should acknowledge that it is no more repugnant to reason that, say, a baseball's trajectory should consist in a vast sum of motions and rests, than that a butterfly's nectar-gathering foray through a flower garden should do so. But two questions loom in response to the hypothesis of multiply-interrupted motion: (1) What would account for the evident unity of the motions, such that we are certainly inclined to call them one motion; and (2) Why posit the multiplicity of motions in the first place, since the unity of motion taken as a whole seems evident? I believe the first question is answered by appeal to the underlying continuity of matter, in conjunction with the persistence of agent causality as it enters into the complete account of a given series of motions. Moments of rest on the way to a particular telos need not destroy a certain overarching unity among the "interrupted motions," inasmuch as the power of a moving cause proves sufficient to co-ordinate those motions, as when marble is removed chip by chip in the "movement" toward statuehood, or when a body of water shrinks through the evaporation of molecule by imperceptible molecule.

244 The second question brings us back to the consideration about kinds of local motion in a discretely structured continuum. For while any number of natural motions give evidence of occurring by displacement of other bodies - one thinks of air flowing around an airplane, or a piece of wood splitting before the advancing wedge - at deeper levels of structure the "marquee theory" begins to seem more plausible. There is experimental reason to suppose, for instance, that as light passes through transparent matter it is being absorbed and re-emitted by the constituent atoms of that medium. The "motion by displacement" idea seems to imply, in order to work at all, a certain elasticity of the medium. Were the structural units of the medium inflexible, motion simply could not occur because there would be no way for the units to "move aside" - there being no three-dimensional (or even two-dimensional) geometry that allows of such displacement. Moreover, we would be faced, in a cosmic plenum, with a sort of "Chinese puzzle" problem: absent a void somewhere, how could motion be initiated, since no displaced part of the medium would have any "where" to go? Thus the least parts of the medium would seem to have to be, not rigid, but compressible: variable enough in their dimensions to allow a body to "squeeze" them aside in its own progress. (Think of a room full of inflated balloons, wall to wall and floor to ceiling, packed so closely that there is no space whatever between the balloons. The only way an extraneous object - say, a marble - could make its way through the massed balloons is by virtue of the balloons' compressibility.) For all the difficulty attendant on a displacive theory of local motion, the other idea, that a mobile could be "actuating" the surrounding medium, least part by least

245 part, in defiance of all sensible evidence, must sound like rant. Yet the problem of motion through a continuum, startlingly ignored by Newtonian and post-Newtonian physics, demands solution. As I will have occasion to suggest in the final chapter, there is a certain appropriateness in the hypothesis that motion at higher levels of information is largely displacive, since it is "furthest" from the substantial in its accidentality, while motions at the quantum level may turn out to be transformative or marquee-like, at least in many instances, in so far as they involve substantial alterations.

L. Action at a distance Once the possibility of void space is ruled out ontologically (pace Newton), the vexed question of whether there can be "action at a distance" resolves into this: can one body act upon another, that is not in spatial contact with it, without regard for any intervening matter, i.e., as */nothing intervened? The question thus expressed admits of two parts: [a] can a physical influence propagate across a distance independently of what constitutes the intervening plenum? and [b] can a physical influence be instantaneous, i.e., non-propagating?88 "No action of an agent, however powerful it may be, acts at a distance, except through a medium."89 What does it mean for one hylomorphic substance to act on an-

88

On the history and philosophy of actio in distans see Mary B. Hesse, Forces and Fields: The Concept of Action at a Distance in the History of Physics (New York, 1962). Much useful scientific material on the subject, blended with decidedly unAristotelian philosophizing, is found in Marc Lange, An Introduction to the Philosophy of Physics: Locality, Fields, Energy and Mass (Oxford, 2002). 89 Summa theologiae la, q. 8, a. 1 ad 3 ("nullius agentis, quantumcumque virtuosi, actio procedit ad aliquid distans, nisi inquantum in illud per media agit" - Leon. 4.82).

246 other? It is for the one to effect accidental or (by way of the accidental) substantial change in the other. As the accidents involved are inseparable from spatiality or extension, so must be the operations which occur through them. That is to say, that the interactions of cosmic (nonintellectual) beings are in essence spatial (and therefore spatiotemporal): they involve that which characterizes the spatial as such, i.e., "parts outside parts," extendedness and adjacency. For one hylomorphic being to act on another (and for that other to "receive" the action of the one), there must be an ontological ground or commonality which is located precisely in their spatiality; they must "share space," not in violation of the principle of unilocality but along a common boundary, thereby forming a unity through relation, i.e., "existing with respect to one another." Since body is by definition a substance which has extension, bodies which are related precisely as bodies must form a whole according to extension.90

m

James Tallarico ("Action at a Distance," The Thomist 25 [1962], pp. 252-292) presents (p. 257) a reduction argument from P. Henry Van Laer (Philosophico-Scientifw Problems, translated by Henry J. Koren [Pittsburgh, 1953], pp. 59-114) against action at a distance, which I here paraphrase with some modification: Suppose that body A is located in void space, and that body P is now brought into its vicinity. If P is acted on by A, then either A's activity "across" the intervening space pre-existed P's arrival, in which case an action existed without an object and without a correlative passion, both of which run counter to the ratio of action; or A's activity only occurred when P became present to it, in which case A would somehow have to have "known" P's becoming present, which is not consonant with the nature of mere body as such. (I have modified the argument to refer to "object" and "passion" where Van Laer and Tallarico had "an accident. . . existing] without a substantial support." For, while the latter is no less inadmissible in natural philosophy, and would certainly invalidate the idea of action at a distance, it is more properly the premise of a prior argument, that against void as such.) Unfortunately Tallarico goes on to develop a faulty critique of Van Laer's argument to the effect that, having made spatial contiguity a prerequisite for the "quantitative whole" implied in a hylomorphic relation, Van Laer has reduced relation, in this case, to contiguity - or at least made relation as such dependent on contiguity - rendering the argument against action at a distance circular (pp. 259f.). In an attempt to "understand the truth which Van Laer touches upon but does not honor" (p. 262), Tallarico argues that relation between two things entails a new formal effect in

247 Note that such considerations do not depend on a conception of "body" as sharply delineated in the sense of Newton's "hard, massy particles." On the contrary, the modern view of elementary particles as concentrations of charge or other properties within an extended (conspecific) field tapering off indefinitely in the surrounding space makes all the more plausible a theory of physical contact as prerequisite for interaction. Particles can, in theory, be "in contact" (and therefore potentially interactive) at arbitrarily great distances, yet undergo specific changes only at some threshold distance which might depend on the environment no less than on individual particle properties. If all particle interactions (including interactions between larger masses of particles, whether molecules or planets) are local in nature, a further question is, how localized is the interaction between two bodies, as compared with their spatial extent as bodies? The recognition that form is the principle of activity - operatio sequitur formae - precludes any necessity of identifying the locus of activity with the full extent or locus each thing related ("Relation depends upon existence, not upon surface contact," p. 270), and that this formality pre-empts mere contact to the extent that any two bodies that are related are by that fact not "at a distance" but capable of transient action/passion. "Of course we have had to recast such notions as distance, direction, medium [construing all of these non-spatially!]; but evidently, this can be done in such a way that inherent absurdity and self-contradiction are removed from the notion of 'action at a distance without the use of a medium'" (pp. 290f.). Tallarico's concern to justify action at a distance is based on his reading of texts in Aquinas that make action essentially dependent on power, not contact. But he gives a strained interpretation, it seems to me, in so far as he attempts to read quantitative (extensive, spatial) aspects out of consideration altogether. What is true of the divine agency (which Tallarico analyzes at length, pp. 283-290) is not necessarily true of hylomorphic agency. In fact a more careful reading of Van Laer discloses that even though "agent and recipient cannot form one quantitative whole unless they are locally related to one another (cited in Tallarico, p. 256), the conclusion is simply that "for the interaction of bodies material contact is a necessary condition" (ibid). This does not obviate the existential relation between two bodies, in virtue of their respective formal principles, as the root cause of their interactions, while acknowledging spatial contiguity as necessary condition of that interaction.

248

of the body as such. A whole can act through one of its parts. (Were those "parts," on the other hand, only so many wholes, independent members of an aggregate, the aggregate could not "act" except via the combined actions of its members.) This observation is trivial at the level of sensible being: every interaction of (say) a being with its environment is more localized than the being itself, even when it involves the being as a whole: think of a child recoiling from a pinprick, or an inflated balloon's "response" to the same. A being with formally distinct parts or organs acts only through those parts; this is because the being's interactions with other beings are specialized in accordance with the powers of the several organs or parts. A simple being, on the other hand - 1 am thinking of "element" under some form - having extension but no distinction of parts according to function, can only act as a whole. But there is, even in this case, no a priori reason why its locus of activity cannot be more restricted than its locus qua being. Hence a particle of volume X may act upon another particle of volume Y somewhere "within" the volume Z, even though the entirety of Xand Tare substantially or quasi-substantially involved in the interaction:

The situation does not correspond to anything we observe macroscopically. When we speak of the whole acting through the part in composite beings, we are invariably describing accidental changes directly, even if substantial changes are indirectly conse-

249 quent (and attendant) on them. But at the truly elemental level, there are (I propose) no purely accidental changes; every change, even though disposed and effected through the accidents, is substantial. (Because the elemental body is irreducibly simple, having no formally distinct parts, there can be no possibility of parts acting as such.) Hence X and 7 must act as wholes, not as when one part of a body moves the whole per accidens, but essentially as proceeding from the whole.

M. Conclusion This chapter's survey of the formal structure of hylomorphic beings has had as its aim, not any new development of the doctrine of the philosophic* perennis in this regard, but simply the compilation of those features of a coherent account which may cast the Aristotelian-Thomistic view of matter in a light favorable to modern physics, and in particular may enable us to apply the doctrine, as set forth in the previous chapter, to some aporiai of quantum physics in the next.

Chapter Five The New in Light of the Old

A. Introductory In the two preceding chapters, I have sought to present and reflect upon the AristotelianThomistic understanding of matter and form as a coherent analysis of cosmic being. Now let us see how this understanding can be brought to bear upon certain features of quantum physics, focusing on the aporiai limned in Chapter Two. I am not "doing physics" in this chapter - not, that is, in the sense that a quantum physicist understands "doing physics." There is no working out of mathematical relations or concocting of theoretical entities, no development or technical analysis of experiments. Rather, the goal is interpretation of some key elements of a scientific theory that has abundantly proven its worth as a physical construct - here, again, taking "physical" with its contemporary implication of "mathematical manipulation of the quantitative aspects of mobile being." The philosophical approach which I take cannot of course advance this kind of physics in a direct sense; but it is my hope that the approach will be seen as indicating a deeper basis for understanding what quantum physics is concerned with - and, in so doing, at least hint at what, in quantum theory, needs closer examination, in the interest of attaining a truer grasp of nature itself.

250

251 The philosophical analysis of mobile being is not premised upon measurements or particular quantitative determinations of that being. It is a development of the implications of mobility as such, and thus looks at change and motion from a perspective that is different from, and complementary to, that of mathematical physics which works out the implications of quantitative measurements themselves. As indicated in Chapter 2, the two approaches are compatible because every mobile being, in virtue of its materiality, is extended, and, in virtue of its specific nature, exists under a specific range of quantitative determinations. Hence to know its quantitative variations is to gain an insight, albeit a partial one, into its nature. Nowhere is this truer than in respect of entities at the quantum level, where the difficulty of quantitative measurement betokens a closeness to the nonquantitative aspect of such entities. In undertaking this rapprochement of the ancient physics and the new, I also emphasize that I am drawing no conclusions beyond those of compatibility and plausibility. I will not "conclude," for instance, that photons are substantial particles, because I am doing philosophy, not physics, and photons as such are only accessible to the measuring apparatus and techniques of physics. One can hardly draw philosophical conclusions, which are by nature certain and immutable, from data which are by no means certain and immutable. What one can do, and what I try to do in the sequel, is to show that such and such physical data are, or are not, illuminated and rendered more intelligible by a perduring philosophical insight.1

1

For original statement of the aporiai to be addressed in the next five sections, see Chapter Two, section L.

252 B. The wave-particle duality This is the central fact that gave rise to quantum physics: that spatiotemporal being exhibits both wavelike (continuous) features, and particlelike (discrete) features. The seeming paradox of this duality - since a wave is manifestly not a particle, and vice versa — has led Copenhagen-inspired theorists into epistemological extravagances of a positivist cast, with operationalist overtones at best and wild subjectivism in more extreme cases. "Complementarity," widely accepted as the governing philosophical idea of quantum mechanics, simply posits that the two manifestations must be taken at face value, not as coexistent so much as equally plausible - with the kind of observation made being assigned a determinative role vis-a-vis the features that exhibit themselves in any experimental situation. The question of intrinsic ontological compatibility is skirted altogether, by "Copenhagen" thinkers, or referred to some underlying, hidden and unifying reality, by thinkers in the Einstein-Bohm line. I say there is no ontological incompatibility between wave and particle, if the two are simply understood as different modes of being at the substantial or quasisubstantial level. Supposing, as is indicated by several lines of physical evidence, that quantum entities such as electrons and photons are not resolvable into subordinate levels of structure (virtually present forms), they would be expected to exhibit properties that are "directly" radicated in their substantial character. Of course, all such entities are observed precisely through their accidents; but those accidents will be relatively few and relatively invariant, inasmuch as they do not represent the virtual presence of other forms

253 (the elements being infima forms). (Analogy: a tree can exhibit a wide range of accidental determinations compatible with its substantial unity, whereas a one-celled alga is much more restricted in this regard, and a chlorophyll molecule more restricted still.) In short, quantum particles such as photons or electrons seem to exhibit properties characteristic of elements that are actually, as opposed to virtually, existing. But the ratio of element does not preclude all corruptibility, inasmuch as they are material.2 That the elements cannot, by definition, corrupt into lower beings that were virtually present does not rule out their being transformed into other elemental beings, beings essentially distinct but on more or less the same (i.e., "primordial") ontological level, under the influence of extrinsic causes. Whether the termini a quo et ad quern of every such elemental transformation are distinct substances or different "modes" of a substance - entia vialia - is perhaps not of urgent importance. (A difference of mode - something not investigated in the present study - might be analogous to, say, a butterfly existing in either the butterfly or the caterpillar mode, or sulfur existing under different allotropic forms, where only the arrangement of the atoms differs, resulting in a considerable variety of macroscopic properties.) But in transitioning from one substance, or substantial mode, to another - a transition which involves the infima level of accidents grounded in the substance - elements will not only exhibit different sets of properties, but will also effect the reverse transition with relative ease, since the substance itself, being elemental, was not resolvable into multiple component forms

2

Summa contra gentiles III, c. 23: "elementorum corpora sunt simplicia, et non est in eis compositio nisi materiae et formae." Leon. 14.57:38a-40a.

254 each with its own potential claim on existence. In other words, we would expect that truly elemental entities will act, not like an elephant which, having died, permanently reverts to a plethora of lower forms, but more like a water molecule which, however often it decomposes into hydrogen and oxygen atoms, can return, with relatively little difficulty or unlikelihood, in its original (though perhaps not numerically identical) essence. The further removed from elementarity and prime matter is a given composite, the less likely is it to be "reversibly" composed. In terms of hylomorphic analysis, this is due to a sort of "entropy" principle: cosmic beings, in virtue of their material principle which is a potency to numerous forms, decompose into that which is now poised to become any of numerous of kinds of being, and not just the one from which it derived through the decomposition. The ground of decomposition is materiality, but materiality is an existential openness to many kinds of information. Beings very close to the elemental level, on the other hand, can only decompose minimally, and are ontologically closer to the entities into which they have decomposed. And elements themselves, whether considered as transforming into other elements or only undergoing modal changes within the one substantial identity, constitute the "limiting case" in this regard: they corrupt (rather than "decompose") into beings that are, if not essentially the same, at least on the same ontological level qua elements and therefore most likely candidates for "recomposition." There is also the question of efficient causality here, as in all cases of change: the efficient causes operative at or near the infima level are themselves so general that they are maximally "available" for reversible elemental transitions, whereas the effi-

255 cient cause that can bring, say, an elephant back from its heap of elephant-matter is so highly specified in its action that it can only operate under conditions that are far removed from those of the elephant's decomposition. I posit, then, that a quantum entity such as a photon, precisely as an elemental entity and therefore as displaying substantial characteristics (or, more precisely, the accidental characteristics most proper to substance), can either (a) corrupt, reversibly and relatively easily, into a related element, or (b) pass between different modalities of the one elemental substance, again reversibly, under some (not necessarily specified) agent causality. These two modes of elementary existence (for as such I will posit them) are none other than the wavelike and particlelike manifestations. The two, per the intimations of modern theory, are certainly not wholly unlike, since the "particle" is most often represented as having a wavelike nature even in its particleness (one thinks of Schrodinger's physical interpretation of the "wave packet," but there are also other interpretative avenues assigning to "particles" something of a wave nature), and the wave appears to have a quantized (i.e., discrete) aspect, even as wave. ("Discrete" aspects of material being, in other words, are not absolutely opposed to "continuous," though the convenient terminology might suggest as much; rather, there is a question of the degree of localization and motion.) On this hypothesis there is no mystery in the disparity between wave and particle properties - no more, at any rate, than between the properties of, say, ice and water vapor: wave and particle are modalities of the one elemental substance, or closely related (because both elemental) substances, perhaps in one or the other case best de-

256 scribed as ens in via, with their duality of manifestation following easily from the reversibility of their substantial or modal transformations. Under some extrinsic causality, evidently quite general, the wave mode readily shifts into the particle mode and vice versa. Nothing in the empirical data precludes such an interpretation. No experiment has ever shown complete randomness in the exhibition of the wave or particle properties respectively; certain situations entail the one behavior, and certain other situations entail the other, univocally and consistently. What the Copenhagen theorists tend to describe as "different kinds of observation" is more objectively described as "different kinds of interaction with other entities" (as, for instance, whether a given interaction with matter is causing light to be refracted, dispersed, absorbed, etc.). Some kinds of interaction will engender the wave mode, others the particle mode. The two can be essentially one but existentially exclusive, in the sense that water vapor and ice are exclusive; either one exists or the other, however easily each state may revert to the other. Of course the observing apparatus, and therefore the observations being made in the laboratory, affect the modality of the elementary entity under examination; but this need call for no bizarre theory of observer intervention as somehow "producing" the reality of what is observed, nor for an elaborately holistic account of the "implicate order" with its not-so-different subjectivist baggage. The recognition suffices, that if you do x to electrons they become X, and if you do y to them they become Y instead, with X and /interchanging as often as you choose to switch x and>>. Against Bohr and most quantum mechanicians today: complementarity should be taken to imply, not some unintelligible propensity of quantum entities to display,

257 now continuous properties, now discrete, despite the evident contradictions - depending simply on how our observations are conducted. Against Bohm and most "hidden variables" theorists: the apparently incompatible sets of properties need not be supposed to coexist in virtue of an underlying ontological stratum which in some unknown way negates the contradiction implied at the level of observable reality. Rather, the two sets of properties belong to modes of being, which do not coexist and therefore do not entail contradiction, even as they freely interchange in virtue of their material principle and formal dispositions, under the appropriate conditions of extrinsic causality. (More on this causality below, in treating of probabilism in quantum physics.) It should be obvious from experimental considerations that, sticking to our paradigmatic example of photons and electrons, there is a connaturality between them. The mere fact that light interacts with matter in so many ways indicates, even at the macroscopic level, a relatedness between them; and the realization that photons are closely correlated with electron orbital energies, as evidenced in phenomena of light absorption and emission by atomic matter, drives the point home. It should strike us as no more surprising, in a word, that a photon can have both wavelike and particlelike manifestations, than that light can be absorbed (not "stored," but somehow transmuted) and then re-emitted (transmuted again) by matter. That is an "alternating duality," evident to sense, that is hardly less remarkable than the one contemplated by quantum physicists, and as easily explained.

258 In closing this section, I glance at one of the most vexed instances of so-called complementarity, the two-slit experiment discussed in Chapter Two. How can we interpret, on the account offered here, the appearance of interference bands from single photons traversing the apparatus? Again, I am not presuming to play the physicist, but I must note at least the plausibility of a light-quantum in continuous mode passing through both slits, and thereby engendering interference inasmuch as it is still a wavelike entity, while its energy is quantized such that it will leave but one highly localized trace when it reaches the recording end of the apparatus and, in virtue of the kind of interaction occasioned by the recorder itself, reverts to the discrete or localized mode. (It need hardly be emphasized, that there must be, in virtue of the continuity of matter, some spatial continuity: the particle cannot be located outside the spatial region previously occupied by the wave.) The "mystery" of the two-slit experiment, dramatized for generations of physics students by Feynman's hyperbole,3 is no mystery at all once one grants the interchangeability of wave and particle properties, as grounded in a substantial relatedness or identity and elicited by different environmental (causal) situations. Indeed let us go further and suggest that the real "anomaly" in conventional attempts to explain two-slit interference phenomena has been the tacit supposition that only wave properties might be exhibited. We cannot import into our analysis of light waves the analogy of constructive and destructive interference as it applies to, say, water waves, because water waves are composed of many particles. Theories of light, on the other hand, have proposed either a continuous (non-particulate) medium, or a par3

See Chapter Two supra, p. 42 and n. 37.

259 ticulate (non-mediated) entity. Short of a multi-particulate medium like that of water waves (and which, so far as I know, makes no sense in the theory of light), neither of the proposed structures can possibly account for interference phenomena at all; both are needed, in the complementary (transformative) account I have proffered here.

C. Discontinuity in quantum phenomena A characteristic feature of quantum-level phenomena is the discontinuity that obtains between continuous and discrete states. There is both a spatial and a temporal aspect to these discontinuities. The quantization of so-called "radiant energy" is seen in its interactions with matter (absorption/emission) via the Compton effect, discrete spectral lines (frequencies), and so on. Between the discrete energy states there seems to be no continuum; transitions between states either occur or do not occur in toto, no "partial transitions" being recorded. Moreover, transitions which are quantized as to energy values (including mass, charge, and so on) are also instantaneous with respect to time, at least to within current errors of measurement. Perhaps most striking, the spatial configurations (shapes, volumes) corresponding to successive quantum states change no less instantaneously. If state A yields to state B (for example, if an atom gains an electron, or an electron is boosted to a higher energy level within an atom, as a photon is absorbed), the volume, shape, charge distribution and other parameters do not "swell" or "shrink" from one state to the next; they simply are in one state and then, in an instant, are in another.

260 Now this kind of mutation is not observed anywhere macroscopically except in cases of substantial change, which is not motion in the strict sense. Between successive substantial informations there is not, and cannot be, an observable continuity, there being no possibility of an entity which is partly one substance and partly another. (Thus when an elephant dies, reverting to the atomic and molecular entities whose forms had been present virtually in the living organism, there is no period of time when "elephant" is partly there and partly not. There is no "time during which" the substantial change is occurring; the accidents may evolve continuously - although there is reason for doubting this as well - but in any event the substantial transition can only occur instantaneously. Nevertheless, when a composite substance (by which I mean one into which prior forms had entered virtually) decomposes, its successor substances will not vary initially in their spatial configuration, until their own principles of activity cause dispersal and reformation. The reason is that the quantitative accidents which now serve to individuate and determine the lower entities in their own right also served to determine the higher composite per accidens, as we have seen. The volume that becomes collectively proper to all the substances into which an elephant has just decomposed is the volume that was proper to the elephant alone, in virtue of those numerous substances having been virtually implied in its substantial unity. But when dealing with structures at the inflma level, there are no virtual entities to carry on, as it were, the spatial characteristics of the prior entity once it has corrupted; it cannot be resolved into inferior beings, but yields absolutely to the accidental determinations of the new substance. This situation entails the possibility of a spatial discon-

261 tinuity (a successor substance being larger, or smaller, or differently shaped or oriented, with no transitional size or shape). Such an interpretation would make little sense in a Newtonian space "through which" every motion is understood to occur; but we have seen that such space is an ens rationis, an abstraction, and in reality it is hylomorphic being which constitutes space. On this account there is no inconsistency in, say, a larger entity resulting from a smaller one, without any process of growth between the two. Each entity entails its own spatiality, its own extension and quantitative determinations, and apart from any dispositiones materiae that may be present it is under no constraints arising spuriously from space as such. At the quantum level, then, I propose to view discontinuities and instantaneous transitions in spatial configuration, energy level, and other physical parameters (as evidenced, for example, in every wave-particle transition), as evidence of the substantial nature of those entities and the transitions between them. More particularly, it is because the informations giving rise to successive quantum states are substantial or quasisubstantial in character - one substantial form yielding to another, as mode transforms into mode - that (a) the states themselves must not admit of a continuum of partial realizations, (b) the transitions must be instantaneous rather than temporal, and (c) the spatial configurations, like the energy and other physical parameters, must also vary discontinuously. What was described in terms of continuous change, classically speaking, was always accidental in nature - not just in the general sense, noted in Chapter 2, that

262 physical science is concerned only with quantities and therefore with accidental manifestations of being, but in the narrower sense as well, that the changes which were being investigated per accidens were themselves accidental changes, specifically local motion in one mode or another. Since accidental changes presuppose substantial continuity, there could be a semblance of continuity in the changes themselves. At the quantum level (since it is, on my hypothesis, a deeper level than those involving virtual composition of complex beings) we now confront change that is substantial in character; the accidental flux corresponds directly to a succession of substantial rather than merely accidental forms, and hence not simply to local motions which suppose substantial continuity. In this realm quantitative accidents are still what the physicist investigates, but they are no longer the accidents associated only with accidental change. Physics has confronted substance almost head-on, and the mathematics of continuity and determinism will no longer suffice. The preceding will, I hope, give an idea of the relevance of the Aristotelian substance/accident distinction, as applied to elementary being, vis-a-vis quantum states and transitions that should appear "strange" only in the context of classical physics' premature reification of the continuous in nature. If I may single out an instance in quantum physics where a greater intelligibility obtains in virtue of the Aristotelian doctrine of formal determination: consider Bohr's atomic model (long since abandoned, of course, but not without its heuristic value, especially in view of the need for a reassessment of quantum theory). He postulated that the quantization of orbital energies (as evidenced in the Balmer line series) implied a prohibition of any orbits not satisfying the discrete en-

263 ergy parameters; thus he sidestepped the radiative-loss problem that was plaguing the "planetary orbits" theory of atomic electrons. If, I suggest, electronic energy levels are considered as so many formally different modes of elemental being, then we have an ontological basis for the quantitative discontinuities which Bohr could only posit ad hoc. Analogously, any quantum transitions evoking discreteness and discontinuity may best be understood as substantial, because elemental, in nature. And, to reiterate a qualification mentioned above: even if we are not dealing with substantial (elemental) changes in the strictest sense, but with modal changes within a given substantial configuration, similar principles may obtain, since there need be no continuum between different existential modes of a substance.

D. Probabilistic outcomes of quantum events There are two kinds of probability-governed events in physics. One, which already dominated the statistical mechanics of Boltzmann et al., involves the probabilities associated with one event from among a (typically vast) number whose parameters (trajectory, energy, etc.) are distributed randomly over a range of real values. Probability in this sense does not connote indeterminism of a radical sort; in principle each component, e.g., each trajectory leading to a given event could be known, though in practice the task exceeds our capacities through the sheer number and complexity of the interactions. (Today's "chaos theory" seems to be an extension of this.) Fortunately, given appropriate boundary conditions, even the most complex of these many-factored systems

264 can be reduced to statistical laws. (The same type of probability and statistical analysis governs affairs in the everyday world, such as gambler's odds or actuarial studies.) But another, albeit related, kind of probabilism is associated with events whose several parameters we do not know entirely, even in theory. Probabilities of this sort are not usually recognized at the level of ordinary sensible being, although in fact they underlie the first kind of probability. But they do assume prominence in the quantum world. In each case a probabilistic and statistical interpretation is imported because of the preponderance of individually unknown factors; but whereas, in the first category, the factors are knowable even if unknown, in the second category the factors considered individually are, to some extent, inherently unknowable. This can arise only through a principle refractory to intelligibility; and this we have seen to be prime matter. Indeed, in accordance with principles laid down earlier, we must expect to find the potentiality which is grounded in prime matter come into greater prominence according as a being's substantial form is closer to that primordial potentiality, i.e., less mediately constitutive as form. (Conversely, the more numerous the prior informations that stand "between" a substantial form and its matter, the more "layers" of virtual presence that dispose the matter and thereby restrict or determine its potency, the less evident will be potency as such, as an undetermined receptivity.) Elementary entities, on transforming, do not resolve into (formerly) virtual components but only into other elements, with minimal spatiotemporal continuity. Since their changes are both substantial (precluding the continuity of an underlying subject, as in local motion) and elementary (precluding the continuity afforded by the virtual-to-

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real analogy of primitive forms in higher substantial changes), there is relatively little of actual being to afford us the intelligibility of classical deterministic physics; transformative events at this level must have a correspondingly high degree of spatiotemporal unpredictability. And this is, of course, the hallmark of certain quantum events: considered individually, they are highly indeterminate in the sense of resisting our predictions as to when and how they will occur. Yet the statistical laws governing the occurrence of many such events point unmistakably to an underlying causality. In fact, both individual unpredictability and statistical laws are consonant with the role of prime matter in elementary transformations. Because of a relatively "undisposed" potentiality at the elementary level, intelligibility is minimal and predictability necessarily low. But because every potency is a potency to some actuality, i.e., is not wholly undetermined, the "direction" of elementary transitions can be indicated in a general way, and here we invoke the fixity of probabilistic laws. The precisely defined half-life of a particular radioisotope is as indicative of an underlying determinative causality, as the unpredictability of a given atom's decay is indicative of matter's indeterminacy in that event. The probability function in quantum mechanics, as we have seen, has acquired a purely epistemological role in the Copenhagen interpretation beginning with Born. And de Broglie and others sought to give it an ill-fated physical interpretation (the "pilot wave") in the context of maintaining wave-particle simultaneity. The latter approach had the advantage of aiming at scientific realism. But if we view continuous and dis-

266 crete aspects as non-simultaneous existent modes, it becomes an even simpler matter to situate the probabilistic outcomes of quantum transitions in the context of an "unmitigated unintelligibility" of matter: what can be expressed quantitatively as (no more than) probabilities can be seen as grounded, physically, in the relative absence of dispositiones materiae (dispositiones adformam) at this ontological level.

£. Uncertainty relations Thus far I have suggested solutions to three aporiai, in what I take to be a natural ontological order: (a) that of the wave-particle duality is referred to the substantial nature of quantum entities, (b) that of discontinuity and instantaneity in quantum transitions is referred to the role of substantial form in those transitions, and (c) that of probability in individual outcomes is referred to prime matter. Let us now turn to a fourth topic, that of the Heisenberg uncertainty relation that obtains between conjugate quantum parameters. This is one of the more problematic issues in quantum interpretation, if not for being intrinsically more difficult, at least for having led thinkers into the most varied, and seemingly desperate, attempts at resolution. The centrality of the uncertainty problem was highlighted early on, as we have seen, in the Einstein-Bohr debate. Because "ontological indeterminacy" was a sensational and novel philosophical implication, seemingly of a piece with the more properly scientific, but no less revolutionary, conclusions of quantum theory - and one to which the positivism of the early quantum theorists left them vulnerable - uncertainty in

267 physical phenomena became an unabashedly philosophical issue. But the problem can be defined in different ways. Is empirical uncertainty merely a matter of measurement? Heisenberg's own early inclination, as instanced in his "microscope" gedankenexperiment, was to view it thus. Note that this would not mean that the problem is unreal; it would not entail relegating it to the category of technical shortcomings that may eventually be overcome. It is entirely possible in principle that our means of observing and measuring phenomena at the quantum level are such that they inevitably disturb the system being measured. Whether this kind of "inaccessibility" of physical reality must be governed by a precise quantitative relation is not clear to me. In any event, opinion polarized toward more extreme views. For the Copenhagen thinkers, uncertainty is not simply a function of measurement, i.e., of macroscopic interaction with quantum phenomena, but of quantum states themselves, which cannot but be reflected in any attempt to perform measurements. For "hidden variables" theorists, on the other hand, such an ontological uncertainty is anathema: they tend to be convinced that a deeper level of quantum reality will restore deterministic intelligibility to a physics that is only temporarily incomplete. On the basis of what has been said about elemental substantial being and the role of prime matter in its interactions, I hypothesize that uncertainty is an objective feature of quantum phenomena, but is due to the potential nature of the material substrate, rather than to any indeterminateness in being fully constituted as such. Hence the great

268 debate mentioned above invites solution by compromise, i.e., by acknowledging that each side is in partial possession of the truth. With Bohr and his followers, the Aristotelian-Thomist can readily grant a measure of objective indeterminacy to being itself; this is the indeterminacy that underlies all contingency and chance in the material world, but it is an indeterminacy that is manifested only in becoming, not in being as such, and a fortiori there is no question of its being "resolved" by acts of observation as such. The psi-function of quantum mechanics is not given a "purely mathematical" interpretation, but is understood as somehow describing the reality. With Einstein and his allies, on the other hand, the realist philosopher can as easily discern an objective "hiddenness" in nature; but since this is understood of the material principle, rather than of lower levels of actual being, it is a hiddenness that is inevitable and insuperable. I propose, in brief, the following indication of a solution to the dilemma:

Copenhagen-type interpretations a. nature radically indeterminate

\

b. observation determines reality

Hidden-variables interpretations c. nature radically determinate

7

d. reality hiddenfromobservation

Resolution of the dilemma a. nature indeterminate (in part)

d. reality hiddenfromobservation (in part)

269 Interminable controversies over "quantum reality," prominent though these are in the literature of the subject, occur on what is to me an alien soil, the terra incognita of post-Kantian philosophy; too often they are fueled, not by the data of quantum physics, but by the anti-metaphysical suppositions of quantum physicists. Here, at the epicenter of the debate, I will simply invoke, as a most plausible foundation for the uncertainty principle, the role of material causality as follows. Every application of Heisenberg uncertainty involves a comparison or transition between two quantum states. And I submit further that the uncertainty relation does not govern pairs of variables which are both associated with a continuous mode, or both associated with a discrete mode only, but only with pairs of which one member is associated with the continuous and one with the discrete mode. But I have posited that continuous and discrete are related as substantial modes or even as distinct substances; and hence they transform in ways characteristic of substantial change, with concomitant discontinuities and probabilities as noted above. It then becomes plausible to suppose that uncertainty enters in precisely with regard to these transformations - the reductions of continuous to discrete and vice versa. Let us again consider the formation of an interference pattern by light passing through two slits. Traditionally this has not been considered problematic except in the case of single photons. I submit that the only way to understand it aright is in the context of photons acting singly. A single photon is often thought of as a finite bundle of energy, but the language intimating particulateness should be reserved for those situations in which the particulate (highly localized) nature is in fact displayed. A light quan-

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turn in transit, interacting with matter (e.g., double slits in an interferometer) in a nonparticulate way, manifests its discrete energy through its frequency, frequency being of course a wave characteristic, and waves being extended phenomena which are capable of interference. As a finite amount of radiant energy propagates toward and through the double slits, it does what any wave is expected to do - it diffracts while passing through the slits, and to some extent self-interferes on leaving them. And so a complex pattern of wavelets is now heading for the recording apparatus ("screen"). There the wave is reduced instantaneously to a much more localized mode, i.e., an excitation state in an atom, due to the physical nature of the recording. And the precise locus of the particularization depends upon the quantitative characteristics of the incoming wave, the wavefunction familiar from quantum mechanics, in other words, but here given a purely physical rather than probabilistic interpretation. In other words, the dynamics of the wave unfolding through time are such that they entail a wide range of possible localizations - not because the particle "existed" in superposed states only to have one of these brought to our awareness by observer-induced collapse of the wavefunction, but because the potential existence of the particle is predisposed by the actual characteristics of the wave and how it interacts with the matter of the recording apparatus. Since the wave represents a wide range of potential localizations, one cannot say, from knowing the wave as such, precisely which localization will result. To the extent that one knows the momentum, a continuous parameter of the wave as such, one will not be able to anticipate the position of the particle when it is formed. Conversely, one cannot say, from observing the locus of the resultant particle, what its momentum in

271 the wave mode is, or rather was. For there is no momentum associated with position as such. Similar reasoning holds with respect to other conjugate variables, either directly or indirectly: the knowledge of one variable precludes knowledge of the other, because the one pertains to one mode and the other toward another mode of being, each standing to the other as potency to act. The light wave is in potency (not is a potency, but has a potency) to become an excitation state of an electron, and vice versa.4 Nevertheless, the range of possible localizations - the potentiality for localization, as disposed or determined by the formed matter of the wave - is finite, and this range is represented statistically by solutions of the wave equation. Given enough photons passing through the slits, more and more of the probabilities are statistically realized and so the "interference pattern" builds up. Interestingly enough, the interference pattern is an artifact of individual photons (waves in transit, reduced to particles at the screen), but only as statistically revealed. It remains to be seen whether theory will eventually identify the mechanism whereby an extended entity in wave mode collapses to this point and not some other. It would have to do, I believe, with the principle alluded to in Chapter 4, whereby an extended being acts as a whole within a more circumscribed space than it occupies as a whole.

4

While on the topic, another example of the uncertainty relation: the length of time during which an atom remains in the excited state before the electron drops to a lower level and a photon is released is related to the excitation energy of the electron. This energy is subject to tiny variations, and the range of variation is related to the excitation time by Heisenberg's principle. Again, the half-life of a radioactive particle, which is only an averaged lifetime of many similar particles, is related by Heisenberg's principle to the mass of the particle, or rather to the variations in that mass.

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Again, it is not our task to "do physics" here; but it can be noted in passing that the quantitative form of the uncertainty relation, expressed in terms of Planck's constant (the quantum of action), is a consequence and a sign of the quantization of energies and analogous physical quantities. It stands to reason that since the elements exist under finite and quantified determinations, whether in particulate or extended mode, their reciprocal transformations will find quantized expression. Uncertainty, then, is posited, in accordance with what was said in the three preceding sections, as a consequence of the reduction of continuous to discrete or vice versa, a reduction which in the nature of things must involve a range of possibilities which are so many finite (quantifiable) expressions of the potentiality of the material being. If my underlying assumption seems too bold, I only ask to see an instance of quantum particles as such exhibiting wave characteristics, or quantum wave entities as such exhibiting discrete aspects. But such instances do not exist, however facile transformations between the two states may be. In closing this all too brief discussion I will emphasize that throughout I am talking of the potential aspects of actual being in virtue of its material principle. At no point are we suggesting that prime matter has independent existence; anything whatsoever that is spoken of in quantitative terms, however abstract, is by that token already forme d matter (secondary matter): this would apply to fields, for instance, as well as to forces and to wave phenomena. To refer once again to our concrete example, the light wave is not the potentiality of'the localized energy of the atom, but an entity bearing that potentiality within it.

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F. (Non)Iocality It will be evident, from my thinking in the realist tradition of Aquinas and Aristotle, that the subjectivist overtones of a Copenhagen-inspired "observer determination of reality" are philosophical anathema. At the same time, it is to be conceded that the Copenhagen claim of ontological indeterminacy can be accommodated to the hylomorphic version of potentiality in nature. That same potentiality precludes, on the other hand, a "complete" description of physical reality in the sense that Einstein and Bohm evidently wanted, while the "hiddenness" of their hidden variables seems to be referable to matter properly understood. In view of this proposed guide to a resolution of the dilemma that has polarized quantum-physics interpretations, what is to be said of the locality issue? Perhaps we should begin by noting that neither the Copenhagen theories (on epistemological principle), nor the hidden-variables theories (per Bell's theorem, with its apparent experimental confirmation) can be local theories as that term is commonly construed - i.e., as entailing the transmission of a physical influence across or through an arbitrarily large expanse of space. I observe further, that neither the several quantum theories themselves (so far as I am aware), nor the philosophical interpretation here being proposed, offers at least directly - a solution to the locality conundrum. But we can rule out one evident extravagance, and eliminate also a couple of the leading "obstacles" to a nonlocal solution. By "extravagance" I mean the sort of language one frequently encounters in the literature, whereby the possibilities of quantum-system "communication" are discussed

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in almost superstitious fashion - as if particles might be "knowing" (not to mention devious!) entities. There is no plausible physical mechanism, and no evident ontological principle, whereby one spatially separated entity should be expected or even hypothesized to "communicate" to another the results of a change induced in it by an act of measurement. Einstein rightly deplored every hint of a conspiracy in nature to thwart man's investigation thereof. But while remaining firmly committed to an objectivist account of physical reality, we can still point to a couple of real weaknesses in the Einstein-Bohm rejection of nonlocality. The first of these is primarily physical, though not without philosophical implications, namely the question of the status of special relativity and thus in what context the speed of light, c, really is a limiting velocity. A treatment of this problem is beyond the scope of this dissertation; suffice it to say that, in the face of what appears to be experimental support for quantum "entanglement" we cannot rule out the possibility of some kind of superluminal transmission of a physical influence from one part of a quantum system to another - again, on the supposition that such an influence would have to be entirely physical in the sense of satisfying an exclusion principle, rather than a "spooky action at a distance" implying more fanciful notions of particle "awareness." Secondly, and more in line with the analysis I have presented in Chapter Four, the possibility must be entertained that any "quantum system," for example one consisting of two entangled "particles," is arbitrarily larger than we are accustomed to thinking. That is to say, that on the hypothesis that entangled entities are more extended, perhaps much more extended, than they have typically been supposed to be, their

275 "sphere of influence," or the region within which they can act instantaneously on each other as a whole, will be correspondingly extended, with no violation of locality as entailed by the principles of material interaction set forth in Chapter Four. What we view as conformable to an Aristotelian and Thomistic account of informed matter is, in other words, a local theory of interactivity, but it supposes that quantum entities are constitutive in some way of what we call space, rather than merely existing therein. There is no logical absurdity in conceiving of a relatively extended quantum system as being instantly transformed, in consequence of some interaction which occurs through accidents located in a relatively tiny region of space (e.g., the region in which a pointlike event is recorded). This would be, not the quantum-mechanical "collapse of the wavefunction" but a purely physical analogue - the localized effect of a materiated active principle (form) which is not, in and of itself, so localized.5 It may be added, that conceiving of quantum systems as thus extended into the macroscopic domain requires a nuanced account of such systems as coexistent without being collocal. The natural philosopher can establish the possibility of such existence; it remains for the mathematical physicist to determine whether such a configuration obtains in fact.

5

A fruitful field for Thomistic exploration remains the "holistic" conception of a physical universe actively unified through its conspatiality. Is the universe itself, after all, only a barely connected "heap," a sorosl One need not embrace the diametrically opposite view of an organismic cosmos in order to conceive the possibility of cosmic cause-effect relations on a scale undreamed of by mechanistically-minded scientists and philosophers. Nor are the holistic implications for the metaphysics (and ultimately the theology) of human nature to be overlooked.

276 G. Matter and quantum physics I am occupied in this study with a perspective on reality that, while already meaningful at the sense-level, should be no less applicable to quantum phenomena - that implies, after all, no radical break between the kinds of changes occurring in the quantum domain and those occurring at higher levels of cosmic structure. The principles of material continuity and substantiality, of existential potentiality and individuation, of spatiality and corruptibility, all converging in the doctrine of matter as presented by Aristotle and Aquinas, are wedded to the principles of elemental form, virtual presence, and dispositiones materiae - leading to a conception of modified atomism, locality and physical interaction which I have sought to apply, consistently if superficially, to the physics of the quantum world. If one were to summarize as briefly as possible the implications of matter, understood as a principle of physical being rather than its actuality, one might reasonably affirm: whatever is studied in physics is constituted, in part, by an existential potentiality, which serves to condition every determination brought about through formal activity. Matter, as conceived by Aristotle and Aquinas, is the existential condition of all cosmic being; and physics, in the modern sense, is the quantitative study of that being. Matter and form as such are not quantitative, but in cosmic being they are inevitably associated with the quantitative, such that a close study of the quantitative provides a real, though partial, insight into the essential natures, activities, and relations among things. This quantitative insight becomes more problematic and less determinative as

277 the potential aspect of matter becomes more prominent, i.e., at ontological levels closer to prime matter itself. Classical physics, in departing resoundingly from the Aristotelian paradigm, lost a viable conception of existential potentiality and reduced matter to the status of a basic "stuff," always and only actual, the elements being irreducible particles of that stuff. Quantum physics has driven us back, once again, to embrace the conception of potential entities with all of their unpredictability. I now revisit the proposed definition of the subject-matter of quantum physics put forward in Chapter Two. There I suggested that quantum physics has to do with entities so close to the primordial level of physical being that their interactions are ordered directly to (quasi-)substantial change, and dominated accordingly by prime matter in a less attenuated way than is evidenced in macroscopic changes. Thus expressed, I believe that all four causal elements of a complete definition are present. The matter of the definition is "physical entities" (i.e., mobile being qua mobile), and its formal specification is "primordial" - what I have elsewhere referred to as the elementary or inflma level of structure. The efficient cause appears in the definition as "interacting," since it is only through interaction (always involving motion, and indeed local motion) that physical entities fall under scientific consideration at all. And because every change, quantum or otherwise, is ordered to an end and the end in this case is, per my thesis, the realization of substantial rather than merely accidental form, we appear to have an adequate definitional allusion to final cause as well. The material and efficient causes in this definition do not of themselves delimit the subject matter of quantum physics. But the two essential-order causes, formal and

278 final (i.e., "elemental" and "substantial," as these terms are used in the definition), when taken together, give us the aforementioned subject matter; and they point the way, in so doing, to an understanding of what distinguishes quantum physics from its classical precursor.

H. Bohm, Heisenberg, and Wallace on potentiality In Chapter Two David Bohm's name was mentioned in connection with a realist (hidden-variables) interpretation of quantum theory. In fact, Bohm's involvement with both quantum physics and the philosophical interpretation thereof is much too great to be dealt with adequately in these pages. But now that we are approaching the end of my own attempt to highlight the relevance of matter as the potential aspect of cosmic being, it will be appropriate to at least sketch Bohm's own handling of the idea of potentiality. In his Quantum Theory, written just before he parted ways with the Kopenhagener Geist, Bohm used the term "potentiality" in a sense that seems easily reconciled with our Aristotelian account: [T]he quantum theory leads us to a new concept of the inherent properties of an object to replace the classical concept. This new concept considers these properties as incompletely defined potentialities, the development of which depends on the systems with which the object interacts, as well as on the object itself. To demonstrate this concept we consider, first, an electron with a broad wavelike packet, of definite momentum and, therefore, of a definite wavelength. Such an electron is capable of demonstrating its wave-like properties when it interacts with a suitable measuring apparatus, such as a metal crystal. The same electron, however, is potentially capable of developing into something more like a particle when it interacts with a position-measuring device, at which time its wave-like aspects become correspondingly less important. But even while it is acting more like a particle, the electron is potentially capable of again developing its wave-like aspects at the expense of its particle-like aspects, if it is allowed to interact with a momentum-measuring device. Thus, the electron is

279 capable of undergoing continual transformation from wave-like to particle-like aspect, and vice versa.6 Although this sounds like Bohr's complementarity, it is rather less positivist in tone, with its focus on the apparatus of observation instead of the act of observation. Indeed, the account of wave-particle duality that I outlined above, in terms of an alternation of modes of being, is essentially akin to Bohm's in this respect. The Copenhagen influence on Bohm is perhaps more evident in what follows. The quantum properties of the electron differ from those described in classical theory not only in that they are latent potentialities, but also in that these potentialities refer to developments, the precise outcome of which is not related completely deterministically to the state of the electron before it interacts with the apparatus....Thus, before the electron has interacted with a measuring apparatus, the wave function defines two important kinds of probability; namely, the probability of a given position and the probability of a given momentum. But the wave function by itself does not tell us which of these two mutually incompatible probability functions is the appropriate one. This question can be answered only when we specify whether the electron interacts with a positionmeasuring device or with a momentum-measuring device. We conclude that, although the wave function certainly contains the most complete possible description of the electron that can be obtained by referring to variables belonging to the electron alone, this description is incapable of defining the general form (wave or particle) in which the electron will manifest itself.7 Here we see an intimate dependence of the quantum system upon the macroscopic measuring apparatus with which it happens to be interacting, such that the quantum system cannot, in principle, be described without reference to the measurements made upon it - not because they are measurements (the pure Copenhagen approach), but be-

6

David Bohm, Quantum Theory (Englewood Cliffs, N. J., 1951), p. 132. pp. 132f. Compare, inter alia, p. 385: "Thus, each observable has two aspects, since it may exist either in a definite form or as an incompletely defined potentiality"; p. 415: "a quantum system should be described in terms of incompletely defined potentialities, which are more definitely realized only in interaction with appropriate external systems."

7

280 cause the macroscopic measuring apparatus is holistically bound up with the quantumlevel phenomena under consideration.8 Only later - commencing shortly after the publication of Quantum Theory — would Bohm develop an approach based on hidden variables, through which the need of referring to the observation apparatus or "environment," as somehow determinative of a quantum state, would be obviated. As of 1951, Bohm's idea of potentiality was still such as to rule out hidden variables, on the premise that the latter are not "potentialities" but actualities: Wefirstnote that the assumption that there are separately existing and precisely defined elements of reality would be at the base of any precise causal description in terms of hidden variables; for without such elements there would be nothing to which a precise causal description would apply....Thus, the analysis of the world into precisely defined elements and the synthesis of these elements according to precise causal laws must stand or fall together.9 By the time his mature reflections on quantum reality had been incorporated into The Undivided Universe, Bohm saw fit to make only glancing reference to his own much earlier anticipation of Heisenberg's interpretation of the wave function in terms of potentialities.10 The term "potentiality" appears but seldom in Undivided Universe, and

Bohm {op. cit., pp. 609f.) makes his objectivism clear: "a quantum-mechanical system can produce classically describable effects, not only in measuring apparatus, but also in all kinds of systems that are not actually being used for the purpose of making measurements. Thus, under all circumstances, we picture the electron as something that is itself not very definite in nature but that is continually producing effects which, whether they are actually observed by any human observers or not, call for the interpretation that the electron has a nature that varies in response to the environment." 9 Bohm, p. 622f. 10 David Bohm and Basil Hiley, The Undivided Universe (London, 1993), p. 18. To a brief discussion of Heisenberg's idea we find appended - perhaps by Hiley, since the work appeared after Bohm's death - the still briefer footnote: "This point of view was indeed proposed earlier by Bohm," with a reference to his 1951 treatise.

281 it is clearly no longer considered to be exclusive of a physical actuality, whose quantum-level manifestation is recognized as only partial.11 Meanwhile, a third of a century after having made his own seminal contributions to quantum theory, Werner Heisenberg - who had remained a proponent of the Copenhagen interpretation - penned some few but widely noticed remarks on the fruitfulness of the Aristotelian concept of matter, specifically as potentia, in understanding quantum physics.12 "The probability wave... .was a quantitative version of the old concept of 'potentia' in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and actuality."13 Heisenberg observed that the notion of potentia is an entirely objective one, not dependent on the intervention of the observer as such; for him, it enters nevertheless into the probability function as understood by the Copenhagen theorists - along with a subjective element, just as it had for the early Bohm. "The observation itself changes the probability function discontinuously; it selects of all possible events the actual one that has taken place. Since through the observation our knowledge of the system has changed discontinuously, its mathematical representation also has undergone the discontinuous change and we speak of a 'quan-

11

See for instance pp. 107f. Also p. 25: "It is true that in some sense, at least, the quantum of action is neither divisible nor analysable at the level of the phenomena....Vrom this however it does not follow that there is no more complete description perhaps at a deeper more complex level in which this process can be treated as continuous and analysable." 12 Physics and Philosophy: The Revolution in Modern Science (New York, 1958), pp. 40f., 53f., 147f., 160. 13 Heisenberg, Physics and Philosophy, p. 41.

282 turn jump.'" 14 Here we can see that the objective role of potentia is implicit in the notion of "all possible events" - a range that is finite, not infinite. Thus far we can indeed recognize the Aristotelian origins. Heisenberg is no less correct in recognizing later that Aristotle's matter is "in itself not a reality but only a possibility, a 'potentia'; it exists only by means of form."15 But having come so tantalizingly close to a principle that could provide the solution to dilemmas he discusses so lucidly, Heisenberg stops short of the full Aristotelian insight. All the elementary particles can, at sufficiently high energies, be transmuted into other particles, or they can simply be created from kinetic energy and can be annihilated into energy, for instance into radiation. Therefore, we have here the final proof for the unity of matter. All the elementary particles are made of the same substance, which we may call energy or universal matter; they are just different forms in which matter can appear. If we compare this situation with the Aristotelian concepts of matter and form, we can say that the matter of Aristotle, which is mere "potentia," should be compared to our concept of energy, which gets into "actuality" by means of the form, when the elementary particle is created.16 The problem with Heisenberg's formulation is that it does not sufficiently divest matter of actuality. The concept of "energy" in physics is indeed abstract: an ens rationis, standing for a wide range of entities precisely in their capacity of interacting with one another. Hence "energy" seems very closely allied to "matter" in the sense in which I use the term in these pages. But energy is quantifiable, while matter is not. "Energy," polyvalent concept that it is, denotes an actuality - even though its actuality is appre14

p. 54. p. 147; cf. p. 148: "The matter of Aristotle is certainly not a specific matter like water or air, nor is it simply empty space; it is a kind of indefinite corporeal substratum, embodying the possibility of passing over into actuality by means of the form." It is not clear whether Heisenberg understands by "corporeal" here any degree of actuality at all - which would be inconsonant with Aristotle rightly understood. 16 p. 160. 15

283 hended as a potentiality to some other actuality. It is, in a word, secondary matter, not the "mere potentia" to which Heisenberg has been making reference. We may concede that all elementary particles "are made of the same substance, which we may call energy" - but we are already at least one structural level above that of prime matter. One need not make too much of Heisenberg's terminology; clearly he found Aristotle's thought appropriately suggestive; but in any event he went no further with it than my citations have indicated. Absent a more developed doctrine of form and the several interwoven concepts that we have presented in Chapters Three and Four, Heisenberg could not have been in a position to make Aristotle's matter constitute an essential basis for understanding quantum phenomena, as being no different in kind (but only "in manifestation") from phenomena of change encountered at the sensible level. Such is not the case for William A. Wallace, who since the 1960s has worked toward re-integrating Aristotelian-Thomistic and modern physical thought on many fronts. In papers published a few years after Heisenberg's comments appeared, Wallace situated Heisenberg's idea more explicitly in an Aristotelian-Thomist context. Rephrasing Heisenberg's solution, one could say that the explanation of massive, kinetic, and electromagnetic phenomena, all of which may be regarded as real, requires some underlying substrate or ultimate matter or protomatter that itself is real but only in a potential way. This ultimate level of ontological depth is, of course, unpicturable, unvisualizable, and unobservable. One might almost say it is unintelligible, if by this is meant that it is in itself unintelligible and only intelligible in terms of the various forms or determinations it can be made to assume. Similarly, it is not existent in itself, and in this sense is not fully real and actual, as are tables and chairs and other determinate objects.17

"Elementarity and Reality in Particle Physics," reprinted in From a Realist Point of View: Essays on the Philosophy of Science, 2nd edition (Lanham, Md., 1983; this essay originally published 1968), p. 204.

284 Wallace went on to echo Heisenberg's apparent reduction of elementary actuality to the so-called elementary particles: "the forms or determinations that this protomatter can be made to assume are what we now know as elementary particles, and thus they are a second-level manifestation of the basic elementarity that is protomatter itself."18 I submit that a qualification is in order, namely, that the term "particle," with its connotation of extreme localization, is too restrictive. As noted elsewhere, I believe that we need not posit a mysterious coexistence of particle and wave, as long as the alternating-modes model has not been definitively ruled out. The foundational level of informed matter may well be so polymorphic as to include particle-like and wave-like modalities. Such a polymorphism is in effect recognized by Wallace elsewhere: The sense in which these are elementary or primary states of matter can be further clarified by inquiring whether all the so-called elementary particles are truly elementary or whether some are more fundamental than others. Heisenberg uses the term elementary to designate the primary manifestations of a basic potency represented by the psi-function. Thus he does not deny that elementary particles can be divided. They can be divided, and still remain elementary, if the fragments into which they divide have characteristics similar to their own, enabling these in turn to be called elementary particles. On this broad interpretation, it is possible to refer to all the particles of which physicists speak as truly elementary.19 Heisenberg himself, on having been acquainted with Wallace's speculations in the 1968 article I have cited, commented (letter to E. K. Gora, December 3, 1965) that Loc. cit. "Are Elementary Particles Real?" reprinted in From a Realist Point of View (this essay originally published 1964), p. 181. Wallace also cites V. Weisskopf, as distinguishing "between particles that represent fundamental states of matter and those that are named particles but are in reality field quanta. The most familiar field quantum is the photon. Just as this is the light quantum of the electromagnetic field, so Weisskopf identifies the pi-meson and the k-meson as quanta of the nuclear field. He also suspects, somewhat along the lines suggested by Heisenberg, that underlying both is something different from the particle and from the field. This he describes as 'some new thing, which is as farfromthefieldas the field isfromthe particle, consequently something new, but that embraces the whole'," loc. cit. 19

285 "I have read the manuscript of Father Wallace's lecture with interest, and have not really felt any need for serious protest." But he added that "neither my studies of Aristotle nor of Aquinas have been thorough enough to permit me the formulation of a wellfounded opinion concerning the concepts 'potency' and 'prime matter.'"20 For Wallace, the discussion of potentiality was situated in the context of charting a realist course between the extremes of neo-empiricism on the one hand, with its emphasis on "merely logical principles that serve to organize a mass of experimental data,"21 and a strong realism such as that of N. R. Hanson, for whom every physical actuality could only find explanation in some other order of physical actuality.22 It is my hope that the present study will in some small way advance Wallace's basic insight and conviction concerning the relevance of a realist doctrine of nature to the fuller understanding of everything considered under physics.

I. Wolfgang Smith's "Hidden Key" W. Smith's The Quantum Enigma is perhaps the most sustained effort since Bohm's to re-interpret quantum physics in terms of ontology, rather than "mere" (and therefore more or less positivistic) epistemology. This book has the merit, which Bohm's work does not, of hewing fairly close to an Aristotelian-Thomistic understanding. That said,

20

Cited in an Appendix to Wallace, "Elementarily and Reality," p. 208. Op. cit., p. 185. 22 Op. cit., pp. 190-2. On his "dematerialization" thesis - which seems sound in so far as it discerns the need of avoiding circularity in explaining features of physical entities, but (I believe) goes too far in refusing to acknowledge any univocity between the macroscopic and microscopic domains - see N. R. Hanson, "The Dematerialization of Matter," Philosophy of Science 29 (1962): 27-38. 21

286 however, Smith also blends in ideas from what appear to be the phenomenological as well as Platonic traditions; and we shall find him less than entirely Thomistic as he takes up the discussion of the doctrine of matter. I originally expected that my work would amount to something of a continuation of Smith's thought; but I came to realize that his contribution is better viewed in contrast to what I am attempting. Still, given the significance of that contribution and the discussion it has engendered, it is appropriate that I draw the aforementioned contrast and let the reader judge of the merits in each case. Smith begins from the "startling fact.. .that every quantum-reality position thus far enumerated hinges upon one and the same ontological presupposition," namely the Cartesian division of the world into res externa and res cogitans, with implications radically destructive of cosmic intelligibility.23 The removal of this fallacy, he avers, must pave the way to a solution of the quantum-reality problem, which is "beyond doubt the most universally significant question hard science has ever posed."24 For Smith, removal of the Cartesian dichotomy will take the form of a holistic recognition of interconnectedness among observers and things observed; in Aristotelian terms (which he does not always use consistently), the form of things really is grasped by the knowing intellect.25 Since the res externa can no longer be treated, in virtue of

23

Wolfgang Smith, The Quantum Enigma: Finding the Hidden Key (Peru, 111., 1995), pp. If. Smith, Quantum Enigma, pp. i-iii. "At the top of the list of 'strange facts' that demand an explanation stands the phenomenon of state vector collapse, which could be well be termed the central enigma of quantum physics," p. ii. 25 Op. cit., pp. 14f.: "In the perceptual act the image is viewed, not as image, but as a part or aspect of the object; it is seen, in other words, as something that belongs to the object....We have as a rule forgotten that there is an intelligence which is intuitive, direct and instantaneous 24

287 the discredited Cartesian "distancing," as of little or no intelligibility, it becomes germane and indeed essential to recognize, within the order of objects themselves {res extensae), a different and most significant dichotomy. Thus Smith will distinguish, in order to unite, the "corporeal world" of direct perception and the "physical universe" known "through a complex modus operandi based upon measurement" in conjunction with theoretical representation.26 He regards every corporeal object as the "presentation" of an associated physical object, and emphasizes that scientific observation is concerned with correspondences between the two.27 "There can be no knowledge of the physical domain without presentation - even as there can be no knowledge of the corporeal world in the absence of sense perception."28 As for the "resemblance" - what might also be called the analogy - between the two, i.e., the connection that will obviate a new (non-Cartesian) "bifurcationist" skepticism, Smith points to "geometrical continuity," i.e., the evident fact that what is perceived and what submits to scientific measurement

in its operation, an intelligence which has no need for dialectic or discursive thought, but flies straight to the mark like an arrow; and much less do we realize that this high and forgotten faculty - which the ancients termed 'intellect' - is operative and indeed plays the essential role in the act of sense perception." 26 "It appears as though physics, at long last, has broken through to its own fundamental level; it has discovered what I shall henceforth term the physical universe - a world that seems to defy some of our most basic conceptions. It is a world (if we may call it such) that can be neither perceived nor imagined, but only described in abstract mathematical terms." Wolfgang Smith, "From SchrQdinger's Cat to Thomistic Ontology," The Thomist 61 (1999): 49-63, cited text p. 51. Cf. Smith, Quantum Enigma, p. 25: "Strictly speaking, no one has ever perceived a physical object, and no one ever will." An apple, for example, "is once again recognized as an external object. That perceptible entity, moreover, is to be distinguished from what may be called the 'molecular apple,' a thing that, clearly, cannot be perceived, but can be known only through the methods of physics." "From Schrodinger's Cat," p. 56. 27 Quantum Enigma, pp. 27-30. 28 p. 31.

288

can be shown to occupy one and the same space.29 The spatial connection does not suffice, however; "the very apprehension of the model or representation entails a certain intellective insight, and thus involves the intellect" - in a way often singled out, I might add, by Einstein.30 Smith maintains that, since "physics deals with...existentiated mathematical structures" it must beware the idolatry of imagination: "reification" of the physical object, i.e. the direct inference from mathematical entity to physical entity, "is always illegitimate; in contrast to a genuinely symbolist use of visual supports it spuriously projects sensible qualities into a domain where such qualities have no place. In a manner of speaking, reification 'corporealizes' what is inherently incorporeal and thus confounds the physical with the corporeal plane."31 This illegitimate reification "was rife throughout the Newtonian era," and it is one of Smith's main contentions that excessive reification of mechanical models (as opposed to a necessary and fruitful use of those models as models) became a habit of scientific thought that still remains to be shaken of, if we are to gain insight into the mysteries of the quantum realm. By virtue of the wave-particle dualism, "particles" in the microworld "cannot be consistently pictured as waves. Consequently they cannot be pictured at all - and this is precisely what puzzles us....It has yet to be recognized that there is an ontological difference between the physical and the corporeal domains, and that the gap cannot be closed through the mere aggregation of so-called particles."32

29

pp. 3If. p. 35. 31 pp. 37f. 32 pp. 4If.

289 By this avenue Smith arrives at a more detailed discussion of indeterminacy, to which I shall turn in a moment. But it is relevant to ask here: is his distinction between the perceived and the measured - between corporeal and physical reality - as essential as he would make it? Granted, that the reality contemplated by physics is radically beyond our powers of sense-perception, and can only be indirectly attained through instruments which serve as a sort of bridge between sensible and insensible; I do not see that this line of demarcation can be considered as other than accidental or relative in nature. That is to say, that even a permanent direct inaccessibility of the "physical universe" to our senses, operating as they do on the "corporeal" plane, does not entail an ontological divide between "physical" and "corporeal" - any more than would exist, say, because someone's eyes were so hypersensitized to light that he must always view the world through a dark filter and learn to make appropriate "corrections" to the altered sense data thereby received. The use of instruments in physical science accomplishes two things: it extends the natural range of the senses within a given qualitative order (e.g., the use of optical equipment to gather more light and provide magnification), and it "translates" other qualitative aspects of being that elude primary sensibility into secondary manifestations that can be sensed (e.g., the use of Geiger counters to "detect" radiation via its effects). The relation between the quantitative and qualitative is not simply that between what is measurable and what is not, but between one aspect of the measurable and another. Smith's duality, though it is not the bifurcating one of Cartesianism, and indeed is posited against the latter, is nonetheless a duality which is overcome only in and

290 through the ratiocinative observing subject, because of a discontinuity between the qualitative (which is measured) and the quantitative (which is only inferred). It is our contention, in a more Aristotelian vein, that this appeal to the measurement process is not necessary in order to maintain a unity of sensible and physical experience: that a primitive "physical" (i.e. quantitative) experience is already occurring when one "sees " the difference in speed of two moving objects, ox feels the difference in heft (mass) of two bodies, and that the corporeal-physical dichotomy should rather be drawn in terms of a proportion, or lack thereof, between the range of physical objects and the functional range of the sense-powers. To return, then, to an area of physics where Smith expects his dichotomy to shed the most light: his argument in Chapter III, "Microworld and Indeterminacy," begins with the denial that there is a "quantum strangeness" in the microworld. For example, it is by no means the case that the electron is sometimes a particle and sometimes a wave, or that it is somehow particle and wave at once, or that it "jumps" erratically from point to point, and so on. For indeed, this kind of "quantum strangeness" stems quite simply from a failure to distinguish between the microsystem as such and its observables (the electron, in this instance, and its position, momentum, and other dynamic variables). In effect, one treats the latter as classical attributes of the electron, which they are not, and cannot be. Or to put it another way, one spuriously projects the results of distinct and interfering measurements upon the electron itself, which consequently seems to combine logically incompatible attributes. It is thus that the electron may appear to be both wave and particle, or to engage in a regimen of "jumping" which does indeed defy comprehension. One could say that this kind of "quantum strangeness" results from an uncritical and spurious realism - a realism which in effect confounds the physical and corporeal planes.33

pp. 48f.; cf. "From Schrodinger's Cat," p. 57: "What is special about measurement is the fact that it realizes an ontological transition from the physical to the corporeal domain....State vector collapse is inexplicable on a physical basis because it resultsfromthe act of a corporeal entity."

291 The indeterminacy of quantum phenomena, then, arises from the juxtaposition (effected through observation) of physical and corporeal domains. As for the former, so far from being "indeterministic," quantum mechanical systems evolve in a way that is specified by the Schrodinger equation itself: "To be precise, it is the Schrodinger equation that guarantees determinism, even as the Heisenberg principle guarantees indeterminacy."34 As Smith develops his analysis, it is evident that he places much weight on the primordial quantum-mechanical notions of superposition and state vector collapse. There are, then, these two ontological planes, and there is a transitionfromthe physical to the corporeal resulting in the collapse of the state vector. The collapse, one could say, betokens - not an indeterminism on the physical level but a discontinuity, precisely, between the physical and the corporeal planes.35 By the act of measurement a particular element from the given ensemble of possibilities has been singled out and realized on the empirical, that is to say, the corporeal level. The physical system, as an ensemble of possibilities, has thus been "actualized." But only in part! For whereas the value of a particular observable has now been determined, the system remains in a superposition of eigenstates for most other observables. And therefore, despite partial actualizations effected by measurement, the system is and remains an ensemble or synthesis of possibilities. In the words of Heisenberg, it is not in reality a "thing or fact," but rather a potency, a kind ofpotentia. As the Aristotelian terminology itself suggests, the conception of physical systems and state vector collapse at which we have arrived is in a way classical, and can in fact be understood from a traditional metaphysical point of view.36 And, more explicitly: Measurement, thus, is the actualization of a certain potency. Now the potency in question is represented by the (uncollapsed) state vector, which contains within itself, as we have seen, the full spectrum of possibilities to be realized through measurement. To measure is thus to determine; and this determination, 34

Quantum Enigma, p. 51; cf. p. 52: "Obviously enough, this quantum mechanical determinism is a far cry from the classical. However, what has been forfeited is not so much determinism as it is reductionism: the classical supposition, namely, that the corporeal world is "nothing but" the physical. It is this axiom that has in effect become outmoded through the quantum mechanical separation of the physical system and its observables." 35 Ibid. p. 55.

292 moreover, is realized on the corporeal plane: in the state of a corporeal instrument, to be exact. Below the corporeal level we are dealing with possibilities or potentia, whereas the actualization of these potentiafej is achieved on the corporeal plane. We do not know how this transition comes about."37 The first thing to note in this analysis is its startling concession of the reality of quantum superposition. Elsewhere Smith is quite clear on this. Consider, for instance, a physical system consisting of a single particle, and then consider two states, in which the particle is situated, respectively, in two disjoint regions A and B, which can be as widely separated as we like. A linear combination of these two states with non-zero coefficients will then determine a third state, in which apparently the particle is situated, neither in A nor in B, but somehow in both regions.... [T]he state of the physical system corresponding to the third state vector can in fact be produced experimentally, and when one does produce that state one obtains interference effects which could not be there if the particle were situated in A or in B. In some unimaginable way the particle seems thus to be actually in A and B at once.38 Smith's solution to the conundrum thus posed is to identify the reality of superposition with that of potentia, thereby wedding ontology and mathematical physics. But it will not do; the invocation of Aristotle is premature. First of all, the very determinacy implied in the Schrodinger equation is opposed to the pure indeterminacy of matter as such. In other words, eigenstates are themselves quantitatively determinate: at most they could only correspond physically to what we have described as dispositiones materiae, which are actually formal in character, and not to matter (potentia) as such. Secondly, even if we see in his use of the term "measurement" the purely objective connotation of "interacting with a measuring instrument," there is insufficient warrant for restricting the "collapse of the state vector" to situations involving measurement. (Here we are back to my earlier criticism, that the boundary between sensible and measurable is in-

"From Schrodinger's Cat," p. 51.

293 correctly drawn by Smith.) Even less satisfactory is Smith's remark that we "do not know" how the transition from potential to actual comes about. Not that one can reasonably demand that everything in physics be "known" - rather, Smith's agnosticism on this point stems from his view that the potency which is being realized in the act of measurement is a potency of the quantitative as such to be manifested qualitatively: in other words, it is a potency, as he elsewhere makes clear, on the part of that which is radicated in matter (quantity) to be actualized as that which is radicated in form (quality) - or, in his terminology, of the physical to be actualized as the corporeal. Echoing Heisenberg, Smith notes that there is nothing in the state vector itself that could explain or account for this determinative act....[T]he transition from potency to actuality requires invariably a creative act - a creative flat, one could say - which nothing in the domain of potency can account for or explain. Nothing within the physical plane, therefore, could cause a state vector to collapse - distressing as this fact may be to those who imagine that there is nothing beyond the physical.39 I fail to see the cogency in this. Granted that no potency explains its own actualization, and that quantum mechanics cannot be expected to include, any more than any other physical theory could include, a description of efficient causality as such (since efficient causality is at best implied, never described, by the quantitative spatiotemporal relations studied in physics), it seems all too apparent that "state vector collapse" can be (and generally is) as humanly unmediated or unmeasured an occurrence as one could desire every time a photon is absorbed by matter, or a radioactive nucleus decays, in some laboratory or on the other side of the galaxy far from any human intervention, one out of a manifold of quantum possibilities is being reduced, through the interplay of cosmic 39

Quantum Enigma, pp. 57f.

294 causalities, to actuality. There is hardly a need to move conceptually from the efficient causality that is implied in every reduction of potency to act, to a "creative fiat"!40 Smith appears to have absorbed that very preoccupation with the subject, or inability to consider physical phenomena in abstraction from the act of observation, that characterizes the Copenhagen theorists he set out to criticize; I shall return to this in a moment. What I am saying of Smith, it will be evident, applies no less to Heisenberg (with whose interpretation, indeed, Smith concurs up to a point).41 Furthermore: there is no compelling basis for relating Smith's physical and corporeal domains as potency and actuality respectively. They can be so related only with reference to an observing subject, and this is not the basis on which Aristotle distinguishes potential from actual in physics. Smith rightly opposes himself to Heisenberg's view that (as Smith puts it) "the transition from the 'possible' to the 'actual' is effected simply by the 'physical act of observation'" - since this forces Heisenberg "to conclude Speaking of the paradigmatic wave-particle transition, Smith says ("From Schrodinger's Cat," p. 53): "Prior to this interaction, the particle will in general be in a superposition state involving multiple positions; we must think of it as spread out over some region of space....At the moment of impact, however, this deterministic Schrodinger evolution is superseded by another quantum-mechanical law, a so-called projection, which singles out one of the positions represented in the given superposition state - apparently for no good reason! - and instantly assigns the particle to the chosen location....It is as though the trajectory of the particle, let us say, were suddenly altered without an assignable cause." 41 Quantum Enigma, pp. 63f.: "Thus far Heisenberg's position and my own appear to be very close indeed - to the point of being indistinguishable. Is not Heisenberg's 'world of potentia' tantamount to the microworld, as I have conceived of it? And his realm of 'things and facts' to what I term the corporeal world?" "Upon closer examination, however, a major difference comes into view. The crux of the matter is this: In the philosophy of Heisenberg we find no sharp distinction between the physical universe on a macroscopic scale and the corporeal world, properly so called. The distinction between the world of potentia and the actual world must consequently be understood in terms of size or scale alone....I maintain that the descent from actuality to potency takes place already on a macroscopic level: it takes place the moment we pass from a corporeal object X to its associated subcorporeal object SX....This is just the crucial point, to say it once more: SX exists as a potency, whereas X exists as a 'thing or fact.'"

295 that the physical act cannot explain the so-called collapse of the state vector; for this he needs to bring 'the mind of the observer' into the picture:"42 but Smith's distinguishing of physical and corporeal manages to re-insert the unwanted subjectivity at another point: not in the act of observing, but in the definition of the observable as such. Physical is in potency to corporeal because the quantitative as such is in potency to the sensible, i.e., the qualitative. In Chapter IV Smith pursues this line of thought further and observes that "we have been led to distinguish between the physical and the corporeal planes; and now, it seems, a third ontological stratum has come into view - which in fact appears to be more fundamental, more basic than the two aforementioned planes [since it grounds the unity between them]. What, then, is the nature of this third domain?"43 In the conviction that we are looking "beyond the space-time continuum" to find the fundamental domain we seek, Smith cites the nonlocality implied in entanglement ("interconnectedness") phenomena, per Bell's theorem. Such nonlocal behavior leads Smith (rightly, as I believe) to observe that everything points to the fact that a particle cannot be fully known by empirical means....a particle may transcend its manifested locus, and thus its phenomenal identity as well. In a word, there may be more to the particle than meets the scientific eye - and by the same token, more than can be made to fit into a fourdimensional continuum. I should make it clear, however, that what stands at issue here is not the dimensionality of the containing manifold, but the absoluteness or relativity of containment itself....It boils down to this: Nature, though not spatio-temporal in its own right, presents itself as spatio-temporal under observation.44

p. 68

296 This reality transcending the spatiotemporal, this Nature, is unknowable as a "thing" in its own right, though it is known "by way of the spatio-temporal universe."45 Smith goes on to identify Nature, in strictly Aristotelian fashion, as the matter-form composite or materia secunda.46 Thus substance underlies, and "projects" ontologically onto, both the quantitative and qualitative orders. After reminding us that these last are related as the physical and the corporeal respectively, Smith completes his Aristotelian analysis with an analogy between physical/corporeal and matter/form. It is this analogy which had earlier led him to posit the act of measurement (i.e., that whereby the physical is rendered corporeal) as an actualization. Now he can (rightly) conclude that, inasmuch as the corporeal is concerned with the qualitative, and therefore with form or essence as such (since the category of quality is radicated ex parte formae), the Cartesian bifurcation can be seen most ominously as a rejection of essences themselves. With all this I stand in agreement. I find Smith's analysis in places difficult of access; working from the standpoint of the mathematical physicist, he seems to have arrived at a largely Aristotelian perspective by a difficult path - that of conceding rather too much to the philosophic presuppositions of conventional quantum mechanics. I have presented Smith's argument at length to better enable the reader to see if I will have done justice to it, when I say that it falters earlier, in regard to its assessment of the

45

p. 71. The physical object as such is "a particular manifestation of the total reality," ibid. p. 78. In adding that "Nature, thus, turns out to be a materia quantitate signata" (ibid.), Smith is careful to note that his use of this term is not precisely that of Aquinas.

46

297 physical-corporeal divide as somehow implying a potency-act relation. If I may presume to diagram Smith's view of the situation: "corporeal" = qualitative (sensible)

\ T—

quantitative (theoretical) = "physical"

\ Nature / (Form - Matter)

Here I try to indicate that, while Smith understands (with Aristotle and Aquinas) that the qualitative and quantitative are grounded in the formal and material aspects, respectively, of underlying substance or "Nature" (thin arrows), he also wants to have the quantitative and qualitative ordered as potency and act, and to be realized as such in the very process of measurement (fat arrow) - not, to be sure, because measurement is a cognitive act (that would be the positivist-Copenhagen interpretation), but because the manifestation of quantum (quantitative) reality in a phenomenal (nonquantitative) context entails, by nature (although somewhat mysteriously) a transposition from one ontological plane to another - from that which we can only infer to that which we sense directly. Underlying Smith's view, as I have indicated, is the quantum-mechanical idea that the superposition of eigenstates stands for all possible localizations of that which cannot be observed to be other than in one location. Wresting, in the spirit of Heisen-

298 berg and others, the wave-particle duality unto some semblance of intelligibility without giving up the simultaneous reality of the wave and particle aspects - and compounding, laudably enough, his difficulties by refusing to walk with Heisenberg down the path of raw subjectivism, Smith locates the "hidden key" to understanding the quantum enigma in the interpretation of observation (measurement) as a unique actualization of the manifold potency represented by the wavefunction, i.e., by the potentialities of the quantitative domain as such. And this is where I cannot follow him; for the ontological relation of quantitative to qualitative - despite their being radicated in matter and form respectively - is not such that the one stands in potency to become the other, but rather that the one is receptive of the other in the simultaneity of their composition. It is not a dynamic ordering, but a constitutive one; not like the potency-act relation that obtains between, say, a faculty and its exercise, but like that which obtains between an essence and its existence. Quantity does not pre-exist the qualities that manifest it - but this is exactly what Smith, it seems to me, is driven to say. No wonder that he must express puzzlement as to how the manifestation comes about in the process of measurement, i.e., in the projection of the quantum event onto the phenomenal level. Smith's understanding comes close to that presented earlier in this thesis; but the differences are significant. It will be recalled that I conceive the continuous and discrete aspects of quantum reality to be related to one another as potency and act only in the sense that either can transform, elementally or quasi-elementally, into the other, as their respective material principles subject them to the activity of other hylomorphic entities,

299 and the dispositiones of their matter (i.e., forms virtually present in them) condition them toward one transformation or another. On my reading there need be, and perhaps can be, no "more" of inherent potentia in the continuous than there is in the discrete manifestations of quantum reality (we must not, in other words, allow the purely mathematical connotations of the terms to mislead us); the characterizations of continuous and discrete are relative and not absolute, there being no such thing as a discrete entity devoid of any extension, or a continuous entity lacking all discreteness. In a word, my construction of quantum phenomena along Aristotelian and Thomistic lines does not "privilege" either complementary aspect, as Smith's seems to do. Both aspects participate fully in the substantial, quantitative, and qualitative aspects of hylomorphic being. The unobservability of the one in comparison to that of the other is a matter only of proportion to our sense faculties. In summary, then: while following Heisenberg's lead in supposing a role for Aristotelian potentia, and agreeing in considerable measure with Wolfgang Smith who has explicitated an understanding of potentia in the context of quantum-mechanical superposition, I submit nonetheless that we can make even better sense of the quantum world by discerning in quantum complementarity the evidence of matter's inherent dynamism, a dynamism that pre-exists all our attempts to observe and measure it.

J. Conclusion In this thesis I have sought to present the Aristotelian-Thomistic doctrine of informed matter not only as consistent and insightful in its own right, but as fruitful with respect

300

to understanding contemporary physics. In particular, the realization that "secondary matter" at the elemental level will exhibit more strongly those characteristics grounded in prime matter itself, potentia pura, should inspire confidence in the intelligibility of quantum phenomena which seem to embody just those characteristics. Ultimately, a unified doctrine of matter as principle of change, of individuation and spatiality, and even of intelligibility, enables us to apprehend the fabric of spatiotemporal being as entirely causal, even if it is not - contra the presumptions of earlier determinists - entirely intelligible to ourselves, who by divine Providence are very much a part of it.

Appendix 1: The Ultimate Boundary of Matter

Given the impossibility of void, and the constitution of cosmic "space" as materialized being in its extended totality, I offer an argument concerning its own boundary. To begin with, the Aristotelian-Thomistic argument against an infinite space will be seen to be the argument against actually infinite being.1 Some have tried to draw the same conclusion from the standpoint of quantitative physics: the mass of the universe, it is said, must be either finite or infinite. But if the mass is infinite, then the net gravitational potential must be infinite, contrary to experience. If the mass is finite, then the net gravitational potential, in a Newtonian (Euclidian) universe, must be such that all the mass of the universe would be collapsed in the center, again contrary to experience. Finally, in the finite but unbounded universe of Einstein and Minkowski, this paradox would be resolved through the peculiarities of the geometry. Therefore the universe is finite and non-Euclidian. All three conclusions, however plausible, suffer from defects proper to the order of mobile being as such. For given the possibility (not ruled out by physics) of a universe of finite age, there may not have accrued enough time for the gravitational potential to have "reached" infinity (under the first scenario) or to have effected the collapse of the universe (second scenario). As for the third conclusion, it suffers from the fallacy of reification of a purely geometrical order of being and drawing from it 1 2

See Chapter Four, Section H. See, inter alia, Stanley Jaki, The Paradox ofOlbers' Paradox. 301

conclusions of physical significance. The fact that Riemannian geometry may be most convenient for the description of spacetime in relativistic cosmology does not mean that spatiality, the extendedness of cosmic being, is in fact other than what it appears aboriginally, three-dimensionally Euclidian. (Arguments for non-Euclidian space often appeal to analogies of ^-dimensional space in [n+l]-dimensional hyperspace; the analogies fail because the radical primordiality of three-dimensional space allows us to conceive of no higher-dimensional analogue except in the abstract; they rest on an illicit inference from mental to real being.) Here is a different approach. The sum total of cosmic being is finite, and this means, in accordance with the very nature of spatiality, that it has finite dimensions. The boundary of the cosmos will be "where" dimensionality ceases. (The universe, of course, cannot really have a place, a "surrounding body," since it includes every body.) Now the dimensive order of being is terminated either by nothing, or by something. It cannot be nothing, "nothing" being an ens rationis. Therefore it is something. But since it cannot be dimensive or material being, it must be immaterial being. From a purely logical standpoint this could be angelic (separate) substance. Thus far the philosopher can proceed, through a certain via negationis. But can he go further? Even armed with the philosophical conclusions that the universe depends upon a creative cause "which all men call God," I do not see how we can conclude that this First Cause is what constitutes the delimitation of the physical order. It seems that the cosmos could terminate "in" angelic being, even as both the material and the immaterial

302

are created and conserved in being by God, angels not being implicated in the creative activity. But it is surely intriguing that, as man extends his vision further and further into space, and so (it would seem) draws ever closer to the boundary thereof, he simultaneously - in virtue of his status as recipient of light and other transmissions, coming from those cosmic depths with finite velocity - is "taken" further and further into the past, perceiving an ever younger cosmos. Any "line of sight," speaking loosely, which thus takes the observer further into the distance and into the past must, in principle, continue on (whether or not "vision" in any sense remains possible) to a "furthest" in both space and time. This ne plus ultra of cosmological penetration, the point where matter and time end - or, seen in the perspective of coming-to-be, begin seems readily identifiable with the creation point, creation being the moment in which the universe comes to be, a boundary between its non-existence and its existence. But again, to conclude that, at this boundary between cosmic being and non-being, one necessarily encounters God (in the creative moment) rather than finite immaterial substance (as somehow present at the creative moment) is more than I am prepared to say.

3

Paradoxically, the further we see "out" in every direction, the smaller the universe we are seeing; the cosmic expansion, an expansion of spatial being as such (not of "things in space"), is extrapolated backward to a singularity, a dimensionless point. 303

Appendix 2: On Matter's Place in a Larger Scheme of Ontological Principles

I here introduce a schema collating the various principles of hylomorphic being - those which are called causes and those which are not - in order to situate matter as completely as possible in the spectrum of physical reality. The four causes which come to us through the Aristotelian-Thomistic tradition are readily divided into intrinsic and extrinsic, and cross-divided into essential-order and existential-order causes. (This division is not affected by variations in how the essence-esse distinction is interpreted.) Extrinsic

Intrinsic

Existential

EFFICIENT

MATERIAL

Essential

FINAL

FORMAL

The placing of form as an essential cause, and agent as existential cause, should not occasion controversy among Thomists. The other two placements are validated thus, [a] The end, even considered as forma ad quern, is nonetheless extrinsic to the being of which it is the final cause, considered not absolutely but in fieri (i.e., as constituted hie et nunc)} [b] As discussed in Chapter Three, matter, though no more "existential" than form considered with reference to the existential act that is distinguished from essence 1

Deprincipiis naturae §3: "Materia et forma dicuntur intrinsece rei eo quod sunt partes constituentes rem, efficiens et finalis dicuntur extrinsece, quia sunt extra rem" (Leon. 43.42:4851). 304

at the foundational ontological level, is, considered within the hylomorphic essence and with reference to the primary essential principle (form), "existential" in so far as it constitutes, not the intelligible determination but the existential condition thereof namely, the dynamic, mediately dependent, and contingent mode of existing peculiar to the spatiotemporal order. Now there are other principles of hylomorphic being which, though entering into the Thomistic metaphysical analysis, have been called "cause" either problematically or not at all. One of these, privation, was distinguished by Aristotle from the properly causal principles of nature on the basis of functioning per accidens while they (matter and form) are per se principles of change. Another principle, whose "causal" status has been much debated, is the exemplar which Aquinas readily adopts from Neoplatonic thought. Then there is esse itself, surely not to be denied the status of "principle of being" inasmuch as it is distinguished from essence in the very first metaphysical composition. Finally, though perhaps the least provocative of discussion historically, there is the active potency in the agent, a principle that must be distinguished from, as it is prior to, agent causality as such. My thesis is a simple one: I offer a schema in which each of the four Aristotelian causes (to which all other causes are reducible), together with each of these four noncausal principles, is properly situated in its manifold relation to the others. To accomplish this all eight principles are unified, even as they are divided, by three principles of division: the aforementioned existential-essential and intrinsic-extrinsic divisions, and a third one according to being and becoming. This latter principle of

305

division is warranted on the basis of the discernment, in our intellectual apprehension of being, of principles which are not present across the whole range of finite being but only in that which is constituted in fieri. Taking all three pairings into account we find that they constitute a symmetrical "eightfold way." There are far too many interrelations among the eight principles to include within the compass of a single diagram, but I hope the fruitfulness of such a diagram, with respect to the ordered analysis of cosmic being, will be evident: Extrinsic

Intrinsic

of being

EFFICIENT

esse

of becoming

active potency

MATERIAL

of being

exemplar

FORMAL

of becoming

FINAL

privation

Existential:

Essential:

The role of the three principles of division, cross-dividing the eight principles, can be more readily visualized in a three-dimensional diagram: imagine a cube divided in half in all three dimensions, yielding eight smaller cubes. Those on the upper half, say, can be represented as intrinsic, those on the lower half as extrinsic; those on the right half as existential, those on the left half as essential; and those on the front half as referred to being simply, those on the rear half as referred to being in fieri. Among the aporiai which call for resolution in the presentation of such a schema are: Why are four, or five (if we count the exemplar) of these eight principles

306

traditionally called causes? Can the designation "cause" apply properly to any of the others, and why? Here I present only an outline of the solution. Aquinas defines cause as "a per se principle of the existence of a thing." His definition can be validated in all its parts by dialectical investigation; that is, the common denominator of what philosophers have meant by "cause" can be reduced to these parts. They are, in fact, the causal elements of the very definition of "cause": per se - the formal specification of what a cause is, namely, principle - the material element, that which is so specified; of existence - causes are referred to esse as such, and to the esse of a thing - i.e., the thing precisely of which they are the cause.2 Now each of the four traditional causes answers to all four notae of the definition. Each is a cause through its own quasi-essence, not in virtue of something else with which it is associated. Each is a principle contributing to existence, rather than existence itself. Each is a factor with reference to the esse immediately, not merely with reference to esse's co-principle, essence, or to some posterior principle. And finally, each is (analogously) a cause with respect to the thing itself, not through some other thing. How do the other four principles fall short of this full definition of cause? Again very briefly, I note that: privation, as Aristotle argued, is not a per se principle; esse is not a principle of existence, but existential act itself; the exemplar is not directly referred to the existence of the thing caused, but only indirectly through form's participation in it; and active potency in the agent is not referred directly to the thing 2

De principiis naturae, 18: "causa dicitur solum de illo primo, ex quo consequitur esse posterioris." 307

caused, but to some other thing that could supplant it in existence. Thus each of the four non-causal principles, as I am calling them, falls short with respect to one of the defining characteristics of cause properly so called. Perhaps the most controversial of these assignments will be the exemplar. Aquinas himself refers to it as a cause, although surprisingly infrequently given the number of times he discusses this principle in his works. A full defense of my position would entail showing that, inter alia, [1] "cause" is used with analogical flexibility in Aquinas's lexicon, as evidenced by his describing the exemplar now as formal, now as final cause - when these causes clearly have different rationes in his most formal discourse; and [2] some of the texts about the exemplar refer to a principle that is causal only in a sense broader than that conveyed by the definition of "cause." I leave it to the reader to trace the many reciprocal relationships that clamor for attention in the diagram here presented. The fuller development of this schema and the symmetrical relations implied in it can only shed further light on the nature of causality and the interconnections among all the great metaphysical principles - to say nothing of its usefulness in pedagogy.

308

Appendix 3: Materiality and Temporality

If matter is primarily a principle of existential dependence, of existing substantially (as well as accidentally)1 through interaction with other finite beings, then it need not follow that such existence be temporal, i.e., entail motion. It is true that we only know material existence as spatiotemporal - that hylomorphic being exists in such a way that its being is not fully present to itself, but is distended, through imperfect actualization, in what we know as time. But the ratio of "substantial dependence in being" is prior to that of mobility and temporality. A thing can exist in substantial dependence upon the causality of other finite beings, without such dependence being constituted through the "act of the potential as such" that defines change or coming-to-be. The universe as constituted in the present instant is the result of all the motion that has characterized it from the beginning; could that instant be frozen, all the relations of causality that presently obtain in time would still obtain in that eternal moment, though they would not be displayed temporally. Such considerations take on more than abstract significance in view of the question, why is there a temporal order? What could temporal succession add to the brute

1

1 say "substantially as well as accidentally" because the Angels or separate substances, according to Aquinas, exist with accidental dependence upon one another: they mediate knowledge, and thus accidental perfections, in hierarchical order to one another. But material beings come to be and pass out of being not only with respect to accidents but also in their substantial wholeness through the causal action of other beings - certainly material beings, and perhaps angelic as well. Man, of course, is a special case inasmuch as he possesses an immortal form. The Church teaches that each human soul is a direct creation, not educed from pre-existing matter. 309

materiality of the cosmos? It does not enrich the being of a material thing to be "distended" through time; no ontological advantage accrues to the thing itself, nor (adopting a theological perspective) would there seem to be, from the standpoint of the Creator, any difference between the distended or partial existence of spatiotemporality and summary existence in the moment - all is present to God. He knows the material being no less fully, in the eternal creative instant, than he knows the immaterial and atemporal. The irrational creature, not knowing itself intellectually, cannot compare itself through time, and therefore knows itself neither as imperfect nor as perfect. But with man the case is different. For man, possessed of an intellectual principle which transcends the material order, possesses an awareness of being, including his own, which takes into account not only the present but also the past and (contingently) the future; so that he can act with reference to not only the present, but also the past and (contingently) the future. So while God knows man and all creatures fully in their ultimate realization, and while irrational creatures know themselves not at all, man knows himself - yet, in statu viae, only as imperfectly realized, through a comparison that takes into account past and future as well as present. It is precisely through knowing himself as imperfect (ontologically imperfect, even before moral imperfection enters the scene) that man acts toward his own perfection, consonant with his possessing intellect and will. And corollary to this is that the cosmic order of flux and temporality is constituted as that whereby man's self-perfection occurs. In other words, the temporal order of being is that manifestation of the material (and spatial) order of being whereby man's

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spiritual nature, his intellect and will, perfect (or fail to perfect) themselves, under divine agency. More briefly still: the cosmos is spatiotemporal for the sake of man's selfperfective activity. I leave it to the theologians to consider whether time will exist in "a new heaven and a new earth," i.e., whether matter will remain as a principle of corruption, after man's perfection is accomplished.

311

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