The Aristotelian Tradition of Natural Kinds and Its Demise 0813230411, 9780813230412

Table of contents :
Contents
Acknowledgments
Prologue
1. Origin of the Idea of Natural Kinds
2. Eidos and Genesis I: Plato
3. Eidos and Genesis II: Aristotle
4. And the Word of God
5. Lex and Motus I: Galilean Science
6. Lex and Motus II: After Descartes
7. Darwin
Selected Bibliography
Index

Citation preview

THE ARISTOTELIAN TR ADITION OF NATUR AL KINDS & ITS DEMISE

THE ARISTOTELIAN TRADITION OF NATUR AL KIND S & ITS DEMISE

STEWART UMPHREY

The Catholic University of America Press Washington, D.C.

Copyright © 2018 The Catholic University of America Press All rights reserved The paper used in this publication meets the minimum requirements of American National Standards for Information Science—Permanence of Paper for Printed Library Materials, ANSI Z39.48-1984. ∞ Library of Congress Cataloging-in-Publication Data Names: Umphrey, Stewart, 1942– author. Title: The Aristotelian tradition of natural kinds and its demise / Stewart Umphrey. Description: Washington, D.C. : The Catholic University of America Press, 2018. | Includes bibliographical references and index. Identifiers: LCCN 2018007869 | ISBN 9780813230412 (cloth : alk. paper) Subjects: LCSH: Species—Philosophy—History. Classification: LCC QH380 .U47 2018 | DDC 576.8/6—dc23 LC record available at https://lccn.loc.gov/2018007869

In memory of William Edgar philosopher & friend

CONTENTS

Acknowledgments ix Prologue 1 1

Origin of the Idea of Natural Kinds

18

2

Eidos and Genesis I: Plato

44

3

Eidos and Genesis II: Aristotle

78

4

And the Word of God

118

5

Lex and Motus I: Galilean Science

145

6

Lex and Motus II: After Descartes

181

7 Darwin

218

Selected Bibliography

245

Index 257

vii

ACKNOWLEDGMENTS

Of those who helped me think about the subject matter of this book, I wish to single out for special thanks the following people: Bill Edgar, who prompted me to study anew the Aristotelian tradition of natural kinds; David McNeill, Alan Pichanick, and Thomas Cleveland, with whom I discussed several Platonic dialogues relevant to this theme; Jason Tipton, for conversations about Aristotle’s understanding of living things; Joe Macfarland, for relevant comments while I was revising parts of chapter 4; Chester Burke, with whom I have enjoyed many conversations about Leibniz, Galileo, Huygens, Newton, and Maxwell; and Nick Maistrellis, for helpful comments while I was preparing to write chapter 7. I wish to thank the anonymous reviewers who read the manuscript in its entirety and made a number of useful recommendations. For any remaining errors and omissions I am, of course, solely responsible.

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THE ARISTOTELIAN TR ADITION OF NATUR AL KINDS & ITS DEMISE

PROLOGUE PROLOGUE

Prologue

In philosophy there have been two great waves of natural-kinds realism: the premodern tradition instituted by Aristotle, to which Avicenna, Maimonides, Albertus Magnus, Thomas Aquinas, and Duns Scotus belonged; and the modern tradition instituted by John Stuart Mill, to which John Venn, Charles Sanders Peirce, Saul Kripke, Hilary Putnam, and Brian Ellis all belong. Philosophers interested in natural kinds have for the most part operated within one or the other of these two traditions. A good example is Ian Hacking, who in two seminal essays, “A Tradition of Natural Kinds” (1991) and “Natural Kinds: Rosy Dawn, Scholastic Twilight” (2007), interwove topical remarks on the concept of a natural kind and its applicability with historical remarks on the Millian tradition of natural kinds.1 My interest, like Hacking’s, is both topical and historical. Unlike Hacking, however, I have chosen to separate topical from historical as much as possible, and to present the former in a recently published 1. Ian Hacking, “A Tradition of Natural Kinds,” Philosophical Studies 61 (1991): 109–25, and “Natural Kinds: Rosy Dawn, Scholastic Twilight,” Royal Institute of Philosophy Supplementary Volume 82 (2007): 203–39. Hacking’s account of the Millian tradition of natural kinds has been criticized. See, for example, P. D. Magnus, “No Grist for Mill on Natural Kinds,” Journal for the History of Analytical Philosophy 2 (2014): 1–15. But these details need not concern us here.

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book entitled Natural Kinds and Genesis: The Classification of Material Entities.2 And unlike Hacking’s, my historical remarks, presented in the companion volume now before you, concern the Aristotelian tradition of natural kinds, its rosy dawn, Scholastic twilight, and eventual demise. Although this book can be read on its own, without having undertaken any prior investigation of such kinds, it will help the reader to gain some familiarity with the contents of my Natural Kinds and Genesis, if only to become acquainted with some of the technical terms I will be using here. I offer therefore the following summary.

REVIEW In that book I raised two questions—“What is a natural kind?” and “Are there any natural kinds?”—and argued that there is nothing peculiarly philosophical or scientific about these questions. Both may emerge in the course of everyday life, as may the questions, “What is justice?” and “Is any political society or human being truly just?” This is but one sign that the concept of a natural kind, like the concept of justice, has its native home in everyday thought, prior to any philosophical reflection or scientific theory.3 Our everyday understanding of natural things presupposes that their reality does not depend on how we regard them, and that the way we ordinarily regard them is heuristically if not cognitively valuable. Natural philosophy, as I conceive it, begins under the guidance of these two suppositions, and is thus akin to natural history. There is today, however, a kind of philosophical antirealism which rejects the first of these presuppositions, and a kind of philosophical naturalism which rejects the second. The antirealism in question agrees that natural things exist, but denies that they exist independently of the 2. Umphrey, Natural Kinds and Genesis (Lanham, Md.: Lexington Books), 2016. 3. Umphrey, Natural Kinds and Genesis, chap. 1.

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way we conceptualize them. It combines, in other words, immanent or metaphysical realism with transcendental or protometaphysical antirealism—the claim that natural kinds exist, for instance, together with the claim that their existence depends on our distinctive way of thinking and speaking about what we perceive.4 The naturalism in question claims that philosophy without natural science would be blind to the empirical world as it is; hence, if philosophers are to discover anything at all about natural kinds, they should regard the relevant scientific theories as simply authoritative, and regard as irrelevant at best our pre-scientific understanding of such things. I argued that protometaphysical realism (our first supposition) has yet to be refuted, and that the way we ordinarily regard natural kinds and their members is first in the order of inquiry (our second supposition), even if the scientific understanding of them should prove superior in the order of knowledge.5 Kinds may be understood as classes or as types. As types they are universals. Hence there are natural kinds as types only if there are universals. The ontic status (reality or unreality) of universals is a perennial issue in metaphysics, one which philosophers have yet to resolve once and for all. I argued, nevertheless, for tentative acceptance of realism with respect to universals understood as multiply exemplifiable entities “in” or “beyond” the particulars (tokens) which exemplify them. Universals may be generic or specific. They are generic just in case they are further determinable as types, specific just in case they are not. I argued that a generic universal Ug and any specific universal Us “under” it cannot both be real. Hence, if Us is real, Ug is unreal, and conversely. To say that one or the other is unreal is to say it does not exist independently of our ways of typifying and classifying things; 4. Protometaphysical antirealists include Immanuel Kant, Michael Dummett, Nelson Goodman, Hilary Putnam, and Panayot Butchvarov. I consider Kant’s transcendental “idealism” in chap. 6.3 of this volume. 5. Umphrey, Natural Kinds and Genesis, chap. 2.

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but this does not imply that it has no basis in reality, for it may be a concept well founded in the natures of things. Finally, I argued that there are no conjunctive or disjunctive universals, and no meta-level universals such as universality itself, save perhaps in our thought or speech.6 From the hypothesis that there are real types it does not follow that there are any real natural kinds. It may be that all natural kinds are simply classes of resembling particulars—which we define, distinguish, and relate by means of sortal concepts having no existence independently of our ways of typifying and classifying things. Realism regarding universals is thus consistent with antirealism regarding natural kinds as types as well as classes. How is one to distinguish natural kinds from other kinds of kinds? First, a kind is natural only if it exists independently of our thoughts and practices. Mythical or fictional kinds (unicorns, dementors) are not natural, nor apparently are artificial or conventional kinds (laptops, spouses). But there are complications. Chattel slavery is not a natural kind, apparently, yet slaves as humans may well belong to one. And there are chemical substances (PVC, Bohrium), samples of which are all synthetic, which seem nonetheless to constitute natural kinds. Second, a kind is natural only if its tokens or members exist in the natural world. Let it be true, as some Platonists allege, that there are mathematical kinds (Euclidean cubes, Lobachevskian horospheres) whose types are real and yet the tokens of these types do not and perhaps could exist in physical space or spacetime. Then cubicality and horosphericity are not natural-kind types. And if the usual interpretation of quantum mechanics is correct, there are no natural kinds whose members are geometrical solids having closed or determinate boundaries. How are we to determine which kinds are natural? Philosophers generally agree that one should proceed naturalistically (phusikôs, as 6. Ibid., chap. 3.

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Aristotle used to say), but have recommended two very different procedures. According to some, we should regard as natural all and only those kinds which are relevant to the theoretical interests of natural scientists today. These interests are now exceedingly diverse, ranging all the way from particle physics to cosmology, quantum chemistry to climatology, molecular biology to medicine. No less diverse are the types and tokens admitted in their implicit ontologies; they include quantities, relations, events, processes, and particulars as various as electrons, organisms, weather systems, black holes, and galaxies. So diverse are these tokens and their types that there no longer appears to be any such thing as the concept of a natural kind. Why, then, should we not conclude that all talk of such kinds is otiose at best? According to others, we should regard some putative kind as a natural kind, in the primary sense of the term, only if its members are enduring things or masses—in other words, only if its members are continuants. The substance called “water” and the class of all and only H2O molecules are then natural kinds. So too, apparently, are the class of humans, the class of hurricanes, and the class of electrons. In virtue of what is a human being a genuine continuant and not merely a continuant-like succession of cellular or molecular multitudes which we, for practical purposes, regard as singular? And how are we to decide that human beings so resemble one another that they constitute a single natural-kind class or exemplify a single natural-kind type? These are difficult questions. Yet regardless of how we answer them, there does appear to be such a thing as the concept of a natural kind. It appears, moreover, that many of the kinds recognized by scientists today are natural kinds only in some derivative, analogical sense of the term, if at all. Which of these two naturalistic procedures should we prefer? The first prevails in natural-kinds studies today.7 The second is more tradi7. In addition to Hacking’s, the following works are representative of this trend: John Dupré, The Disorder of Things: Metaphysical Foundations of the Disunity of Science (Cam-

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tional. I prefer the more traditional way for two related reasons. First, it accommodates our everyday understanding of things natural, according to which continuants and their kinds are ontologically as well as pragmatically basic. Natural kinds such as animal, vegetable, mineral are plainly relevant to our pretheoretical interests; and even if many of the kinds we ordinarily take to be natural turn out to be unreal, either because their members are not genuine continuants or because they do not form disjoint classes, it will still be the case that there is one concept of a natural kind, and that this concept plays a distinctive and important role in what philosophers today call “folk naturalism” or “folk metaphysics.” My other reason for preferring this monistic conception of natural kinds is more historical. It was John Venn (1834–1923), closely following John Stuart Mill (1806–73), who first introduced the term “natural kind” into our discourse. Mill had set out to reform Aristotelian logic. He began by replacing the traditional nine or so categories of being with just two, namely, subjects and classes. Classes he then divided into two sorts, manmade and real. The members of a manmade class have only one or a few distinguishing properties in common; or, if they have many such properties, these are all interrelated by some discoverable law. The class of red things is manmade, as are the classes of women and of white men. The class of humans on the other hand is real, as are the classes of animals, of plants, and of minerals such as phosphorus and sulfur.8 What Mill called “real classes” Venn called bridge, Mass.: Harvard University Press, 1993), 60–84, 103–5; Richard Boyd, “Realism, AntiFoundationalism, and the Enthusiasm for Natural Kinds,” Philosophical Studies 61 (1991): 127–48; P. D. Magnus, Scientific Enquiry and Natural Kinds: From Planets to Mallards (New York: Palgrave Macmillan, 2012), 43–49; M. A. Khalidi, “How Scientific Is Scientific Essentialism?,” Journal for the General Philosophy of Science 40 (2009): 85–101, and Natural Categories and Human Kinds: Classification in the Natural and Social Sciences (New York: Cambridge University Press, 2015), 42; and M. Ereshefsky and T. A. C. Reydon, “Scientific Kinds,” Philosophical Studies 172 (2015): 969–86. 8. John S. Mill, A System of Logic, ed. J. M. Robson (Toronto: Toronto University Press, 1973–74), 1:27–40, 46, and 133.

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“natural kinds,” and as members of such kinds he too mentioned human beings, animals, and plants—all of which appear to be exemplary continuants.9 Aristotle used very similar examples when clarifying what he meant by ousia (entity, substance), the primary category of being. What Mill called “subjects” Aristotle called “primary ousiai”; and what Venn called a “natural kind” he called an eidos (“species”) or “secondary ousia.” The words are different but the concepts are the same.10 This is no mere coincidence, for Aristotle’s logic and Mill’s revision of it originate in our everyday understanding of things, and it is from this common root that the two great traditions of natural kinds have sprung. It may be true, as Hacking says, that the Millian tradition is already in its twilight, in part because philosophers working in this tradition are trying to accommodate the great diversity of contemporary theoretical interests.11 But from this it follows not that our monistic conception is unduly restrictive, but that the concept of a natural kind no longer seems to have much theoretical use. So closely linked is the concept of a natural kind to the concept of a continuant that one cannot elucidate the former without providing some elucidation the latter as well. Exemplary continuants change and yet remain the same as long as they exist. To understand how this is possible, metaphysicians have distinguished between what a continuant is and how it is, or between the invariant nature (substance, essence) of a thing and the thing’s varying attributes. A continuant x 9. John Venn, The Logic of Chance: An Essay on the Foundations and Province of the Logic of Probability (New York: Chelsea, 1923), 55. 10. The principal differences between the two traditions are these: (1) Aristotelians were very interested in the ontic status of natural-kind types, and in continuants as entities, whereas Millians generally speaking are not. In this one respect, if no other, my account is more Aristotelian than Millian. (2) Aristotelians tended to assume that natural kinds are linked conceptually with final causes and not laws of nature, whereas Millians tend to assume the reverse. I agree that natural kinds should help to explain the characteristic behavior of their members, but deny that natural kinds are linked conceptually with either laws of nature or final causes. 11. Hacking, “Natural Kinds: Rosy Dawn, Scholastic Twilight,” 203–39.

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changes in virtue of its accidental attributes and yet remains numerically identical in virtue of its unchanging nature nx ; and these variations and this invariance are both real. It follows that the distinction between what is essential and what is accidental in x cannot depend on the way in which we regard it, nor can it be a mere distinction of reason.12 Nor on the other hand can it be a real distinction (distinctio realis) in the traditional sense, as what varies and what is invariant in x cannot exist apart from each other. It follows that metaphysical essence statements of the form “x is nx” (“Socrates is his soul,” “water is H2O”) are to be distinguished not only from protometaphysical essence statements (“This garrulous old man is Socrates,” “Hesperus is Venus”), but also from numerical identity statements (“Hesperus is Phosphorus,” “This garrulous old man is the one Athenians put on trial for impiety and corrupting the youth”) and ordinary predicative statements (“Socrates is snub-nosed,” “Water is tasteless”). Nor, finally, is the intrinsic nature or essence of a continuant x to be identified with the attributes x has necessarily; for necessary attributes belong to the how rather than the what; and what something is, its essence, cannot be an attribute of x, even though we must speak of it as it were. The being of a continuant, we see, is not easy to articulate.13 To further elucidate the concept of a continuant, I noted that continuant-like material objects are involved in the world metabolically, inasmuch as they are ever-changing; compositionally, inasmuch as they have parts; and situationally, inasmuch as they depend on their surroundings for their continued existence. Of such involvement there are three possible grades. Grade I: the object is intrinsically invariant, individual, independent, and only extrinsically varying, “dividual,” dependent. Grade II: the object is intrinsically both invariant and varying, 12. Compare, e.g., W. v. O. Quine, Word and Object (Cambridge, Mass.: MIT Press, 1960), 199, and “Reference and Modality,” in his From a Logical Point of View (Cambridge, Mass.: Harvard University Press, 1961), 139–59. 13. Umphrey, Natural Kinds and Genesis, chap. 4.3.

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individual and dividual, independent and dependent. Grade III: the object is intrinsically varying, dividual, and dependent, only extrinsically invariant, individual, and independent. The worldly involvement of immanent universals and Leibnizian monads is grade I; of Cartesian bodies and many physical systems, grade III; of genuine continuants, grade II. Grade II entities are beings-in-becoming. It appears that every being-in-becoming is a continuant, and that every continuant is compositionally and situationally as well as metabolically grade II. To understand such entities proves difficult; one tends to reduce them to grade III objects (as Descartes seems to have done in his account of material things), or to grade I unities (as Leibniz almost did in his monadology), or else to regard grade II itself as grade I plus grade III (as Aristotle seems to have done when he analyzed every entity constituted by nature into a combination of form and matter).14 On the basis of these partial elucidations, I offered the following answer to our first question: A natural kind is a type whose tokens are all and only those continuants which exemplify it in virtue of their natures or essences, and which constitute therefore a single natural class. Alternatively, a natural kind is a class whose members are all and only those continuants which exemplify, in virtue of their natures or essences, a single type. The second formulation is preferable to the first, inasmuch as such classes are natural, whereas the types their members exemplify are universals and universals as such are transnatural. Natural kinds are, first of all, classes of resembling continuants. And continuants are members of a natural kind just in case they closely resemble one another in virtue of their essences, their what rather than their how. In other words, the requisite resemblance relation is between substances as such, rather than their attributes. Natural kinds are, first of all, s-resemblance classes whose members are individual continuants.15 14. Ibid., chap. 4.4. 15. Ibid., chap. 5.1.

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We now see how natural-kinds realism entails essentialism. A class is a natural kind only if its members are continuants, and something is a continuant only if it has an essence; only if it is a grade II and not a grade III object; only if there is some identifiable or substantial there there. It follows that natural kinds, unlike abstract sets, may gain or lose members and yet remain numerically the same. A natural-kind class, like any of its members, is invariant in its variations, as long as it exists; and it exists as long as there is at least one continuant x which exemplifies the corresponding natural-kind type in virtue of its essence or nature nx .16 My answer to our first question seems unduly restrictive. May there not be natural kinds of stuff such as water? Yes, but these would not be natural kinds in the primary sense, for the following reason. The mass-type water is multiply exemplifiable only in the sense that its tokens are numerically diverse portions of one and the same entitative stuff, not in the sense that they are diverse entities.17 It may seem to follow that the natural kind water is really a singleton class whose sole member is one of a kind. But this too is not accurate, for mass terms as such have no plural forms and hence no genuine singular forms either; they do not designate objects.18 Therefore, strictly speaking, water does not constitute a singleton class. Nor is it a class having two or more continuants as members in virtue of their natures. 16. Cf. Monte Cook, “If ‘Cat’ Is a Rigid Designator, What Does It Designate?,” Philosophical Studies 37 (1980): 61–64. In Aristotle’s metaphysics, the link between natural-kinds realism and essentialism is clear. It is also clear in the writings of Kripke and his followers. Early Millians and Mill himself were not essentialists, I suggest, because their empiricistic tendencies made it difficult for them to distinguish grade II from grade III material objects. 17. Call all the gold in the world G1. Suppose G1 perishes, and then, at some later date, some gold (G2) comes into being. If G1 and G2 were individuals, it would be reasonable to ask whether they are one continuant or two: cf. the case of Lazarus and Lazarus* in Umphrey, Natural Kinds and Genesis, chap. 4.5. As gold is presumably a mass, G1 and G2 are nothing more than spatiotemporally scattered portions of one and the same continuant. 18. Henry Laycock, Words without Objects (Oxford: Clarendon Press, 2006), and Dean Zimmerman, “Theories of Masses and Problems of Constitution,” The Philosophical Review 104 (1995): 53–110.

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It is not a natural-kind class at all. Yet it is sufficiently like exemplary natural-kind classes that it would be more illuminating than not to classify it as one. The same may be true of the class of red dwarf stars, and perhaps even the class of natural kinds. But all these applications of the concept would be secondary, derivative, by analogical extension; they are not natural kinds in the primary sense of the term.19 Having thus declared what a natural kind is, I turned to our second, more empirical question: Are there any natural kinds? There are only if there are genuine continuants. Yet so difficult is it to recognize the nature or essence of a given material thing x—that in virtue of which it is invariant in its variations, individual in its dividuality, and independent in its situational dependence—that antirealism with respect to continuants is a plausible philosophical position. I argued nevertheless for tentative acceptance of continuant realism with respect to some if not all living organisms.20 The question, then, was whether these supposed continuants form disjoint classes in virtue of their intrinsic natures. Apparently they do not, but it does not follow that there are no natural kinds at all. To answer our empirical question, I suggested, we should put aside our everyday understanding of things, and make use of scientific theories.21 To this end, I examined theories in physics, chemistry, and biology. In fundamental physics, the only entities are quantum fields (supposing there are several of them), and quantum fields are best understood not as continuants (“endurants”), but as four-dimensional occurrents (“perdurants”). There are also field quanta, indefinitely many of them, but their situational involvement in the fields to which they belong is grade III. Hence, if continuants and their kinds exist, they must be emergent entities; they must have come into being. To identify which continuants are admitted in natural science, one 19. Umphrey, Natural Kinds and Genesis, chap. 5.1. 20. Ibid., chap. 4.7. 21. Ibid., chap. 5.3–4.

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must turn to the special sciences. Here we found putative continuants of several sorts: in biology, living organisms; in chemistry, individual molecules and atoms; and in particle physics, perhaps some hadrons (e.g., the quark-composites called “free protons”). Living organisms and single molecules, atoms, protons, and the like are all thought to be continuants. All of them appear to have emerged within the cellular, molecular, atomic, subatomic, or quantum-theoretical situations on which they depend. One can order these particulars in the following way: free protons depend directly on field quanta; atoms, on subatomic particles; molecules, on atoms; primitive biota, on abiotic molecules; multicellular organisms, on diverse populations of living cells. We may order the natural sciences accordingly: physics at the bottom, then chemistry, then biology. Natural science thus resembles a layer-cake whose different levels are explained in part by the heterogeneity of the subject matter proper to each layer.22 As we descend from ethology to quantum field theory it becomes more and more difficult to argue that the particulars we find at a given level are genuine individuals: organisms, yes; atoms, maybe; field quanta, no. And as we ascend from fundamental physics to biology, it becomes more and more difficult to argue that the lawlike statements we find are expressions of genuine laws of nature in the primary sense of the term: E = mc2, yes; chemical reaction equations, maybe; Dollo’s Law, no. It also becomes more difficult to argue that tokens of sortal types fall neatly into disjoint classes: protons and atoms, yes; macromolecules, perhaps; living organisms, no. For us this constitutes a dilemma: exemplary individuals do not form well defined kinds, and well defined kinds do not have exemplary individuals as members. 22. The different “levels” may not stack up in a unique way. In string theory, for some specific theory T there may be an equivalent theory T* such that objects regarded as simple in T are regarded as composite in T* and vice versa. So, for instance, in one theory quarks are simple and solitons (monopoles) are quark-composites, whereas in the “dual” of this theory solitons are simple and quarks are soliton-composites.

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Working against this layer-cake picture are the reductionist tendencies in natural science. Biologists tend to regard living things as nothing more than systems of cells or molecules; chemists, to regard molecules as nothing more than systems of atoms or subatomic particles; particle physicists, to regard elementary particles as nothing more than normal states of quantum fields. This tendency and the widespread opposition to it have given rise to the following dilemma: we either embrace the idea of a grand theory of everything and give up the idea that some continuant-like objects are genuine continuants or else embrace the idea that there are genuine continuants and give up the idea that a grand theory of everything will be a theory of every thing.23 Scientific theory, I concluded, does not make it easy to decide that there are, or are not, natural kinds in the primary sense of the term. I made the following suggestion: There are genuine continuants only if, in the history of the universe, substantive emergence (genesis) has occurred; and substantive emergence has occurred, if at all, in the course of what scientists call “symmetry-breaking events.” Therefore, if one decides, as I have, that there are genuine continuants, one must agree that they have come into being, that substantive emergence has indeed occurred as the universe expands and cools. The task, then, is to discover whether there exist any singular things which arguably are such that (1) the concept of a continuant applies to them and (2) they constitute well defined s-resemblance classes. And the place to begin looking for such things is in theoretical chemistry. It can be argued that the class of H2O molecules is a natural kind, provided these molecules are free, and provided their atomic constituents are not different forms of H and O. This is not a class in which chemists have any interest: it is 23. Cf. P. W. Anderson, “More is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science,” Science 177 (1972): 393–96, and R. B. Laughlin and D. Pines, “The Theory of Everything,” Proceedings of the National Academy of Sciences 97 (2000): 28–31. Both are reprinted in Emergence, ed. A. A. Bedau and P. Humphreys (Cambridge, Mass.: MIT Press, 2008).

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not an exemplary chemical kind. Chemists however would acknowledge the existence of such a class, and probably agree that its members resemble one another very closely in virtue of their structural natures.24 This completes my review. I now offer a few words about the present volume.

PREVIEW As Wilfrid Sellars once wrote, “The history of philosophy is the lingua franca which makes communication between philosophers, at least of different points of view, possible. Philosophy without the history of philosophy, if not empty or blind, is at least dumb.”25 Moreover, by using philosophical traditions as heuristic guides, one can expand one’s horizons and better view the presuppositions buried in present-day doctrines, including one’s own. In particular, by considering the emergence of Aristotelian natural-kinds realism and its eventual demise, we shall open ourselves up to philosophical points of view quite unlike our own, and better understand the philosophical milieu within which today’s natural-kinds realism and antirealism have emerged. But this book is not so much a detailed history of the Aristotelian tradition of natural kinds as it is a series of soundings, or excavations, which together reveal in outline the full story yet to be told. Readers will note that my treatment of medieval Aristotelianism, in particular, is hardly a full account of the different ways in which philosophers then modified, while still preserving, Aristotle’s conception of natural substances and their species. My account resembles a sketch of a story that is hard to tell because it involves so many characters whose intentions are often far from clear. I invite readers to try filling in the 24. Umphrey, Natural Kinds and Genesis, chaps. 6.2 and 7.4. 25. Wilfred Sellars, Science and Metaphysics: Variations on Kantian Themes (New York: Humanities Press, 1968), 1.

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gaps and otherwise improving the somewhat potted account I am about to give. My approach, though not as thoroughgoing as some might like, will serve nevertheless to reveal three things of great importance to us as natural philosophers, things which Aristotle scholars and philosophers of science, among others, are liable to overlook or downplay in their attention to details. In the event these things prove insufficiently conspicuous even in my account, I highlight them here. First, no philosophical claim concerning natural kinds occurs in a historical vacuum. Two examples: (1) Aristotle renewed pre-Socratic natural philosophy in the light of Socrates’s turn to invariant forms and their definitions, together with the Socratic-Platonic insistence that we pay close attention to what is first for us. His natural-kinds realism combines, as it were, a quasi-Platonic realism with respect to (in rebus) universals with a quasi-Empedoclean realism with respect to those naturally constituted entities which remain (eidetically) invariant in their many variations, as long as they exist. (2) William of Ockham undertook to preserve Aristotelian logic and physics, the true via antiqua, by purging them of what he took to be their Scholastic accretions. In doing so, however, he emphasized antirealism with respect to all species as types, and maintained that every distinction is a distinction realis, thereby doing away with the key distinction between a material individual x and its specifiable essence or nature nx . Thus did he inadvertently pave the way for the demise of Aristotelian natural-kinds realism with the advent of Galilean science, arguably the true via moderna. Second, there have been two major revolutions, two Kuhnian “paradigm shifts” in the history of natural philosophy. One was made by Aristotle when he replaced pre-Socratic outlooks with his bio-centric and eido-centric conception of the natural order: see chapter 3, where I describe his focus on invariant forms or essences in varying material things. The other was made by Galileo and other seventeenth-century

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natural philosophers, when they replaced Aristotle’s outlook with their nomo-centric and mechano-centric conception of the natural order: see chapter 5, where I describe their focus on invariant functional relations among physical quantities or events. The Galilean outlook remains predominant today; and, as we shall see, it is no more hospitable to natural-kinds realism than was pre-Socratic natural philosophy. Third, natural philosophy has always been subject to crisis. I will describe four such crises, whose prime movers were Parmenides, Socrates, Scholastic theologians, and Kant. (1) According to Parmenides, being is one, indivisible, ungenerable, immovable, and absolutely independent. Things natural on the other hand are mere seemings, not real at all, and efforts to understand them are doomed to failure from the outset: natural science is a rational-seeming expression of delirium. (2) According to Plato’s Socrates, the investigation of nature is a distraction from the more important work of trying to understand the beautiful, the just, the good, and the like. In trying to understand such “forms,” moreover, one should focus on what each is, and not on how it becomes present in or to us. The proper study of man is the forms (being), our soul, and the broadly political setting within which alone such studies can be made. Investigations of nature that do not take place within this framework are bound to go astray. (3) According to some medieval Schoolmen, natural philosophy must subordinate itself above all to the authority of church doctrine, and secondarily to the authority of Aristotle’s physics. So, for example, because creationism is true according to church doctrine, no philosopher should think otherwise; and because the world is hierarchically ordered according to Aristotle, no natural philosopher should think otherwise. Nothing good can come from investigating nature directly, without a safety net, or from using Aristotelian and church doctrines as heuristic guides only, not also as final authorities. (4) According to Kant, Newtonian physics can be put on a solid foundation only if we suppose that nature itself is empirically real but transcendentally ideal. And because the study

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of empirical reality is the province of natural science, natural philosophy has no independent role to play; it must subordinate itself to the authority of scientific theory. Although Kant’s transcendental idealism is no longer widely espoused, the twofold challenge he posed lives on, having metamorphosed into the two mutually independent doctrines I call “protometaphysical antirealism” and “philosophical naturalism.” Renewing natural philosophy in the face of this double threat is both desirable and difficult. In Natural Kinds and Genesis and The Aristotelian Tradition of Natural Kinds and Its Demise my aim has been to pave the way for such a renewal.

CHAPTER 1

Origin of the Idea of Natural Kinds

The first natural-kinds realist appears to have been Aristotle; and Plato, his teacher, appears to have been the first to reject natural-kinds realism in full awareness that he was doing so. Neither Aristotle nor Plato thought in a philosophical or cultural vacuum. The milieu within which they thought and wrote included the songs of Homer and Hesiod, as well as the writings of the pre-Socratic philosophers. To what extent did natural kinds become a theme for these philosophical and prephilosophical predecessors? To answer this question is my aim in this chapter.

EARLY GREEK POETRY Homer and Hesiod were the fathers of ancient Greek sophia.1 Even the first philosophers, who openly rejected this wisdom, tacitly relied on it, so much so in fact that what they assert can be little understood apart from what they reject. 1. Plato, Lysis 214a1–2.

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ORIGIN OF THE IDEA ORIGIN OF THE IDEA

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The songs of Homer and Hesiod mention kinds of various sorts. To designate humankind they used the noun anthrôpos (human), always in the plural and often in the same breath with theoi (gods). To designate kinds more generally they used three words: ethnos (band, herd, flock, swarm), phulon (tribe, race, stock), and genos (race, stock, family).2 There is an ethnos of concubines, another of Achaeans, the people, or waterfowl; and ethnea of comrades, young men, young pigs, or the dead. There is the phulon to which Helen belongs, another of professional singers, women, gods, human beings, or dreams; and phula of auxiliaries, gods, human beings, giants, or savage flies. There is a genos of Cretans, another of men, gods, human beings, cattle, or gray flint, and a double genos of strifes.3 The members a kind are continuant-like things, never events or inanimate artifacts, and the kinds themselves are extensions taken collectively, never universals or shared essences.4 The genos of gods is heterogeneous, as is the genos of humans.5 Foremost among them, however, are the Olympian gods and humans here and now. The former ingest ambrosia and nectar. Instead of blood 2. See Homer, Iliad 2.87, 2.91, 2.362, 3.32, 4.58, 5.441, 7.115, 9.130, 13.165, 13.495, 14.361, 15.54, 15.691, 17.442, 17.552, 19.30, Odyssey 3.245, 3.282, 7.307, 8.481, 10.526, 11.34, 14.68, 14.73, 16.401; Hesiod, Theogony 21, 33, 44, 161, 212, 336, 590, Works and Days 12, 90, 110, Shield of Heracles 3, 163; also the Homeric Hymn to Demeter 35, 310, 352, Hymn to Apollo 470, Hymn to Hermes 309, Hymn to Helios 18. Of these three terms, genos occurs most frequently, ethnos the least. Whereas Homer often uses phulon in the plural, Hesiod tends to use it in the singular. Both tend to use genos in the singular. And both use adjectives to specify such kinds: the savage phula of flies, the sacred genos of gods, etc. 3. Cf. Homer, Iliad 1.3, 1.290, 1.339, 1.494, 2.447, 2.641, 3.182, 5.340, 5.870, 6.170, 7.446, 11.68, 18.61, 24.99, Odyssey 1.143, 1.263, 1.373, 5.7, 5.136, 5.197, 5.306, 6.154, 6.287, 8.306, 8.365, 12.371, 12.377, 15.433, 23.336; and Hesiod, Theogony 21, 33, 277, 305, 949, Works and Days 11–13, 141, 549, 718, Shield 79. 4. Some have argued that Homer’s Iliad begins by admitting a real property, namely, wrath (mênis). But there is no evidence he took it to be a universal, and not just a characteristic proper to Achilles. 5. Gods: Homer, Iliad 6.180, 14.199, 14.231, 14.259, and Hesiod, Theogony 116, 123, 217, 337, 756. Humans: Homer, Odyssey 9.106, 10.80–132, and Hesiod, Theogony 44, 50, 590, Works and Days 109.

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like ours, they have ichor. Evidently they have no souls (psuchai), and live forever without growing old. Often they are called “blessed.” Humans on the other hand ingest meat, bread, and wine. They all have souls, grow old and die, after which they are said to be no longer. Only rarely and by analogy are a few of them called “blessed.” Humans are naturally mortal, it seems, whereas gods are immortal and ageless: the presence or absence of soul makes almost all the difference in the world.6 But when a human loses his life (psuchê) and becomes a corpse, his soul does not then cease to be; rather, it comes into its own and endures forever.7 Mortal and immortal are polar opposites—as are male and female, right and left, light and dark, east and west, sky and earth—and yet, partly for this reason, Olympians and humans form a pair.8 They converse, have similar shapes, interlocking aims, and sometimes form alliances. Both live on or near the surface of the earth. Both fall under the sway of eros, sleep, night, and fate. And it is in war, above all, that both sides come together in their differences and acknowledge Zeus as father of gods and men.9 But their commonality goes deeper than this. For not only are some men godlike or divine, mortals and immortals are also said to mingle in love and produce offspring.10 More importantly still, Olympian gods and human beings have come to be, perhaps from the same remote ancestor.11 The relationship 6. Cf. Homer, Iliad 1.3, 1.290, 1.339, 1.494, 2.447, 2.641, 3.182, 5.340, 5.870, 6.170, 7.446, 11.68, 18.61, 24.99, Odyssey 1.143, 1.263, 1.373, 5.7, 5.136, 5.197, 5.306, 6.154, 6.287, 8.306, 8.365, 12.371, 12.377, 15.433, 23.336; and Hesiod, Theogony 21, 33, 277, 305, 949, Works and Days 141, 549, 718, Shield 79. Cf. M. L. West, Indo-European Poetry and Myth (New York: Oxford University Press, 2007), 124–34. 7. Cf. Homer, Iliad 23.102 with 1.3, 7.79, 7.84, 16.62, 21.264, 21.379, and Odyssey 11.490. 8. Cf. G. E. R. Lloyd, Polarity and Analogy (New York: Cambridge University Press, 1966), 26–48. 9. See especially Homer, Iliad 12.94, 14.231, 14.258, 14.294, 18.516, 20.7. In Hesiod’s Works and Days, Zeus is the giver of justice in our political age (227–40). 10. Usually their progeny are mortal: the one-drop rule holds as a rule. Cf. Homer, Iliad 19.105, 19.111, 20.232–35, Odyssey 5.136, 5.209, 11.601–4, and Hesiod, Theogony 277, 940–69. 11. Cf. Pindar, Nemean Odes 6.5. Compare Hesiod, Works and Days 110, 127, 144, 169, and see below, notes 14 and 15.



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between kind and origin is evident in the word genos, which means both “kind” and “birth” or “source.” When Hera tells Zeus that notwithstanding their difference in rank they are of the same genos, she is declaring not only their membership in the same class but their common ancestry. The Olympians are one in kind not only because they are other-than-mortal but because they are akin. A genos is a kinship group.12 Whence did these gods come to be? An answer can be found in book 14 of the Iliad, where, during an erotic interlude in which Hera briefly gets the better of Zeus, the Muse digresses to say that Ocean and Tethys are the origin (genesis) of all immortals. Tethys is a rarely mentioned water-goddess, Ocean the all-encompassing river. Both are non-Olympian. The genos of gods, then, has its origin in this ambient perpetual flow. What is first for us is not first in generation.13 A similar answer can be found in Hesiod’s Theogony. There, in response to our question, the Muses speaking through the poet declare that Chasm (Khaos) first of all came to be, followed by other dark divinities; only later did the generations of humans and Olympians appear. On this account, the various kinds of things depend ultimately on the emergence of some pregnant emptiness without gender or form. Once again, all real differences in kind are derivative.14 Later in Hesiod’s Theogony, the Muses give an alternative account. Having paused to describe a prison for immortals, they digress to declare the world as a whole. Deep down there is a great chasm, they say, whence grow the roots of earth and unfruitful sea. There lie the sources and limits of Earth, Tartarus, Sea, and Heaven, the four divine 12. Homer, Iliad 4.58; see also 6.58, 21.186, Odyssey 1.216, 17.373, and Hesiod, Theogony 21, 336, 869. The cognate words geneê, genethlê, gonê, and gonos are all similarly ambiguous. On the genos of gray flint (Theogony 161), cf. Iliad 2.857 and M. L. West’s commentary in his Hesiod: Theogony (Oxford: Clarendon Press, 1966), 215. 13. Homer, Iliad 14.201, 14.246, 14.302, 18.607; cf. Hesiod, Theogony 335, 518. The origin of humans is unclear; cf. Homer, Iliad 22.146, Odyssey 19.162; Hesiod, Theogony 35, 185–87, 277, 522–52, 563, 590. 14. Hesiod, Theogony 116. Compare Aristophanes, Birds 690–94.

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world-masses or places.15 This account is topographical rather than genealogical, and put in terms of being rather than becoming. Which are we to accept?16 But let us not exaggerate the differences between them. The verb einai (“to be”) has vital and locative senses, and in epic poetry these predominate: to be is first of all to be alive and present, whereas to be no longer is to be dead and gone.17 Homer and Hesiod do not distinguish being from becoming. The gods, who are forever, are forever becoming.18 Humans are ephemeral. The difference between these kinds is a difference between two modes of becoming. Homer and Hesiod make no reference to anything not in space or time, and Homer in particular suggests that nothing is truly everlasting, unless it be the very flow of things together with a certain fatefulness. Common to these origination accounts are two difficulties. First, each posits as the ultimate source (archê) of things either a first beginning or a lowest place. But whence did Chasm or Ocean come to be? What lies below the lowest place? Where in the world could the source of the world be? These three “archaeologies” prompt such questions but do not answer them. Second, Homer and Hesiod present two very different views of the world. In one, there is the genos of humans and the genos of Olympians, their significant others. It is a world full of clarity and light. There are marriages, cities and war, beautiful forms, virtue and vice, the Muses and the poets. Here the Olympian gods rule. In the other view, this world-order is but a recent flowering or gloss. The well-formed depends on the formless, 15. Theogony 721–819, esp. 728, 736–39, 807–10; also Iliad 8.15, 8.479. 16. The Muses warned Hesiod that they were capable of giving two accounts—one true, the other only seemingly true (Theogony 27). We wonder whether their double origination account is a demonstration of this. 17. Cf. Charles Kahn, The Verb BE in Ancient Greek (Boston: Reidel, 1973), esp. 233–45. 18. Homer, Iliad 2.400, 3.296, 6.527, 7.53, 14.244, 14.333, 16.93, 20.104, Odyssey 2.432, 14.446, 23.8, 24.373; Hesiod, Theogony 548, 893, 993. See also Hymn to Demeter 36, 322. In these poems the word aieigenetês (“forever becoming”) is used only in the plural and only of gods. Note also the verb pelô (used interchangeably with eimi), which means “turn out,” “happen,” or “come to be,” as well as “be.”



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darkness is prior to light, and in that darkness there is no clarity, no beauty, but rather something so monstrous that even gods shudder to look upon it.19 Is the real world the one in which the Olympians have limited rule, or the one in which they are wholly derivative with respect to time or place?20 The one in which there are stable kinds (genea) or the one in which there are not? The Muses focus on the world of clarity and light, the beautiful foreground of things, but in these archaeological asides they make the background prior to the foreground. To get at the reality of things we must uncover their hidden sources or roots; and yet in turning from genos to genesis we must not lose sight of the variegated surface of things here and now. No homecoming could be more difficult. The word genesis is formed from the verb gignesthai (“to become”). The –sis ending makes it a process noun. Process nouns are rare in early epic poetry. The word genesis occurs only three times, all in Homer’s Iliad 14; and the word phusis, from phuein or phuesthai (“to sprout forth or grow”), occurs just once, in Homer’s Odyssey 10. There, Odysseus was on his way to Circe’s place when Hermes intervened to show him the phusis of a plant. It was black in its root and white in its flower, and had the power to make one immune to Circean bewitchment.21 In this context, as often in later Greek, the word phusis refers not to the growing or nascence of a natural thing but to its inner nature; it is not being used as a process noun. Was its verbal root then forgotten? Homeric men are often described in terms of their physique (phuê) as well as their form (eidos).22 One warrior, Glaucus, links mortals with plants (phuta) when he says to Diomedes: “As are the generations of leaves 19. Theogony 738, 744, 810. See also Iliad 20.65. 20. It is by no means clear that they will rule forever: consider Aeschylus, Prometheus Bound. Even now the power of Zeus is limited: he cannot master fate, he can be seduced, and when he commands all gods to assemble, Ocean does not obey (Iliad 20.7). 21. Odyssey 10.303. 22. Iliad 1.115, 1.58, 3.208, 22.370, Odyssey 5.209, 5.212, 6.16, 6.152, 7.210, 8.134. The word phua occurs nine times in Pindar’s odes, where it means “natural ability” or “talent.”

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[geneê phullôn], so are those of men. The wind scatters some leaves upon the earth, but the burgeoning wood puts forth [phuei] others. . . . Even so does one generation of men spring up [phuei] while another passes away.”23 The plant’s phusis, I suggest, is its nature as something that has come into being, and can no more be understood apart from that process than a genos can be understood apart from its genesis.24 The nature of the plant is described in terms of polar opposites. The task is to see light and dark, flower and root together as one, and to do so one must see the whole plant, including the part that usually remains invisible. Hermes already knows its nature, though not because he made it: the nature of a thing is not an artifact of any kind. Humans come to know it only rarely and with difficulty. One reason, perhaps, is that moly, as the gods call it, contains a drug that enables us to keep our mind together with our human form, something few of us need while we are alive. Yet mortals seem oblivious to the natures of things generally, perhaps because they identify wisdom with the knowledge of things past, present, and future—the province of inspired poets and seers. To see the nature of a thing, one must look beyond the course of events. What Hermes showed Odysseus on the path to Circe is not the sort of thing a seer declares.25 Early Greek poets have some idea of kinds, and Homer at any rate has some idea of nature, yet they seem unaware of natural kinds as such. They do not understand ethnea, genea, or phula in relation to the natures of their members. They show no interest in the distinc23. Iliad 6.146–49. 24. Cf. Émile Benveniste, Noms d’Agent et noms d’action en indo-européen (Paris: Adrien Maissonneuve, 1948), 78–80; David Daube, Roman Law: Linguistic, Social and Philosophical Aspects (Edinburgh: Edinburgh University Press, 1969), 59–61; Charles Kahn, Anaximander and the Origins of Greek Cosmology (New York: Columbia University Press, 1960), 201; G. S. Kirk, Heraclitus: The Cosmic Fragments (New York: Cambridge University Press, 1970), 227–31. The verb phuô occurs throughout epic poetry, usually but not exclusively of plants. Cognate words include autophuês (self-growing), phusizoos (life-giving), as well as phullon (leaf), phuton (plant), phulon (tribe), and phuê (bodily form, physique). 25. Cf. Iliad 1.70–72, 2.119, Odyssey 8.579, 12.190. Cf. Theogony 32–38.



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tion between classes and lineages, or between kinds that are natural and kinds that are not. Concubines, professional singers, Cretans, women, human beings, wildfowl: these are all kinds. To us, they are also a hodge-podge; we want to sort them out into the natural and the merely conventional. But while Homer and Hesiod might have agreed that some such distinction can be made, it is not one they see any need to make. It is as if the disparity between what is natural and what is not has been flattened out in their poetry. This impression is confirmed by considering Homer’s use of the words dikê and themis. There is, he says, the way (dikê) of kings, mortals, female slaves, suitors, gods, or old men, and the established way (themis) of women, men and women, human beings, or strangers.26 Again we find no attempt to distinguish ways that are merely customary from ways that are not. This does not mean that Homer put them all on a par. In the Odyssey, whereas the conduct of the Olympians is beyond reproach, that of the suitors is perverse; it belongs to an inverted world which Odysseus aims to set right with Athena’s help. Yet there is no evidence that while sorting out and ranking such ways, Homer had in mind the distinction between natural and unnatural.27 I conclude that the idea of natural kinds did not originate with Homer or Hesiod. To find its origin, we turn to the philosophers who first sprang up in opposition to them. 26. Homer, Iliad 9.134, 9.276, 14.386, 19.177, Odyssey 4.691, 9.268, 11.218, 14.59, 14.130, 18.275, 19.43, 24.255. See also Hymn to Apollo 458, 541, and Hesiod, Works and Days 275. 27. Pindar and Aeschylus, too, “fail” to distinguish natural ways from mores. Something may behave in the way (dikên) of a wolf, a dog, a man, a Persian, a diver, the moon, dreams, a child, a swallow, a young wife, a swelling wave, a driven ox, a swan, sailors, a messenger, or a fawn (e.g., Pindar, Pythian Odes 2.84, and Aeschylus, Suppliant Maidens 409, Agamemnon 3, 233, 297, 491, 724, 920, 979, 1050, 1093, 1180, 1182, 1298, 1444, Libation Bearers 195, 202, Eumenides 111). They also admit “genera” and “phyla”—familial, political, national, mortal, and divine—most of them kinship groups of one sort or another, but show no interest in sorting out those kinship relations which determine natural groups from those which do not. Cf., e.g., Pindar, Isthmian Odes 1.30, Nemean Odes 6.1, 10.38, 10.54, Olympic Odes 6.25, 6.71, 13.58, Pythian Odes 4.52, 4.58, 4.256, 5.125, 9.14, 12.3; and Aeschylus, Suppliant Maidens 155, 544, Seven against Thebes 188, 236, 256, 604, 654, 691, 833, Agamemnon 1566, Eumenides 912, Prometheus Bound 232, 549.

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EARLY IONIAN PHILOSOPHY Under this heading I put the work of Thales, Anaximander, Anaximenes, Heraclitus, and Xenophanes.28 They were called philosophoi, phusiologoi (those who discourse about nature), or phusikoi (natural philosophers), and their writings were said to be peri phuseôs (about nature).29 Did Thales and the rest accept these designations? No one today knows.30 It seems reasonable, however, to regard them as natural philosophers. Take Heraclitus. Scholars agree that much of his book has survived, and in the bits of it we have the word phusis occurs more often than in all of archaic poetry put together. He claims moreover to distinguish each thing according to its nature and declare how it is.31 The other Ionian philosophers shared this aim. And unlike poets and seers, they did not seek divine assistance when trying to declare things: most of them wrote prose, in the extant fragments of which no Muse is ever invoked; and though preferring to write verse, usually in epic meter, Xenophanes too was pushing off from Homer when he said, “Indeed not from the beginning did gods show all things to mortals, but in time those who search find out better.”32 Ionian natural philosophers were intent on finding out for themselves what Odysseus needed Hermes to see. Appeals to authority have no place in their thinking. 28. Though Xenophanes lived much of his life in Italy, and his theology sets him apart from the others mentioned in this list, some of his fragments are “Ionian” and it is on these fragments that I focus here. 29. Aristotle, Physics 184b17, 187a12, 205a5, Metaphysics 986b14, 988b27, 990a3, 1005a34, On the Soul 403a25, 406b26, 426a2, Parts of Animals 641a7, a21, and Plato, Lysis 214b4–5, Phaedo 96a8. Also E. Schmalzriedt, Peri Phuseos: Zur Frühgeschichte der Buchtitel (Munich: Fink, 1970). 30. Heraclitus B35. Cf. W. Burkert, “Platon oder Pythagoras? Zum Ursprung des Wortes ‘Philosophie,’ ” Hermes 88 (1969): 159–77. Cf. Diogenes Laertius, Proemium 12 and VIII, 8. 31. Heraclitus B1, B106, B112, B123. 32. Xenophanes B36.



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To grasp what they were thinking, consider the following Xenophanean fragment: What they call “Iris,” this too is naturally [a] cloud, Purple and crimson and yellow to look at.33

Assertions of this sort were not entirely new. In Iliad 6 Diomedes encounters a worthy opponent and asks, “Who are (essi) you among mortal human beings?” To which the other replies that he is Glaucus, son of Hippolochus, from Lycia.34 “I am Glaucus” and “Iris is a cloud” are protometaphysical essence statements: they assert that this object before you in perception or thought esti (is) the entity e.35 Xenophanes’s statement, of course, is the more surprising. Many no doubt rejected it. Yet from the poets, as well as their own experience, ancient Greeks knew that appearances sometimes deceive. Olympian gods were the most beautiful of deceivers, as Homer had made clear in poetry that was expressly musical, which is to say, of the Muses. For instance, in Odyssey 19, Odysseus enters his own house, having disguised himself as a beggar with Athena’s help. No one recognizes him until an old nurse notices an old scar. “You are (essi) Odysseus,” she says, lifting her hand to his chin, “I did not recognize (egnôn) you until I had touched my lord all over.”36 In Iliad 3, having plucked Alexander from the battlefield and returned him to where he belongs, Aphrodite went in the likeness of an old maid to summon Helen. But Helen saw through (enoêse) the mortal appearance and balked, afraid that Aphrodite was again leading her astray.37 Protometaphysical essence statements can express discoveries, and when they do we may 33. Xenophanes B32. Cf. Anaxagoras B19. 34. Homer, Iliad 6.123–211. It was customary to identify oneself by name and geographical or genealogical origin. Diomedes knows that Glaucus is mortal because Athena has removed from his eyes a mist, thereby enabling him to recognize (eu gignôskein) who is a god and who is not: Iliad 5.126, 20.130, 20.205. 35. Cf. Umphrey, Natural Kinds and Genesis, chap. 4.2. 36. Homer, Odyssey 19.392, 19.468, 19.475. 37. Homer, Iliad 3.396.

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call them “recognitional” or “noetic.”38 That this beggar is lord Odysseus and that old woman really Aphrodite are good examples. So too is Xenophanes’s assertion that what poets and others call “Iris” or “Rainbow” is really a cloud. Yet it differs from its Homeric antecedents in two respects. First, the verb is not esti but pephuke, a perfect form of phuô: the philosopher is focusing on something natural apart from its enchanting aura. Second, the discovery it expresses is deflationary; it reduces an awe-inspiring presence to something altogether mundane albeit wondrous to look at, whereas its poetic counterparts turn something apparently lowly into a lordly agent. Modern-day reductionism has its remote ancestor here. To get a better idea of what early Ionian philosophers were thinking, consider these Heraclitean fragments: “Having listened not to me but to the logos it is wise to agree that all things are one,” and “This world-order (kosmos), the same for all, neither god nor human made, but it always was and is and will be, everliving fire, kindling itself in measures and extinguishing itself in measures.”39 The first is a statement of holistic monism: all things are so interrelated that together they are one rather than many. The second is three statements in one: (1) This kosmos is no artifact, (2) it did not come into being and will never perish, and (3) it is everliving fire. The third is a nature statement: it declares the nature of the world-order without denying the reality of this order. That it is not a protometaphysical essence statement becomes clearer still when one considers fragments in which Heraclitus describes the strife-filled attunement (harmoniê) of things.40 Attunement requires things attuned and strife requires that the differences among them be real. Though real, however, these things are not enduring entities, or continuants; Heraclitus calls them 38. Mourelatos calls them “speculative”: Route of Parmenides, 57–61. 39. Heraclitus B50, B30. 40. Heraclitus B8, B51, B53, B54, B76, B80, B90. Only one Heraclitean fragment, B67, suggests that (3) is a protometaphysical essence statement.



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gignomena (“becomings,” “processes”).41 They are, I suggest, dynamic modes of the stuff or process he calls “everliving fire,” kindling and extinguishing itself in measures. The others made comparable nature statements: that all things are water (Thales), or mist (Anaximenes), or the indefinite (Anaximander).42 Not one of them seems to have argued that his nature statement is true, or helped his readers to understand what it is to be a nature statement; they spoke from on high to no one in particular, leaving the rest of us to our own devices. Yet we can safely make a few remarks about their teachings generally. First, they are comprehensive: all things are X. They resemble, in this respect, the three archaeologies found in the Iliad and the Theogony. But while X, the archê, may still be called ageless and divine, it is not the oldest or most fundamental deity; what things are is not first in time or place but in being. Cosmology and ontology replace genealogy and topography as philosophical reflection replaces poetic musing or religious awe.43 Thales, Anaximenes, and Heraclitus agree that X is to be designated by a mass term. Theirs is a monistic mass or process ontology.44 They agree also that X is sempiternally restless. And although they disagree about which term is most suitable—Heraclitus preferring pur, Anaximenes aêr,45 Thales hudôr, Anaximander to apeiron—this disagreement may not be fundamental. All except Anaximander, per41. Heraclitus B1, B80. 42. For these three statements we rely on early commentaries, e.g., Aristotle, Metaphysics 983b20 (DK 11A12), and Simplicius, In Aristotelis Physica commentaria 24, 26 (DK 13A5), 24, 13 (DK 12A9). Xenophanes declared that all things that come to be and grow are earth and water (B29), but without the context we cannot be sure that he was a dualistic mass ontologist. 43. The first extent use of the word archê in this sense is in Anaximander B1. 44. Cf. Peter Simons, Parts: A Study in Ontology (Oxford: Clarendon Press, 1987), 153– 66, José Benardete, Metaphysics: A Logical Approach (New York: Oxford University Press, 1989), 35, and Alexander P. D. Mourelatos, “Events, Processes, and States,” Linguistics and Philosophy 2 (1978): 415–34. 45. M. L. West describes aêr as the stuff of invisibility, having no fixed location in the Hesiodic world framework: see his Hesiod: Theogony, commentary on line 697.

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haps, were speaking metaphorically of something very subtle. Phenomenal fire, mist, and water are among the things that are X, hence none of them is what all things are: nature statements are not identity statements. Anaximenes took X to be more mist-like than fire-like; Heraclitus, to be more fire-like than mist-like. The former understood change in terms of condensation and rarefaction; the latter, in terms of strife and war. All change, said Anaximander, occurs in accordance with fitting necessity (kata to khreôn) or the ordinance of time (kata tên tou khronou taxin).46 Heraclitus, too, said that everything occurs in conformity with fitting necessity or the logos (kata ton logon) or measures (kata metra) or the attuned tension that is strife (kat’ erin).47 Is his understanding of the world nomocentric? Certainly it is logocentric and ratiometric.48 Are everliving fire and the logos two principles or two complementary ways of declaring what there is? The latter, I suspect, but the answer is unclear. Finally, did these first natural philosophers admit natural kinds? No. They had little use for the word genos, which occurs only twice in all the fragments of their writings, or the words phulon and ethnos, which occur not at all.49 One might argue that water or mist or fire is one of a kind; but there is no evidence they would have agreed. So were they antirealists with respect to natural kinds? Did they think that all classification has its basis in the semblance (dokos) which poets and people generally have wrought upon 46. Anaximander B1. On time, cf. Pherecydes B1. 47. Heraclitus B1 and B80 with B10, B30–31, B36, B50–51, B54, B62, B67, B90, B94, B102. The ratios 2:1 and 3:2 figured prominently in Anaximander’s astronomy as well. 48. The logos is not said to be a law (nomos); but consider B114 with B2, B82, B94, as well as Felix Heinimann, Nomos und Physis: Herkunft und Bedeutung einer Antithese im Grieschischen Deken des 5. Jahrhunderts (Basel: F. Reinhardt, 1945), 66. Heraclitus (and Anaximander) may have had the idea of a law of nature—as Eva Brann argues in her The Logos of Heraclitus (Philadelphia: Paul Dry Books, 2011), 28—but not yet the term. I will touch on this issue in chapter 5.2 of this volume. 49. Heraclitus B82. Anaximander described the generation of animals and may have thought that humans come from nonhuman animals; but the words alloeidôn and homogenê (DK 12A10, DK 12A30) are probably not his.



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everything and everyone?50 Perhaps, but it seems more accurate to say they had no idea what a natural kind is, and would have regarded as misguided any attempt to introduce this idea into natural philosophy. The discovery of nature preceded the discovery of natural kinds.

THE PARMENIDEAN CRITIQUE Parmenides of Elea wrote one work, a short poem in epic meter, most of which seems to have survived. In it, an anonymous youth recounts a fantastic journey he used to take, at the end of which he received not a vision but a speech. This speech, delivered without interruption by an anonymous goddess, has two parts. In the first she declares “the untrembling heart of well-rounded [or persuasive] truth.” In the second she offers a critique of “the opinions of mortals, in which there is no true trust.”51 The poem is obscure, yet most scholars agree on one point: Parmenides thought the idea of nature to be no more admissible than any other idea belonging to the way of mortals. The challenge for natural philosophy was to block this conclusion by showing that realism with respect to the natural world is acceptable. Trying to meet this challenge brought about the first major renewal of natural philosophy. By a route shrouded in myth, the youth has reached the point of having to decide between is and is not, or between two ways of inquiry for thinking: the first, how it is and how it cannot not be; the second, how it is not and how it needs must not be.52 The choice, in other 50. Cf. Xenophanes B34, in which he may have been alluding to Homer, Iliad 18.483, and possibly 14.215. 51. Parmenides B1.28–30. 52. Parmenides B8.15 and B2.1–5. There are several possible translations of the latter passage, none interpretation-free. Unresolved questions include: should hôs be taken to mean “that” or “how”? Is the verb esti (“is”) solely or even primarily existential? Should this verb be taken to have an implicit singular subject? Does the second, modal clause in each case modify or merely explicate the first clause?

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words, is between thinking about necessary being and thinking about impossible being. Left out, it seems, is thinking about contingent being. But this option, though logically distinct from the other two, is no different from the way of mortals. Were the young man to choose it now, he would short-circuit his own journey. The goddess orders him to hold back his thinking from the second way, as it is unintelligible. Being unintelligible, it is less a path on which inquiry can proceed than a dead-end: take even one step in that direction and your thinking would cease. The youth, however, is to decide for himself by means of reason (logos).53 Supposing one agrees with the goddess, there remains only the way about being (to eon) or truth (alêtheia). On it, she says, there are many signs, among them ungenerable, imperishable, untrembling, now altogether one, indivisible, immobile, and complete.54 These signs cannot be real properties, yet they must be predicable of being if her account is properly descriptive. They are signs (sêmata) on the way about being; they belong not to being but to the semantic field in terms of which discursive thought can get a fix on being. Parmenides’s ontology is explicitly ontological.55 It is shot through with negativity, as it must be if mortals are to have any chance of apprehending being in speech. It is also pervasively and explicitly poetic. The ontological situation, apart from which we could not discover what there is, must be onto-mytho-logical.56 About this teaching it suffices here to make two points. First, the usual criticisms of Parmenidean ontology—that it cannot account for falsehood or fakery, that it tacitly admits nonbeing, and that it refutes itself—depend on a failure to distinguish the metaphysical from the 53. Parmenides B2.6–8, B6.2, B7, B8.8. More detailed reasons for rejecting the second way are offered in Plato’s Sophist 236d–241c. 54. Parmenides B8.1. 55. See Umphrey, Natural Kinds and Genesis, chap. 2.2, and 2, 8 of this volume. 56. For elaboration of these points, cf. Stewart Umphrey, “Not Is Not,” in The Envisioned Life: Essays in Honor of Eva Brann, ed. P. Kalkavage and E. Salem (Philadelphia: Paul Dry Books, 2007), 350–74.



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protometaphysical. Parmenides expressly distinguishes being from seeming. Seemings are not just nothing. Instead, says the goddess, they needs must seemingly be (dokimôs einai).57 We tend to accept them as genuine. We believe that a human being named “Parmenides” wrote a poem, fragments of which still exist, and assume that nothing is real if not these conditions under which alone reality can be described. We are radically misguided; we fail to distinguish being from what, for us, must seemingly be, so we have trouble distinguishing pragmatic self-refutation from logical contradiction. Following the logos is not easy for anyone rooted in the way of mortals. Second, although no one has refuted Parmenides once and for all, it does not follow that he was right about being. For one thing, not every step in his argument is clear, so we are in no position to say that the argument is sound. It is also indirect, and as Kant and others have noted, indirect proofs cannot exhibit what was to be demonstrated. Why should one believe that being must be complete if it cannot be incomplete, or that it is logically definite, like the bulk of a well-rounded ball?58 The Parmenidean elenchus is no less a via negativa than its Socratic counterpart; and in neither case is it easy to see how something positive can come out of it. About Parmenidean being, then, we should remain undecided. The subject matter of natural philosophy may still be real. The goddess tells the young man that he must also learn about mortal opinions, in which there is no true trust.59 She speaks of a way “on which mortals who know nothing wander double-headed, as 57. Parmenides B1.32. Recent scholars have interpreted the adverb dokimôs (which occurs here for the first time in extent Greek texts) in conformity with later usage to mean “genuinely” or “acceptably.” In this poem, however, it means “seemingly.” Ionian philosophers also downgraded the epistemic or ontic status of things designated by dok- words. See again Xenophanes B34.5; and on the meanings of such words in Heraclitean fragments, cf. Charles Kahn, The Art and Thought of Heraclitus (New York: Cambridge University Press, 1979), 29n, 67n, 69n, 102, 210. 58. Parmenides B8.32, B42. 59. Parmenides B1.28–30 and B8.51.

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helplessness in their breasts guides their vagrant mind and they are carried deaf and blind alike, dazed indecisive tribes [phula] for whom being and not being are held to be the same and not the same.”60 Those who wander in this way, plying “an aimless eye and an echoing ear and tongue,” are wedded to it by the force of habit rooted in experience. They will likely persist in regarding as real the seemings (dokounta) which pervade all things.61 What underlies this mortal delirium? The goddess makes three interrelated suggestions. First, we refuse to decide between is and is not. By holding onto being and not being as the same and not the same, we remain of two minds about everything and so wander in circles.62 Second, while discoursing about what there is, things will be mere names, as many as mortals posit, convinced that they are true: becoming and perishing, being and non[being], and changing place and exchanging bright color.63 Language bewitches us if we assume that our names and descriptions used referringly do in fact refer. In truth none of them do. The goddess reasserts this radical nominalism later in the poem, when she claims that all things occur in conformity with opinion (kata doxan) and suggests that the whole world (kosmos) exists only in the arrangement of our words or beliefs.64 Remove this arrangement and the world-order would collapse. Third, of mortals she says, 60. Parmenides B6.4–9. These are mortals who know nothing. The youth, we infer, is one who knows something, because otherwise he would not be on the way of the goddess (B1.2, B27). The phrase “are held” translates nenomistai, a verb related to the noun nomos (“law”). Similarly, the Olympians were held to be gods in the cities of Greece, and anyone held to disagree about this ran the risk of being charged with impiety. 61. Parmenides B7.3–5 with B1.31. On the different ways of construing B1.32 and B7.3, cf. D. Gallop, Parmenides of Elea (Toronto: Toronto University Press, 1984), 21, 37n64, 53, 63. 62. Parmenides might have found in my account of continuants an exemplary instance of this error. 63. Parmenides B8.38–41. I choose the manuscript reading adopted by L. Tarán. For a summary of alternatives, cf. Gallop, Parmenides of Elea, 71. 64. Parmenides B19.1–3 and B8.52, 60.



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for in their minds they posited two forms for naming, of which it is not right [to posit] one—wherein they have gone astray—65

These two forms she calls “light” and “night.” That mortals should not have posited one of them I take to mean, “They should not have posited even one.”66 What there is cannot be understood in terms of light or night, either singly or as a pair (even though, in her discourse about being, the goddess must employ language that intimates otherwise). They are postulates in terms of which we try to make sense of everything that seems real, including ourselves and the milieu in which we proceed. Mortals elaborated this error by distinguishing corporeal opposites and positing diverse signs (sêmata): light as gentle and ethereal; night as dark and dense. To show what follows once this beginning has been made, the goddess presents a “likely” cosmology. It looks like a late entry in the Ionian cosmology competition. Does she not imply that Ionian monism should be rejected in favor of dualism? But an interpretation along these lines would be mistaken.67 For her cosmology admits becoming and perishing, sexual generation, nature and nascence, natural powers, and duration, all of which were disallowed in her just65. Parmenides B8.53. 66. Cf. M. C. Stokes, One and Many in Presocratic Philosophy (Washington, D.C.: Center for Hellenic Studies, 1971), 146. 67. Also mistaken, in my view, is the interpretation according to which Parmenidean being is a single, ungenerable, imperishable, immobile, homogeneous, spherical mass, a finite block-universe. This interpretation is not without textual foundation; cf., e.g., D. Sedley, “Parmenides and Melissus,” in The Cambridge Companion to Early Greek Philosophy, ed. A. A. Long (New York: Cambridge University Press, 1999), 113–33. It may also be regarded as part of the recent scholarly effort to heal the break which Eleatic philosophers appear to have made with Ionian natural philosophy; cf. P. K. Curd, The Legacy of Parmenides (Princeton, N.J.: Princeton University Press, 1998), and D. W. Graham, “Empedocles and Anaxagoras,” in Cambridge Companion to Early Greek Philosophy (ed. Long), 159–80. Notice, however, that this interpretation depends on taking a statement of likeness (between being and the bulk of a well-rounded ball, in B8.43) to be a statement of identity; cf. G. E. L. Owen, “Eleatic Questions,” Classical Quarterly (New Series) 10 (1960): 84.

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completed account of what is.68 Its verisimilitude has no truth in it (she calls it “deceptive” as well as “likely”), and its purpose is expressly prophylactic: the youth is to learn it so that no mortal judgment will ever outstrip him.69 Her cosmology, I suggest, is better understood as a diagnostic tool which, like the moly plant Hermes showed Odysseus, makes its user immune to bewitchment. For example, it helps one see that Anaximander needs the ordinance of time and the indefinite; Heraclitus, the logos and everliving fire; Aristotle, form and matter; Newtonian mechanics, force laws and bodies in motion; quantum mechanics, mathematical structure and indeterminate field-disturbances. Naturalists need two “forms,” one clear and distinct, the other obscure. Their problem is then twofold: to elucidate the murkier “form” without explaining it away, and to understand how these “forms” can be both two and one. The whole enterprise is misconceived. Natural philosophy wanders indecisively, with echoing ears and tongues, its profound double-talk exemplifying the double-headedness of mortals generally. The goddess provides this cosmology not in order to beat out the competition in a mug’s game, but to complete her critique of mortal opinion. Yet there is a sense in which Parmenides completed the monistic tendency in Ionian natural philosophy.70 It appears in retrospect that Heraclitus and the others were trying to declare what is, but got hung up on making nature statements of the form “All things are X.” Their inquiries carried them only partway out of the house of mortal opinion. Parmenides completed the journey they began, but in so doing found that there could be no nature of anything, that gignomena were mere semblances. In fulfilling natural philosophy he also finished it off. 68. Becoming and perishing, sexual generation: Parmenides B10.3, B11.4, B12.4–6, B13, B17–18, B19.2 (cf. B8.6–28). Nature and nascence: B10.1, B10.5, B16.3, B19.1 (cf. B8.10). Causal powers: B9.2, B10.6, B18.2 (compare B8.30, where the necessity is logical rather than natural). Duration: B19.1–2 (cf. B8.5). This cosmos is also full of life, whereas being could not be alive or dead. 69. Parmenides B8.51, B61. 70. Cf. Aristotle, Metaphysics 984a27 (also 1028b2–4).



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NEO-IONIAN PHILOSOPHY Under this heading I put the work of Anaxagoras, Leucippus, Democritus, and Empedocles. All were natural philosophers who reduced change to local motion, denied that anything corporeal is self-moving, and affirmed plurality with real variety. They appear to have made these innovations in response to Parmenides’s critique. Did they think he allowed for things mixing and unmixing, combining and separating?71 Or that his position was self-refuting?72 Did they correctly estimate the strength of his critique?73 We cannot say with certainty. What is certain is that these Ionians renewed natural philosophy, and in so doing admitted heterogeneous individuals or masses. Did they, unlike their pre-Parmenidean predecessors, also admit natural kinds? To find out, we must look more closely at their several teachings.

Anaxagoras Anaxagoras holds that in the beginning all things were so mixed together that nothing was clear. Mind put this confused mass into rotary motion. It began to separate out and become clear. Eventually the hot and the dry were concentrated mainly in celestial phenomena, the cold and the moist in terrestrial phenomena.74 Thus was the primordial mishmash turned into a cosmos. Yet there was no substantial 71. That Parmenides, unlike Zeno, admitted pluralism as a possibility: Mourelatos, The Route of Parmenides, 130–33, and J. Barnes, The Presocratic Philosophers (London: Routledge and Kegan Paul, 1979), 1:204–10. That he, unlike Zeno, admitted locomotion as well: Graham, “Empedocles and Anaxagoras,” in Cambridge Companion to Early Greek Philosophy (ed. Long), 165–77. 72. That this was their objection to the Parmenidean critique: A. A. Long, “Parmenides on Thinking Being,” Proceedings of the Boston Area Colloquium in Ancient Philosophy 12 (1996): 125–62, and S. Trépanier, Empedocles: An Interpretation (New York: Routledge, 2004), 140–44, 152. Trépanier finds a hint of this objection in Empedocles’s poem. 73. That this was the case: Barnes, Presocratic Philosophers, 2:5, 11–15, 139. 74. Anaxagoras B1–2, B4, B9–10, B12–13, B15–16.

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emergence (genesis): becoming and perishing, though held (nomizetai) to be real, are mere nomizomena; in reality all change is locomotive.75 Nor was stuff of any sort separated completely from stuff of any other sort; now and always there is everywhere a share of everything.76 However cold the earth may become, it will never become simply cold, as it always contains some admixture of the hot. Nor are there any ultimate parts; any portion of the world, however small, is equal in multitude to the entire world, which is boundless.77 As befits his mass ontology, Anaxagoras uses the language of magnitude rather than multitude, of portions rather than proper parts. But he speaks also of unnamed multitudes and uses the count-noun khrêmata (“things”) to designate such phenomena as the sun and the moon, human beings, and other living things, and the count-noun spermata (“seeds”) to designate, perhaps, those portions that are on the verge of becoming distinct phenomena.78 Regarding such things we have two questions. One concerns the constitution of each. Take for example the sun. The hot and the cold pervade it, and yet it is hot, we say, because its share of the hot is much greater than its share of the cold. Now consider the hottest part of the sun. Though very hot, it is not simply hot; there must be in it a share of everything else, including the cold. The hot, we say, is very hot because within it there is a very high concentration of—what? The hot? Our account is circular or infinitely regressive.79 The solution, I believe, is to argue that the regress is innocent. Anaxagoras employs ordinary language, which is geared to things rather than stuff, in order to present an ontology in which there is inhomogeneous stuff all the way down. Difficult it is 75. Anaxagoras B17. 76. Anaxagoras B4, B6, B8, B11–12. 77. Anaxagoras B1, B3, B6–7. 78. Anaxagoras B1, B4, B6–7, B12. The word khrêmata also meant “money.” 79. Cf. J. Barnes, Presocratic Philosophers, 2:24, 27. There is no evidence that Anaxagoras distinguished between stuff that is hot (to thermon) and the property of being hot (what Plato will call auto to thermon or what Aristotle will call thermotês).



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for us to say that a thing contains the hot and the cold without imagining that it could be analyzed into these two constituents. In reality, however, there is no such thing as the hot or the cold: there are no elemental masses. How then can we still maintain that some things are hotter than others? One way is to think of the hot as an ideal mass which some regions approach more closely than others as mind turns the primordial mishmash into a centrifuge.80 Our second question concerns the ontic status of these khrêmata. Anaxagoras takes the material world to be an indeterminate manifold that is heterogeneous and altogether actual.81 What we call “things” are either derivative on local motions or dependent on human usage. Anaxagoras seems to regard celestial bodies, human beings, and the like as supervenient phenomena, none of which has come into being. There are no individual continuants and no natural kinds in the primary sense. Not once does the word phusis occur in the extant fragments of his work. 80. A mathematical model unavailable to Anaxagoras may help. (1) Imagine any finite region of the mixture. Let it be spherical. This region contains 2^‫ א‬0 infinitesimals. Dividing it into hemispheres, let the infinitesimals in one of them be hot, those in the other be cold. Then, of all the infinitesimals in the region, 2^‫ א‬0 are hot and 2^‫ א‬0 are cold. (2) To model the primordial mixture, we suppose our infinitesimals to have been so thoroughly mixed that in any sub-region, however small, the hots and the colds are “equal in multitude.” To us the region appears lukewarm throughout. A force we call “mind” now causes hots to move toward the periphery, colds toward the center. Let this motion occur in such a way that eventually we have in the middle a spherical subregion containing 2^‫ א‬0 colds but only ‫ א‬0 hots distributed uniformly throughout, while about it we have an annular subregion containing 2^‫ א‬0 hots but only ‫ א‬0 colds distributed uniformly throughout. In our central region the colds have thus become clear, while in our peripheral region the hots have become clear. We count them as two, and may call them Earth and Heaven respectively. (3) To dispel the illusion there are real uncountable multitudes, we take very seriously the claim that there are no smallest parts. We supposed that our sphere contained 2^‫ א‬0 infinitesimals— which made them equinumerous with the real numbers. We contrive a better approximation if instead we say that it contains 2^2^‫ א‬0 infinitesimals—making them equinumerous with the hyperreals—or rather 2^2^2^‫ א‬0 , or rather, and so on to infinity. This incompletable series becomes a pointer to the variegated reality whose elementary units we cannot identify because they do not exist. 81. A similar ontology is entertained in Simons, Parts, 157.

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Leucippus and Democritus Only a little of what Leucippus and Democritus wrote remains, yet from this detritus together with ancient commentaries we gather the following. Reality comprises the full and the empty. The empty is identified with void and described as if it were something in which the full is forever distributed. Democritus calls it “nothing,” but adds neologistically that nothing (mêden) is no less than thing (den).82 The full comprises infinitely many particles having infinitely many different shapes and sizes, each of them everlasting, massy, indivisible, and immutable except with respect to place.83 These atoms move incessantly, impelled by repeated collisions to enter into different configurations.84 Sun and earth, human beings, and other living things all supervene on the transient arrangements of atoms. Are they thus real in a sense, or only by convention? The extent fragments provide no clear answer. Leucippus and Democritus were the first natural philosophers to admit individual continuants, to which they ascribed a variety of fixed shapes. Did they also admit natural kinds based on their different forms? Aristotle and Plutarch imply that they did.85 Simplicius, however, says that it was the principle of sufficient reason which led them to posit myriad shapes.86 In fact, Leucippus and Democritus seem to regard all such kinds as convention-laden. Nor do they say what an atom is in its nature. Only once in the many fragments of his writings does Democritus use the word phusis in an ontological context. He prefers the neologism eteê (“reality”).87 82. Democritus B156. See also DK 68A37. 83. See DK 67A6, 8, 11, 13–14, 37, 68A14, 38, 43, 47, 57, 60–61, 135. 84. Leucippus B2, DK 68A14, 123, and C. C. W. Taylor, The Atomists: Leucippus and Democritus (New York: Cambridge University Press, 1999), 188–93. 85. Aristotle, Metaphysics 985b17–20 and Plutarch, Against Colotes 8, 1111a–c. 86. Cf. Simplicius, In Phys. 28.27 [DK 70A3] and Taylor, Atomists, 72, 168, 173. The word ideai (“looks”) in DK 68B167 [= Taylor D7] need not refer directly to atoms, as Taylor supposes. 87. Democritus B168 (which may not be a genuine quotation). The other twelve oc-



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Empedocles Like Anaxagoras, Empedocles is a mass ontologist who admits no void, but like Democritus he posits a determinate plurality: there are, he says, four “roots”—fire, air, water, and earth—each everlasting and unchanging, save with respect to place.88 He also posits two sources of motion: love, which mixes together the four roots, and strife, which separates them. When love rules, they form a sphere whose constituents are “grown together” and “submerged.”89 Were strife to rule, would they form four nested spheres? The extant fragments do not say, nor do they say how love and strife cooperate to form a cosmos. There is mention of a “broad oath” or “oracle of necessity” which seems to govern all events.90 Perhaps love and strife submit to it. In any case, their reciprocal actions are such there is an endless cycle in which the four roots commingle and separate. The cosmos we inhabit is a transient state in one or another phase of this cycle.91 Empedocles, like Democritus, was a realist with regard to continuants. Primarily there are fire, air, water, and earth—four everlasting masses, each with its own distinctive character (êthos) or nature (phusis) in virtue of which it remains the same throughout all its changes of place. He calls them “beings” (onta).92 Derivatively there are plants, currences of the word phusis are in fragments having to do with ethics, human physiology, and human affairs generally. How Democritus understood the relation between these parts of his teaching and his atomism is unclear. For his use of the word eteê, cf. B6–10, 117. That he and Leucippus did not admit natural kinds: DK 67A8, 68A41. 88. Empedocles B6–7, B11–14, B17.4–8, B17.13, B17.18, B21.9, B21.14, B22.4–5, B26.3, B26.12, B27, B29, B30.1, B35.7, B35.11, B35.31, B36.16, B98.1–2, B109, B129.5. 89. Empedocles B17.19, B109. He sometimes suggests that the roots are self-moving (e.g., B35.6, B59.1, B62.6), but in these cases he probably means the roots qua strife- or love-infused. Compare Hesiod, Theogony 728, 736–39. 90. Empedocles B30, B115.1, and Aristotle, Physics 252a31. The word anankê (“necessity”) occurs also in Democritus B181, Leucippus B2, and Parmenides B8.30, B10.6, but not in the extant fragments of works by the earlier Ionian philosophers. 91. Empedocles B17, B26–29, B35–36, B61, B71, B134. The four roots would be most clearly distinguished when Strife alone rules, but then we would not be around to notice it. 92. Empedocles B17.28, B63, B110.4.

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animals, and long-living gods—myriad individuals. He calls them “mortals” but not “beings.”93 Are they then merely by convention? Perhaps; yet Empedocles ascribes to each a distinctive form (eidos), a nature (phusis), a fixed ratio (logos) in virtue of which it remains the same throughout the vicissitudes of its little life.94 Of course, they did not come to be: there can be no substantive emergence, no genesis or nascence in that sense.95 Yet even the roots “become” in the sense of mixing and unmixing, in consequence of which mortals sometimes emerge and endure as long as their bodily parts remain attuned in the fixed ratios proper to them.96 They are continuants in some derivative sense of the term. Does he also admit natural kinds? Fire, air, water, and earth are his paradigmatic beings. They are enduring masses, with their own distinctive natures, and seem to differ from one another in kind, not merely in number. One might then take the sortal term “root” to stand for a generic kind whose four members are each one of a kind. Empedocles, however, might not have agreed. As for the swarms of mortal things that exist now and again, they are said to be members of different genera: Empedocles was the first natural philosopher to use the words genos, phulon, and ethnos frequently and in ways that seem 93. Empedocles B47. 94. Empedocles B22.7, B23.5, B71.3, B115.7, and B63, B110.4. The nature of a mortal is not to be identified with its psuchê: B138 (the sole occurrence of this word in the Empedoclean fragments). 95. Empedocles B7–9, B11–12, B31; B63; B26.3; B9.5, B26.3 (and note the painting analogy in B27.1–8). The use of phusis as a process noun is new. Plato and Aristotle will also use it this way, though sparingly. 96. Empedocles B17.3, B17.27, B17.30, B17.34, B26.3–7, B35.11, B61.1, B63, B110.5–9; B21.14, B22.5–7, B26.10, B38.10, B71.3; B98, B96.4 (cf. B23.4, B71.4, B107.1), B115.7, and DK 31A78; and note the occurrence of epigignetai (“supervenes”) at B17.30. Cf. A. P. D. Mourelatos, “Quality, Structure, and Emergence in Later Pre-Socratic Philosophy,” in Proceedings of the Boston Area Colloquium in Ancient Philosophy, ed. J. Cleary (Lanham, Md.: University Press of America, 1987), 163–94; Brad Inwood, The Poem of Empedocles (Toronto: University of Toronto Press, 1992), 31–39.



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not merely concessionary or poetic.97 Did he understand these genera typologically as well as genealogically? Probably, though we cannot be sure. There is no evidence that he distinguished universals from particulars, or that he classified mortals according to their natures; but one need not be an Aristotelian or scientific essentialist to have grasped the idea of a natural kind; and it is in Empedocles’s poem that we find the first evidence of philosophical reflection on natural kinds.98 Two circumstances fostered this development. One was the Parmenidean critique, which compelled natural philosophers to distinguish being from becoming and to notice that their prephilosophical notions of genesis and phusis may be problematic. A second factor was their desire to explain natural phenomena in all their multiplicity and variety, which led them to embrace pluralism with irreducible heterogeneity. The one thing still lacking is attention to kinds as universal types. This came with Socrates and Plato, but it came at a price; for the Socratic turn, and Plato’s appropriation of it, brought about a second major crisis in natural philosophy. This crisis, together with kinds as universals, will be our twin theme in the next chapter. 97. Empedocles: B9.2, B124; B74 (compare Parmenides B6.7); B26.4, B36.5–6, B121.2; see also B17.28, B62.4. 98. Herodotus, another neo-Ionian, may be included in this group. That he, like Empedocles, linked eidos and phusis in his accounts of animal genera: Seth Benardete, Herodotean Inquiries (The Hague: Martinus Nijhoff, 1969), 87–93.

CHAPTER 2

Eidos and Genesis I Plato

To the dying Plato there came a dream in which he had become a swan that flew from tree to tree, frustrating the efforts of archers who wanted to shoot it down. What this meant, said Simmias the Socratic, is that interpreters of Plato’s writings will forever be unable to get a fix on his teaching.1 Indeed they have; for Plato wrote dialogues in which different characters speak, never the author himself, and although these artifacts are not inkblots or clouds into whose features we may read whatever we wish, it is also true that no single teaching can be extracted from them. My procedure here will be indirect. I first consider some dialogues in which one or another of three philosophers (Socrates, the Eleatic stranger, Timaeus) is the leading character and then give reasons for thinking that Plato was a natural-kinds antirealist.

1. Cf. Olympiodorus, Commentary on the First Alcibiades of Plato, ed. L. G. Westerink (Amsterdam: North-Holland, 1956), 6.

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SOCRATES Opening a Platonic Socratic dialogue is like stepping into another world, or so one feels when coming to it directly from the pre-Socratics. Socrates has turned away from what interested them—the cosmos, being, the nature of things—focusing instead on things human; and he does so in conversation with other human beings, most of whom are not philosophers. How is one to understand this Socratic turn?

Take One Socrates describes it in Plato’s Phaedo. Having failed to understand how two things become one or one thing two, and having found that Anaxagoras failed to present the comprehensive teleology his book promised, he undertook a “second sailing.” No longer would he try to explain how something comes to be, or show that what occurs is generally for the best; nor would he attend directly to things seen or done. Instead he would try to discover the truth of the beings (ta onta) by taking refuge in speeches (logoi), hypothesizing certain forms (eidê), and seeing what follows.2 Socrates does something like this in other dialogues. In the Eu­ thy­phro he asks Euthyphro to give an account (logos) of the holy; in the Hippias Major he asks Hippias to give an account of the beautiful; and in the Meno he asks Meno to give an account of virtue. What sustains each interrogation is a question of the form “What is X?” And the X in each case he calls a “being” (on, ousia) and a “form” (eidos).3 The words eidos, ousia, and logos are here being used in extraordinary ways: X is invisible, immutable, has little to do with real estate, and the 2. Plato, Phaedo 99d4–100b7. Cf. Hippias Major 299b9, 302e12. That Socrates abandons cosmology in particular: Apology 20d9–e3, Euthyphro 6a6–b2, 15e5–16a3, Republic 382d1–2. 3. Plato, Euthyphro 6d10–e1, 11a8, Hippias Major 286d7–e2, 287c1–288a11, 289d4, Meno 71b1, 72a8–d1, 80a5.

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account of it is to be definitional. As beings, moreover, these forms are distinguished strictly from things seen or done, and more generally from things in the process of becoming (gignomena).4 As forms they are also distinguished from such kinds as monkeys, humans, and gods, for these are said to be genê rather than eidê, whereas X is said to be an eidos and never a genos.5 The aim is to say what the being or form is, not how it becomes “present” to something or how something comes to “have” it. And as definitions (logoi) the answers being sought are distinguished from myths (muthoi). Mythical accounts are proper to becoming, Socrates implies, hence to everything that is by nature. Rarely does he say that an eidos has or is a nature (phusis).6 Socrates’s onto-eidetic turn seems Parmenidean. Yet there are differences. (1) By hypothesizing forms and asking what each of them is, Socrates sets aside the requirement that one decide between is and is not. He can do so because his interlocutors almost never doubt the 4. The distinction between being and becoming need not be explicit; often it is the language used that shows it. In the Euthyphro, forms of gignesthai (“to become”) occur twenty-one times, five in the brief passage leading up the “What is X” question, seven in interludes or at the dialogical meta-level, the rest in sentences presenting illustrative instances or analogies. The eidos in question is independent of Euthyphro’s “definitions” and the dialogical flow in which they come to be and pass away. In the Hippias Major, a much longer dialogue, the verb gignesthai occurs only eighteen times, very few of them in passages having to do directly with the beautiful itself. In the Meno, it occurs over sixty times, but only ten of them are in passages having to do directly with virtue itself. 5. Plato, Hippias Major 289a–c, Meno 74d, Lysis 216c–d, Cratylus 393b–394e, Phaedo 77c, 79a–b. Socrates sometimes uses the words eidos and genos almost interchangeably: Republic 435b9–444b5, 507b2–509b10, and Phaedrus 247c8, 250b5, 263b8–c5, 270d5–277c5. In the first two of these passages, it serves to highlight the limitations of the soul-city and the good-sun analogies. In the second, it may highlight some difference between eidos and idea. In the third, it reminds us that we are reading a myth. I have no explanation for the fourth and fifth. 6. The few exceptions include: Republic 476b6 and possibly 501b1–3; possibly Hippias Major 293e4; Phaedo 103b5 (the sole occurrence of phusis in 99d–107d). For nature belonging to the domain of myth, cf. Phaedo 107d5, esp. 108c4–109a6 and 111c5–113e8 with 110e1. Only in this part of the Phaedo is the verb phuô used to signify growth (110a4, d4). On the use of the word muthos more generally in Plato’s dialogues, cf. Robert Zaslavsky, Platonic Myth and Platonic Writing (Lanham, Md.: University Press of America, 1981).



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reality of what is in question.7 For Socrates, however, this assumption is a quietly instated hypothesis, not a conviction. By his nonassertoric stance and refusal to face directly these forms as beings, he distinguishes himself from other “friends of the forms” and makes himself less vulnerable to misology. (2) Socrates admits a plurality of forms, each of which he takes to be immutably one and the same in all its manifestations.8 He is the first philosopher to propose realism with respect to universals. (3) According to Parmenides’s goddess, the things in which these forms appear are dokounta, mere seemings, in which there is no true trust; to suppose otherwise, she implies, is to remain delirious on the way of mortals. For Socrates, gignomena are not necessarily unreal. He never questions the assumption that he and his interlocutors are agents capable of making choices, examining their ways of life and modifying them. What he calls “our soul” is somehow between mere semblances and being. (4) According to Parmenides’s goddess there is no real relation between changeable things and being; our usual names for them do not refer to anything real. For Socrates, gignomena are related ontically as well as heuristically to the forms they manifest. How he understands this relationship is unclear. He sometimes seems to regard universals as immanent in things (in rebus), at other times as transcendent (ante res). Whereas some commentators take this to be a sign of Plato’s evolving thought, to me it seems rather to depend on those with whom Socrates is conversing and to what end.9 In any case, insofar as the question “What is X?” determines what is said, and X is identified as a form, Socrates re7. In Hippias Major 287c4–d1, Socrates asks whether “that eidos” is something that is (on ti). He does so, I suggest, because Hippias is a sophist and many sophists held that beauty or nobility, like justice, is merely by convention. Hippias is exceptional in this regard, and Socrates lets stand the claim that the beautiful itself is real. 8. Plato, Euthyphro 6d9–e6, Meno 72c1–d1. 9. For a good account of how a strong one-over-many theory suits the Republic as a whole, cf. David McNeill, An Image of the Soul in Speech: Plato and the Problem of Socrates (University Park: Pennsylvania State University Press, 2010), 178.

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peatedly urges his interlocutors to “look away” from things becoming and attend to what X is. Questions about the “participation” relation remain marginal, as do questions about the ontic status of the forms themselves and their participants. Why does Socrates call X an eidos or idea? The word eidos is used ordinarily to designate the bodily form of a human being (especially one who is young and beautiful), but no one objects to his calling eidê the different kinds of persuasion, speech, cognitive abilities, regimes, pleasures, or the like.10 Socrates may also have in mind analogous uses of the word in the works of mathematicians, physicians, and historians, as well as the linguistic relation between eidos and eidenai (“to know”), idea (“look”), and idein (“to see”).11 What we call “universals” are the invisible looks of things. To become aware of them resembles coming to see clearly some one thing obscurely manifest in many things seen and done. So, at any rate, he suggests. How many such forms are there, and how diverse are they? In the Euthyphro, Hippias Major, and Meno Socrates speaks of the holy, the beautiful, and virtue, each of them a single eidos. Are these three names for three forms? Should we count the just and the good as a fourth and a fifth? But the Euthyphro also suggests that what we call “holiness” is nothing other than justice insofar as it becomes manifest in our dealings with the gods; and according to the Hippias Major, Symposium, and other dialogues, the beautiful can hardly be under10. Eidos as bodily form: Charmides 154d5, e6, Lysis 204e5, 222a3, Meno 80a5, Protagoras 352a2, Phaedo 73a1, 76c12, Phaedrus 249b6, c2. Eidos as class: Laches 191d3, Gorgias 454e3, 473e2, Symposium 205b4–d8, Republic 376e11, 392a2, 397b4, 401d1, 406c2, 432d1, 432b3–5, 434a3, 477e1, 544c8, Phaedo 77c3–7, 79a6–b11, 100b4, Phaedrus 265a9, c9, Philebus 19b2. Notice that these sorts are of states, processes, or activities, and not of things which are in these states, involved in these processes, or engaged in these activities. In other words, there are eidê of predicates but not of subjects. 11. Cf. A. E. Taylor, Varia Socratica (Oxford: Clarendon Press, 1911), 178, and J. Klein, A Commentary on Plato’s Meno (Chapel Hill: North Carolina University Press, 1965), 50n43. For uses of the word eidos in early mathematical writings, cf. Euclid, Data def. 3 and prop. 58, Elements VI.27–29, and Apollonius, Conic Sections I.11–13, III.45.



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stood apart from the good.12 So even though these beings resemble unconnected islands in streams of dialogical discourse, they may not be as diverse as they seem. Yet, just as he sets aside the Parmenidean requirement that one decide between is and is not, so too Socrates restrains our desire to have a synoptic overview of the forms. Finally, what justifies his hypothesizing these beings? He seems to rely on the fact that his interlocutors are intent on distinguishing right from wrong, good from bad, fine from disgraceful; and in making these distinctions they appeal to certain ideals. These ideal standards they regard as real, not merely subjective or conventional, and yet people have very different opinions about them. Debates about right and wrong, good and bad, fine and disgraceful are likely to occur; and because they are about serious issues and no established art or science can resolve them, these debates tend to become heated.13 Socrates draws attention to the presumed standards themselves and urges his interlocutors to replace their inadequate opinions about them with knowledge. But again, why should one grant, even provisionally, that these ideals are genuine universals? To better understand Socrates’s onto-eidetic turn, we need to look more closely at his pragma, what it is he does when doing his own thing.14

Take Two The verb dialegesthai, like the noun eidos, has both a “lower” and a “higher” sense in Plato’s dialogues, for it means not only “to engage in conversation” with another human being, but also “to engage in dialectic” about what is. In Plato’s Socratic dialogues these two meanings are inextricably linked.15 Socrates’s philosophical activity is inherently 12. Plato, Euthyphro 11c4–12e8 and, e.g., Hippias Major 295c, Symposium 24c. 13. Cf. Plato, Euthyphro 7b7–d10 and, e.g., Laches, Charmides, Republic I. 14. Plato, Apology 20c5. 15. Cf. Plato, Republic 454a5 with 511c5, and, e.g., Theaetetus 161e6, Parmenides 126c2, 135c2, d2.

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dialogical as well as dialectical. The Platonic “dialogues” in which he leads the way are thus bi-directional. There is on the one hand an upward movement toward something impersonal, transhistorical, everywhere and always the same, and on the other hand an interpersonal back-and-forth between Socrates and other humans, each as mutable and particular as Socrates himself.16 In dialogue Socrates examines his interlocutor’s opinions about what X is. Insofar as these opinions are his own, their examination becomes an investigation of the interlocutor himself and his whole way of life. And insofar as they prove inadequate, the interlocutor feels as if his very soul is being exposed. By making this ethico-psychological turn, Socrates cannot avoid appearing meddlesome and divisive. Conversational interaction with him is the “second-sailing” analogue of Baconian experimentation. Socrates converses with politicians, generals, poets, a few sophists, and many youths. All except the sophists are Athenians. Most are nonphilosophical. Hence Plato’s Socratic dialogues, however elevated they may become, are free of that academic air which now imbues philosophy. Why does he proceed in this way? One reason is that he has brought philosophy down from the heavens and compelled it to study things human.17 In other words, he has made what is first for us the ongoing focus of his investigations.18 What is first for us includes political affairs, what we praise or blame, admire or denigrate, and things erotic. It is the very milieu within which philosophers must proceed. Pre-Socratics regarded this opinionated, convention-laden 16. According to Socrates (Phaedrus 249d), erôs also manifests itself in this twofold way. 17. Cf. Cicero, Tusculan Disputations V.10, Xenophon, Memorabilia I.i.16, IV.vi.1, vii.3–5, and Aristotle, Metaphysics 987a29–b7, 1078b17–31. 18. Whoever wrote the Lovers (or Rivals) understood this. On entering a grammar school Socrates sees two boys engrossed in some astronomical inquiry. He begins speaking with two onlookers, rivals in love with the boys. Their conversation turns to philosophy itself, what it is and whether it is a fine or good thing.



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milieu as a great barrier to the truth. Socrates agrees that the pretension to know things one does not know (doxosophia) pervades “the way of mortals,” yet supposes that only by examining such pretensions can one become wise. This supposition would be incorrect if what is first for us were like a cave in which the only recognizable eidê are visual or willful, in which the greatest eros is tyrannical rather than properly daemonic, or in which no dialogue could be dialectical as well as conversational. Socrates’s political turn makes sense only if what is first for us points to what is first simply. So interested is Socrates in the good or useful that he appears to be an exemplary lover of gain. This agathological turn may not set him apart from his philosophical predecessors, however theoretical they seem by comparison, yet Socrates has also concluded that the unexamined life is not worth living for a human being, and that the self-knowledge attained by examining one’s own life involves knowing that one does not know anything important. Such knowledge he calls “human wisdom.”19 The attainment of human wisdom does not bring complete satisfaction, as Socrates shows, for he still wants to know those important things; he remains openly erotic, manifestly philosophical in the moderation that comes with knowing that one is not yet wise. He must then have realized that if the unexamined life is not worth living for a human being, it does not follow that the examined life is worth living. The utility or goodness of human wisdom, or philosophy itself, remains in question. It is the central question lying just beneath the surface of Plato’s Socratic dialogues. Socrates’s “second sailing” is at once dialectical and conversational, onto-eidetic and ethico-psychological, and thus comprehensive in its own way. It is also reflective in the sense that it busies itself with the human things, or with the broadly pragmatic situation in which alone philosophy itself or any other human endeavor can occur. And aside from 19. Plato, Apology 20d5–23c1, 37e3–38a6.

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any therapeutic benefits his diagnostic procedure may have for others, the most notable achievement of such reflection is self-knowledge or moderation in the sense just described. That the Socratic turn presents a fundamental alternative to the naturalistic and ontological turns of his philosophical predecessors is obvious. We should not think of these alternatives as branches of philosophy existing happily side by side, for each claims to be what philosophy is or should be. The Socratic turn presents not only an alternative to natural philosophy but a challenge to it, one that is no less formidable than the Parmenidean turn to being. Natural philosophers must henceforth find a way of sailing safely between these two troublemakers.

On Nature It does not follow that Socrates has nothing to say about nature. In fact he refers to it often, but always obliquely in relation to something near or dear to us. Take for example the Lysis. There, in dialogue with two boys, he presents himself as wanting to discover, not what friendship is, but how one becomes a friend to another. To this end he first describes a pre-Socratic transformation of some poetic wisdom,20 then sketches a physics of friendship according to which there are three kinds (genê): the good, the bad, and the neither good nor bad. The neither good nor bad befriends the good, he says, when and only when the bad becomes present to it without yet making it bad.21 Socrates does not take this bit of physics to be true simply: it is explicitly 20. Plato, Lysis 213c5. Whereas Homer says that the god always leads like to like and makes him known, those who discourse about nature say that the like is of necessity always dear to the like. For god they substitute necessity; for leading they substitute being; and the references to intentionality they expunge. 21. Plato, Lysis 215c4, 216c1. What is between the bad and the good has no intrinsic appetite for the good. It is thus quite unlike the daemonic according to Diotima in the Symposium (201e–203a), and quite like the friendship between Lysis and Menexenus. Their friendship is liable to be dissolved, therefore, when one of the boys falls in love or when Socratic interrogation spurs him to seek what is good.



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a projection onto nature of something very human, which he reflects back upon its source in order to advance the discussion. This is not to say that it is merely pragmatic, that it says nothing about the genesis or nature of friendship, but merely to note that it belongs to his “second sailing” and not to the naturalistic philosophy he has abandoned. Consider also Plato’s Republic. There it is Glaucon who first mentions phusis and genesis, eidos and ousia (being). Having set out a conventionalist account of justice, he challenges Socrates to show that the perfectly just man would be happier than the perfectly unjust man.22 Socrates takes up the challenge but does not refute conventionalism directly. Instead, he invokes an analogy between justice in the individual man (or soul) and justice in the city; and the city in which justice will be displayed is one expressly generated in speech. In the end it is unclear whether any political society is strictly by nature or whether man is naturally political, and the true standard of justice turns out to be transnatural. There is no natural right, according to Socrates in this dialogue. Yet there are, he implies, natural constraints on the manifestations of right. With Adeimantus it is agreed that each citizen will have just one job, namely, the one that accords with his nature. They assume moreover that human nature comes already specialized: if you are naturally suited to farming, you are not naturally suited to merchandising as well; and if you are naturally suited to farming, you are naturally a farmer and nothing else.23 With Glaucon it is agreed, first, that an enriched city will require soldiers and police who, like noble dogs, are both spirited and philosophical in their nature; and secondly, that members of their city will be steeped in a great myth. This tall tale has two parts. The first ascribes autochthony to the citizens and serves to instill patriotism. It has no basis in nature. The second part has a god mixing different metals into them at birth—into some gold, into others silver, into the rest bronze or iron. The golden 22. Plato, Republic 357c5, 359a5–361d5. 23. Plato, Republic 370a7–c6, 395b4, 415c1, 423d2–7, 433a5, 443c4–8.

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ones are to rule, while the silver ones are to be their auxiliaries.24 This does have some basis in nature; they agree, at any rate, that there are three natural kinds (genê tôn phuseôn) hierarchically ordered in this way.25 Finally, having noticed the obscurity in which Socrates has left the relationship between the purified city and the actual world, his interlocutors make three waves of objection, all of them pertaining to the generation in deed of this city in speech. Socrates responds by introducing the philosopher-king, whose nature or soul little resembles the city in speech.26 He also agrees that men and women differ in kind (genos), but denies that our nature is therefore double. The sexual dimorphism of humans is secondary in nature to their functional or erotic trimorphism as suitable rulers (lovers of wisdom), auxiliaries (lovers of victory), and the rest (lovers of money).27 Thus does he put into question the conventional understanding of human nature. Consider also the Philebus. It begins in a debate between Socrates and Philebus, the former a proponent of mind, the latter a fan of pleasure without limit. Philebus soon bows out, letting Protarchus take his place. Unlike his teacher, Protarchus insists on remaining human, and Socrates lets this constraint govern what follows. Their task becomes one of showing that there are different kinds of pleasure, most of which have no place in the best human life. But there is a problem: pleasures are indefinite in their nature; given any such manifold, what is limited in it can hardly be discerned from what is unlimited. How then can there be any eidetic analysis of it? In book 10 of his Elements, Euclid dealt with a similar difficulty: having shown that there are infinitely many irrational magnitudes (aloga), he tried to classi24. Plato, Republic 374e4–376c6 (note the plural “natures” at 374e7, 375d7). It is here that Socrates begins to focus on the souls of the citizens; see also Timaeus 18a4. 25. Plato, Republic 431b5, 435b5. 26. Plato, Republic 486d10, esp. 487a5, 490b3, 501d1–e2, 518d9, 535a–537c; see also 403c4. 27. Plato, Republic 451b9–457b6, esp. 451c1–5, 455c5–456b4 with 459b12, 473d6, 540c5– 9, 581c6, 585d11.



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fy them.28 Socrates is dealing with a problem at once more human and less amenable to reason (logos): having admitted that pleasures are indeterminate in number, degree, and type, he tries to divide this class (genos) into sections (trêmata), thereby discerning in it a number of subclasses (eidê).29 Whether he succeeds is unclear, because he accepts so many of Protarchus’s questionable convictions. They assume, for instance, that measure prevails in the natural world, and that animals are beings that have come to be. On these assumptions it is argued that deviations from an animal’s being (ousia) are contrary to nature and painful, whereas returns to it are according to nature and pleasant.30 This works for Protarchus but not for anyone who, like Socrates elsewhere, doubts that substantive emergence (genesis eis ousian) is possible, and wonders whether things by nature are really so well ordered in relation to our reason. According to Aristotle, Plato as a young man associated first with Cratylus, who taught that all perceptible things are in flux and therefore unknowable, and then with Socrates, who sought definitions of things knowable but not perceptible. As a result, Plato become a Her28. Euclid, Elements 10.21–35 and 10.115 with 10.36–72, 10.73–114; compare Plato, Theaetetus 147d3–148b2. A similar problem appeared in modern mathematics with the discovery of transcendental irrational numbers. There are uncountably many of them and they resist eidetic analysis. Notice, too, that from the standpoint of Galois Theory, Euclid’s classification of “algebraic” irrationals appears ad hoc, his geometrical approach too weak to succeed. 29. Plato, Philebus 12c4–13c5, 31b2–55c3. Pleasure as a genos: 11b5, 31a5, b4, 32d1, 44e7, 63b8, 65e2. That it can be sectioned: 12e7, 27d10, 61e6. That there are eidê of it: 19b2, 20a6, c4, 32b6, c4, 33c5, 51e5. In the Philebus, so-called Platonic forms are called “henads” or “monads,” never eidê or ideai. The word eidos does not occur in 53c4–55c3, where Socrates distinguishes between genesis and ousia, or in 55c4–59c9, where he distinguishes what is precise or philosophical in the sciences from what is conjectural or demiurgic. At 23d, he shifts from eidos to genos as he begins to describe the cause; here too genos appears to be the more comprehensive term. 30. Plato, Philebus, 28e1–6 with 31d1–33c4, and 26d8, 27b8–9, 32b1–4 (cf. 54a5–d8). For a detailed account of the ways in which Protarchus’s convictions determine the course of the dialogue, cf. Seth Benardete, The Tragedy and Comedy of Life: Plato’s Philebus (Chicago: University of Chicago Press, 1993).

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aclitean Socratic, dissolving perceptible things into roils and eddies of unlimited becoming while dividing being into eidetic universals.31 The Cratylus represents a meeting between these two formative influences. Yet Socrates’s treatment of them is characteristically oblique. For one thing, his theme throughout is linguistic rather than metaphysical, and eventually he and Cratylus agree that no sensible person would try to find out what there is by focusing on names. It is Socrates, moreover, who presents both sides. That the being of things (ousia tôn pragmatôn) is endless flux he establishes through an etymological excavation of the Greek language. This account he calls “inspired.” The alternative account, according to which the truth of the beings (alêtheia tôn ontôn) comprises immutable eidê, he calls a “dream.”32 He seems to prefer the dream, yet could we not pick both, or neither? While in etymological flight Socrates notes the possibility that ancient name-givers, like many of the wise today, got dizzy turning about in their investigation of the beings (onta) and ended up reading their own vertigo into things (pragmata).33 Is it not also possible that Socratics, busying themselves with things human, get carried away and end up reading into being the idealism without which there would be no morality, no arts and sciences, no human society? The Cratylus leaves both sides of Plato’s “teaching” up in the air. Consider finally the Theaetetus. Again Socrates finds in Homeric poetry, as well as Protagorean relativism, a commitment to Heraclitean fluxism. But this time the leading question is “What is knowledge?” and the interlocutors are two mathematicians. Of all the oddities in this dialogue, the two most relevant to our theme are (1) the fact that Plato pairs experts in two very different fields—namely, mathematics, 31. Aristotle, Metaphysics 987a29–b9. 32. Plato, Cratylus 386c3, 393d4, 401c4, 431d3, 436c4, 438d7–c4. 33. Plato, Cratylus 411b3–5; see also 439b10–c6. Socrates shifts attention from onta to pragmata in Cratylus 385c4, and does not use the two words interchangeably until he has made his Heraclitean turn at 401d.



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represented mainly by Theaetetus, and maieutics, represented by Socrates—and (2) the fact that Socrates claims to have an art.34 Regarding (1), we ask whether knowledge of number and knowledge of soul can be subsumed in a single comprehensive account, and whether experts on either side are competent to offer it. Regarding (2), we notice that Socrates elsewhere claims expertise in the art of love (erotics) and seems adept in the art of questioning (erotetics).35 How different are these arts? Certainly they are nature-arts in the sense that they— like medicine, agriculture, and gymnastic—concern things tumbling about between being and nonbeing.36 About such things there can be no knowledge, Socrates elsewhere says.37 The epistemic status of his own expertise is likewise problematic. But if we pay attention to what he does, not merely to what he says, we see that Socrates’s dialectic is not about the beings alone. Of course, something like an eidetic analysis of gignomena would be impossible if nature were wholly indeterminate in number and kind; but Heraclitean fluxism is untenable, and by refuting it in the Theaetetus Socrates has restored a necessary condition for the whole business (pragmateia) of posing and trying to answer questions of the form, “What is X?”38 This business, his pragma, must involve classifications of things natural as well as eidetic analyses. Are these classifications not mythical? Socrates may regard them as mytho-logical.39 Consider, for instance, his account of pleasure 34. Plato, Theaetetus 149a7, 151b1. 35. Plato, Symposium 177a8, 198d1, 212b1–8, Lysis 204b8–c2, Phaedrus 257a7, Cratylus 398d2–7. In the Gorgias (521d7) he says that he is attempting the political art, not that he has it. 36. Cf. Plato, Laws 889d4–6. Socrates mentions the same three arts when examining Nicias’s account of courage in Laches 198d1–199a9. It may be significant that there is no mention of an eidos of courage in the Laches or of moderation in the Charmides. 37. Plato, Republic 478a6, 508d3, Philebus 57d6–59d9 with 56d9–c6 and 15a1–c8, Phaedo 75c7. Plato’s Athenian Stranger seems to agree: Laws 889b1, and Epinomis 975e2–976a6. 38. Plato, Theaetetus 161e5. 39. Cf. Plato, Phaedo 61c2 with 70b6; Republic 376d9, 392c2, 415a3, and 501c4 with 379a2, 588c2. Compare Homer, Odyssey 12.450–53.

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and pain in the Phaedo, according to which they are neither two nor one but an indivisible pair.40 The true analysis of our soul into parts, or of things natural into genê, may likewise be quasi-arithmetical: our soul as indeterminately triadic, erôs or Platonic-Socratic dialegesthai as indeterminately dyadic, etc.

THE ELEATIC STRANGER The day after their conversation in the Theaetetus, Socrates again meets Theodorus, Theaetetus, and young Socrates. This time Theodorus has brought along a “very philosophical man” from Elea. Socrates notes how hard it is to tell real philosophers apart from their various lookalikes—statesmen, sophists, and men utterly mad—and asks the stranger whether his fellow Eleans regard sophist, statesman, and philosopher as one, two, or three in kind. As three, says the stranger, although it is no easy task to say what each of them is. Theodorus and Socrates urge him to undertake this task. He will do so, he says, but in dialogue rather than one long lecture. The result is what we read in Plato’s Sophist (in which, with Theaetetus, he defines the sophist) and Statesman (in which, with young Socrates, he defines the statesman). In his recourse to argument and attention to human affairs, the stranger appears Socratic. Yet there are differences. First, like Herodotus, he is a traveler; he has observed things about which Socrates has only hearsay. And although Elea is in some sense his home, he 40. Plato, Phaedo 60b3–c7. The Aesopian alternative given here, according to which they are two things joined at the head by a god, is wholly mythical. Socrates elsewhere notes the tendency of spirited men to insist on making clean cuts (Republic 439c7–440a3 with 436a8). Notice that the principle of noncontradiction (Republic 436b8–c2) and the evident multiplicity of our activities do not jointly entail the partition of our soul into any definite number of parts. Even if the city’s division into three distinct classes were natural, it would not follow that that our soul is similarly divided. Whether Socrates’s analysis of the human being into body and soul is mythical or mytho-logical is a question present, though never actually posed, in the Phaedo.



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gives the impression of being a man who passes through many cities without belonging to any. He seems moreover to know the answers as well as the questions. Socrates does not bother to learn his name and we feel no need to form an image of him. For us, he is faceless, anonymous—the Stranger. Second, he enters into dialogue more from a sense of social propriety than any philosophical necessity. Nor is he intent on examining and refuting his interlocutors, that they may come to realize how ignorant they are about the most important things. Nor is he openly erotic or interested in gaining what is good for himself and others. Consequently the Sophist and Statesman lack that ethico-psychological tension which characterizes Socratic dialogue. They are less lively, more theoretical. Third, he seems less receptive to the idealism of those around him. In the Statesman, he notes that clothing is for the sake of protection against the elements, but ignores its connection with our sense of shame and desire to look good; and he downplays the role of music in civil society, whereas Socrates plays up its capacity to open up our souls to what is noble or fine.41 He also leaves mostly undisturbed our preconceived notions of virtue and knowledge. He accepts, for instance, the idea that courage and moderation conflict, and the idea that there are already many genuine arts and sciences. He admits even an art of sophistry, whose practitioners suspect they do not know what they are talking about. For Socrates, their suspicion points to the truth about sophistry, that it is no art at all but a mere knack.42 With respect to our standards of knowledge and goodness, the Stranger is less inclined than Socrates to set the bar high, to engage in what many regard as “high redefinition.” He seems more down-to-earth as well as more theoretical. 41. Compare Plato, Statesman 279c8 with Republic 372c2, and Statesman 287c2, 304a7, 306d7 with Republic 403c4–7. 42. Plato, Statesman 258b3, 307d6. Compare Sophist 268a3 with Gorgias 463a–466a, but consider also Sophist 254a5, Statesman 277d2–7.

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Fourth, he does not separate being from becoming. Being is coextensive with the power to affect or be affected, he says, and something is only if it “has mind,” and mind implies life, and life implies motion.43 It is not surprising, then, that he calls “beings” (onta) things in the process of becoming (gignomena, pragmata), or that he regards the production of an artifact as a case of substantive emergence (genesis eis ousian), or that he employs such phrases as “the indispensable being of becoming.”44 Nor is it surprising that he makes little distinction between eidê and genê, eidetic and genetic kinds.45 Fifth, he focuses on eidê as classes (extensions) rather than immutable types (universals). Look at the language he uses. An eidos is said to have parts; it can be divided or sectioned; it may be manifold or many-tribed.46 And when he speaks of a “participation” relation it is always of one kind in another, never of tokens in a type.47 For Socrates, the focus is primarily on some one eidos and the particulars which may or may not partake of it. He never says of such an eidos that it is manifold; and although on one occasion he speaks of making cuts in accordance with eidê, he never speaks of cutting an eidos.48 So 43. Plato, Sophist 247d–e, 248c–249d. 44. Plato, Sophist 219b4, c4, 234c4–d6, 250a8, 264b4, Statesman 266c5, 283d8, 284d4, 287d7 with 285a2–4, 306b10 with 307a9; and Sophist 219b4, Statesman 283d7–e6. But consider also Statesman 286a5, which comes closer to the sort of statement we expect from Plato’s Socrates or Parmenides. 45. Plato, Sophist 235c5–d1, 253b8, 254b7, d4, and 259b2 with 254c2, 255c5, and d4; Statesman 306a8 with e2. (Plato’s Parmenides uses the word genos only when examining Socrates, never when displaying his way of hypothesis.) 46. Plato, Statesman 287e9, 288d4 (cf. Timaeus 76a7, 87a5), 291a8. 47. Plato, Sophist 251b9, d9, 252d3, 254b7–d2. 48. That Socrates does not cut eidê: Phaedrus 265e1 and Philebus 48d4 are not counterexamples, because in the former passage the cutting is said to be only in accordance with eidê, while in the latter it is not explicitly eidetic. (Plato’s Parmenides, too, does not employ the cutting metaphor.) That Socratic forms or ideas do not have parts: the word meros or morion does not occur in Republic 475e–480, 502c–511e, or in Phaedo 99d–107e. Socrates does sometimes speak of eidê as classes, and occasionally engages in eidetic analysis of the sort we find in the Sophist and Statesman: e.g., Euthyphro 11e4–12e8, Philebus 12e7, 27d10, 61e6.



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whereas Socrates appears to be a realist with respect to universals, the Stranger does not. Is he then an antirealist, as some commentators have inferred? He cannot be an extreme nominalist, as he maintains that not every extension for which we have a name is a genos, and not every “genetic” cut is eidetic (kat’ eidos).49 Nor can he be an ante res realist, as he denies that there are any entities apart of living things. With respect to universals, then, he is either a moderate antirealist or a moderate realist. We cannot say which, because his extensionalist turn gives him a way of bypassing the issue altogether. It also gives him a way of “killing” his “father” and pinning down the sophist. For if one shifts as he does from being (ousia) to being this or that entity (to on), one may then regard nonbeing (to mê on) as being something other than this or that being. Suppose for example that one such entity is the just. Then the non-entity would be whatever is not just, that is, other-than-the-just. And if we agree that whatever is must be accessible to thought or speech, then whatever is not will also be accessible to thought or speech.50 The sophist had taken refuge in nonbeing, and Parmenides maintained that nonbeing is unthinkable and unspeakable. By making his broadly semantic turn, however, the Stranger has found that what is not is in a sense—which contradicts Parmenides—and that it can be an object of thought or speech—which makes the sophist definable. Thus has he extended the reach of both counting and accounting. But he has also paid a price, for now being is but one of several coordinate classes, another of which is nonbeing construed as alterity: being and nonbeing are on a par. Also leveled are disparities central to Socratic inquiry: between being and becoming, and being and seeming. Whatever is just only by 49. Plato, Statesman 261d3–263b11. Note also his use of the words idea and phusis when describing each of the five greatest kinds in the Sophist (250a). 50. Plato, Sophist 247d–259a (note especially 250d7, where the genus being is said to be in the soul). A similar turn is made in Parmenides 160b5–163b6, where, having supposed that the one is not, Parmenides argues that it is nonetheless discernible, knowable, selfsame, unlike other things, and so must be in a sense. His argument is explicitly semantic.

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partaking of the just itself, or seems just but is not, is no less than the just itself.51 In sum, the Sophist and Statesman do not display Socrates’s ontoeidetic or ethico-psychological turn. Yet the Stranger appears to have undertaken a second sailing. No one would mistake him for a pre-Socratic natural philosopher, and his semantic-extensionalist turn sets him apart from Parmenides and Zeno as well. The Sophist and Statesman display the Socratic turn modified. One could hardly find a better illustration of the slipperiness of likenesses than in the resemblance between Plato’s Eleatic Stranger and Plato’s Socrates as philosophers. The Sophist and Statesman contain the Stranger’s response to three questions provoked by Socrates: “What is the sophist?,” “What is the statesman?,” and “What is the philosopher?” These questions have the form “What is X?” They appear to be Socratic. For Socrates elsewhere, however, “X” is a noun or nominalized predicate signifying some quantity or normative quality (“the holy,” “piety,” “the beautiful,” “virtue”), whereas for the Stranger it is here a subject term signifying some kind of agent (sophistês, politikos, philosophos). Yet he considers them not as continuants or natural kinds but as activities, arts, or sciences.52 One might argue that the nature of a living thing is art- or activity-like, but the Stranger makes no such argument. He shows little interest in sophists or statesmen as natural entities. He, like Socrates, engages in the complementary activities of division and collection—that is, dialectic—but unlike Socrates he knows at each juncture which cut to accept, which to set aside, and when the sequence of cuts is complete. Whereas dialectic in the Socratic dialogues can seem hit-or-miss, even inspired, here it more nearly resembles a technique. But why does he require that divisions be di51. Consistent with such leveling is the fact that the Stranger’s divisions are usually of like from like, rarely of better from worse. 52. Plato, Sophist 218c2, 233a8, Statesman 258c3, 292d4, 297a4. Cf. Daube, Roman Law, 2–13, 17–19, 36, 46–48.



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chotomous and down the middle as much as possible?53 He insists that the cuts be made in accordance with eidetic differences (kat’ eidê), but offers little reason to suppose that bisection will yield the desired results. In fact, he posits five greatest kinds in the Sophist and divides the co-causes of statesmanship into seven kinds in the Statesman; and these results, being odd in number, cannot be the result of dichotomy alone.54 The Stranger divides not only in accordance with eidetic differences, I suggest, but also in accordance with the abilities and limitations of his interlocutors. Theaetetus and young Socrates are mathematicians for whom measures of relative more-and-less are quite familiar; already they are skilled in the geometrical procedure of cutting lines or areas into two equal parts.55 Yet they are unfamiliar with sophists and statesmen, and with the situations in which these agents operate—situations in which measures of relative more-andless take a back seat to measures of fittingness. The Stranger tries to awaken these budding mathematicians to this fact. When for example young Socrates immediately divides the class of animals into humans and beasts, he is made to realize that he must slow down and become more dialectical, less anthropocentric.56 Dividing like from like down the middle serves this purpose. The Stranger proceeds in a way that befits both what is in question and who is being questioned. In this respect, he closely resembles Socrates. He also resembles the statesman, who must legislate effective rules of distributive and corrective justice: the lawful distributions and penalties must be equitable, otherwise they will not be just; and they must be describable in quantita53. Plato, Sophist 219a8, d4–e5, 220b7, e6, 223d6, 225a9, 266a10, Statesman 262a8–b7, 265a4, 266a2, 276d8, 284e3, 289a6, 302e7. 54. Plato, Sophist 254d4–255e2, Statesman 287b4–289c3. 55. The expression dicha temnein (to cut in two or bisect), used frequently by the Stranger, is also found in the writings of ancient Greek geometers. Cf., e.g., Euclid, Elements I.9–10, 34. That one should not expect eidetic division and collection to exhibit mathematical precision: J. Lenkowski, “Definition and Diairesis in Plato and Aristotle,” St. John’s Review 56 (2014): 58. 56. Plato, Statesman 261d3–263b11; cf. 264a8–b2, 285d4–286b3, and Parmenides 130c5–e4.

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tive terms, otherwise they will not appear just to the people governed by them.57 When young Socrates divides all animals into human beings and beasts, he exhibits a tendency to leap to conclusions coupled with a prejudice in favor of being human. To moderate the former and put the latter out of action, the Stranger undertakes first to shake the young man into a state of greater wakefulness, then to help him divide the class of animals step-by-step in a way that puts humans back into the animal world.58 This longer way exhibits the Stranger’s own tendency to be highly theoretical about barnyard realities. We may set out the result in a treelike fashion as shown in figure 2-1: This way of classifying humans resembles the taxonomic “keys” we find in field guides to plants and animals. Plato’s Sophist and Statesman are field guides to fauna of two very peculiar sorts. Yet while such keys may help us to identify a thing, the definitions they provide are criterial rather than essential or real; they classify things in terms of their observable attributes rather than their natures. The Stranger distinguishes humans from pigs by noting that the square on the diagonal of the one-foot square is two (square) feet, whereas that on the diagonal of the two-foot square is four (square) feet. Telling this joke is his way of sidestepping while indicating the problem of human nature. It befits his purpose, which is not that of a natural philosopher discerning natural kinds, but rather of a dialectician defining the political art in conversation with a young mathematician who, through a combination of theoretical daring and political naiveté, is liable to go badly astray.59 57. Cf. Plato, Laws 719e4, 737e, 757d4–e3, 934b3–c6. That dikaion (“just”) and dicha (“in half ”) are etymologically related seems to have been accepted at the time: Aristotle, Nicomachean Ethics V.4.1132a31. 58. Plato, Statesman 263c1–267c4. 59. Observable attributes may be clues to a thing’s nature. Perhaps our bipedality is a more revealing than many believe, our kinship with pigs deeper than we like to think. In Homer’s Iliad and Odyssey, only (dying) human beings and a (dying) wild pig are said to have souls; cf. Odyssey 14.426.



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living

wild tamable



[solitary]



herd nurturing

aqueous



dry land

winged footed



horned hornless



split-hoofed single-hoofed or or mixed generation unmixed generation



FIGURE 2-1.

porcine human

Yet the Stranger, too, sometimes mentions nature. In the Sophist, the word phusis occurs twenty times. Thirteen of them are in his account of the five greatest classes, where it serves to highlight the unity of each. Its connotations of generation and growth are there stripped away.60 Six of the seven remaining instances are in the last few pages of the dialogue. Here, by a remarkable piece of non-reasoning, Theaetetus concludes that all so-called natural things are by divine art.61 So when, finally, they say what the sophist is in its “proper nature,” it is a 60. He uses the word especially in connection with alterity: Sophist 255d9, e5, 256e1, 257c7, d4, 258a8, a11, b10, d7. 61. Plato, Sophist 265d1–5 (compare Philebus 27b7-c3). In 265a–266e, the word phusis occurs four times. Only here in the Sophist does the verb phuô occur in nonperfect forms.

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divine artifact they have defined, a work of art whose stated function (ergon) may or may not be the one god intended for it. In the Statesman, the word phusis occurs thirty-seven times, nine of them in a myth told by the Stranger to help young Socrates realize where he is.62 The world, he says, alternates between two periods. In one, the Age of Kronos, god is in charge. There are no cities, no sexual generation or death as we know it, and all of nature is under the thumb of divine providence. In the other, the so-called Age of Zeus, god has withdrawn. Natural things come into their own. There is sexual generation and irreversible being toward death. And humans, left to their own devices, live in cities. It is in this period that artisans and scientists, poets and sophists, statesmen and philosophers have emerged—kindred agents who cooperate, or not, in their pursuit of the good.

TIMAEUS Plato’s only natural philosopher is Timaeus of Locri, and the Timaeus is his only dialogue traditionally said to be about nature. Most of it is a lecture on the generation of the cosmos and the first human beings. We cannot be sure that, had he spoken in less constraining circumstances, Timaeus would have explained the nature of things in just this way. Be that as it may, he owes Socrates a debt of gratitude, his Athenian host thinks it best to satisfy Socrates’s request in a roundabout way, and he himself makes a point of being polite.63 Why did Plato pick this natural philosopher and place him in this context? Why did he have Socrates remind us right away of the Republic and then sit quietly, all dressed up (kekosmēmenos), while Critias outlines 62. Plato, Statesman 268b8–277a2 (where the word phuô occurs ten times out of a total of eighteen, all but one in some nonperfect form). On why the word phusis may be comparatively frequent in the Statesman, cf. Laws 889d6–e1. 63. Plato, Timaeus 17b1–4, 20c4–d6, 27b8–d1, 40d6–41a3.



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his grand scheme and Timaeus plays his part in its execution? How is one to interpret the fact that cosmology thus mediates political theory and political history? To these questions there are no clear answers. We cannot be sure that the Timaeus is supposed to show how the “first sailing” can be renewed post-Socratically, or whether the kinds it posits are to be regarded as natural.

Cosmology The world according to Timaeus depends on principles that lie beyond the world. He admits three such “causes”: a model, place, and a divine craftsman. The model (paradeigma) is the being to which the craftsman looked when producing the cosmos. Timaeus calls it “the intelligible animal” and “that which animal is,” but it cannot be alive and is not said to be divine.64 It is beautiful if not good, and complete in that it comprehends all four genê or ideai of animals. Like a universal, it is always, eternally, and really.65 Whether animal itself is the only such being remains unclear.66 Place (chôra) is that which the craftsman fashioned into a likeness of the model. Timaeus calls it “mother,” “nurse,” “receptacle,” and “wandering cause,” and links it with necessity.67 It is amorphous, he says, yet full of dissimilar powers (dunameis), four in kind, which are always being shaken out by a seismic motion.68 Were this motion to take its course, the fiery would become concentrated at the periphery, the earthen at the center, the watery and airy in between; but never, he implies, would they come to rest in a state of equilibrium. And although it tends to sort itself out in this way, place has no intrinsic end or purpose. Timaeus never calls it beautiful or good. Finally, by mak64. Plato, Timaeus 30c7, 39e1, 39e8 (cf. Phaedo 75d1, 92d9). 65. Plato, Timaeus 27d6, 28a3, 30c6, d2, 31a4, b1, 37d1, 39e7. 66. Plato, Timaeus 50c5, 51a1, b6–8, d4–5, 52a1–3, 53d6–7. 67. Plato, Timaeus 47e5–48a2, 49a6, 50d3, 51a5, 52d5, 68e1, 88d6. 68. Plato, Timaeus 50a3–51b2, 52d4–53a7, 57c5.

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ing time a moving image of eternity and thus a feature of the cosmos, he makes place prior to time. Yet before the cosmos was generated there was place, and place itself is forever becoming. It must then be temporal in a sense, even though cosmological time is for it a mere ornament. The craftsman (dêmiourgos) made of place a spatiotemporal likeness of the model. He is said to want, reason, devise, and believe (nomizesthai), and to ordain, persuade, beget, construct, stamp, and paint.69 Yet he has no body, and seems indeed to be nothing but active, productive mind. Timaeus calls him a god. This god wants what is good and is himself good if not beautiful. And he is forever.70 Yet Timaeus does not classify him as an intelligible being, or call him wise, or ascribe to him any science.71 Of these causes Timaeus offers two expositions. In the first (27d– 31b), he distinguishes being from becoming. In the second (47e–53c), he distinguishes the cosmos from place. Only in the second does he say that the causes differ in kind: the matrix is one eidos or genos, the father or model a second, the cosmos a third.72 Thus does he draw attention to the analogy on which his entire account depends; for in any case of production there is the producer himself, the materials on which he works, the pattern he wishes to realize in them, and the product itself. In Timaeus’s account, the cosmos belongs to the class of products; the model, to the class of patterns; the matrix, to the class of materials; and the craftsman or father, to the class of producers. But the cosmos is a living god, at once beautiful and good; the 69. Plato, Timaeus 28c6, 29e1–e3, 30a2, a5, b1, 33a6, b7, 34a8, c1, c4, 37d4, e3, 39e7, 41a8, b4, 50c5, d4, 55c6, 69b3. 70. Plato, Timaeus 29e1, 30a2, a6–7, 34a8, 37a1, 39e7–9, 46c8, 47e4, 56c5, 69b3. 71. There must be such a cause, he says, if there is to be any created thing (Timaeus 28a4–c3). The necessity is hypothetical, and depends on taking the natural world to be something made. 72. Plato, Timaeus 48a7, 48e2–49a4, 50c7. Timaeus often uses eidos and genos interchangeably. The most obvious exception occurs when he posits three generated eidê, not genê, of time (37e4).



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matrix can be apprehended only by a sort of bastard reasoning without sense perception; the pattern is an eternal being; the producer, a transcendent deity.73 How illuminating, then, is the analogy on which his cosmology depends? Timaeus does not take up this question. Instead, he hews to the task Critias has imposed on him and therefore subordinates natural philosophy to physical theory. The craftsman found place to be chaotic, measureless, irrational, and “persuaded” it to receive a world-order modeled after animal itself. This Big Persuasion theory is no less puzzling than today’s more explosive counterpart. Timaeus calls it a “likely muthos.”74 One thing is clear: the resulting cosmos is everywhere and always full of the “workings” of mind and the “becomings” of necessity. This complexity easily eludes us. On the one hand, we may think that we are describing the cosmos when in fact we are describing the model or its mathematical schematization. Timaeus avoids this error. The cosmos only resembles an intelligible entity, he says, and its coming to be is not a case of substantive emergence (genesis eis ousian).75 On the other hand, we may think that we are describing the cosmos when in fact we are trying to describe the receptacle. Timaeus avoids this error as well. The cosmos is something finished, he says, a self-sufficient whole and not a mindless dream moving mysteriously over the deep. He thus resists the perennial temptation to reduce cosmology to (mathematical) ontology or (unmathematizable) chorology.76 73. Plato, Timaeus 29b3, e3, 30a4–5, b8, 31b3, 34a1–b9, 36d8–37d1, 48a2, 53a8, 56c3–7, 68e2, 69b3, 92c8–9. The relation of cosmos to model is that of image to original. Timaeus does not call it a case of communion or participation, and seems unaware of the “Third Man Argument” advanced in Parmenides 131e8–133a10. 74. Plato, Timaeus 48a2–3 with 29d4, 30b7, 48d2. In its native indifference to reason and capacity to be persuaded by reason, place resembles the spirited part of our souls according to Socrates (Republic IV). 75. Consider Timaeus 50a–c, 80e4, and note the different verbal aspects of the participles he employs at 47e4–5. 76. Plato, Timaeus 28b1, 29a5–7, 33b4–34b9. The term “chorology” I take from John Sallis, Chorology: On Beginning in Plato’s Timaeus (Bloomington: Indiana University Press, 1999).

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His account of bodies comes in two iterations. First, the divine craftsman reasoned that to be both tangible and visible the cosmos must be composed of fire and earth, and that fire and earth could be bound together beautifully by two middle terms, air and water. So, using all available stuff, he made the cosmic body out of fire, air, water, and earth, in amounts determined by a continued proportion.77 Second, Timaeus himself conjectures that particles of fire, air, water, and earth could be constructed by schematizing the four sorts of precosmic powers; and that the divine craftsman might have done so by imprinting in these powers four of the five regular solids. Timaeus distributes these solids so that particles of fire are pyramidal; those of air, octahedral; those of water, icosahedral; and those of earth, cubical.78 About this account it suffices to make four points: (1) Timaeus, like some social-contract theorists, uses his Big Persuasion theory as a heuristic device to help him distinguish what in bodies is rational, and therefore beautiful, from what is not. He calls this part of his lecture a “likely logos.”79 (2) The genê or eidê of body are defined in terms of precosmic powers (traces, affections) and the five regular solids. But these solids are defined in terms of their surfaces, which are themselves defined in terms of constituent triangles of two sorts. The principles of body, then, are these triangles and those potentialities, neither of which are bodies. (3) This account makes no reference to the model and it is hard to see how there could be any similarity between animal itself and geometrical figures or ratios. Perhaps, like Kant, the 77. Plato, Timaeus 31b–34b. Expressed algebraically, the proportions are a3:a2b::a2b: ab ::ab2:b3 (e.g., 8:12::12:18::18:27). The craftsman must have constructed all four terms out of a given amount of stuff, a problem far beyond the scope of Euclid’s Elements. Earth is probably the least term, fire the greatest, yet Timaeus does not say which is which (cf. Republic 509d–511e). The divisions of body are made partly in accordance with geometric rather than arithmetic or harmonic means. 78. Plato, Timaeus 52d–61c, esp. 53a2–e7, 54b3–d7, 55a2–56d1, 57c7–d6. See also 28b8, 69c1, 79d5–e6, 80c5. Whereas the first account of body introduced a problem in ratio theory, the second introduces an exercise in solid geometry. Timaeus says nothing about how these two accounts are to be put together. 79. Plato, Timaeus 53d5, 56a1, b4, 59d1, 67d1, 90e8. 2



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craftsman realized that in order to construct a spatiotemporal likeness of the model he had to invent mediating schemata. (4) As socialcontract theorists distinguish between prepolitical (uncivilized) and political (civilized) man, so Timaeus distinguishes between precosmic (ungeometrized) and cosmic (geometrized) kinds. The difference between them is like the difference between tamed and untamed nature, or between cosmological and precosmological time. One may think that only cosmological time is time properly speaking, and that men are human only insofar as they have become civilized. But one may also think that bodies are natural only insofar as they are potentialities not yet geometrized. His account of soul has three parts. First the craftsman made the cosmic soul. Its constituents are right out of the Sophist 245e–259d, but their forced combination and subsequent divisions and motions are distinctly Timaean.80 Second, the craftsman mixed up another batch of immortal souls—same ingredients but qualitatively inferior—and sowed them into the different “organs of time.”81 Third, his subordinates receive these souls, invent a mortal class of souls that prove double, and allocate them all to three different places within the human body.82 Again it suffices to make just a few points. (1) Soul, unlike body, is associated with the good and not the beautiful.83 (2) Counting the eidê or genê of soul proves difficult because Timaeus introduces without explanation a distinction between immortal and mortal. Whereas immortal souls dwell in our heads, he says, even though they are inherently placeless, our mortal souls are not really distinct from their proper places: his account of them is entirely physiological.84 (3) In his 80. Plato, Timaeus 34b–36d, 39ab. Only here in the dialogue does the word ousia cluster. Only here is the craftsman said to use force (35a8). The divisions of soul are made in accordance with arithmetic or harmonic rather than geometric means. 81. Plato, Timaeus 41d–42e. 82. Plato, Timaeus 69c. 83. Cf. Plato, Timaeus 37a1, 42b2–3, 69e5, 70b8. 84. Plato, Timaeus 42b7, 69a3, c6–8, d5, 77b4, 81c6–e1, 84a7, 89b6–c4, 89e4–90a4. The kinds of soul are usually called eidê, not genê. A notable exception occurs at 73c3–4.

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psychology, too, Timaeus makes no reference to the model. Although souls and bodies of various kinds are necessary conditions for the presence of mind in the world, and for the instantiation of animal itself, they are not likenesses of anything eternal. His account of animals is in three acts. In Act One, mind saw such and so many ideai in animal itself and decided that the cosmos should have as many of these sorts. There are in fact four: the celestial genos of gods, a winged airborne genos, an aqueous eidos, and a footed dryland eidos.85 Why do these animal-kinds correspond to the four kinds of body? Perhaps Timaeus has observed that animals occupy different elemental niches, and inferred that the craftsman must somehow have deduced this arrangement from an inspection of animal itself and inhomogeneous place. In Act Two, the craftsman tells members of the celestial class that they are to make the other three kinds, imitating his example. Only now do we learn that the others are to be mortal and that the master craftsman will not make them.86 Does the difference between immortal and mortal reflect any distinction within the model? And what about the different ways in which immortal and mortal animals are related to the cosmos as a whole? Do these reflect different ways in which the ideai are related to animal itself? Timaeus does not say. In Act Three the celestial craftsmen go to work, producing the first humans and the barely ensouled plants which are to be their food.87 These humans are our ancient phusis, the exemplary mortal genos. All were males lacking genitals as well as navels. They were built for nobility, their heads sphere-like, their thinking attuned to the circling 85. Plato, Timaeus 39e–40d, esp. 39e7–40a2. Animal kinds are usually said to be genê rather than eidê. 86. Plato, Timaeus 41a–42e. The distinction between immortal and mortal is first introduced at 41b2–7. Celestial animals are qualifiedly immortal. All other animals are mortal even though their souls are partly immortal. 87. Plato, Timaeus 69c. Although plants are alive, their ideai in no way reflect ideai in animal itself (77a3–5). There are only two other references to plants in the dialogue: 60a1, 90a6.



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of heaven. Yet some became disordered in their minds and devolved into women. Our phusis having thus become double, the craftsmen fashioned and attached male and female genitals, plant-like things enabling us to reproduce. Eventually some of their descendants became still more disordered and devolved into the genos of birds, from which came the genos of other terrestrial beasts, from which came the aqueous genos including the tribe of fish. Thus did the cosmos become complete.88 Throughout this long finale there is no reference to the model. The begotten craftsmen, working almost entirely on their own, produced a mankind that is now extinct, and not any of the mortal kinds that now exist. These appear to be a cosmic accident, one that perpetuates itself sexually. In fact, however, they came to be because the souls of their ancestors, ultimately our ancestors, became corrupt. For this, we or they bear responsibility; the present order is just. Yet the original craftsman, seeing that the cosmos would not be complete unless its mortal parts were defective, so devised the celestial makers and our immortal souls that the requisite degeneration was inevitable. This secret Timaeus has revealed; but he has not explained why the present order of animal kinds is stable, as it must be if the cosmos is to remain complete.89 The relation between cosmic and eidetic kinds could hardly have been presented in a more riddling fashion.

Philosophy and Piety Timaeus says that cosmology is for the sake of relaxation from the rigors of ontology, as it is about becoming rather than being and about becoming there can only be opinion with sense perception.90 He also says that his cosmology mixes myth with reason, and that it can only 88. Plato, Timaeus 90e–92c with 42a1–d2, 90d5. Compare Symposium 189d. 89. Cf. Plato, Timaeus 92c1–3. Consider also 18d8–19a5, 42a3–44c4, 73b6, 76a6–b1, d7–e6, 81a4–5. 90. Plato, Timaeus 59c5–d2 with 27d5–28a6.

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be likely. But it does not follow that his account is false, or that natural philosophy is a waste of time. In fact, not only does he imply that his cosmology is more likely than its competitors, he claims that the study of nature is necessary for human happiness.91 The similarities between his lecture and the Republic are striking. There, proceeding mytho-logically, Socrates produces a city in speech —a city containing three or four classes, ordered hierarchically, with some possibility of movement from class to class. A city resembling it will be realized, he says, only if a philosopher looks to something eternal and, like a craftsman, turns a bunch of youngsters into a beautifully ordered whole. Similarly, Timaeus reproduces a world in speech—a world containing four classes of animals, ordered hierarchically, with some possibility of movement from class to class. This world came into being when a craftsman, looking away to an eternal model, turned a bunch of potentialities into a beautifully ordered whole. Timaeus even describes us as being fettered in a sort of cave; for the craftsmen have rooted our minds in the stars, he says, and otherwise so enveloped us in time and place that we are likely to be the most god-fearing and dream-ridden of animals.92 Yet between his account and Socrates’s there are differences, one being this: for Socrates, the city in speech is a model “laid up in heaven.” It does not imitate Athens, the city in which he produces it. Compare Timaeus, for whom the cosmos in speech is a representation of the very world in which he and the rest of us live. It can be shown that Socrates would have no place in a city like the one he has generated in speech, but from this it follows only that there must be some tension between Socratic philosophy and a good political order, not that Socratic philosophy is impossible. Compare Timaeus. His own thinking transcends the cosmos, and yet his cosmology limits human 91. Plato, Timaeus 29c4–d3, 68e6–69a5. Cf. Parmenides B8.51 and Plato, Phaedrus 272d2–273a1. Cf. W. K. C. Guthrie, A History of Greek Philosophy (Cambridge: Cambridge University Press, 1965), 2:64. 92. Plato, Timaeus 27a8, 42a1, 47e5, 52b3, 55d7, 70a2–d6, 71a3–72b5, and Critias 106a4. Cf. Republic 369c6–d3 and 484c6–d3, 500e3–4, 540a9.



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thought to things cosmic; it supplies no basis for philosophical eros or dialectic. Timaeus thus fails to make room for himself in his own account.93 It is a failing to which physical theory is perennially prone. Yet it may be that he made the natural world a sealed cave in order to supply Critias with humans of the sort he wants. Critias identifies this world with the all (to pan). No, says Timaeus, it is only this all; but in the final round of his account, as references to eternity disappear, this world seems to be all there is.94 Critias is also a pious man. He must like it that Timaeus bookends his lecture with prayers, first to gods and goddesses, and then to the god. But goddesses are only by convention, Timaeus says, and the god to whom he finally prays is this very cosmos in speech.95 Does he not realize that by elevating his representation of a likeness, he seems to be praising himself even as he succumbs to an idol of the cave? Timaean piety is as perplexing as the physical theory it imbues.

PLATO What did Plato, the maker of these dialogues, think about natural kinds? He entertained seriously the proposition that there are real types (eidê), attendant difficulties notwithstanding. He also entertained seriously the proposition that things by nature are not beings-in-becoming, and that the disjoint kinds (genê) into which such things seem to fall are artificial or conventional rather than real. Was Plato then a realist with regard to universals and an antirealist with regard to natural kinds? I think so, yet one cannot be sure, as he chose to show rather than tell, and different dialogues show different things. Do any of them suggest that he was ever a natural-kinds realist? 93. Consider Plato, Timaeus 36d8–37c5 with 34a2, 41e1–b5, 47b6–c4, 68e6–69a5, 88e, 90a2–b1, and 46d7–8 with 92a1–d5. Erôs emerges only with the degeneration of aboriginal humans into sexually differentiated men and women (90e6–91a5). 94. Plato, Timaeus 27a4 and 29d7–8; cf. 88e4, 90c8, d3, e2, 92c4. 95. Plato, Timaeus 27c6 with 40d–41a and Critias 106a4 (cf. Timaeus 92c4–9).

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There is one “late” dialogue, the Sophist, in which a semantic turn allows its leading interlocutor to smudge the line between being and becoming, eidos and genos, substantial and nonsubstantial emergence. But there is no indication here or elsewhere that Plato thought this could be used to establish natural-kinds realism. In the Laws, a “late” dialogue, the distinction between being and becoming has almost disappeared, and yet its leading interlocutor emphasizes the difference between eidetic and genetic accounts and shows how difficult it is harmonize the two.96 The Timaeus may indicate that Plato took the natural world to be a beautifully ordered whole (kosmos) only if some rational agency has made it so; but if he did, it would not follow that he took things by nature to be divine artifacts; and as we have seen, Timaeus himself implies that bodily kinds have no basis in what is, and the way in which animal kinds represent eidetic differences is quite mysterious. Consider, finally, Socrates’s alphabetic analogy in the Cratylus and Philebus. The stream of linguistic utterance is indefinite yet somewhat articulate. A divine alphabetist, studying this stream, discerned in it vowels, semivowels, and consonants. Consonants are audible only in syllables such as BA, BU, KE, KO, PI, PAW, TAY, TEE, and so forth; in themselves they are soundless mutes. One might think that natural kinds are like different syllabic types in the flux of nature, and that the universals in which their members participate are like the mutes to which these types correspond. But again, the problem is to show that this is so without invoking a divine articulator who invents as well as discovers these divisions and collections. The Cratylus and Philebus give no indication that Plato thought this could be shown.97 96. Plato, Laws 631b–632d, 645a4, b1, 720e11, 963e5, 965c2. Cf. Seth Benardete, Plato’s “Laws” (Chicago: The University of Chicago Press, 2000), 18–21, 75, 86, 181, 329, 344. 97. Plato, Philebus 18a7–d2, Cratylus 393d1–e9. The Philebus is the only dialogue in which Socrates mentions natural kinds as types (15a4), but he calls them “henads” rather than eidê, and it appears that these henads may be concepts rather than real universals (compare 15a4 with 54c10, 55b1). The Eleatic stranger also makes use of an alphabetic analogy



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He was, it seems, non-dogmatically and self-consciously a naturalkinds antirealist. That he was self-consciously so sets him apart from the pre-Socratic philosophers, most of whom had nothing to say about natural kinds one way or the other. That he was non-dogmatically so means that his writings continue to provoke thinking about natural kinds and their members. While reading them, we feel as if our minds were waking up to what still lies beyond our comprehension. Of all the dramatis personae Plato produced, Socrates is the most powerful. Consequently, while reading his Socratic dialogues we may come to regard this character as our role model, and become convinced that his second sailing in the only way to go in philosophy. Yet Plato has not shown this conviction to be true; it is the rhetorical power of his writing, as much as any argument it contains, which leads us to join in the Socratic turn. We need to be careful, then, lest we become enchanted. Aristotle did take proper care, as we shall see. (Statesman 275c5–d6) but his interest is primarily in discerning stoicheia (elements, letters) “in the long and difficult syllables of the pragmata,” and only secondarily in discovering immutable types in the things that are by nature; see also Sophist 261d–e with 252e–254a and Theaetetus 201d.

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CHAPTER 3

Eidos and Genesis II Aristotle

Aristotle was the first natural philosopher to embrace natural-kinds realism, and it was his conception of natural kinds that was generally accepted by medieval philosophers. In this chapter I consider the way in which he effected a “paradigm shift” in natural philosophy; his acceptance of the widespread belief that living things are paradigmatic entities; his account of their natures or essences, and of their place in the cosmic order; his conception of the natural kinds, or “species,” to which many if not all living things belong; and his explanation of how such entities come into being.

NATURAL PHILOSOPHY RENEWED Socrates, said Aristotle, busied himself with ethical matters, not at all with nature as a whole, and with respect to things ethical he sought the universal (to katholou) and was the first to focus on definitions of what things are. He also said that Plato was a metaphysical dualist: beyond the world of perceptible things, which are in flux and unknow78



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able, there are certain universals, called “ideas,” which are immutable, knowable, and separate from everything perceptible.1 This presented a challenge to natural philosophy, one which Aristotle undertook to meet by criticizing its Parmenidean and Heraclitean roots. He did not say that the Socratic turn presented a comparable challenge, but spoke rather as if it was irrelevant to any theoretical undertaking. In renewing natural philosophy, however, Aristotle did not simply rejoin the pre-Socratics. He was the first philosopher to say that horses, humans, and the like are entities in their own right; the first to claim that such entities are to be explained in terms of intrinsic formal causes; the first to maintain that there are natural kinds in the full sense of the term; and the first to make the what-it-is (to ti estin) central in things by nature. His way of investigating such things also appears unlike that of any pre-Socratic philosopher. Explicitly, repeatedly, he began with what is first for us. What is first for us are the phenomena, comprising not only what we perceive (aisthêta, phainomena kat’ aisthêsin) but also what we or the experts find plausible (endoxa).2 Aristotle engaged accordingly in much empirical research and paid close attention to the ways in which people talk about things. He did so not because he took what is first for us to be first simply or because he wished to defend our ordinary understanding of the world. In fact he distinguished between what is first for us and what is first simply, and acknowledged that what we take to be exemplary realities may have “little or nothing of being.”3 1. Aristotle, Metaphysics 987a29–b9, 1078b17–30, 1086b3, and Parts of Animals 642a24– 31 with Metaphysics 987b1–2. 2. Aristotle, Nicomachean Ethics 1145b2–20, 1146b8; see also 1095b14–1096a5 and Topics 100a18–b23, 104a8–11, 108b13, 119a38, Prior Analytics 24b12, Art of Rhetoric 1352b27–32, On the Heavens 270b6–20, 279b6–7, 287b31–288a2, 297b23–298a20, 308a4–7. Cf. G. E. L. Owen, “Tithenai ta Phainomena,” in Aristote et les problems de méthode, ed. S. Mansion (Louvain: Publications Universitaires de Louvain, 1961), 83–103; C. P. Long, “Saving Ta Legomena,” Review of Metaphysics 60 (2006): 247–67; and Jason Tipton, Philosophical Biology in Aristotle’s Parts of Animals (New York: Springer, 2014), esp. 10–12, 21–24, 28–29, 45. 3. Aristotle, Posterior Analytics 71b34, Nicomachean Ethics 1095a30–b4, Physics 184a16– 18, Metaphysics 992b24, 995a24–36, 1029b3–10.

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Yet he realized that we must begin with things as they first appear or seem to us; and these phenomena, he supposed, reveal as well as conceal the truth.4 Such in brief was his peculiar way of investigating nature and the peculiarly biocentric ontology to which it led him. What explains these peculiarities? I make the following suggestion. Aristotle’s theoretical response to the Socratic turn was not to ignore it, but to appropriate it by noticing that natural phenomena are among the things first for us, by relying on a different analysis of how such things are declared in speech, and by setting aside for the time being, at least, the suspicion that sense perception blinds us to things as they really are. The Aristotelian return to nature follows in the wake of Socrates’s second sailing and depends on it. It is post-Socratic in the way that neo-Ionian natural philosophy was post-Parmenidean. And it was in this way that Aristotle brought about the first of two revolutions, or “paradigm shifts,” in the history of physics. He shows rather than tells us how his return to nature is Socratic. To see how it led him to natural-kinds realism, let us begin by considering Books I.1–II.1 of his Physics.

THAT THERE ARE INDIVIDUAL ENTITIES Aristotle begins his treatise on nature by focusing on inquiry. About it he makes two points: (1) if our goal is scientific knowledge (epistêmê), we must seek out the principles or causes; (2) the course of inquiry is naturally (pephuke) from things more familiar to us to things clearer and more knowable in their nature. Natural things more familiar to us 4. Aristotle, Metaphysics 993a30; cf. Kurt Pritzl, “Aristotle’s Door,” in Truth: Studies in a Robust Presence, ed. K. Pritzl (Washington, D.C.: The Catholic University of America Press, 2009), 15–39. That sense perception is cognition of a sort: Generation of Animals 731a33, Prior Analytics 46a17–22, Posterior Analytics 72a1–3, 74b32–34, 100b3–5, Parts of Animals 639b5–10, 640a13–15, On the Heavens 306a5–17, Metaphysics 980b28.



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include concrete wholes we perceive, generic classes we take for granted, and things we have named but not yet articulated.5 We expect Aristotle to begin here, but in fact he turns away to examine the opinions of Parmenides and other pre-Socratics; it is not until Book II.1 that we get the sort of inquiry he led us to expect in Book I.1. Why did he not begin directly in the natural, neo-Socratic way? He cannot do so, I suggest, because his philosophical predecessors have established a tradition within which he and his auditors must operate, and he knows that their teachings are inadequate, in part because they tended to disregard, even denigrate our everyday understanding of things. To begin properly, therefore, he must first free himself and his auditors from this tradition by refuting or appropriating it through argument. The natural beginning of natural philosophy must be retrieved, and it cannot be retrieved naturally.6 The principles in question are either one or many, and if one either movable or immovable. Parmenides held that being is unqualifiedly one and immovable. His inquiry then was not about nature, save in showing that there can be no such thing as nature because it involves becoming and becoming is unintelligible. To refute Parmenides, Aristotle invokes his categorial understanding of being. Being is either something predicable of a subject or a subject of which something is predicatable. Being according to Parmenides cannot be the former, because it would then be predicable of nonbeing, and it cannot be the latter, because nonbeings would then be predicable of it. His ontology is therefore unacceptable.7 But notice, this categorial understanding of being is an articulation of the ways in which we ordinarily talk about what there is: Aristotle’s refutation of Parmenides assumes the 5. Aristotle, Physics I.1. 6. Throughout this chapter I suppose that the traditional ordering of a given Aristotelian treatise does not seriously misrepresent Aristotle’s thought. Some scholars have questioned this supposition. 7. Aristotle, Physics I.2–3.

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reliability of the “way of mortals who know nothing,” and thus begs the question. It is true, however, that our categorial understanding of being comes first in the order of inquiry. Aristotle is quietly returning us to our proper starting point.8 Earlier natural philosophers posited contraries, two in number, and agreed that all change can be understood in such terms. Supposing these contraries to be dispositional states, it is necessary to hypothesize as a third principle that which underlies and persists in these changes of state. Call it the phusis or ousia (substance) of changeable things. The principles of everything natural are then three—hot and cold, or the like, and the substance which becomes hotter and colder.9 Aristotle, in recovering the subject matter of natural philosophy from the Parmenidean elenchus, is recounting what his predecessors said about nature, not what he himself is going to say. His account is also schematic. It does not tell us which contraries are basic, or offer any reason to affirm (or deny) that the third principle is more than one in number: the word ousia has not yet been used in the plural. Nor, finally, does it imply that there is any substantial change, or that the ousia of things is not everlasting. Having thus recounted the ontology of pre-Socratic natural philosophers, Aristotle uses it to present what we say about change in general.10 Now, more than before, he mentions such familiar changes as bronze becoming a statue, stones or timbers becoming a house, someone unmusical becoming musical, and a mixture of seminal fluids becoming a human being. For the first time he characterizes the contraries generally as the form and the privation thereof, and what underlies them as matter (hulê, which ordinarily means “wood”). He 8. One might claim that that if being were transcategorial, it would be ineffable. But Aristotle is in no position to make such a claim, for not only does he invoke the transcategorial relations of inherence and predication, in order to articulate the different categories of being, he also admits the existence of an entity so simple that what one predicates of it is no more real than the “signs” describing Parmenidean being. 9. Aristotle, Physics I.4–6, esp. 189a9, a28–33, b16. 10. Aristotle, Physics I.7.



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also begins using the word ousia in the plural, allows for substantial as well and nonsubstantial change, and says that it is not yet clear whether the matter or the form is the ousia of a thing.11 Finally, he emphasizes that every becoming is to this or that enformed being from something lacking this form and yet nevertheless qualified. There is no unqualified being, and no reason to think that becoming is possible only if there is unqualified nonbeing.12 At the end of Book I we are exhorted to begin again from another beginning.13 This new beginning turns out to be the one he described at the outset, the one which opens up a natural way of investigating things natural. Book II of the Physics begins as follows: Of the things that are, some are by nature, whereas others are on account of other causes. Of things by nature, some are the animals and their parts, and the plants, and the simple bodies—for instance, earth and fire and air and water—for we affirm that these too are by nature. And all these differ evidently [phainetai diapheronta] from things not constituted by nature. For each of them has in itself a source of movement and standing still . . .14

Such movement or standing still may be qualitative, quantitative, or local. Aristotle thus accepts our usual understanding of motion and rest. He does not immediately reduce all movement to locomotion, as did the neo-Ionians. And although he still admits substantial change, he does not mention it here; his focus now is on what there is (to on), not on the genesis of what there is. Do simple bodies have their sources of movement in themselves? Suppose an ape picks up a clod of earth, holds it for a moment, then lets it go. Is the source of its freefall evidently within it? No, it is not plainly in anything. At the outset, then, simple bodies are not exemplary cases of things constituted by nature, whereas apes and other 11. Aristotle, Physics 190a31–b17, b25–27, 191a7–12, a19. 12. Aristotle, Physics I.8. 13. Aristotle, Physics 192b2–4. 14. Aristotle, Physics 192b8–14. Cf. On the Soul 412b16.

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animals are. In the order of inquiry, at least, Aristotle’s physics is going to be zoöcentric.15 The downward movement of earth is according to its nature, whereas its upward movement is contrary to nature, by force. Had something impeded the development of the embryo that came to be this ape, the ensuing deviation would likewise have been contrary to its nature.16 Not every occurrence in the world is natural. And whereas apes and the like are constituted by nature, artifacts and things by convention are not. Not everything in the world has a nature.17 In Aristotelian physics, as in our everyday understanding of the world, “nature” is a term of distinction. Aristotle proceeds to categorize things having natures as entities (ousiai).18 This too accords with common opinion. Yet he would admit that our perception of such things is fallible,19 and it is not immediately evident to us why we should regard horses as entities but not beds. Why then does he not try to prove that things constituted by nature are entities? The answer is simple: he attempts no such argument because it would be absurd to “prove” things more evident by appeal to things less evident. That some if not all things constituted by nature belong to the category of ousia is more evident to us than any reasons we might now have for accepting or rejecting this metaphysical proposition. Hence, to require such an argument right away, 15. Cf. Aristotle, Metaphysics 1040b5–10. He does not now mention celestial beings, as they are cognitively remote (cf. Parts of Animals 644b22–28). 16. Aristotle, Physics 192b22–193a2 with 215a1, 230a29, 254a9, b21, On the Heavens 300a23; and Sarah Waterlow, Nature, Change, and Agency in Aristotle’s Physics (Oxford: Clarendon Press, 1982), 5. 17. Aristotle, Physics 192b17–193a2 with Metaphysics 1003a24–b19, 1025b7–1026a10, 1064a2, On the Soul 412a6. 18. Aristotle, Physics 192a33; also 185a24 and Metaphysics 992a24–28, 1032a19, 1034a3, b22, Categories 1b28–2a19, History of Animals 491a23. 19. Aristotle, On the Soul II.6, III.1. Experience is not just sense perception: Metaphysics 980b27–981a1. When Aristotle speaks of perceptible substances he need not mean that they are sensible (aisthêta) in the narrow sense of term introduced in On the Soul III.1. Consider, e.g., Posterior Analytics 78b39.



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as some of his predecessors would surely have done, shows poor judgment.20 Given the Parmenidean and Socratic turns, in particular, we need to recover our robust sense of nature. That there appear to be things by nature, some having sources of movement and standing still in themselves, is an uncontroversial phenomenological point. That these balky self-movers are usually spoken of as entities is an uncontroversial semantic point. This is where we all begin.21 Aristotle’s return to nature has yielded the following: (1) There are beings constituted by nature. This existence statement introduces “the if ” (to ei). (2) Those having natures are entities. This category statement introduces “the that” (to hoti). (3) Paradigmatic natural entities are horses and the like. This paradigm statement indicates the order of inquiry: though elementary masses and the heavens will not be ignored, we focus now on individual animals like us, and do not worry right away about how to understand water, stars, or oysters.22 (4) The inquiry will be empirical as well as conceptual, for statements (1)–(3) have opened up a domain known to us only in outline; we need to get better acquainted with these beings in all their variety and complexity. Our inquiry will therefore involve a good deal of natural history. We must not let any squeamishness or contempt for what is lowly or shameful cause us to look away from our proper starting point.23 Natural history is not yet natural science (phusikê). To know some20. Aristotle, Physics 193a4–9 and 191a24–27 with 191a33–b13 and Metaphysics 984a30– b1, 992b18–20, 1039b27. One might claim to have primary, nondeductive knowledge of such entities; but Aristotle makes no such claim and no such knowledge is required at this stage of the inquiry. 21. Aristotle, On the Soul 412a11, Metaphysics 1028b28, and Physics 192a34 with Categories 1a20, 4b17–19, Topics 103b29–31, Metaphysics 1017a24–30. Also Metaphysics 993a30–b7, 995b14, 997a34, 1028b2–7 with Posterior Analytics 72a18–20. 22. Aristotle, Metaphysics 1032a18, 1034a2–4, 1043b22. Cf. James G. Lennox, Aristotle’s Philosophy of Biology (New York: Cambridge University Press, 2001), 18–25. 23. Cf. Aristotle, Prior Analytics 46a17–27, Topics 102b35, Physics 193a5, Generation and Corruption 316a5–10, History of Animals 491a7–14, Parts of Animals 639b20, 640a14, 646a11, 650a31, Generation of Animals 704a10, 719a20, 746a15, On Respiration 478b1.

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thing scientifically is to know the why (to dioti) as well as the that (to hoti), and we know why these natural entities are as they are just in case we know their causes.24 Natural science is what we now seek, not merely from some preconception of what science is, but because living things are so wonderful and perplexing: the phenomena themselves induce us to ask “Why?” And in trying to answer this question we tend naturally to look within (entos) these entities, as that is where their natures appear to be.25

INDIVIDUAL ENTITIES EXPLAINED Aristotle was the first natural philosopher to make the word “cause” a key technical term. We often answer why-questions by statements meant to declare what is responsible (aition) for some occurrence or state of affairs—to declare, in other words, the cause (aitia) of something’s becoming or being what it is. Aristotle found in these everyday because-answers a fourfold typology of causes: type I, that out of which X came to be and of which it is constituted (e.g., the silver of which this cup is made); type II, the form or pattern of X (e.g., the ratio 2:1 that a musical octave has); type III, that whence X is primarily initiated (e.g., the begetter of a child); and type IV, that for the sake of which X is (e.g., health, for the sake of which one eats right).26 Aristo24. Aristotle, Physics 184a24–26, 194b17–19, Metaphysics 981a12–b3, Posterior Analytics 72b28–30, 89b23–25, 92b5–8, 93a20, On the Soul 413a11; also Nicomachean Ethics 1095a30– b13, 1098b5, Topics 105a10–19. Cf. David M. Balme, “Aristotle’s Use of Division and Differentiae,” in Philosophical Issues in Aristotle’s Biology, ed. A. Gotthelf and J. G. Lennox (New York: Cambridge University Press, 1987), 89; Montgomery Furth, Substance, Form, and Psyche: An Aristotelian Metaphysics (New York: Cambridge University Press, 1988), 60. 25. Aristotle, On the Heavens 268a19, and History of Animals 511b19 with Physics 192b13, 19. When seeking to understand the good life for a human being, Aristotle also looks within, to the exercise of good character. His ethics focuses on individual agents, the virtues proper to them, and their characteristic behavior. Similarly, his physics focuses on natural entities, their natures, and their characteristic movements. 26. Aristotle, Physics 194b16–195a3, also Metaphysics 983a26–32, 1013a24–34, b4, Posterior Analytics II.11.



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telian physics mentions causes of all four sorts. Tokens of types II, III, and IV often coincide.27 Having classified as entities beings constituted by nature, Aristotle begins to explain each in terms of its nature, which he takes to be its matter together with its form.28 The matter is a type I cause, the form a type II cause. So far, then, he is offering an explanation of the sort we expect. Yet already there are difficulties. First, the entity’s nature appears indistinguishable from its inner source of movement, but this source seems irreducible to matter or form alone.29 Moreover, he speaks as if the entity in question had two natures, which is impossible.30 Above all, why should we think that its nature is more formal than material, as he now claims?31 It may be true that we identify a bed in terms of its shape (morphê) rather than the wood (hulê) of which it is made; but why should we think that this hylomorphic conception, whose native home is in the productive arts, can be extended to things constituted by nature? Aristotle has just distinguished such things from artifacts, and if the form and matter of a horse were really like the structure of a bed and the wood of which it is made, this would only reinforce the pre-Socratic thought that a horse is not really individual at all, for just as this wood need not have been a bed and the bed’s shape need not have been realized in wood, so too are the form and matter of a horse mutually independent, their union merely conjunctive, like soul and body in Plato’s Phaedo. Yet Aristotle takes this hylomorphic analogy to be illuminating. To see why, we turn to the central books of his Metaphysics.32 27. Aristotle, Physics 198a21–26 (the material cause is plainly the odd fourth). See also Metaphysics 1015a12. 28. Aristotle, Physics 193a9–b6, cf. Parts of Animals 641a17–27. 29. That its nature is to be identified with this source: Aristotle, Physics 192b21–23, On the Heavens 268b16. 30. That it seems to have two natures (phuseis): Aristotle, Physics 194a16, 27. 31. That it is more form than matter: Aristotle, Physics 193b6, 200a33, Parts of Animals 640b28, 641a30, 642a17. 32. Physics according to Aristotle considers movable beings insofar as they are movable,

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Matter and Form We tend to regard matter itself as formless, but when we try in thought to strip away everything that makes matter this or that enformed thing we find that nothing remains. Matter as such is neither separable nor a this (tode ti), yet the material entity is both separable and a this.33 Matter is always already enformed, and its form is not extrinsic. Hence matter and form, as two intrinsic causes, must not be regarded as two mutually independent constituents of the entity in question. Aristotle has several ways of thwarting our tendency to accept this misconception. One is to regard matter adjectivally: a table is not wood but wooden, a human being not flesh and bones but fleshy and bony, and the matter of a natural entity generally is not “that” (ekeino) but “thaten” (ekeininon).34 Another way is to insist that we attend always to the proximate matter: although this horse is composed of (equine) flesh and bones, and in these material parts there are portions of water and earth, it is not therefore just watery and earthen, and to think otherwise is to lose sight of the entity you wish to explain.35 The material is unintelligible apart from the formal cause. But form, says Aristotle, is not only prior in being to matter, it is also most perplexing.36 We are inclined to agree when we read that the form of a living entity is its soul (psuchê). What is formal about the soul of an individual organism? To clarify what he means by the eidos in this context, Aristotle describes it first as the thing’s essence (VII.4–12), whereas first philosophy considers them insofar as they are beings, yet one should not conclude that it offers no explanation of natural entities as such. Aristotelian physics is primarily the science of those beings which have in themselves a source of their movements, and only secondarily a science of motion generally. 33. Aristotle, Metaphysics 1028b36–1029a28 with 1014b29, 1024b9, and Physics 193a11. 34. Aristotle, Metaphysics 1033a5–23, 1035a8, 1049a18–24, 1058b5–15, Physics 245b10–12. 35. Aristotle, Metaphysics 1049a18–27, On the Soul 423a12. Cf. J. Beere, Being and Doing: An Interpretation of Aristotle’s Metaphysics Theta (New York: Oxford University Press, 2009), 268–83. 36. Aristotle, Metaphysics 1029a29–33, cf. 1022a17–19, 1029a6.



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then as the principal cause of its being (VII.17), and finally as its ownmost activity (VIII.1–IX.8).

Form as Essence Let the entity in question be Socrates. His nature is his soul. And his soul, regarded conceptually (logikôs), Aristotle calls to ti ên einai proper to Socrates. Translated word for word, this neologism means “the what-it-was-to-be.” But to einai is an articular infinitive meaning “being,” as in the phrase to hippôi einai, “the being proper to a horse”; and although the verb ên is imperfect, here it probably expresses recognition.37 Therefore, a statement which managed to declare Socrates’s being what it is would be what I call an “essence statement.” Such statements are either protometaphysical (“This is Socrates”) or metaphysical (“Socrates is his soul [and his soul is x]”). Aristotle is now interested in what statements or definitions of the latter sort declare— the individual’s nature or essence—the what-it-is (to ti estin) proper to it. This essence cannot be a real or a logical property (e.g., being male or being identical with Socrates). Nor can it be a bare monad.38 Nor can it be just the material entity whose being we wish to explain, for whereas this being is divisible, particular, and as such indefinable, its intrinsic essence is indivisible and definable without reference to 37. Aristotle, Metaphysics Z.4. Other instances of ên used recognitionally: Generation and Corruption 328b2, On the Heavens 313b8, Parts of Animals 640a33. On its use more generally, cf. W. W. Goodwin, Syntax of the Moods and Tenses of the Greek Verb (New York: St. Martin’s Press, 1965), §39. The expression to ti ên einai appears to be Aristotle’s refinement of the expression to ti estin. Both may be regarded as embedded questions: “the what-is-it?” and “the what-was-it-[going-]to-be?” Some have interpreted them in just this way. Cf. e.g., Lenkowski, “Definition,” 64. On the relevance of the fact that ên and estin are both durative in aspect: C. P. Long, Aristotle on the Nature of Truth (New York: Cambridge University Press, 2011), 192, and L. A. Kosman, The Activity of Being: An Essay on Aristotle’s Ontology (Cambridge, Mass.: Harvard University Press, 2013), 268n4. 38. Aristotle, Metaphysics 1035b14, 1044a8. Cf. Frank Lewis, How Aristotle Gets By in Metaphysics Zeta (New York: Oxford University Press, 2013), 141–43.

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the thing’s matter.39 Concrete entity X and the essence of X are not the same simply. Aristotle regards the name “Socrates” as ambiguous, designating a categorially primary, mobile ousia and a causally primary ousia that is immobile save insofar as it is the essence of this individual. Call these “Si” and “Se” respectively. Si is material, changeable, rather indefinite, an “entire this” (hapan tode), whereas Se is immaterial, never in a process of becoming, definite, “just this” (hoper tode).40 Should we regard them as different entities? No, for Socrates the man is essentially though not simply his soul. As Aristotle says, there is a sense in which material entity X and the essence of X are the same, and a sense in which they are not.41

Form as Cause of Being Proceeding again from the beginning, Aristotle asks, “Why are these materials an individual human being?” He introduces the following analogy. Let there be the syllable AB. Its constituents are the letters A and B. In virtue of what do these letters constitute a single syllable? It cannot be the letter A or the letter B. Nor is it some third thing C, for then we would ask, “Why are A, B, and C a single syllable and not just three elements?” and so on to infinity. Similarly in the case of a natural entity like Socrates, we begin with the individual man. His constituent parts include flesh and bones, etc. What is primarily responsible (prôton aition) for the fact that they constitute this individual? 39. Aristotle, Metaphysics 1016a33–35, b2, b33, 1032b14, 1035b14, 1039b20, 1052a32–36. 40. That “Socrates” signifies doubly: Metaphysics 1043a29 with 1031a15–18, b2, b31. That his soul moves only incidentally in virtue of being so embodied: On the Soul 408a30–b18. That his soul or form is his essence: Metaphysics 1032b1, 1035b2. On the distinction between the “just this” and the “entire this”: Metaphysics 1007a20–33, 1030a3, 1033a3, 1045b1, 1051b30, 1052b16 with 1033b2–1034a5, 1041b11, 1045a4. On categorially and causally primary ousia: Categories 3b36, Topics 103b22, Posterior Analytics II.2, Metaphysics 1014b35, 1017b21–23. In Attic Greek, interrogative ti can mean both “What?” and “Why?” 41. Aristotle, Metaphysics 1031b18–20, 1033a24–b19, 1037a1, b1–7, 1038b2–30, 1039a3–7, and 1045b6.



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It cannot be any one of these parts or all of them together; it must be something else beyond them. This something else, which explains the being (to einai) of Socrates, is the essence or form proper to him.42 Accordingly, when Aristotle says that a natural entity is “composite” (suntheton) or “out of both” (ex amphoin), he does not mean that it has matter and form as elements, components, or parts. It is clear also that flesh and bones constitute a whole and not a heap only if they are united by a single formal cause that is intrinsic to them. Statues and the like are individuals only in appearance or by convention.43

Form as Essential Activity We regard ourselves as agents, and to determine who we are we attend to what we do. What one does is his ergon, his work or job, and the activity in which he is engaged while doing his job is his energeia, his being-at-work or activity. The ways in which one may be at work are manifold, yet we have some idea of how they are to be ranked. If for instance he devotes his life to politics even apart from fame or fortune, his political activity (praxis) is probably what that most reveals who he is.44 Aristotle takes this understanding of people as agents and presses it analogically in two directions. On the one hand he uses the terms ergon and energeia to describe living things generally. For example, sight is the ergon of an eye, what it does naturally; and seeing is its energeia, the enactment of this function. A plant nourishes itself and generates offspring: that is what it does naturally. And when, as we say, it actively does these things, these operations are instances of its being-at-work.45 On the other hand Aristotle regards the essence of a 42. Aristotle, Metaphysics VII.17, On the Soul 415b12–14. 43. Aristotle, Physics 193a15 and Parts of Animals 641b13 with Metaphysics 1035a7, 1041b12, 1043b21–23. 44. See Umphrey, Natural Kinds and Genesis, chaps. 1 and 7.3. 45. On the interpretation offered here, the words ergon and energeia have their home

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living thing as an energeia. At first this seems farfetched, for how could an agent be an activity? The metaphorical strain diminishes, however, when we notice his distinction between first- and second-order activities. Seeing is the being-at-work of an eye’s capacity to see, and this capacity to see—eyesight—he takes to be the being-at-work proper to that bodily part which is capable of seeing. Call this bodily part an eye. Then, as seeing is the enactment of eyesight, so is eyesight the enactment or actuality or be-ing of the eye. Were an eye a living entity, he says, the eyesight proper to it would be its soul.46 Being-at-work differs from movement. In the case of any movement as such, the end (telos) is extrinsic to the movement itself. For example, if I am looking for something, finding it is the goal and this goal lies beyond my search. But if I am just looking, the goal is intrinsic to my seeing and my seeing is an activity rather than a movement.47 Aristotle calls this being-at-work an entelecheia. The soul of a living thing, he says, is its first-order entelechy. Hence the formal cause of a material entity is also its intrinsic final cause, the end for the sake of which it actively persists in being itself.48 Hence, insofar as it is enformed, a material entity cannot be in a process of coming to be or perishing. But insofar as its essential activity has (like any instance of seeing) a finite duration, it has come into being and will eventually perish.49 in Aristotle’s account of human affairs. Both occur frequently in his Nicomachean Ethics and Politics. So powerful are these analogies that biologists today still employ them, though rarely with as much insight into their role as analogies. 46. Aristotle, On the Soul 412a8–18, b15, Metaphysics 1049b5–10. That the essential activity of a naturally constituted entity is its form or ousia: Metaphysics 1043a20–28, 1050a4– b34. On the centrality of being as essential activity in Aristotle’s Metaphysics, cf. Kosman, The Activity of Being, and Beere, Being and Doing. 47. Aristotle, Metaphysics 1048b8, 18–33, Nicomachean Ethics 1174a14–b6. Movements may be but necessary accompaniments. They may also be conceived as incomplete activities: Metaphysics 1048b18–35. 48. Aristotle, Metaphysics 1015a12, 1050a15–13, also Nicomachean Ethics 1094a16–18, a36, Physics 198a22–24, Topics 145a25–27. Cf. Furth, Substance, Form, and Psyche, 156–61. 49. Aristotle, Nicomachean Ethics 1174a14–29, Physics 192b1, 219b2–7, 222b16, 225a34,



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Let us review. Aristotle wishes to explain a natural entity in its being as distinguished from its becoming. His explanation is in terms of two causes. One of them, the type II cause, he regards first as the form of an entity, then as its essence, then as the cause of its being an enduring this, and finally as its substantial activity. These four construals seem mutually incoherent. How could a form and an activity be the same? And how could either of them be what the entity is? Aristotle, I suggest, uses “form” and “activity” as analogies—the former drawn from the sphere of human production (poiêsis), the latter from the sphere of human action (praxis)—and as analogies they elucidate the same cause from different points of view. Regarding the form of a natural entity “logically” as its essence helped to free us from our tendency to confuse it with the entity’s material structure, but left us wondering how the essence could be a cause. Regarding it as the principal cause of being helped in this regard, but failed to highlight the way in which the entity is essentially an agent. Regarding it as the very “act-uality” which its proximate materials are potentially has also helped; though harder to grasp, it has brought us closer to the entity as it is. As for the type I co-cause, Aristotle regards it first as the proximate matter of the entity, then as what makes it an indefinable particular, then as its several constituents, and finally as its capacity (dunamis) to persist in being what it actively is, and to perish.50 Again there seems to be a progression, from the body as something already enformed to the body as something already at work in being alive. Were these materials independent of all form, they would be nothing at all; 240b8–10, Metaphysics 1027a29, 1033b11, 1034b7–19, 1039b20–1040a8, 1040b2–4, 1043b14– 21, 1044b21–24, Generation and Corruption 335b4, On the Heavens 280b16–23. 50. Aristotle explains both coming into being (genesis) and being (ousia) in terms of capacity (“potentiality”) and activity or operation (“actuality”), but does not always tell us which of the two explanations he is offering. On the importance of making this distinction, cf. Metaphysics 1042a27, 1060a20, and, e.g., L. A. Kosman, “Substance, Being, and Energeia,” Oxford Studies in Ancient Philosophy 2 (1984): 121–49.

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the Megarians would be right to deny that there is any potentiality, any change, anything accidental. And were the forms independent of matter, as Platonists believe, physics would be like geometry. Aristotle rejects both options.51 Things natural, he says, are “for the most part,” and what is for the most part is not a consequence of the accidental together with the necessary, as the accidental is a consequence of it.52 Form and matter must therefore be very intimately related in entities constituted by nature. To clarify this quasi-relation, Aristotle proposes another analogy drawn from the productive arts. Something is a saw, he says, only if its sawing capacity is realized in materials of a certain sort. Similarly, something is a human being only if its soul is realized in an organic body of a certain sort.53 Aristotle would have agreed with Wittgenstein that the living human body is our best picture of the human soul.54 Its complex constitution, together with its manifold life-activity, is our best evidence of its inevident nature. And it is most revealing, Aristotle would have added, when the specimen before us is mature and healthy, not mutilated or otherwise incomplete. His research program is now clear. For an illustration of it, consider his Parts of Animals. There, having picked out an apparent part, he asks two questions: (1) “What are its constituents and how are they 51. Aristotle, Metaphysics IX.3, and Physics 193b5. Though Aristotle sometimes says that the essence can be defined without reference to the matter, he also says that the animal cannot be defined without movement (1036b28–32)—and there could be no movement without matter as the capacity to be otherwise—and that the proximate matter and the form are identical (1045b16–22). In his biological writings he says that having blood is in the ousia of blooded animals, being winged is in the ousia of a bird (Parts of Animals, 646a8–12, 669b11–13, 678a32–35, 682b28, 693b13). He emphasizes the advantages of studying the form together with the matter in Physics 194a12, On the Soul 403b1–11, Parts of Animals 641a15–32, Metaphysics 1025b31–1026a7, 1037a10–20. 52. Aristotle, Physics 198a35, 199a33–b7, Metaphysics 1026b30, 1027a10–15; cf. 1049b8–10. 53. Aristotle, Physics 194b9 with 199b34–200b8 and Metaphysics 1035b15–16, 1044a18, Parts of Animals 639b24–640a9, 642a14–16, On the Soul 414a22–26. 54. Wittgenstein, Philosophical Investigations, trans. G. E. M. Anscombe, 3rd ed. (New York: Macmillan, 1968), 178. That the range of bodies that can be human is much narrower than the range of materials that can be made spherical: Metaphysics 1036a31–b7, b26–28, Parts of Animals 646b15.



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structured?” (2) “What is its function [ergon]?” While the answer to (1) mentions proximate type I causes, the answer to (2) mentions type IV rather than type II causes.55 This is because a bodily part is not itself an entity; its being consists rather in the contribution it makes to the life of the animal as a whole. This end, the animal’s essential activity, Aristotle likens to an art (technê) always at work in its body. He refers often to the inner nature (phusis) which has designed, produced, and uses these bodily parts. These terms, too, are analogical. The “designer” is the animal’s essential being-at-work, not some agent extrinsic to it.56 As the parts of an animal consist primarily in what they are as parts, one should explain them primarily in terms of their functions, and only secondarily in terms of their matter. Every such part Aristotle calls an organon (“instrument”). The principal parts of animals are their organs. Is everything in the animal body organic? Nature does nothing in vain, he says, but this turns out to be a heuristic maxim: “Having discerned something that appears to be a part, always look for its function.” More often than not, Aristotle thinks he has found it; but not always. For instance, the fat around the kidneys seems on reflection to have no function at all; it is not conditionally necessary for what the kidneys do, but rather an inevitable consequence of what they do.57 One of the difficulties in Aristotle’s research program is to 55. In Parts of Animals, as elsewhere, “the nature” can mean either the material constitution or the function (that for the sake of which). The latter is prior to the former: Parts of Animals 640b28, 641a29–32, 693a15–17, 694b12–15 (cf. Physics 199a25–32). 56. Aristotle, Physics 199b28–33, On the Soul 420b16–23. Parts of Animals 634a19, 652a31, b21, 654b32, 656b26, 657b37, 661b29, Generation of Animals 753a19 (notice that these various verbs of making and ordering are usually perfect in aspect). The entire animal body is called an organon (instrument) in Parts of Animals 642a11 (cf. 645b15–20). 57. Aristotle, Generation of Animals 734a30, b24–27, 788b20–25, On Animal Locomotion 704b12–18. On the limits of functional explanation: Parts of Animals 663a8–15, 670a29–31, 672a1–16, 677a12–30, 683a22–26, Generation of Animals 776a15–777a3, 778a31–b1. Cf. Allan Gotthelf, “Notes towards a Study of Substance and Essence in Aristotle’s Parts of Animals ii–iv,” in Aristotle on Nature and Living Things, ed. A. Gotthelf (Pittsburgh: Mathesis, 1985), 41; S. Marc Cohen, Aristotle on Nature and Incomplete Substance (New York: Cambridge

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ascertain the scope and limits of functional explanation. The very different research program established by Galilean physicists will have difficulties of its own, but this is not one of them.

GLOBAL VERSUS LOCAL Aristotle’s post-Socratic physics puts organisms at the center of things to be observed and explained. Yet not everything natural is organismal. Eventually he must enlarge the scope of his inquiry to include things inorganic, among them the heavens and the ultimate constituents of everything organic; his thinking must become cosmological. As we saw in our study of Ionian natural philosophy and epic poetry, however, the cosmological perspective threatens to undermine the status of things right before us. To see how Aristotle deals with this threat is our next task.

Elemental Masses The nonuniform parts of an animal are resolvable into uniform parts, which in turn are resolvable into still simpler materials and so on until we arrive at things so elemental that nothing simpler exists in nature. There are four such elements, Aristotle argues: earth, water, air, and fire.58 Each has a place to which it naturally moves: fire, toward the periphery of the cosmos (it is very light); earth, toward the center of the cosmos (it is very heavy); water and air, to intermediate locations.59 Intrinsic to each, moreover, are a pair of basic qualities University Press, 1996), 138–57; Lennox, Aristotle’s Philosophy of Biology, 63, 205–23; and Tipton, Philosophical Biology, 42, 74, 98, 104, 123–26, 141–44. 58. One argument, from the number of simple local motions, is presented in On the Heavens III.1; the other, from the number of primary affections, is presented in Generation and Corruption II.1–2 and Meteorologica IV.1. Empedocles agreed that there are just these elemental masses, but his account of them is said to be deficient. For one thing, he “said nothing” about their natures (Generation and Corruption 333b13–18). 59. Aristotle, On the Heavens 310a2, a24, and Physics 208b11.



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or affections: the hot and the dry (fire), the cold and the dry (earth), the cold and the moist (water), or the hot and the moist (air). Each involves the possibility of being otherwise, substantially as well as attributively.60 Portions of each are coming into being and perishing all the time.61 Difficulties attending his account of elemental masses include the following. (1) Some proximate matter must be common to all four of them, as they are capable of changing into one another.62 But this underlying stuff cannot be a still simpler mass, for then earth, water, air, and fire would not be elemental and their changing into one another would not be substantial. Nor can it be nothing at all, for then these four masses would be immutable. How then are we to elucidate “it”? By analogy, Aristotle says, and yet available analogies provide little illumination at this depth.63 (2) Each element must be enformed, but his account of their forms is inchoate at best. In On the Heavens, the cosmic place proper to an element is said to be its form and act-uality, whereas in Generation and Corruption the essence of an element is said to consist in its paired affections or powers. But in no extant treatise are these diverse conceptions unified.64 Nor is it anywhere shown that 60. Aristotle, Generation and Corruption 319b3–320a7, 329a29–330a26, 331a8, On the Heavens 286a31–b1, Metaphysics 1032a20–22, 1071a10–11. His doctrine of elements thus depends on his conception of opposites. 61. Aristotle, Generation and Corruption 329a35-b1, On the Heavens 283b19–22, Parts of Animals 648b2–5, On Longness and Shortness of Life 2. These changes are all reversible (Generation and Corruption 331a26–b11, Metaphysics 994a30–b3). Therefore, when he says that they occur in a cycle (331b2), he must mean that they do so for the most part. The chief stabilizing factor appears to be the annual movement of the sun along the ecliptic (336a14). 62. Aristotle, On the Heavens 312a31–33, Generation and Corruption 320b13–25, 329a25– 31, 332a24, Meteorologica 340b15–17, Metaphysics 1065a28–38. He rules out simple replacement on the ground that something cannot come from nothing. 63. Aristotle, Physics 191a8. One might take the principle in question to be not metaphysical but protometaphysical. Aristotle, however, shows little readiness to accept this option. 64. Aristotle, On the Heavens 307b20, 310a22–b1, 311a4, a20, Generation and Corruption II.9, Meteorologica 339a14, 378b10. Expressions signifying essence or final causality are rarely used in these treatises.

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these differentiae, which appear to be locative and qualitative, are really substantial.65 (3) Why does their dynamic interplay never threaten the overall stability of the cosmos? And how is one to understand the fact that organic beings endure according to their natures only if (portions of) these four masses are held back “violently” from moving according to their natures, and conversely? (4) He has reasons, empirical as well as quasi-Pythagorean, for affirming the existence of these four masses. But why classify them as entities (ousiai)? Something is an entity only if it is essentially independent and a this (tode ti). But no elemental mass is a this, and each is situationally grade III as it depends essentially on the topographical order of the cosmos as a whole.66 One might argue that they are sufficiently entity-like that we may regard them as entities, but how illuminating is this analogical extension? Be that as it may, Aristotle is establishing a hierarchy of entities. The lowest level comprises earth, water, air, and fire, in that order.67 Above it is the level comprising terrestrial life forms. Let us review his “biology” in this new light.

Living Things Plants are only marginally alive. They sometimes live when divided; their essences are comparatively obscure; their souls consist only in the capacity for self-nourishment and reproduction.68 Animals are 65. For one thing, the dry has an opposite, namely the moist, whereas ousia has no opposite: Categories 3b24–27, Physics 189a32, 225b10. 66. Aristotle, Metaphysics 1040b8–10, 1056b16 (cf. 1017b10, 1028b10, 1042a8); M. Matthen and R. J. Hankinson, “Aristotle’s Universe: Its Form and its Matter,” Synthese 96 (1993): 426–30. 67. Among these, too, there is a hierarchical order, fire being the most form-like, earth the most matter-like: On the Heavens 310b14, 312a12–21. 68. Aristotle, On the Soul 409a9, 411b19–30, 413b16, b20, 415a4, Length and Shortness of Life 476a18, Generation of Animals 735a35–b4, On the Heavens 292b1–18, Meteorologica 390a17–21.



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superior; yet so plant-like are sea cucumbers and sponges that they seem scarcely to have the power of sensation. Molluscs are also plantlike in their natures, and some “bloodless” animals survive division.69 It is among “blooded” animals that real individuality and psychological complexity appear. Above all there are humans, the most complete animals, the least dwarfish, the most according to nature, and the only ones having a share in intellect.70

Celestial Beings Humans are not the highest beings in the cosmos; celestial entities are still more divine, apparently because they are everlasting, their movements uniformly circular.71 Whereas before the principal distinction was between animate and inanimate, now it is between celestial and sublunary. This is the most revisionary consequence of Aristotle’s cosmological perspective. Yet his account of celestial entities is remarkably sketchy. Being natural, they must be hylomorphic.72 But of celestial matter, which he calls “aether,” he says only that it cannot be heavy or light, hot or cold, dry or moist, and that it admits of no change other than uniform circular motion.73 As for their forms, we 69. Aristotle, Parts of Animals 681a1–18, Generation of Animals 715b11–18, 732a11–23, b28, 735a35–b4, 761a19–32, History of Animals 537b32, 538a18, 539a4, 548b10, 549a8, Metaphysics 1040b13, On the Heavens 292b1–8. 70. Aristotle, Parts of Animals 656a7–8, 686a25–b2, History of Animals 588a29–32, 612b18, On Animal Locomotion 706a19; also Nicomachean Ethics X.7–8 and Politics 1256b21. The human being is naturally so constituted that it can have active intellect. Whether it has active intellect by nature is unclear. 71. Aristotle, Nicomachean Ethics 1141a20–23, a33–b2 (cf. 1154b28–31 and Metaphysics 982b29), On the Heavens 281a3, 282a23–27, 283b19–22, 286a9–12, 290a32, 300a20–27, Metaphysics 1069a30, 1074a30. 72. Though Aristotle clearly supposes as much, he rarely calls them ousiai. An exception: On the Heavens 298a31. 73. Aristotle, On the Heavens 288b20, 301a23, Metaphysics 1044b7, 1069b3, b25. It follows that all heavenly occurrences are necessary, none accidental or merely for the most part (cf. On the Heavens 287b24–26). Celestial matter has just those characteristics needed

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must regard celestial beings as ensouled, he says, because the god is alive and by sharing in the divine life they too are alive, and because they have their sources of motion in themselves.74 But not only does this depend on the questionable supposition that to be is above all to be alive, it implies that these beings have bodily organs, which is impossible.75 He also says that they are moved by transcendent movers to which they comport themselves as lover to beloved, which suggests that each is moved extrinsically by an end it can never attain, even though each is also said to be always in its telos.76 It is also unclear whether these entities are the celestial spheres or the stars in them.77

Gods The mover of the outermost heaven Aristotle calls “the god.” His account of it is threefold. First, as supranatural it must be altogether immobile, impassive, immaterial, and incomposite. Second, by analogy with the highest way of being alive available to us, it is the simple activity of self-thinking thinking. Finally, as supreme in the order of beings, it is the sovereign good.78 Whereas before the principal distinction was between sublunary and celestial, now it is between natural and supranatural. This is the most revisionary consequence of Aristotle’s theological perspective. Yet his account of gods is sketchy. to preserve the phenomena. It thus resembles the luminiferous aether posited in classical electromagnetism. 74. Aristotle, On the Heavens 275b25, 285a29, and 286a10 with 285a29, 292a18–21, Physics 265b32–34, Metaphysics 1072b26–29. 75. Aristotle, On the Heavens 291a27, b13 with 290a27–b11, Physics 250b14. Self-movement is properly speaking vital (zôtikon: Physics 255a5–10)—a notion that seems to have its home in his “zoology.” Cf. Waterlow, Nature, 260. 76. Aristotle, Physics 255a5–10, 259b6–20, On the Heavens 284b30, 285a3, Metaphysics 1072a26, b3. Compare Meteorologica 339a25; but also On the Heavens 270b23. 77. Cf. Aristotle, Metaphysics 1040a33, 1050b24–28, On the Heavens 284a14–18, a27–38. Bear in mind that he has ruled out any void. 78. Aristotle, Metaphysics XII.7, 9, and 10 respectively. See also Metaphysics 1050b7–9, On the Heavens 286a9.



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We find no discussion of what it means for non-discursive thinking to be of itself and nothing else, or how there is thinking without any capacity for thinking.79 And there must be several such beings, it seems, yet he gives no account of how one might tell them apart without recourse to a theory of the heavens, which he does not yet have.80 In Aristotle’s cosmotheological view there is a comprehensive hierarchy of entities. At its top is pure mind (his neo-Anaxagorean conception of the god); at the bottom, elementary masses (his neoEmpedoclean conception of the four roots); and ranged in between are sublunary flora and fauna (the entities with which he began). Together they constitute an ordinal scale according to which any given entity is more or less definite, true, good, or divine.81 Things remote (the heavens and their movers) appear now to be to be paradigmatic in reality, whereas things exemplary for us (living organisms) appear marginal. And so great is the metaphysical distance between these things that we wonder whether the former alone are to be categorized as entities (ousiai). Aristotle takes up this question. He agrees that something is an entity only if it is separate (khôriston) and a this (tode ti). He also agrees that the unmoved mover clearly meets both conditions: it is altogether independent and simply this (haplôs tode). But a terrestrial animal, though held to be unqualifiedly separate (khôriston haplôs), depends on divinities above and elements below: were there no unmoved mover, the natural world would collapse, but not conversely; and were there no earth or water or air or fire, no animal body would 79. Aristotle never says that god has a nature (phusis). He does say that it is an essence (ti ên einai), but not that it is a form (eidos). 80. There will be as many unmovable movers are there are celestial spheres, he says, and how many there are is for astronomers to determine: Metaphysics XII.8. 81. Cf. Aristotle, Metaphysics 1069a3–b3, 1070b3–5 with Categories 14a29–35 and Metaphysics 983a5, 993b27–31, 1007b27, 1010a2–4, 1040b8–10, 1050b6, 1064b3–33, 1072a31–b13, 1075a11–25, Physics 260a2, b17–19, On the Heavens 269a31, b16, 281a3, 282a27, 283a21–30, 288a4, 290a32, 292b17–25, Parts of Animals 648b2–5, Generation and Corruption II.8, 10, Movement of Animals 700b34.

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exist, but not conversely.82 Hence no such animal is unqualifiedly separate. As material, moreover, it is an entire this (hapan tode); only its essence is just this (hoper tode), and such essences are separable only in thought or speech. Hence no such animal is unqualifiedly a this. Finally, when compared with the act-uality that is god, this animal’s soul is only sort of a being-at-work (energeia tis), more like a movement than an actuality.83 Is it then really the case that horses, humans, and the like are beings-in-becoming and not merely supervenient patterns in matter? It is indeed the case, says Aristotle. Against the materialists he maintains that living organisms are emergent entities whose bodily parts cannot be reduced to the elementary masses on which they depend.84 And against the friends of divinities he maintains (1) that the term ousia is a focal equivocal whose secondary senses can no more be reduced to the primary sense than the being of attributes can be reduced to the being of entities, and (2) that one can declare the essence of an animal without referring to anything higher on which it depends. Notice, too, that his cosmotheological teaching relies on analogical outreach from terrestrial animals to elemental masses and to celestial beings and their transcendent movers; that the resulting speculations have about them a conjectural air; and one should not use what is comparatively inevident and not yet well explained to reject what is comparatively evident and still plausibly explained. Aristotle begins in medias res and stretches out circumspectly in all directions. Always he resists the temptation to reduce what is right before us to what is far away, or to systematize his various findings 82. Aristotle, Metaphysics 1042a28–31, 1045b23, On the Soul 413a4, b28, 414a19. 83. Cf. Aristotle, Physics 201a9–15, b31–33, 257b8, Nicomachean Ethics 1174a22–29. Also Topics 125b17, Metaphysics 1029b8–20, 1040b5–10, 1063a10–15, On the Soul 417a16, 431a6, On Prophecy in Sleep 463b14. 84. Cf. Aristotle, Parts of Animals 639a1–641a14, 646b5–14, 648b2–5, Meteorologica 389b29–390b1, On the Heavens 302a21, with Metaphysics 1036b29–32, 1040b5–10. Cf. Mary L. Gill, Aristotle on Substance: The Paradox of Unity (Princeton, N.J.: Princeton University Press, 1989), 6, 77, 138–47, 163–68, 219–21, 240–42.



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and conjectures.85 Aristotelian natural philosophy thus resembles natural science today: both are characteristically many-wayed and on the way, like Homer’s Odysseus. No philosopher has been more Odyssean than Aristotle.

SPECIES Aristotle was a natural-kinds realist. He also invented the term “universal” (to katholou) to designate types as distinguished from tokens (particulars, ta kath’ hekasta), and seems to have been a realist with respect to some if not all of the types mentioned in his physics. Yet, as later Aristotelians observed, he seems to have offered nothing that we would call a “theory” of universals. Consequently, what sort of naturalkinds realist he was remains obscure. Universals may, it seems, be attributive (non-sortal) or substantive (sortal). Among attributive universals there is, for example, whiteness (leukotês, to leukon) as distinct from things that are white (ta leuka).86 Aristotle seems to have held that such universals are in rebus in the sense that none could exist unexemplified; that of such real types there are highest genera and lowest species; and that the highest genera are categories of being, not being or unity or goodness.87 He may also have held that attributive types are real only if determinate—that if whiteness, for instance, is a universal immanent in diverse particulars, then the generic types color and quality are well-founded concepts rather than additional universals.88 85. See also On the Soul, wherein he refuses to reduce soul (psuchê) to mind (nous), and the Nicomachean Ethics, wherein he refuses to reduce moral virtue to prudence (phronêsis) or practical virtue to contemplative wisdom (sophia). 86. Aristotle, Categories 9a31–10a30, 14a7 with 1a27, 2a31. 87. Aristotle, Metaphysics 998a32–35, 1004a4, Posterior Analytics 92b13, Nicomachean Ethics I.6. 88. Did he also admit attributive particulars? He sometimes uses such expressions as to ti leukon and ho tis nosos (Categories 1a25–28, Topics 102b21–29, 123b35, 127a21–26,

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Among substantive types there is, for example, the human being (ho anthrôpos) as distinguished from this or that human being (ho tis anthrôpos).89 Was Aristotle an in rebus realist with regard to any types of this sort? Scholars disagree. To adjudicate their debate, let us first summarize the relevant textual data. (1) An entity (ousia) is a “this,” whereas every universal is a “such” and not a “this.” Hence no entity is a universal. (2) Intrinsic to every material entity is its form (eidos), that in virtue of which it is what it is as long as it exists. (3) No such formal cause is a universal: Socrates’s soul and Callias’s soul are numerically diverse. (4) Yet Socrates and Callias are specimens of one and same speciest (eidos), namely, the human being. They are conspecific, homo-eidetic. (5) Such species constitute a distinct category of being. Although none is a “this,” Aristotle calls the category under which they fall “secondary entity” (deutera ousia). (6) There are higher-order types or classes, called “genera” (genê), to which animals of different species may belong: humans and horses are congeneric. (7) Species are often disjoint, but not always. At any rate, there appear to be typologically amphibious cases, ta epamphoterizonta, which cannot be allocated exclusively to either of two neighboring classes—seals, for instance, and sea cucumbers.90 173b10, 181b38, 182a4, Metaphysics 1025b31, 1030b17–31, 1035a26, 1064a23–25, Nicomachean Ethics 1141a22–28; see also Plato, Phaedo 102d6). Three interpretations of them have been offered. First, each may further specify a quality—a species of paleness (leukotês) or sickness. Second, it may particularize the quality to this or that subject—the whiteness-of-a, the sickness-of-b. Third, it may particularize the quality to this or that kind of subject—the whiteness proper to some animals (e.g., albinos), a disease of the eyes (e.g., ophthalmia)— in which case, like “the snub,” it designates a qualitative universal (whiteness, sickness, concavity) combined with some material sort of thing. I think these expressions are best interpreted in the second or third way. 89. Aristotle, Categories 1b4, 2a13, 3a24. 90. Aristotle, Metaphysics 983a27, 996a10, 1003a14, 1028a12, 1032a24, 1033a4, 1033b4– 1034a8 with 999b21, 1036a26–31, 1037b27–1039a16, 1038b34–1039a3, 1041a4, 1060b21, 1071a18–29 (cf. 1032a24), Categories 2a14, 3a7–25, b10–21, Topics 1.5, On Interpretation 17a4, Prior Analytics 24a17, History of Animals 488a1, 502a16, 538a13, 589a21, Parts of Animals 669a9, b15, 681b1, 689b32, 697b1, 697b1, Generation of Animals 730b35, 767b30–34, 772b1,



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Of these data there are two plausible yet mutually incompatible interpretations. According to one, Aristotle was a moderate antirealist with respect to specific as well as generic types of enduring things. There are material entities which constitute discrete s-resemblance classes in virtue of their intrinsic forms, and some of these classes are such that any further division of them into s-resemblance subclasses would be arbitrary. Call such classes “speciesc.” The human intellect, by universalizing what the members of a speciesc severally are essentially, may form a sortal concept—equivocally called an eidos—and regard every member as an instance of it; yet this eidos, though well founded in the given speciesc  , is in intellectu and not in rebus.91 According to the other interpretation, the homo-eidetic members of the class speciesc are instances of a specific universal speciest ; and this typological species—tellingly called an eidos—is irreducible to any concept we may have, or to the homo-eidetic individuals on which it depends. Aristotle, then, was a moderate realist with respect to some if not all speciest . These competing interpretations agree that Aristotle has admitted material entities, some of which are individual continuants, and some if not all of these continuants form well-defined s-resemblance classes in virtue of their souls. They agree, then, that he was a natural-kinds realist in the primary sense of the term. According to the first, however, he was not a natural-kinds realist in the full sense of the term, 777a16. That intrinsic forms or souls are not universal (katholou) does not entail that they are particular (kath’ hekaston): Joseph Owens, The Doctrine of Being in Aristotle’s Metaphysics (Toronto: Pontifical Institute of Medieval Studies, 1963), 223–27, 347–64, 392–95, 428– 31. See also Rogers Albritton, “Forms of Particular Substances in Aristotle’s Metaphysics,” Journal of Philosophy 54 (1957): 699–708; and Lewis, Metaphysics, 23. 91. One may say, as Aristotle sometimes does, that the human being is this or that concrete human being considered universally (Metaphysics 1035b27–30, 1037a5–10). But humans are substantially alike primarily in virtue of their souls, only secondarily in virtue of their bodies or their bodies and souls taken together. The difference between male and female humans is in the matter rather than the form; otherwise they would belong to different species (Metaphysics 1058a29–b3).

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as he denied the (extra-mental) reality of natural-kind types, whereas according to the second interpretation he affirmed the reality of such types and was therefore a natural-kinds realist in the full as well as the primary sense of the term.92 This is the principal point of disagreement between them. Suppose the second interpretation is correct. Then two questions arise. First, is Aristotle’s immanent realism consistent with the real diversity of conspecific individuals? The human being cannot be in Socrates and Callias in the sense that nx is in x, for then Socrates and Callias would not be two entities; nor can it be in them in the sense that x is in diverse presentations of x, for then Socrates and Callias would not be two entities—or so I have argued.93 Aristotle may have agreed. At any rate, when he says that Socrates and his essence are the same, he is not speaking protometaphysically, and when he implies that Socrates and Callias are essentially the same, he does not mean that their souls are numerically identical. In what sense, then, is he an immanent realist with respect to species? That remains unclear. Second, is he also a realist with respect to genera (genê)? I have argued that generic types cannot be real if specific types are real. Again Aristotle may have agreed, for genera are like matter (hôs hulê), he says, and matter as such does not exist. When seeking real definitions of essences, therefore, he treats putative genera as determinables which are to be “divided” ultimately into species; and when making such divisions he sometimes regards the eidos as the ultimate (specific) difference, sometimes as the genus together with this difference.94 Hence, for Aristotle, genera are natural kinds only secondarily. The primary natural kinds are species, and to determine them 92. See Umphrey, Natural Kinds and Genesis, chap. 5. 93. Ibid. 94. Aristotle, Metaphysics 1038a25, 1057b7; see 998b30–999a6, 1016a27, 1030a17– 1031a14, 1035b34–1036a29, 1038a6, 1045a24–35, 1054b30, 1058a23, Categories 3b13–27, On Interpretation 17a38–b2, Topics 122b16. Aristotle supposes that there is a final (teleutaia) difference: Metaphysics 1034a5, 1038a16, Parts of Animals 642b7–20, 643a8–12, 644a24–26.



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his procedure is twofold. On the one hand, starting from commonly recognized genera of living things, he proceeds conceptually (logikôs) to divide and determine them with a view to zeroing in on ultimate species. On the other hand, starting from commonly recognized parts of living things, he proceeds naturalistically (phusikôs) to determine and correlate their functions with a view to zeroing in on the intrinsic forms. The two procedures are complementary and mutually corrective, and both are inductive in the sense that we proceed Socratically from what is first for us to what is first in reality. Yet Aristotle made little claim to have discovered the real definitions of animal species. And although the definitions he sought are classificatory—like those in Plato’s Sophist and Statesman—he offered nothing that a modern biologist would call a taxonomy.95 He might even have denied that such a system could be fully articulated, on the grounds that genera, like matter, are more or less indeterminate. Aristotle’s response to Plato’s natural-kinds antirealism is becoming clear. It has several interlocking parts. (1) There are cases of genuine emergence (genesis eis ousian). Horses and humans, for example, are natural entities that have come into being and will eventually perish. They are also genuine continuants, beings-in-becoming, whose involvement in the materiality of the world is grade II. This thwarts the Platonic tendency to separate being from becoming. (2) Every such thing is an individual continuant in virtue of its essential actuality or soul, and this principle is rightly regarded as the thing’s intrinsic eidos, that in virtue of which it is definite, definable, knowable. This thwarts the Platonic tendency to seek what is knowable only in what is transnatural. (3) Some such things are also homo-eidetic; they closely resemble one another in virtue of their forms. And of the 95. G. E. R. Lloyd, “The Development of Aristotle’s Theory of Classification,” Phronesis 6 (1961): 59–80; David M. Balme, “ГΕΝΟΣ and ΕΙΔΟΣ in Aristotle’s Biology,” Classical Quarterly 12 (1962): 81–98; P. Pellegrin, Aristotle’s Classification of Animals, trans. A. Preus (Berkeley: University of California Press, 1986), 103–12; and Lennox, Aristotle’s Philosophy of Biology, 7–38, 160–81.

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s-resemblance classes thus constituted, some are such that the types their members severally exemplify are specific universals grounded in the things themselves. This undercuts the Platonic distinction between the eidê and things that are by nature. (4) A genos may be understood as a higher-order substantive type, in which case it cannot exist apart from the specific differences that ultimately determine it. This thwarts the Platonic tendency to move from the more specific to the more general. (5) A genos may also be understood as a kinship group or lineage. Human beings beget other human beings and so on indefinitely.96 They constitute a self-perpetuating s-resemblance class whose members are specimens of one and the same speciest , namely, the human being. This undercuts the Platonic distinction between eidos and genos. Several questions arise. First, have there always been human beings? Yes, because any such entity must have come to be from another such entity; act-uality is prior to potentiality in time as well as in being and definition.97 Second, do all currently existing human beings have a common ancestor? Aristotle does not say, and what he does say is compatible with the hypothesis that humankind comprises more than one homo-eidetic lineage. Third, will there always be human beings? Aristotle seems to think so, but sometimes hedges, and nothing in his account rules out extinction as a possibility.98 Finally, why does he think that Socrates and the offspring he begat with Xanthippe are so nearly alike in their formal natures that we may regard them as instances of one and same species? Having admitted such emergent entities as entities, Aristotle needs to give an account of their emergence. He did so in Generation of Animals, to which I now turn. 96. Aristotle, Metaphysics 1024a29–36, 1032a25, 1070a4–8, Generation of Animals 731b31, Topics 104a1–14, 124b16 with On the Soul 421a16, 23. 97. Aristotle, Metaphysics 1049b10. 98. Aristotle, Generation of Animals 732a1, b21, Generation and Corruption 331a8, 338b1– 19, On the Soul 415b3, Metaphysics 1024a29–31, 1049b17–1050a3. Note the resemblance between the indefinite recurrence of homo-eidetic individuals in a species and cosmic cycles; cf. Generation and Corruption II.11.



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THE PERPETUATION OF SPECIES BY NATURAL GENERATION That animals usually breed true is a commonly held opinion. Aristotle agrees; sexual generation, in his view, is for the most part substantive replication. Biologists today disagree; replication, in their view, occurs only at the molecular level. But they also regard animals as organized heaps of molecules or traits and have trouble defending their assumption of real biotic functions. Aristotle’s way of renewing natural philosophy has the consequence that apparent facts are regarded as facts until further notice. That is why his natural-kinds realism remains commonsensical even today, when the authority of science could hardly be greater. Sexual generation is still called “reproduction.” In turning his attention from the being of such things to their becoming, Aristotle gives greater weight to type III causes. He also tries to explain the apparent fact that some animals emerge spontaneously out of dung or the like. His account of animal generation is therefore double. I first summarize each part, and then show how they fail to explain the persistence of species as natural kinds.

Sexual Generation A housebuilder at work puts bricks and mortar into place, selecting and handling his tools in accordance with his housebuilding skill. Hence, to explain fully the genesis of the house, one must mention (1) the movements and dispositions of things in and about the business ends of the builder’s body, where the rubber meets the road, and (2) the skill that the builder has in his soul, the primary source of his housebuilding activities. Sexual generation resembles housebuilding. During intercourse, at the site of the action, two materials meet, one of them contributed by the male animal, the other by the female animal. Let these animals

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be conspecific (usually they are).99 Aristotle calls these materials “the male” and “the female.” They are the proximate co-causes of the embryo.100 An explanation of sexual generation must therefore mention both. It must also mention the souls of the parents, which are the primary type III causes of the male and the female. Empedocles, by failing to note these primary causes, gave an incomplete explanation.101 Aristotle has already given an account of them,102 but must still describe the proximate causes and their interaction. The male and the female are residues, surplus materials produced directly from the blood of the father and mother respectively. The former is a uniform fluid in the semen, the latter a uniform fluid in the menses.103 Having made these questionable inferences, Aristotle goes on to describe the function of each fluid in terms of two familiar distinctions: between active and passive powers (dunameis), and between type III and type I causes. The male is so constituted that its movement has a certain articulation (logos), which it can impart to the female. The female is so constituted that it can receive this movement and come alive. The male, in virtue of its articulated movement, is the proximate type III cause of the emerging embryo. The female, in virtue of its capacity to receive this movement, is the proximate 99. Cf. Aristotle, History of Animals 606b20, Generation of Animals 738b28–34, 746a19. He has observed that hybrids are often unstable, and is inclined to think they do not occur naturally. As for mules, he notes that they are sterile and says that they are contrary to nature (Metaphysics 1033b26–1034a5). 100. Aristotle, Generation of Animals I.2. 101. Aristotle, Physics 198a26–33, 224a32–34, Generation of Animals 730b8–32, 734b20– 735a29, 740b25–741a4, Parts of Animals 640a10–b4, Generation and Corruption 324a26–b4. 102. Aristotle, Physics 198a26 and Generation of Animals 730b8–32, 734b20–735a29, 740b25–741a4. 103. Aristotle, Generation of Animals I.17–19. See also 736a27, 737a16–18, 738b18, Parts of Animals 689a5–11. Pangenesis theories are therefore to be rejected. To account for the difference between these two residues, he speculates that semen is more fully “concocted” than menses and therefore less blood-like, and that it contains more hot air (pneuma) and is therefore hotter. The connections between heat, motion, and life run deep in Aristotle’s natural philosophy.



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type I cause. The male contributes no matter to the embryo and cannot quicken itself. The female is potentially alive but cannot quicken itself. Hence neither alone is sufficient: the embryo comes into being only when these two fluids cooperate.104 Embryogenesis is initially this very quickening. Before, the female was only potentially ensouled; now it is actually ensouled. Before, it was not yet a naturally constituted being having its own source of movement; now it is.105 To become an animal, however, this young embryo must undergo metamorphosis. For the animal soul involves capacities to sense and move in certain characteristic ways—capacities that no living thing can have unless the appropriate organs are present—and the newly constituted embryo does not yet have such a body. It is rather plant-like, drawing nourishment from the female animal in the manner of a plant rooted in soil. Yet, unlike any plant, it will become an animal if nothing impedes. Accidents do sometimes occur. There may even be errors in the initial constitution. For the most part, however, embryogenesis proceeds to completion, to its proper telos; and when it does, what is now potentially an animal of some kind will have become actually an animal of that kind.106 104. Aristotle, Generation of Animals 716a5–30, 724a30–b12, 726b18–21, 727b10, 729b5, 730a27, 733b24–31, 734b33 (logos), 740b35, 741b7–9, 765b8, 767a16, with Metaphysics 1019a15–19, 1033a25, 1044a35, 1046a10–29. Cf. Alan Code, “Soul as Efficient Cause in Aristotle’s Embryology,” Philosophical Topics 15 (1987): 56–58; and L. A. Kosman, “Male and Female in Aristotle’s Generation of Animals,” in Being, Nature, and Life: Essays in Honor of Allan Gotthelf, ed. J. G. Lennox and R. Bolton (New York: Cambridge University Press, 2010), 147–67. 105. Aristotle, Physics 202a13–b22, 224b34–235a20, Generation and Corruption I.3, 729a9–20, 730b14–35, 736a28, 737a13–18, 738b12, 739b22, 741b7–9, 755a18, 765b10–15. To designate the quickening Aristotle uses the verb sunistanai (“to constitute”). He uses the same word participially in the expression “being constituted by nature,” which figures prominently in Physics II.1. That this quickening is instantaneous and thus not a movement properly speaking: On the Soul 417a32–b9, Physics 225b15–21, and Kosman, The Activity of Being, 62–66. 106. Aristotle, History of Animals 560a10–18, Generation of Animals 734b9–17, 751b31, Metaphysics 1049a3–18, 1050a5, Physics 199b5, Generation of Animals 767b14, Parts of Animals 639b12–642b24. On the goal-directedness of embryogenesis, cf. Allan Gotthelf, Teleology,

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Suppose the animal is human. Then the initiator of embryogenesis had its source in a man. This man, the begetter, is a human in act-uality. So too is the begotten, the mature offspring; they belong to a lineage (genos) whose members are mutually akin.107 Thus begetter and begotten are homo-eidetic specimens of one and the same species. The persistence of humankind, as a class and as a type, depends on the generation of another and another such entity. Eidos and genesis, being and becoming, are here inseparable.108

Spontaneous Generation Some animals are generated out of putrescent mixtures of earth, water, and air.109 Aristotle accounts for such occurrences by extending analogically his account of sexual generation. These mixtures contain pneuma (hot air). When enclosed, they may therefore contain a vital heat (psuchikê thermotês) or vital source (zôtikê arkhê) that resembles the male. And the enclosing stuff may, like the female, have a capacity to be quickened by the male-like stuff within. Suppose these conditions obtain. Then, when quickened, the female-like stuff becomes an ensouled thing having its own source of movement.110 Animals so generated have come into being out of materials that are not, strictly speaking, animate; and they differ in kind because their proximate causes are heterogeneous. Their morphogenesis, though, occurs in three stages: larva, pupa, and mature specimen. Larvae, though eggFirst Principles, and Scientific Method in Aristotle’s Biology (New York: Oxford University Press, 2012), 142–51. 107. Aristotle, History of Animals 539a23–25, 550b32, Generation of Animals 715a23, b3, 734a28–34, b19–22, Physics 202a11–12, 234a32–34, Metaphysics 1024a29 and IX.8. 108. Aristotle, Generation of Animals 731b31–35, 767b32–34, Metaphysics 1070a26–28. Cf. Plato, Parmenides 132c12–133a10. 109. Aristotle, History of Animals 539a18–26, 547b12, 548a7–19, 551b27–552a1, 556b26, 569a11–26, Generation of Animals 715b27, 721a7, 761a14. All molluscs, some insects, and even some fish appear to be generated in this way. 110. Aristotle, Generation of Animals 729b27, 736b3–737a18, 743b3, 762a19–32; see History of Animals 556b26, Meteorologica 379b6, 389b5.



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like, can move from place to place, and will feed on themselves as wholes while undergoing further metamorphosis.111 Difficulties attending Aristotle’s account of spontaneous generation include the following. (1) Act-uality is prior to potentiality in time, he says, and what is potentially x must be understood in relation to what is act-ually x. But the “vital” heat in putrescent matter need not have come from a living being like the one it produces, and does not exist in order to produce such a being. There is a sense, then, in which spontaneous generation is not by nature.112 (2) Analogous to the male in such generation is what Aristotle calls “vital heat” and a “vital source.” Yet this material is inanimate. To admit spontaneous generation is to admit the genesis of life from nonlife. Aristotle’s neo-Empedoclean account of it and today’s biochemical accounts of it are likewise problematic.113 (3) Successive generations of horseflies or the like do not constitute a kinship group (genos), as there is substantive recurrence without eidetic replication.114 Hence, for Aristotle, 111. Aristotle, History of Animals 539b10–13, 547b19, 551a13–552b25, 557b1–13, 569a25– b22, Generation of Animals 715a23–b8, 721a5, 723b3–9, 758b6–759a7, 762a22–27. 112. Aristotle, Metaphysics 1032a12, Parts of Animals 641b29–642a1, Generation of Animals 734b33–735a2. Aristotle realized that there are natural regularities to which his fourfold causal scheme does not fully apply—e.g., eclipses, the movement of the sun along the ecliptic, the seasons, cloud formation, and rainfall. Although such regularities may seem to be for the sake of something, they occur automatically (apo tautomatou), of necessity. He also admitted that some regularities within animal bodies cannot be explained functionally, and refrained from explaining teleologically the transformations of simple bodies into one another. The same is true here: not all animals are generated sexually, and those that are not emerge spontaneously (apo tautomatou), of necessity. Cf. Physics 198a18, b10, Metaphysics 1044b12, Meteorologica 346b36–347a3, 359b34–360a5, Generation and Corruption 337b12, 338b3, Posterior Analytics 95b38–96a7. Also David M. Balme, “Development of Biology in Aristotle and Theophrastus: Theory of Spontaneous Generation,” Phronesis 7 (1962): 91–104; David L. Hull, “The Conflict between Spontaneous Generation and Aristotle’s Metaphysics,” Proceedings of the Inter-American Congress of Philosophy 7 (1967): 245–50; Lennox, Aristotle’s Philosophy of Biology, 229–49. 113. His explanation of spontaneous generation (Generation of Animals III.11) leads directly into an examination of Empedocles on the origin of living forms. 114. Aristotle admits as much in History of Animals 539a21–23, 550b32–551a1, Generation of Animals 723b3–9.

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they are not exemplary natural kinds. (4) So labile are these malelike and female-like materials that the persistence of such species as the horsefly and the flea seems unlikely. As distinct species, however, they appear stable. Aristotle offers little explanation of this phenomenon.115 His account of sexual generation is no less questionable. (1) Perishable animals, like plants, generate their own kind in order to be as divine as possible.116 Each thus has a double end (telos): its essential activity, and perpetuation of the species it exemplifies. These ends are not the same. The former end is intrinsic; it explains why animal a persists actively in being the entity it is. The latter is extrinsic to a; it explains how this entity can participate actively in the lineage to which it belongs.117 We saw that Aristotle’s cosmotheological perspective threatened to undermine the ontic status of emergent entities by subordinating them to elementary masses or divinities; now we see that his genealogico-theological perspective threatens to submerge them in streams of life. Aristotle might respond by saying that, just as a species is a substantive being secondary to the the individual entities instantiating it, so too is perpetuation of the species an end secondary to the act-uality that each individual is. He does say that males and females are plant-like when they copulate, and that the males would be better off otherwise engaged.118 Though basic in the order of becoming, and thus “most natural,” the nutritive-generative soul is posterior in the order of being.119 Aristotle would deny that the animal is primarily the soul’s way of making another soul like itself. 115. Aristotle was aware of the possibility that some animals, having initially come into being spontaneously, begin to generate sexually. He knows that most fish and many insects generate sexually. He has also observed that snails copulate, but not that any offspring result (Generation of Animals 762a32–35). 116. Aristotle, On the Soul 415a23–b2, 416a19, Generation of Animals 731b18–732a1, Generation and Corruption 336b25–34. 117. Do spontaneously generated animals, too, strive to be as sempiternal as they can? 118. Aristotle, Generation of Animals 731a9-b8, 731b18; Nicomachean Ethics 1097b33– 98a1, 1102a32-b12. 119. Aristotle, On the Soul 415a26.



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(2) To become the animal a it is potentially, young embryo e must undergo a process of completion (teleiôsis).120 Now e is either ensouled or not. If not, it is not yet alive, contrary to what Aristotle says. And if alive, what sort of soul does e have? It cannot be simply the nutritive soul, for then e would be a plant and not merely plant-like. Nor can it be the soul of the animal into which e is going to develop if nothing impedes, for then e would already be a in act-uality. But then e is neither ensouled nor soulless, which is impossible. Aristotle might argue that the logos imparted to the female by the male is soul-like in that it explains the present organization of e and the ordered stages in which it “wants” to become a. But why then is e not an entity-like heap on its way to becoming an individual whole? Aristotle needs to say more about this eidos-like logos.121 (3) In the initial constitution (sustasis) of the embryo there are two proximate causes, one contributed by the male animal and called “the male,” the other contributed by the female animal and called “the female.” Aristotle has no theoretical reason for regarding the male as the efficient cause having an active power to constitute, the female as the material cause having the passive power to be so constituted. Indeed there is evidence against this hypothesis: offspring usually resemble the mother as well as the father. Some eggs also appear to be self-constituting. True, these “wind eggs” do not become more than plant-like, yet their existence is enough to admit parthenogenesis as a possibility.122 Moreover, his account of the embryo’s original consti120. For his accounts of this process, cf. Metaphysics IX.7, Generation of Animals 724a25, 741b25, Parts of Animals 640a3–19, On the Soul 412a28–b6. 121. Compare Generation of Animals 737a8, 762a18–21 with the account of soul in On the Soul. 122. Aristotle, Generation of Animals 741a16, 751b1–30. In the former passage, and at 722b13, he seems to rule out parthenogenesis; but consider also Metaphysics 1034a15, b5. Perhaps he derived this ranking of male and female from his political philosophy; cf. Charlotte Witt, “Form, Normativity and Gender,” in Feminist Interpretations of Aristotle, ed. C. Freeland (University Park: Pennsylvania State University Press, 1998), 117–36. In his Politics, but not his Nicomachean Ethics, he says that women are naturally inferior to men in the exercise of their deliberative capacity. And in his Generation of Animals, but not his On the Soul or History of

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tution implies that the male is not like a housebuilder at work on his materials, for once embryogenesis has occurred its work is done. An alternative analogy, also Aristotelian, seems more apt. The female, he says, is like one of those machines so intricately constructed that it will move on its own once a tiny piece has been removed or a string cut.123 The “artfulness” as well as the matter is in it, whereas the male is nothing more than a catalyst. (4) Most problematic for his account of the initial constitution is the similarity between this event and spontaneous generation. In both cases, the male is a warm pneumatic fluid having the power to impart its own structured movement to another, while the female is a less concocted material having the capacity to receive this structured movement. In both cases, the quickening itself is said to resemble the curdling of milk by rennet.124 So why is it that in the case of sexual generation one must mention the primary as well as the proximate causes, whereas in spontaneous generation one need mention only the proximate causes? Is not sexual generation, too, simply “necessary”? But then the perpetuation of species by means of sexual generation would also be inexplicable. So, in addition to showing how “spontaneous” generation can preserve the appearance of species stability, Aristotle needs to show how the soul of the begetting animal is responsible for the initiating proximate cause equivocally called “the male.” He does say that the form of an animal is responsible for the integrated functioning of its bodily parts. Semen is but a residue, yet it may resemble leftover paint which the artist puts to another use.125 Animals, he asserts that females naturally have less vital heat than their male counterparts. Nowhere does he spell out the connection between these two assertions. The relation between his politics and his biology remains unclear. 123. Aristotle, Generation of Animals 734b9–17, 741b7–15. 124. Aristotle, Generation of Animals 729a11–14, 737a13–16, 739b22, 755a18, Parts of Animals 676a16–18, Meteorologica 384a21, 389b20. The “active” ingredient in rennet is rennin, an enzyme, and enzymes are catalysts. Aristotle regards it as a sort of heat that resembles the pneumatic heat which enables the male to exercise its proper function. 125. Aristotle, Generation of Animals 725a24–27. That such residues are scarcely parts



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Still, as in any craftsmanly endeavor, there can be many a slip between the message (logos) received by the semen or menses and the soul it represents. Aristotle agrees that the ability of the male to inform the female is limited—otherwise offspring would resemble the fathers more than they do—yet he supposes that begetter and begotten are usually homo-eidetic, that all substantial deviations are monsters.126 This is plausible. No less plausible, however, is the hypothesis that offspring usually resemble their parents very closely in respect of their forms, and that small eidetic variations may accumulate over generations. Not only has he failed to rule out this competing hypothesis, his explanation of sexual generation seems to favor it. Aristotle’s explanation of emergent entities as emerging, his genetic account, does not square with his explanation of emergent entities as entities exemplifying specific types, his eidetic account. Investigating this deficiency might lead one to reject species as natural kinds, and even to doubt that substantial forms could so master the vagaries of matter as to explain the existence of continuants. Seventeenthcentury philosophers will reject both natural kinds and substantial forms, but their reasons for doing so will not flow from the doubts I have raised here. To understand their way of renewing natural philosophy, we must first consider Scholasticism and the challenge it posed. of the animals that generate them: Generation of Animals 724b28. That some organic parts, owing to certain necessities, do not work very well: e.g., Parts of Animals 764b2. 126. Aristotle, Generation of Animals IV.2–4, History of Animals 560a10–18.

AND THE WORD OF GOD AND THE WORD OF GOD

CHAPTER 4

And the Word of God

Let us pause to take stock. Pre-Parmenidean Ionian philosophers introduced the idea of nature, but not of natural kinds. They were ontological monists. Parmenides introduced the idea of being apart from becoming, and argued that the subject matter of natural philosophy merely seems real. Post-Parmenidean Ionian philosophers reintroduced change, but not substantial emergence (genesis, coming into being). They were ontological pluralists. Two of them, Leucippus and Democritus, admitted everlasting atoms differing in shape and size. And Empedocles admitted four everlasting masses—air, earth, fire, and water—all mixing and unmixing under the influence of Love and Strife. But none of them needed the idea of a natural kind. Leucippus and Democritus seem not to have been interested in the question whether their atoms differed in kind. And although Empedocles may have been the first natural philosopher to admit what Homer called “tribes” or “races” of transient things, there is no evidence that he asked himself whether such things fall into distinct resemblance classes in virtue of their natures; nor does he seem to have been interested in the question whether air, earth, fire, and water were four in kind.

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Although the concept of a natural kind may be hovering in the wings, it still has no theoretical role to play. Plato followed Parmenides in distinguishing between being and becoming, and Socrates in positing not one but several beings, understood as forms or ideas. These forms are universals, as Aristotle noted; and insofar as transient things partake of these universals, they instantiate or manifest them. It is in Plato’s dialogues that we first find a distinction between real types and their tokens. Yet Platonic forms (eidê) are not natural-kind types, as the things partaking of them are not beings-in becoming, and because the different genê into which these things fall are not well defined apart from the classificatory activities of someone’s mind. Plato’s challenge, then, is to show that there are beings-in-becoming, and that some if not all of these entities fall into discrete resemblance classes in virtue of what they are. Aristotle took up this twofold challenge. He first modified the Socratic turn by taking what we perceive, not just what we think or say, to be heuristically valuable. He then proceeded to investigate the natural world, always taking his bearings by how things natural appear to us, or by how we ordinarily apprehend them in opinion or speech. Thus did he find that there are material continuants, that each is an enduring individual in virtue of its intrinsic form (eidos), that some of them beget still other individuals having very similar intrinsic forms, and that the kinship groups to which these homo-eidetic individuals belong are disjoint species (eidê). Whether Aristotle thought that these typological species may also be regarded as genuine universals is a much-disputed question, yet clearly he admitted s-resemblance classes whose members are continuants, and such classes are natural kinds in the primary sense of the term. Aristotle, by effecting this “paradigm shift” in ancient Greek natural philosophy, became its first natural-kinds realist. Yet for the next several centuries his natural-kinds realism remained a minority view. Most natural philosophers in late antiquity endorsed either Stoic phys-

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ics, which was Heraclitean, or Epicurean physics, which was Democritean: they had little need for the concept of a natural kind. Only in the so-called Middle Ages were most philosophers Aristotelians of one sort or another, and natural-kinds realism was part and parcel of the theocentric cosmology they endorsed. Avicenna, Averroes, Maimonides, Albert the Great, Thomas Aquinas, and Duns Scotus modified, in one way or another, Aristotle’s eidocentric conception of natural entities and their species, and yet, by following his lead, they established the first great tradition of natural kinds. Natural philosophy always occurs within a given milieu. Aristotle was in some sense an ancient Greek philosopher, as we have seen; and medieval philosophers lived among and were themselves, it seems, “people of the Book.” Accordingly, just as I began my study of Aristotle’s doctrine of natural kinds by noting some relevant aspects of early Greek epic poetry and pre-Socratic philosophy, so too in this chapter I begin by noting a few things in the Bible that are relevant to our theme. I then consider the Thomistic synthesis and its unraveling in the works of William of Ockham. Finally, I consider the sense in which the fourteenth-century “Calculators” anticipated the Galilean revolution in natural philosophy, and the sense in which they remained Aristotelian in their outlook.

SCRIPTURE References to kinds occur mainly in four Old Testament passages: Genesis 1, Genesis 6–7, Leviticus 11, and Deuteronomy 4. The first two describe the creation and flood; they are pre-Abrahamic. The other two promulgate dietary laws; they are Mosaic. The word for kind is mîyn (genos, genus, or species).1 It means “sort.”2 God has produced 1. I cite first the original Hebrew word in the OT and then the corresponding words in the Greek Septuagint and the Latin Vulgate, or first the original Greek word in the NT and then the corresponding Latin word. 2. It is related to words meaning “out of,” “from,” “portion out,” “part,” “shape,” “likeness.”



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plants and animals according to their different sorts. When invited to name them, Adam invented sortal terms whose meanings reflected those original kinds, and which may or may not have survived the Babel debacle.3 The Old Testament includes sortal terms for things neither animal nor vegetable, but nowhere is there said to be a mîyn of anything nonterrestrial, nonbiotic, or manmade. Nor are humans said to constitute a mîyn. The word for humankind is ’âdâm, whose prototypes God produced “after our image” (s.elem, eikôn, imago) or “according to our likeness” (demût, homoiôsis, simulitudo).4 No mîyn is said to have God-like prototypes. Adam appears not to have named himself. The kinds mentioned in Genesis 1 and 6–7 seem natural; they exist independently of this or that political society and are indifferent to the distinction between permissible and impermissible. Compare the kinds mentioned in Leviticus and Deuteronomy, which seem relative to a particular society: they serve to determine ways in which the children of Israel are to be a people holy and apart.5 But we should be careful. The Hebrew word for nature (teva) does not occur in the Old Testament. It began to appear with Samuel ibn Tibbon’s Hebrew translation of Maimonides’s Guide for the Perplexed, a late twelfthcentury work much indebted to Aristotle, Al-Fârâbî, and Avicenna. Ibn Tibbon used this word to translate the Arabic tabî῾a, which Maimonides and Islamic philosophers used to translate the Greek phusis.6 It is more obviously associated with the idea of distinguishing, partitioning, or separating than are the Greek and Latin words used to translate it. What it designates may but need not be regarded as a universal. 3. Gn 2:19, 11:1–9. Cf. Milton, Paradise Lost, 8.352, and Saul Kripke, Naming and Necessity (Oxford: Blackwell, 1980), 96, 153. 4. Gn 1:26 (cf. Augustine, The Literal Meaning of Genesis, 3.11–12). The word ’âdâm is never used in the plural and is neutral with respect to the distinction between male and female. 5. Certain animals are repeatedly said to be unclean or abominable “for you.” The distinction between pure and impure is also mentioned in Gn 6–7, but there it seems anachronistic, and in any case God instructs Noah to include animals of both sorts. 6. Cf. Jon D. McGinnis, “Natural Knowledge in the Arabic Middle Ages,” in Wrestling with Nature, ed. R. Harrison, R. Numbers, and M. Shank (Chicago: University of Chicago

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The idea of nature thus seems to be a philosophical import. As for the New Testament, the word phusis does not occur in the Gospels or Revelation. It does occur in Paul’s letters, wherein he addresses people, mostly Gentiles, for whom ideas of nature had become commonplace. Yet not once does Paul invoke the idea of a natural kind.7 Although it need not indicate the absence of the corresponding idea, the absence of a key term should give us pause. Our caution is reinforced by two further considerations. First, the Bible says that all animals and plants were originally created. To create (bârâ, ktizein, creare) is an act of God alone.8 No formative process in the world is quite like it—though it does resemble a performative speech-act or the fashioning of a pot. Things created according to their mîyn seem therefore to be like things produced according to a pattern. Once produced by God they reproduce naturally, thereby taking on the appearance of a kinship group (mishpâchâh, genos, genus).9 We should not let this appearance blind us, however, to the fact that their ultimate progenitors were created, and creation is nothing like natural generation. Second, God as creator does not operate in the world, he producPress, 2011), 60–64. Teva comes from the root t^aba meaning “to sink down,” “impress,” “stamp.” The teva of something is its intrinsic character. Much the same is true of the Arabic tabî῾a. They and the Greek word phusis (or Latin natura) thus belong to different semantic fields (cf. chap. 1.1–2 of this volume). That tabî῾a is rare in prephilosophic Arabic literature: Mushin S. Mahdi, Alfarabi and the Foundations of Political Philosophy (Chicago: University of Chicago Press, 2001), 23. 7. Rom 1:26, 2:27, 1 Cor 11:14, Gal 2:15, 4:8, Eph 2:3. Also Jam 3:7, 2 Pt 2:12. Paul’s principal distinction is between the psychophysical and the spiritual. He shows little interest in marking distinctions within nature or among natural things. 8. E.g., Gn 1:1, 1:21, 2:3, Dt 4:32, Is 40:26, Mk 13:19, Col 1:16, Rv 10:6. 9. Gn 8:19. When the kinship group is a family, tribe, or nation of humans, the preferred term is môwledet (sungeneia or phulê, cognatio). In expressions such as “the generations of men” (Gn 9:9), the Hebrew term for generation is is dur, from the verb dûwr, to gyrate, revolve. Recurrence of the same through sexual generation gives humankind a nonhistorical, natural-kind appearance. The Bible warns us against being misled by this appearance, even as it records our tendency to view different human tribes typologically as well as genealogically; cf. Yoram Hazony, The Philosophy of Hebrew Scripture (New York: Cambridge University Press, 2012), 70–74.



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es it; but as king, redeemer, and savior he does operate in the world, protecting, punishing, and rescuing his chosen people, his servants, the elect. Creating and caretaking appear to be two very different operations—the one architectural, as it were, the other historical—yet the Bible contains signs pointing to their underlying unity. In Isaiah 40–54, for example, creation and salvation are regarded as diverse aspects of a single divine operation, one that initiates world history and brings it to fulfillment. Viewed in this light, the world itself appears to be an ongoing creation or miracle. God’s activity, expressed repeatedly in the imperative mood, is usually one of partitioning and holding parts apart: separating light from darkness and determining that plants and animals belong to their proper sorts, separating the children of Israel from kindred tribes, protecting the righteous and punishing the unrighteous, dividing the elect from their families, expelling demons, and so forth.10 Everything is ultimately a divine stipulation. Thus does the Bible undercut ancient Greek distinctions between nature and history, natural and conventional, natural and sacred. Can the idea of nature have any place here? But if not, how could natural philosophy occur in a religious milieu so informed? Homer, we recall, described a plant whose nature, though hidden, is there to be discovered with or without divine assistance. He together with other Greek poets determined a milieu in which sight, insight, the looks of things, beauty, erotic love, and the Muses were all elevated; in which polytheism was taken for granted; in which the Olympian gods were regarded as beautiful deceivers given to unbridled laughter; in which no text was regarded as sacred. It is not terribly surprising that natural philosophy took hold in such an environment, or that Aristotle in particular 10. In addition to passages already mentioned, cf., e.g., Ex 15:17, Lv 19:19, Dt 22:9–11, Ps 93, 104:27–30, Job 39–41, Eccl 12:1, Mt 10:34–38, 24:24, Lk 18:7, Rom 8:23, Ti 1:1. Leviticus as a “book of separations”: Everett Fox, The Five Books of Moses (New York: Schocken Books, 1983), 499.

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should have developed an eidocentric natural philosophy rooted in wonder and culminating in disinterested contemplation. Compare a milieu determined by revealed religion, in which hearing is elevated above sight,11 faith above insight, obedience above contemplation, justice above beauty; in which there are no Muses, no gods other than God; in which reverence rather than wonder is the beginning of wisdom; in which the Tanakh, Bible, or Qur’an is regarded as sacred. How could philosophy thrive in such an environment? But philosophy is always rare and difficult; its relationship with the nonphilosophical milieu on which it depends is always a tense one. In fact, Aristotelian natural philosophy did take hold in this very different soil, and was transformed by it, as we shall see.

THE THOMISTIC SYNTHESIS Thomas Aquinas and other medieval Aristotelians agreed that the natural world includes individual substances, some of which undergo substantial as well as accidental change, and that of such things a hylomorphic explanation is appropriate. Aquinas also agreed that there could be no matter without form, and that even in those cases where the form could not exist apart from matter, the latter is nevertheless for (propter) the former, not conversely.12 Finally, they agreed that these substances belong to different species, about which they were realists in the primary sense of the term. In all this they followed Aristotle closely. But they were also much more explicit. For example, whereas Aristotle wrote little about “the principle of individuation” or substantive universals, the medieval 11. Cf. Hans Jonas, The Phenomenon of Life: Toward a Philosophical Biology (Chicago: University of Chicago Press, 1966), 192, 220, 227, 236. 12. Thomas Aquinas, Summa Theologica [hereafter “ST”] I, q. 66, a. 1; q. 70, a. 3. See also Maimonides, The Guide for the Perplexed, trans. S. Pines (Chicago: University of Chicago Press, 1974), 3.8.



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Aristotelians wrote at length about both.13 The extent to which, in these voluminous writings, they differed from one another and from Aristotle is not easy to ascertain. It suffices here to note the following. (1) For them, natural kinds and universals were not separate issues. (2) They tended to agree with Avicenna that the form or essence of a material substance is universal in the intellect (in intellectu), singular in the thing (in re), but in itself neither singular nor universal.14 (3) They tended also to agree that the species homo, for instance, is this or that human soul taken universally together with this or that human body taken universally.15 (4) Unlike Aristotle, they used one word (forma, s.ûra) to designate the intrinsic formal cause, another word (species, naw῾) to designate the specific natural kind. And what Aristotle called secondary ousia, they tended not to regard as substantia in any sense. Much greater differences within the Aristotelian tradition begin to appear when we compare Aquinas’s account of the human soul with Aristotle’s. When you die, according to Aristotle, your soul ceases to be. What is highest “in” your soul (namely, active mind) is indeed eternal, but it is also impersonal. Consequently, when your soul has ceased to be, so have you, as you are essentially your soul. Aquinas, however, insists on personal immortality. Your soul, he says, is essentially rational or intellective; and although the intellective soul can be embodied only in a human body, it need not be embodied at all. Consequently, 13. For introductions, cf. Individuation in Scholasticism, ed. J. J. E. Garcia (Albany: State University of New York Press, 1994). 14. Avicenna, The Metaphysics of the Healing, trans. M. E. Marmura (Provo, Utah: Brigham Young University Press, 2005), 5.1. 15. E.g., Aquinas, ST I, q. 4, a. 3; q. 29, a. 2, ad 3; q. 75, a. 4; q. 76, a. 3, ad 2; q. 84, a. 4; q. 85, aa. 1–2; Summa contra Gentiles [hereafter “ScG”], 3.24; In VII Metaph, lectio 9; On Being and Essence, ed. A. Maurer (Toronto: Pontifical Institute of Mediaeval Studies, 1961), 40–42; also Avicenna, Metaphyics of the Healing, 5.5; Maimonides, Guide, 3.13, 23a-b, and 3.18, 37b. But compare Averroes, In Metaph 7.21, 7.24, and note that Avicenna and Aquinas acknowledge that a material substance is of some species primarily in virtue of its form (e.g., Avicenna, Metaphysics of the Healing, 6.4.9; ST I, q. 5, a. 5). They agree moreover that genera exist only in species, where “species” means primarily the most specific kinds, species specialissimae.

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when you die, your soul does not cease to be and neither do you, as you are essentially your soul.16 Of course, there seems to be more to the human soul than a capacity for intellection; there are also capacities for imagining, sensing, and assimilating nutriment, without which one would not be human. Should we then say that each of us is essentially several souls? No; a material substance has just one intrinsic form. So you have but one soul and that soul is intellective. Powers of imagination, sensation, and so forth belong to it only because it is now the form intrinsic to the material entity that bears your name. Every human has such powers, necessarily, as long as it exists; but they are not essential to the intellective soul each of them is.17 Here Aquinas has put himself in something of a dilemma. The easy way out would be to reject either the unicity-of-soul doctrine or the personal-immortality doctrine. But he will not reject the former on philosophical grounds, while on religious grounds he will not reject the latter. Instead, he tries to have it both ways by identifying your essence with your intellect. On this point, as on others, his synthesis of Aristotelian philosophy with Christian doctrine is unstable.18 To see how his theological orientation colors his natural-kinds realism generally, let us consider it in relation to his accounts of divine exemplars, providence, the hierarchy of beings, and creation.

Divine Exemplars Exemplarism is the neo-Platonic view according to which natural things manifest ideas present in the divine mind. Augustine adapted this view to Christianity by identifying the divine mind with the Word 16. Aquinas, ST I, q. 75, aa. 2–3, 6; q. 76, a. 1, ScG 2.73, 75–84, 90. That the human soul begins to exist when the living human body begins to exist: ScG 2.85 and Norman Kretzmann, The Metaphysics of Creation (Oxford: Clarendon Press, 1998), 395. 17. Aquinas, ST I, q. 14, a. 11; q. 54, a. 3; q. 76, aa. 1–3; q. 79, a. 1, ad 1; q. 79, a. 5, ad 3, ScG 2.58, 2.90, 2.94, 4.81. 18. Ecclesiastical authorities will soon condemn the unicity-of-form doctrine.



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of God.19 Twelfth- and thirteenth-century Schoolmen were Augustinian exemplarists, Aquinas among them. His exemplarism involves no reversion to Platonism, however, because the Word of God, though ante res, is not composed of really distinct ideas. Nor is it a conceptual illusion to regard archetypes in the mind of God as a plurality of some sort; for though one in relation to him, they are many in relation to creatures. Thomas calls them exemplares or rationes.20 Horses and the like, he argues, are what they are by participation in these eternal archetypes; and they instantiate the species horse, say, if and only if they exemplify the corresponding archetype. So, whereas material substances are prior in being to the species in which they “participate,” divine exemplars are prior in being to the material substances which “participate” in them.21 Yet these substances also come and go, whereas their species do not. Natural kinds thus display what is invariant in their transient members, and as such constitute a permanent manifestation of eternity.22 Aristotle would agree that naturally constituted entities depend somehow on a divine first mover, and that their species are somehow cyclical. But the positing of exemplars in addition to species he would regard as superfluous at best, and deny that horses or the like are what they are by participation in divine ideas however understood.

Divine Providence Whereas god according to Aristotle cares not at all about the natural world, God according to the medieval Aristotelians is both providen19. Augustine, de Ideis, 2; On Free Will, 2.17, 2.46, 3.23.70; Confessions 1.6.9; The Literal Meaning of Genesis, 5.15.33. 20. Aquinas, ST I, q. 3, a. 8, ad 2; q. 14, a. 11; q. 15, aa. 1–2; q. 34, a. 3, ad 4; q. 44, a. 3; q. 84, aa. 4–5, ScG 2.12. 21. For us in this life, the order of discovery is almost the reverse: ST I, q. 84, a. 5; q. 85, aa. 1–2. 22. Cf. Aquinas, ST I, q. 113, a. 2; II, q. 93. Cf. Avicenna, Metaphysics of the Healing, 6.5.29, 9.8.13.

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tial and presidential. Indeed, according to Aquinas, God’s eternal plan for the world is divine providence, particular as well as general, and his execution of this plan is divine governance.23 And because God rules the world and everything in it with a view to himself, divine providence is teleological.24 Aristotle too admits a comprehensive teleology, but it has a different basis and is much less thoroughgoing. Divine providence is the eternal plan (ratio, exemplum) of the world. Aquinas identifies it with God’s Word (Verbum).25 He also calls it lex aeterna, eternal law, as it meets all the conditions for being a law and is in fact the primary law.26 But he has also identified the eternal exemplar (idea, exemplum, ratio) with God’s Word. His accounts of divine providence and the divine exemplar are thus two descriptions of one and the same principle. And because he also held that the divine archetype, though one in relation to God, is many in relation to creatures, it would seem to follow that eternal law is likewise many in relation to the created world. But then, just as there are natural kinds which reflect supranatural archetypes, so too there should be natural regularities that reflect supernatural laws. Aquinas seems to have taken a step in this direction when giving his account of “natural law” (lex naturalis), for having articulated it in terms of those natural inclinations that characterize humans as such, he further describes this law as “a sort of participation in the eternal law in us.”27 Is natural law nothing other than that law of nature (lex naturae) proper to human beings as rational animals? If so, it is the nomological correlate of the species hu23. Aquinas, ST I, q. 14, a. 11; q. 22, aa. 1–3; q. 44, a. 2; q. 103, ScG 3.64–65, 75. His argument from design (ST I, q. 2, a. 3, ScG 1.13, 35) has no counterpart in Aristotle’s writings. General providence is admitted in Plato’s Laws 899, in Stoic writings, and in such neoPlatonic writings as Plotinus, Enneads 6.7, and Proclus, Elements of Theology 120, 122, 133–34, 141. Cf. Al-Fârâbi, Perfect City, 17, Avicenna, Metaphysics of the Healing, 9.3, 9.6, 10.2, Averroes, The Incoherence of The Incoherence, ed. Simon van den Bergh (New York: Luzac, 1954), 82, Maimonides, Guide, 3.16–17 with 2.22, 2.25, 2.29, 2.32. 24. Aquinas, ST I, q. 22; q. 103, a. 2, ScG 3.17–18. 25. Aquinas, ST I, q. 27, a. 1; q. 34, a. 3; q. 103, a. 6; q. 116, aa. 2–3, ScG 3.97. 26. Aquinas, ST I-II, q. 91, a. 1; q. 93, aa. 1–6 with q. 90, aa. 1–4. 27. Aquinas, ST I-II, q. 94, aa. 1–6 and q. 96, a. 3, ad 3.



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mankind. There would also be a nomological correlate of the species equinity—namely, the law of nature proper to members of the species horse—and so forth. The resulting theory would resemble Brian Ellis’s scientific essentialism: so far from being mutually incompatible ways of conceptualizing the world, natural kinds and laws of nature would be directly linked through the essences of powerful particulars.28 But Aquinas does not go down this road. Instead, he treats species and laws of nature (about which he says almost nothing)29 as if they rested on different footings. From the beginning, species point reliably to the divine exemplars they represent. They are nonhistorical types fixed forever in God’s government of the world. Even the species humanitas is not a provisional work-in-progress, despite the fact that the Fall has occurred and the general resurrection will occur, and despite the fact that the Word became flesh in a man who doubtfully instantiated the same natural-kind type as those around him. Natural kinds pertain to what is in God’s creation, whereas laws of nature pertain to what occurs in his government of the world. Such laws are general rules that do not point straightforwardly to the divine plan they represent. Aquinas associates them with secondary causes, which produce their effects naturally and only for the most part. So, for example, it is a law of nature that dead men never come back to life, that human beings are begotten by human beings, and that heavenly bodies move always with uniform circular motion. But these laws hold only for the most part, as the Bible makes clear.30 28. See Umphrey, Natural Kinds and Genesis, 110–12. For Aquinas, natural kinds and laws of nature are grounded theologically in the divine Word, whereas for Ellis they are grounded naturalistically in the things themselves. 29. Aquinas, ST III, q. 77, a. 1, ad 1 (in a discussion of transubstantiation), II-II, q. 85, introduction (in a discussion of sacrifice). Lex naturae is not mentioned in his taxonomy of laws (ST I-II, q. 91). His interests and preferred modes of inquiry direct him instead to man and man’s relation to God. 30. Aquinas, ST I-II, q. 93, a. 5; I, q. 22, a. 4; q. 105, aa. 1, 8; q. 112, a. 2; q. 116, a. 2; III, qq. 73–78 (on the eucharist), ScG 3.72–74, 3.94, 3.100–101. God could annihilate natural kinds if he wished: ST I, q. 104, a. 1. Aristotle would disagree.

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His typological and nomological accounts differ also in their key terms. Species manifest archetypes in God’s intellect; and the terms used to designate these types are idea, exemplum, and ratio—usually in the plural. Laws of nature, on the other hand, manifest God’s providential plan; and the terms used to designate this plan are lex aeterna, ratio, and exemplum—always in the singular. Why is ratio or lex preferred when describing God’s Word as a plan, while exemplum or idea are preferred when describing his Word as an archetype? The latter two terms still carry Platonic connotations. They serve to describe the Word insofar as it is sortal and theoretical. The former two terms serve to describe the Word insofar as it is epitactic and propositional. Even for us, God’s plan is like a single magisterial judgment governing everything.31

Hierarchy Aquinas posits a hierarchy of beings that is reminiscent of Aristotle’s. Yet there are important differences. First, all dependent beings are finite, whereas the supreme being (God) is infinite. Second, among dependent beings, the principal distinction is between spiritual and material substances. A substance is spiritual just in case it is essentially intellective. The supreme created substances are simply intellective, without any material involvement. Each therefore is one of a kind. The Bible calls them “angels,” and so does Aquinas. They form a hierarchy. Humans, too, are spiritual substances, yet they are not simply intellective but material as well, and therefore many in number though one in kind. Humans are subordinate to angels in the order of being, of perfection, of participation in God.32 Material substances 31. See Umphrey, Natural Kinds and Genesis, 107–10, with chap. 5.2 of this volume. Because in Latin there are no definite articles, we cannot always tell whether Aquinas meant an exemplar or the exemplar, a law or the law. Consider, e.g., ST I, q. 22, a. 1, ad 2; q. 22, a. 3; q. 103, a. 6; I-II, q. 93, aa. 1, 3–5; q. 96, a. 3, ad 3. 32. Aquinas, ST I, q. 5, aa. 2–4; q. 15, a. 2; q. 22, a. 1; q. 22, a. 4; q. 50; q. 75, a. 7; q. 76, aa. 1–2; q. 79, a. 1, ad 1; q. 108, a. 1, ScG 2.46, 2.49–51, 2.55, 2.68, 2.93, 2.95, 3.20–21, 3.79–80; On Spiritual Creatures 4, 6.



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are divided into animate and inanimate, and heavenly and sublunary. Their ordering, too, is quite Aristotelian.33 But the place of humans is now unclear. For as terrestrial they are inferior to everything heavenly, and yet heavenly bodies, though moved by angels, are not themselves spiritual, whereas humans are; hence, though corruptible, they are superior to the heavenly bodies. As transitory, moreover, each of us is inferior to our species. Yet our species, though permanent, is inferior to each of us in relation to God. Does not the spiritual order trump the natural order, in his view?34 Aquinas’s order of beings is more strongly theocentric than Aristotle’s and has about it a less conjectural air.35 It prevails moreover in his thinking about things natural. There is in his works, and those of other Schoolmen, little evidence of that biocentric approach which prevailed in Aristotle’s thinking. They admit a role for empirical study but engage in very little of it.36 Natural philosophy for them is not neoSocratic, as it was for Aristotle. Indeed, their approach to things natural resembles that of philosophical naturalists today: they both emphasize commentary and analysis within a pregiven theoretical framework.

Creation God created the world ex nihilo (not from some pre-existing stuff), de novo (not from eternity), and freely in accordance with his intellect (not necessarily or capriciously). The creative act itself involves no motion or time, as it initiates both. It is not properly speaking a genesis 33. Aquinas, ST I, q. 50, a. 3; a. 5, ad 3; q. 65; q. 75, a. 1; q. 76, a. 1; q. 78, ScG 2.68–69, 2.72, 2.93, 3.82. 34. Aquinas, ST I, q. 47, a. 2; q. 68, a. 1; q. 70, a. 3; q. 75; q. 98, a. 1, ScG 2.46–55, 2.82–84, 2.90, 2.93, 3.111. See also Al-Fârâbi, The Perfect City, 8; Avicenna, Metaphysics of the Healing, 6.5, 9.3; Maimonides, Guide, 3.12 (but see also 2.6). 35. See also Maimonides, Guide, 1.72. 36. A notable exception: Albertus Magnus, On Animals, trans. K. F. Kitchell and E. M. Resnick (Baltimore, Md.: Johns Hopkins University Press, 1999). On the relevant background, cf. Lennox, Aristotle’s Philosophy of Biology, 110–25. There is also Avicenna’s work in medicine.

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(generatio). God alone can create and he alone is eternal, self-subsisting being. All other things depend on him as their efficient as well as final cause.37 It follows that species have not always existed, as Aristotle supposed. Nor however did they originate by natural selection together with other natural processes, as Darwin maintained. Instead, they were created in the very institution (institutio) of nature. It follows moreover that the world, being wholly in accordance with the divine Word, is thoroughly intelligible. In Aquinas’s theocentric conception of the world we find the metaphysical counterpart of Vico’s principle that verum (the true) and factum (the made) are convertible.38 Natural philosophers thus have a divine guarantee that the science they seek is possible in principle. Although they must investigate nature the hard way, by empirical and abstractive means, they need not settle for likely stories, as Timaeus supposes. Does it also follow that everything natural is insubstantial, shadowy, vestigial, like figures in a dream? This is certainly one option.39 But so too is the more Aristotelian view, embraced by Aquinas, according to which some creatures are individual substances having real causal powers, some of which have come into being and will eventually perish, some of which can deliberate and alter their lives while seeking knowledge of things natural and supranatural.40 Still, the dis37. Aquinas, ST I, q. 2, a. 3; q. 3, a. 8; q. 8, a. 1; q. 9, a. 1; q. 19, a. 4; q. 19, a. 10; qq. 45–47; q. 65, a. 3; q. 74, a. 2; q. 104, aa. 1–4, ScG 1.17, 2.11, 2.16, 2.20–21, 2.23–27, 2.31–32, 2.38. See also Maimonides, Guide, 2.13, 2.18, 2.20–21, and H. A. Davidson, Moses Maimonides: The Man and His Works (New York: Oxford University Press, 2005), 365–67. 38. G. Vico, The New Science §331, and On the Most Ancient Wisdom of the Italians, trans. L. M. Palmer (Ithaca, N.Y.: Cornell University Press, 1988), 50–52. 39. Cf., e.g., Bonaventure, Commentary on the Sentences, 1.3.1, in Selections from Medieval Philosophers, ed. and trans. R. McKeon (New York: Scribner’s, 1930), 2:118–48, esp. 133. For background, cf. 2 Mc 7:8, Rom 4:17, Heb 11:3, and G. May, Creatio ex Nihilo, trans. A. S. Worrall (London: T. and T. Clark International, 2004), 7. 40. Aquinas, ST I, q. 45, a. 4; q. 105, a. 5, ScG 2.65, 3.69, 3.71–72. Cf. J. R. Weinberg, A Short History of Medieval Philosophy (Princeton, N.J.: Princeton University Press, 1964), 183.



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tinction between things born (nata) and things made (facta) is ultimately erased: the world according to Aquinas is God’s great opus, the Book of Life, whose terrestrial lifeforms can all be traced back to their original institution.41 And he, unlike Aristotle, distinguishes not only between the matter and the form of a material substance, but also between its essence (essentia), what it is, and that by which it is, its being or existence (esse). Though actual in relation to matter, form is potential in relation to the act of existing (actus essendi). And it is this act, rather than its intrinsic form or essence, which is innermost in a creature, even though it is extrinsic in the sense that it comes directly and contingently from God.42 Creation, according to Aquinas, involves a diversification and delimitation of existence into individual substances, spiritual as well as material, whose natures are the different ways in which existence has been delimited.43 It does not follow that the essence of a creature can be reduced to its existence or that its essence existed prior to the creation. But it does follow that the existence of natural things is prior in being to their natures. Hence natural philosophy, in its attention to the natures of created things, abstracts from what is primary in them. It is autonomous within theological science in somewhat the way biology today is autonomous within physical science. In these ways, among others, the Thomistic synthesis seeks to rec41. Aquinas, ST I, q. 65, preamble; qq. 70–71; I-II, q. 93, a. 1. 42. Aquinas, ST I, q. 3, a. 4; q. 4, a. 1, ad 3; q. 8, a. 1; q. 13, a. 11; q. 44, a. 1; q. 45, a. 4; q. 45, a. 7; q. 46, a. 1; q. 50, a. 2, ad 3–4; q. 54, aa. 1, 3; q. 61, a. 1; q. 75, a. 5, ad 1, 4; q. 85, a. 3, ad 1; q. 104, a. 1, ScG 1.20–24, 1.31, 2.39–45, 2.49–54, 3.65, 3.69; De Potentia 7.2, 9.5, De Veritate q. 1, a. 3, ad 3; q. 21, a. 4, ad 4, De Ente et Essentia, 4. Cf. Avicenna, Metaphysics of the Healing, 1.6, 1.8, 5.1, 8.4. Also Kahn, The Verb BE in Ancient Greek, 18. That form is potential in relation to the act of existing explains why angels are not pure actualities even though they are pure forms; and that the act of existing is individuating explains why angels are also singular things, not universal species, even though they are immaterial. 43. Cf. W. E. Carlo, The Ultimate Reducibility of Essence to Existence in Existential Metaphysics (Dordrecht: Nijhoff, 1966), and for a more nuanced account, J. F. Wippel, Metaphysical Themes in Thomas Aquinas (Washington, D.C.: The Catholic University of America Press, 1984).

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oncile Aristotelian with Christian doctrines. Clearly there are residual tensions. But the principal conflict is zetetic rather than doctrinal, as we can see by considering various opinions about the origin of the world: the big bang theory (contemporary cosmologists), the big persuasion theory (Plato’s Timaeus), the sempiternity theory (Aristotle), and the creation theory (Aquinas et al.). They cannot all be true. No one seems to know, demonstratively or non-demonstratively, which if any we should accept.44 Hence natural philosophers are free to examine and reject every one of them. For Aquinas, however, creationism is an article of faith, and articles of faith are to be accepted and defended, never rejected. The natural light of reason has its place, but should operate in conformity with the supernatural light of grace. Physics and natural theology are true as far as they go, but inadequate in relation to divine revelation—just as moral and theoretical virtues are all good qualities of soul, as Aristotle said, but fall short of the theological virtues (faith, hope, and charity) which complete them.45 This conception of the relation between philosophy and sacred doctrine is at the heart of the Thomistic synthesis. And it more than any particular theory about the world caused a third major crisis in natural philosophy, one which was not resolved until the seventeenth century. Yet even among Schoolmen, the Thomistic synthesis proved unstable.46 For even as it was taking hold in the church, theologians and philosophers were taking it apart. Foremost among these deconstructionists was Ockham, whose work I now briefly consider.

44. Aquinas, ST I, q. 45, aa. 1–2, ScG 2.5, 2.46. 45. Aquinas, e.g., ST I, q. 1, aa. 1, 5; q. 2, a. 3, ad 1; q. 12, a. 13, ad 3; q. 46, a. 2; q. 99, a. 1; I-II, q. 4, aa. 2–3; II-II, q. 1, aa. 3–8; q. 2, aa. 1–3; q. 3, a. 6, de Trinitate q. 2, a. 4, ad 5, with M. Jordan, “Theology and Philosophy,” in The Cambridge Companion to Aquinas, ed. E. Stump and N. Kretzmann (New York: Cambridge University Press, 1993), 232–51. 46. That these conflicts were partly institutional: J. A. Aertsen, “Aquinas’s Philosophy in Its Historical Setting,” in Cambridge Companion to Aquinas (ed. Stump and Kretzmann), 24–27.



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THE GREAT UNRAVELING Ockham was a theologian and philosopher who separated theology and philosophy by accentuating the difference between reason and faith and arguing that reason can demonstrate very little about God or the way in which God and world are related.47 Philosophy is then free to investigate whatever can be known by rational and experiential means. Ockham thus helped to establish the modern way (via moderna) in philosophy. Yet his intention was conservative; he sought to purge Christian theology of neo-Platonic and Aristotelian distortions while purging Aristotle’s logic and physics, the true via antiqua, of the metaphysical speculations in which medieval Aristotelians had buried it. Ockham the theologian emphasized God’s omnipotence and the radical contingency of everything created. It follows, he thought, that mundane events are not bound together by any natural necessity. Meanwhile, Ockham the philosopher promoted a linguistic or conceptual turn: we are to focus first of all not on what exists but on our ways of apprehending what exists. And while doing so we are to exercise what came to be called “Occam’s Razor”: if putative entities of some sort are not required to explain any true propositions about the world, we should expunge them from our ontology.48 It follows, he thought, that all things in the universe are radically singular; there are no extramental universals, and no real species or essences of the sort posited by medieval Aristotelians. The relation between his antinecessitarianism and his antirealism with respect to natural kinds is obscure. It suffices here to say a few words about each. His antinecessitarianism: God can do anything that is not formally contradictory. There are no other constraints on his freedom to create or conserve whatever he has chosen to create.49 He does not 47. Ockham, Quodlibital Questions, 2.1.1–2, 2.2.1, 2.3, 3.1, 3.4, 4.1–2, 7.11–18. 48. Ockham, Ordinatio 1.2.1, Quodlibetal Questions 7.2, Summa Logicae 1.51. 49. Ockham, Quodlibetal Questions 6.1, 6.6. Ockham does say that once God has cove-

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therefore act inordinately or randomly.50 But it does follow that the world-order is not the manifestation of some eternal law which God must execute once he has chosen to create the world; for not only would that be a constraint on his will, one whose denial is logically possible, it would also misattribute to his intellect an idea that exists only objectively in the world-order he produces, not subjectively in Him.51 Yet Ockham agrees that creatures are powerful particulars, “secondary causes,” and as such they produce certain likely effects. In other words, given a secondary cause of type C, there will naturally follow an effect of type E, other things being equal; and given an effect of type E, it will naturally have been produced by a cause of type C. But natural causation is not necessary, for God may anywhere at any time intervene.52 Ockham’s position is therefore to be distinguished from Hume’s (which rejects both powerful particulars and natural necessity), and from Avicenna’s or Spinoza’s or Brian Ellis’s (which affirms both), and from Descartes’s (which admits nomic necessity but rejects “secondary causes”).53 Ockham also denies that causation is a relation over and above its relata; for not only are there no necessary connections among things in nature, there are no real connections at all. The world is nothing over and above the particulars “in” it. Its unity is that of a collection—a diversity and not a university.54 Ockham’s antiessentialism: existing things comprise substances nanted never to do something, it will never occur. Would God’s breaking such a covenant violate the principle of noncontradiction? Cf. Armand Maurer, The Philosophy of William of Ockham in the Light of Its Principles (Toronto: Pontifical Institute of Mediaeval Studies, 1999), 260. 50. Ockham, Quodlibetal Questions 2.3, 6.1, 6.6. 51. Ockham, Quodlibetal Questions 6.6, 7.15, Sentences 1.35.5, Ordinatio 1.35.5. 52. Ockham, Quodlibetal Questions 2.1, 4.2, 4.22, 4.32, 5.18. Unlike other Aristotelians, Ockham doubts that sublunary and celestial matter are different in kind: Reportatio 2.18. 53. Compare Marilyn M. Adams, William Ockham (Notre Dame, Ind.: University of Notre Dame Press, 1987), 2.741–58. 54. Ockham, Quodlibetal Questions 6.12, 6.15, 7.3, 7.8, Summa Logicae 1.39, 1.54, 3.27, Ordinatio 1.2.1, 1.24.1. Though Ockham the theologian admits a comprehensive teleology similar to Aquinas’s, Ockham the philosopher has no room for it in his physics.



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and their attributes. All attributes are nonrelational qualities.55 Some belong only contingently (per accidens) to the substances in which they inhere; they are called “accidents.” Others belong necessarily (per se) to these substances; they are called “properties.” Accidents such as Socrates’s paleness and properties such as his capacity to laugh are really distinct from Socrates himself. All distinctions among created things are real distinctions. Yet attributes of either sort would not exist if there were no substances; for them, to be (esse) is to be-in (inesse).56 Substances, on the other hand, do not inhere in anything; they are ultimate subjects. Natural substances are hylomorphic, Ockham says, but he, unlike other Aristotelians, takes matter itself to be something actual and he admits that a material entity may have more than one substantial form. An animal’s soul does not then explain why it is a single enduring thing. Nor is there in it a common nature or an essence that is universalizable in thought. Nor is there any distinction between what it is and that it is. The nature (nx) or existence of a hylomorphic entity is just the hylomorphic entity (x) itself, a radically singular thing.57 No “principle of individuation” is needed to explain the particularity of it or any one of its attributes. Ockham’s conceptualism: there are no universals. The species horse is just the many individuals to which the concept horse applies. Though we may regard this concept as a universal type, we should bear in mind that it is “in the soul”; that as a real quality or act of soul, it too is particular; and that it is universal only in the sense that it naturally signifies many extra-mental things. And though we may regard the cor55. The shapes of things and the straightness or curvature of lines are examples of relational qualities. Insofar as they are relational, Ockham maintains, they are nothing over and above the material parts so arranged. Cf. Quodlibetal Questions 7.2, Summa Logicae 1.55. 56. Ockham, Quodlibetal Questions 5.22, 6.20, 7.2, Summa Logicae 1.16, 1.18, 1.20–25, 1.30, 1.55–56, Ordinatio 1.2.10. 57. Ockham, Quodlibetal Questions 2.7, 2.10–11, 4.19, 4.21, 5.11, 5.15, 5.23.3, 6.15, Summa Logicae 1.7, 1.16, 1.43, 3–2.27, Ordinatio 1.2, Expositio Physicorum 1.1, 1.16, 2.2, 2.9. He does not affirm Aristotle’s distinction between heaps and naturally constituted wholes. A piece of wood is a substance, he says, and when divided in two it becomes two substances.

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responding word “horse” as a universal, we should bear in mind that it exists in the English language, not in the extra-mental reality that includes horses; that insofar as it exists, it is but a token or multitude of tokens, not a type; and this token is a universal only in the sense that it conventionally signifies many things.58 Yet Ockham is not an extreme conceptualist, for he affirms that substances exhibit similarities with one another, that similarities come in degrees, and that these relations among individual substances constitute an objective basis for the application of specific and generic concepts, and for such scientific truths as “Man is a rational animal” and “Every extended substance is composed of matter and form.” He is what metaphysicians today call a “resemblance theorist” with respect to universals. But again we must be cautious. First, he denies that there are resemblance relations in addition to the resembling individuals. Second, these scientific truths are necessary only ex hypothesi: had God chosen not to create any humans, the proposition “Man is a rational animal” would be false.59 Third, we must take seriously his claim that concepts are singular affections or acts of soul. This is true, he says, not only of “first intentions” (e.g., the concept horse, which signifies those extra-mental substances we call “horses”) but also of “second intentions” (e.g., the concept species, which signifies those intra-mental particulars we call “species”).60 Resembling particulars are all there is. You have your naturally signifying ways of classifying them and I have mine. There is no such thing as the concept horse, the concept species, or the concept concept, regarded as classificatory principles we may have in common. 58. Ockham, Quodlibetal Questions 1.13.1–2, 3.12–13, 5.10, 5.13, 5.16, 5.23, Summa Logicae 1.1, 1.4, 1.13–19, 1.33, 1.42, Ordinatio 1.2.4–8. On natural signification, cf. Adams, William Ockham, 1:109–41, esp. 121–33. There are also no divine exemplars, as ideas are in God only objectively in the sense that they are things he knows, and everything he knows is singular. 59. Ockham, Quodlibetal Questions 4.32, 5.15, 5.18, 6.8, Summa Logicae 1.29, 1.54, 3–2.5, Ordinatio 1.3.4, 8.2 (cf. Aquinas), 30.5. 60. Ockham, Quodlibetal Questions 4.19, 4.35, 5.13, 5.21, Summa Logicae 1.1, 1.14–15, 1.25, 1.38, 1.40.



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Ockham’s conceptualism implies that there are no real naturalkind types, and thus natural kinds in the full sense of the term. And his antiessentialism implies that there is at most one natural kind in the primary sense of the term. For K is a natural kind in the primary sense only if its members belong to it in virtue of their natures—in other words, only if K is an s-resemblance class. But Ockham admits no distinction between the essence of a singular thing (nx) and that thing (x), and the only multitude of things that arguably constitutes a natural s-resemblance class is the one consisting of all and only material substances. Any division of this class into kinds must be based on the accidents or properties of its various members. But then the resulting kinds will be a-resemblance or p-resemblance classes and not natural kinds in the primary sense. Hence there are no Aristotelian species as types or as classes. This necessary consequence did not prompt him to give up the term “species.” Nor did he cease believing that coordinate species are generally disjoint, or that there are lowest species (species specialissimae).61 But he could not have justified these beliefs within the austere framework of his natural philosophy, and how he might have justified them theologically is unclear.62 This much however is clear: while proceeding boldly under the banner “Back to Aristotle!” Ockham helped bring to an end the Aristotelian tradition of natural kinds.

RATIONAL MECHANICS The abandonment of Aristotle’s biocentric approach to things natural, the gradual liberation of natural philosophy from revealed religion, and a growing readiness to question Aristotle’s conclusions: these de61. Ockham, Summa Logicae 1.18, 1.21. In his Sentences (3.2.6, 4.4.6) he argues that substantial similarity can be exact, not that it is ever actual. Cf. Maurer, Philosophy of William of Ockham, 456n10. 62. May not God create universals if it pleases him to do so? Ockham nowhere shows that such entities are logically impossible.

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velopments provided an opening in which new ways of considering natural phenomena could emerge. And in the generations following Ockham, a new mathematical science of motion did emerge. Its practitioners (called “Calculators”) still had to deal with the fact that in Aristotle’s physics substances are primary—and as substances unmathematizable—and the fact that Ockham had reduced quantity, relation, time, place, and motion to substances and their qualities.63 These metaphysical constraints they skirted in two ways. First, they concentrated on passages in the later books of Aristotle’s Physics, where his formal-teleological conception of material individuals recedes into the background and mathematics became uncharacteristically prominent.64 Second, they proceeded openly in accordance with the imagination (secundum imaginationem),65 which allowed them to treat material substances and their qualities as if they were quantities, and to regard certain relations among them as if they were real. Ockham might have questioned the point of all this make-believe, but he could not have rejected it on metaphysical grounds; for he acknowledged that material substances are extended, that their qualities are 63. Ockham, Summa Logicae 1.41, 1.44–54, 1.59–61, Quodlibetal Questions 1.5.1, 4.10, 4.26–27, 6.8, 6.10, 6.16, 6.22–23, 6.25, 7.5–6, Ordinatio 1.30, Sententia 4.4.6, and Adams, William Ockham, 2:671, 690–95. Would he have admitted qualities had he not required them to explain the eucharist? Cf. J. A. Weisheipl, “The Concept of Matter in Fourteenth Century Science,” in The Concept of Matter in Greek and Medieval Philosophy, ed. E. McMullin (Notre Dame, Ind.: University of Notre Dame Press, 1963), 157; and E. Stump, “Theology and Physics in De sacramento altaris: Ockham’s Theory of Indivisibles,” in Infinity and Continuity in Ancient and Medieval Thought, ed. N. Kretzmann (Ithaca, N.Y.: Cornell University Press, 1982), 214. 64. These passages included Physics 4.8, 6.1–2, and 7.4–5, with commentaries thereon by Averroes and others. Also serving as points of departure were several passages in his On the Heavens. On the place of mathematics in Aristotle’s Physics, cf. G. E. L. Owen, “Aristotle’s Mechanics,” in Aristotle on Nature and Living Things (ed. Gotthelf), esp. 240–44. 65. E.g., Nicole Oresme, Nicolas Oresme and the Medieval Geometry of Qualities and Motions: A Treatise on the Uniformity and Difformity of Intensities Known as Tractatus de Configurationibus Qualitatem et Motum, trans. M. Clagett (Madison: Wisconsin University Press, 1968), 1.1, 1.3, 1.17, 2.1, 3.1. Cf. Curtis Wilson, William Heytesbury (Madison: Wisconsin University Press, 1956), 24, 115.



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more or less intense, and that each of these things is therefore a quantum. Hence quantification, like specification, can have some basis in reality.66 Metaphysical parsimony, moreover, does not entail semantic parsimony. Just as Ockhamists are free to regard sortal concepts as universals (something we do all the time in everyday life), so too are they free to represent related quanta by magnitudes, ratios, and proportions, and to speak of these as if they were real (something we do all the time in mathematics).67 I now summarize this new science of motion, and determine to what extent it moved beyond the Aristotelian framework it presupposed. Qualities admit of degrees—more or less pale, more or less healthy, etc. They may be regarded as intensive magnitudes and represented alphabetically by letters or graphically by line segments. And the material substances to which they belong are so related that the spatial and temporal intervals between them may be regarded as extensive magnitudes, likewise representable by letters or line segments. All these magnitudes are assumed to be continuous.68 Motion is qualitative, quantitative, or local. It may be regarded as a succession of similar states exhibiting different degrees, as in cases of whitening. This is the intensio-remissio theory of motion. Alternatively, it may be regarded as the gaining or losing of material parts, as in cases of bulking up. This is the addition-subtraction theory of motion. These two theories are not mutually exclusive.69 Both take 66. Ockham, Summa Logicae 1.43–48, Quodlibetal Questions 4.23–24, 4.27, 6.10. 67. They were not the first Aristotelians to make a mathematical turn: Grosseteste, whose interest was in optics (another scientia media), anticipated them. So too did his student, Roger Bacon. 68. Cf. Anneliese Maier, Zwei Grundprobleme der scholastischen Naturphilosophie (Rome: Edizioni di Storia e Letteratura, 1951), 9–64. Also Aristotle, Categories 6–7 and Physics 248b22. 69. Cf. E. Sylla, “Fourteenth-Century Theories of Alteration,” in Infinity and Continuity (ed. Kretzmann), 231–57, and “The Oxford Calculators,” in The Cambridge History of Later Medieval Philosophy, ed. N. Kretzmann, A. Kenny, and J. Pinborg (New York: Cambridge University Press, 1988), 540–63. Ockham favored an intensio-remissio theory of qualitative

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qualitative as well as quantitative and local motions to be continuous. Speed (velocitas) is regarded as a quality or something qualitylike. It too admits of degrees and may be represented alphabetically by letters or graphically by line segments. Given a body in motion, if no intensification or remission of its speed occurs, the motion is uniform, whereas if it does occur, the motion is difform: there is acceleration (velocitatio). Acceleration may be uniform, in which case the motion is uniformly difform, or nonuniform, in which case the motion is difformly difform. So, for example, the rate at which whitening occurs may be uniform or difform, etc.70 Force (potentia, virtus, vis) also admits of degrees. It too may be represented alphabetically or graphically. A body is moving locally only if there is some force acting on it, and this force must be greater than the resisting force of the medium in which it moves. There is no unresisting medium.71 In projectile motion, contrary to what Aristotle thought, the moving force subsists as an impetus within the projectile itself. In gravitational or levitational motion, too, there must be some moving force within the body; final causality alone cannot explain it.72 Aristotle’s distinction between natural and violent motion is thus brought into question, without being rejected altogether. Ratios obtain between magnitudes of the same kind—speed v1 to speed v2 , moving force F to resisting force R, time t1 to time t2 , etc. Magnitudes may be homogeneous in their representations but heterogeneous in themselves. For example, spatial and temporal intervals may be represented by line segments, and it may be that s1:s2::t1:t2 ; but we should not infer that s1:t1::s2:t2 , for such permutations are adchange (e.g., Expositio in Physica 3.2–3), but was receptive to an addition-subtraction theory of quantitative and even local change. 70. E.g., Oresme, De Configurationibus, 2.1–8. 71. Cf. Aristotle, Physics 215b22. 72. The impetus theory seems to have originated with Buridan. Fourteenth-century physicists were inclined to identify the centripetal or centrifugal force in elemental motions with the very heaviness (gravitas) or lightness (levitas) of the moving body.



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missible only if all terms are the same in kind, and distances and times differ in kind: it makes no sense to say that si is greater than, less than, or equal to ti .73 The new scientists of motion did homogenize some magnitudes that Aristotle thought heterogeneous. Bradwardine, for instance, argued that rectilinear and curvilinear motions are comparable with respect to speed.74 Yet he and the others accepted the claim that qualitative, quantitative, and local motions are categorially diverse. They also seem not to have assumed that there could be a ratio scale for every sort of qualitative quantum. One thing may be twice as fast as another, or twice as hot, but can it be twice as healthy or courageous? The answer is unclear. Theorems take the form of proportions that remain invariant even as their terms vary. A dynamical example: Bradwardine found that v∝logn(F/R), where v is understood to be the dependent variable and n = v2/v1.75 This theorem both generalizes and corrects what Aristotle said in Physics 7.5, and the proportionality it describes may be regarded as an instance of formal causality.76 A kinematic example: Oresme found that if a quality Q varies uniformly in “latitude” from qi = 0 to qf = n, over “longitude” d, then the total variation equals (n/2)d. This equality we may call Oresme’s Mean Intensity Theorem. It holds true not only for uniformly varying degrees of speed over temporal interval Δt, but for uniformly varying intensities of heat or 73. Cf. Euclid, Elements 5, def. 4, and Aristotle, Physics 5.2, 7.4, 8.8. 74. Bradwardine, Thomas Bradwardine, his Tractatus de Proportionibus; Its Significicance for the Development of Mathematical Physics, ed. and trans. H. L. Crosby (Madison: Wisconsin University Press, 1955), 4.1–3. Compare Aristotle, Physics 249a29–b19. 75. Bradwardine, De Proportionibus, 2.1, 3.1–2. My way of expressing his theorem is anachronistic. Where he spoke of duplicate ratios and the like, we now speak of exponential functions; and where he said that v follows (sequitur) in a certain way the ratio of F:R, we now say that v depends functionally on F/R. Note also that in the ratio x:y he regarded each relatum as having a certain disposition (habitudo) to the other; he did not posit any relation over and above these relata (De Proportionibus, 1.1 [67]). 76. Cf. Aristotle, Physics 194b27–28, and Weisheipl, Physical Theory in the Middle Ages, 52, 61.

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the like over spatial interval Δx. Galileo’s Mean Velocity Theorem is a specification of it.77 To what extent have these fourteenth-century physicists moved beyond Aristotelian physics? They established a mathematical theory of motion in which specific differences among things tend to disappear in their quantitative and relational representations, in which respect they seem more Galilean than Aristotelian. Their procedure, however, was logical and imaginative rather than observational; they showed little interest in grounding their theorems by taking measurements in carefully controlled situations. In this respect they seem neither Galilean nor Aristotelian.78 They agreed, moreover, that motion is irreducible to locomotion; that natural and violent, voluntary and nonvoluntary motions are to be distinguished; that hot and cold, heavy and light are real qualitative opposites; that substances are categorially primary; and that among these substances are such things as lions and eagles, some of whose qualities are so dissimilar that they can be homogenized only in their mathematical representations. These fourteenth-century physicists would have rejected the claim that natural phenomena are essentially mathematical. In this respect they remained fundamentally Aristotelian. Galileo and other seventeenth-century physicists did not, as we shall see.79 77. Oresme, De Configurationibus, 3.5–8. Compare Galileo, Two New Sciences, Third Day, theorem 1. There is no evidence that Galileo was acquainted with Oresme’s Theorem, also called “the Merton rule.” 78. Cf. Wilson, William Heytesbury, 148–51. 79. E.g., Oresme, De Configurationibus, 1.24 with 1.22, and 2.10. Assuming that earth differs substantially from water, air, or fire, and that these elements are to be understood in terms of hot and cold, wet and dry, it follows that one cannot keep heating or moistening something earthen without eventually transforming it into something watery, airy, or fiery: some phase transitions are substantial changes. In assuming all this, fourteenth-century mechanists remained comparatively close to our everyday understanding of things, as did Aristotle. Cf. Wilson, William Heytesbury, 57.

CHAPTER 5

Lex and Motus I Galilean Science

Ockham threatened the Aristotelian tradition of natural kinds in two ways. First, if antirealism with respect to universals is true, as he argued, then there are no real natural-kind types, and hence no natural kinds in the full sense of the term. Second, if antiessentialism is true, as he argued, if there is no distinction at all between a material substance x and its nature nx , then there is no basis in reality for saying of two materially different things that they are essentially the same, or exactly alike, and hence there are no natural kinds even in the primary sense of the term. Early modern philosophers followed Ockham in denying the existence of universals. They also denied the reality of “substantial forms.” Consequently they regarded the Aristotelian distinction between heaps and naturally constituted wholes as acceptable only if some material things are genuinely atomic. A few did endorse metaphysical atomism, but most did not, preferring instead to suppose that the natural world is at bottom just matter in motion—a view remarkably like that of some pre-Parmenidean natural philosophers. 145

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Yet the division between ancients and moderns is more radical than this. By effecting yet another paradigm shift in natural philosophy, Galileo and others revolutionized our understanding of nature. Aristotelian physics was overthrown, a new way of investigating nature undertaken, a new mathematical physics established. My task now is to disclose the metaphysical foundations of this science and discuss their implications for natural-kinds realism and natural philosophy generally.

THE MATHEMATICAL NATURE OF NATURE According to Galileo, the universe is a great book that we cannot begin to understand unless we have learned to recognize its elements. “It is written in mathematical language and its letters are triangles, circles, and other geometrical figures without which it is humanly impossible to understand a word of it. Without these, one wanders in vain through a dark labyrinth.”1 According to Descartes, the natural world is matter in motion according to certain laws. These laws are expressible algebraically, the motions they govern are local and quantifiable, and matter itself is reducible to extension. Corporeal nature is an object of pure mathematics.2 By taking nature to be essentially mathematical, these philoso1. Galileo Galilei, The Assayer, in S. Drake and C. D. O’Malley, The Controversy on the Comets of 1618: Galileo Galilei, Horatio Grassi, Mario Guiducci, Johannes Kepler (Philadelphia: University of Pennsylvania Press, 1960), 183, and Discoveries and Opinions of Galileo, trans. S. Drake (Garden City, N.Y.: Doubleday, 1957), 237. This passage aligns with Opere di Galileo Galilei, ed. A. Favaro (Florence: Barbèra, 1890–1909), 6:232. See Galileo’s letter to Marsili, 1632, in Opere, 14:386. See also Maurice Clavelin, The Natural Philosophy of Galileo, trans. A. J. Pomerans (Cambridge, Mass.: MIT Press, 1974), 409–17. 2. Descartes, Regulae 14 (AT 10:442–49), Meditations 2–6 (AT 7:17–20, 26, 28, 30, 36, 43, 63, 71, 74, 80), Principles of Philosophy 1.48, 1.55, 1.64, 2.4, 2.11, 2.53, 2.64, The World 5 (AT 11:25), letter to Mersenne, July 27, 1638 (AT 2:268). AT = Oeuvres de Descartes, ed. C. Adam and P. Tannery (Paris: Librarie Philosophique J. Vrin, 1964–73).



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phers removed from the world many of the things we usually impute to it. There are no colors, tastes, or other such qualities, and no volitions or final causes: mathematical objects are not the sort of thing that could be green or red, sour or sweet, or have any inner directedness or spontaneity. There is no place in Galilean physics for the concepts of right or wrong, good or bad, healthy or sick—what Plato’s Eleatic Stranger in the Statesman calls “measures of fittingness” as distinguished from “measures of relative more-and-less”—nor any place for opposites such as hot and cold, moist and dry, or natural and violent. The physical world is the Husserlian Lebenswelt deanimated. To us it seems lifeless, quite unlike the world of everyday experience.3 It is also quite unlike the Aristotelian world it replaced. There, quantities and relations were incidental to the material substances in which they inhere, and the matter of such entities was either heterogeneous (if proximate) or formless (if primary). In the world of Galilean science, by contrast, such geometrical properties as shape, size, number, and arrangement are determinative of the bodies to which they belong; these properties are but modes of matter; and matter is the same everywhere, in the heavens and on the earth. There is no longer any substantial difference between proximate and prime matter, and matter itself is not altogether amorphous; it has an intrinsic structure describable, it was thought, by the axioms of Euclidean geometry. Unlike its medieval precursors, mathematical physics is no scientia media; for it has erased the difference (insisted on by Aristotle 3. E.g., Galileo, The Assayer, 274 (Opere, 6:349–51); Two New Sciences, trans. S. Drake, 2nd ed. (Toronto: Wall and Thompson, 1989), 104 (Opere, 8:146–47); Descartes, The World (AT 11:26, 36), Meditations 3 (AT 7:43), Reply to Sixth Objections (AT 7:440), Principles of Philosophy 1.68, 2.4, 2.11, 2.36, 4.202; Hobbes, de Corpore 9.6–7, 8.19; Robert Boyle, A Free Enquiry into the Vulgarly Received Notions of Nature, ed. E. B. Davis and M. Hunter (New York: Cambridge University Press, 1996), 18, 37–50, 143, 158–60; Plato, Statesman 283–86; and Aristotle, Metaphysics 996a29-b1. On their reduction of heat to the local commotion of parts: Anneliese Maier, “Die Mechanisierung des Weltbilder im 17. Jahrhundert,” in her Zwei Untersuchungen zur nachscholastischen Philosophie (Rome: Edizione di Storia e Letteratura, 1968), 13–67.

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and admitted even by Plato’s Timaeus) between mathematical structure and nature itself.4 That nature is essentially mathematical does not entail that our mathematics is adequate to the task of describing it. Founders of the new physics appear to have recognized as much.5 They made major innovations in mathematics, including algebraic geometry (Descartes) and the calculus (Newton). Perhaps the book of nature is written not in circles or the like, but in “fluents” or ratios whose terms are nascent or evanescent. Perhaps the key terms are not Euclidean objects at all, but rather symmetry relations studied in group theory. And perhaps the structure of space or spacetime is to be described by the axioms of some non-Euclidean geometry. Group theory and non-Euclidean geometry were unavailable to early Galileans, yet quantum field theory and general relativity theory remain recognizably Galilean; founders of the new science would have welcomed them. There is a complication. According to Galilean physics, nature is also essentially mechanical. Physical things are bodies whose interactions are to be understood in terms of immediate pushes or pulls. The physical world is like a great machine, or system of machines, whose elementary components are levers, pulleys, wedges, gears, screws, or the like.6 But a nested system of Euclidean figures is not really ma4. Cf. R. Feldhay, “The Use and Abuse of Mathematical Entities: Galileo and the Jesuits revisited,” in The Cambridge Companion to Galileo, ed. P. Machamer (New York: Cambridge University Press, 1998), 100–120. 5. Galileo, letter to Gallanzoni, July 16, 1611 (Opere, 11:149), with Clavelin, Natural Philosophy of Galileo, 447. 6. Galileo, Two New Sciences, 147, Dialogue Concerning the Two Chief World Systems, trans. S. Drake (Berkeley: University of California Press, 1953), 40; Descartes, Principles of Philosophy 2.24–25, 4.188; Hobbes, de Corpore 9.7; Boyle, Free Enquiry, 13, 39–40, 102, and “Origin of Forms and Qualities,” in Selected Philosophical Papers of Robert Boyle, ed. M. A. Stewart (New York: Barnes and Noble, 1979), 18, 40, 49. On the significance of regarding all change as measurable in terms of linear distances and times: Anneliese Maier, Die Vorläufer Galileis im 14. Jahrhundert (Rome: Edizioni di Storia e Letteratura, 1949), chap. 3, in On the Threshold of Exact Science, trans. S. D. Sargent (Philadelphia: University of Pennsylvania Press, 1982), 40–60. See also E. J. Dijksterhuis, The Mechanization of the World Picture, trans. D. Dikshoorn (Oxford: Clarendon Press, 1961).



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chine-like; and geometrical solids are not bodies, as they are not the sort of thing that could be impenetrable, resistant to change, or moved by shoving or tugging. Therefore, the nature of nature is not simply mathematical; it is mechanical as well. In astronomy, beginning with Kepler, mathematical description was combined with physical explanation, while in terrestrial mechanics, beginning with Galileo, physical problems were shown to be mathematical as well.7 Galilean science thus united within itself two disparate traditions in natural philosophy—one associated with the Pythagoreans, Plato, and Archimedes; the other with Democritus, Epicurus, and Lucretius. Two conceptual anomalies appeared right away. First, if the universe is a machine, and machines are designed and maintained for the sake of some end, cosmology should be teleological. But there is no room for teleology in mathematical physics. Must its founders then deny and affirm the presence of final causes in nature? Second, they were less interested in motion as a state than in acceleration as a change of state. Such changes are to be explained by impressed forces, which seem active. Can Galileans admit active forces without ascribing spontaneity to nature? And can they admit gravitational or magnetic or electrical forces, in particular, without having to accept direct action at a distance? To remove the first difficulty, Descartes and others argued as follows. God is the divine geometer-engineer who created the universe and sustains it from moment to moment. He has his reasons for doing 7. Cf. Kepler, Epitome of Copernican Astronomy, 4.4.2–4, 5.2.1, and the letter quoted in M. Caspar, Kepler, trans. C. D. Hellman (New York: Collier Books, 1962), 140. Galileo, Two New Sciences, 153 (Opere, 8:197) and the essay addressed to Cosmo quoted in Stillman Drake, Galileo at Work: His Scientific Biography (Chicago: University of Chicago Press, 1978), 172; Newton, Principia, preface. Also Ernst Cassirer, Determinism and Indeterminism in Modern Physics, trans. O. T. Benfey (New Haven, Conn.: Yale University Press, 1964), 172–77; Dudley Shapere, Galileo: A Philosophical Study (Chicago: University of Chicago Press, 1974), 67; Clavelin, Natural Philosophy of Galileo, 409–11; Alexandre Koyré, “Galileo and Scientific Revolution,” Philosophical Review 52 (1943): 333–48, reprinted in Koyré, Metaphysics and Measurement (Cambridge, Mass.: Harvard University Press, 1968). See also Koyré, Galileo Studies, trans. J. Nepham (Atlantic Highlands, N.J.: Humanities Press, 1978), 37, 74, 183, 199, 208.

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so, but these reasons transcend nature. Therefore, final causes have no place in scientific explanation. Physicists may consider the universe and systems within it as if they were machines directed to some end, but as scientists they suppose that end to be quite irrelevant to the knowledge they seek.8 The distinction between natural science and theology is thus rigidly enforced. It is still a distinction within natural philosophy, however, and not yet between philosophy and science. The second difficulty proved more recalcitrant. Descartes tried to resolve it by reducing everything mechanical, including forces, to things mathematical. Geometrical solids are the essences of bodies, what they are if they exist. Bodies are existing solids, and they exist because God (re)creates them from moment to moment. What makes these geometrical solids real, then, is the action of God’s will.9 But how is this efficient cause not another occult power, as far beyond our purview as any final cause? Here we must distinguish between causes secundum esse (according to being) and causes secundum fieri (according to becoming).10 Secundum esse, the forces of being in motion or at rest are but expressions of God’s action in maintaining the existence of bodies in their present states. So conceived, they are not geometrizable, not immanent in bodies, and therefore no business of the physicist. Secundum fieri, the forces of being in motion are what we measure, in each instance, by calculating the size of the thing times its speed.11 So conceived, they are immanent in bodies and must be taken into account by the physicist. They are also geometrizable, and 8. Descartes, Meditations 4 (AT 7:55), Principles of Philosophy 1.28, 3.2; Francis Bacon, Advancement of Learning 2, New Organon 1.52, 2.2; Boyle, Free Enquiry, 5. 9. Descartes, Meditations 3 (AT 7:49), Principles of Philosophy 1.53, 1.55–57, 2.36. For discussion of this point, cf. M. Gueroult, “The Metaphysics and Physics of Force in Descartes,” in Descartes: Philosophy, Mathematics, and Physics, ed. and trans. S. Gaukroger (Sussex: Harvester Press, 1980), 196–202, 222n26. 10. Descartes, Reply to Fifth Objections (AT 7:369). On his use of this Thomistic distinction, cf. A. Gabbey, “Force and Inertia in the Seventeenth Century: Descartes and Newton,” in Descartes: Philosophy, Mathematics, and Physics (ed. Gaukroger), 234–38. 11. Descartes, The World 8 (AT 11:50, 58), Treatise on Man (AT 11:193), Meteorology 1 (AT 6:235), Principles of Philosophy 2.43.



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because matter has been reduced to extension there need not be any gaps between “interacting” bodies: mechanical causation is preserved. What happened to the difference between bodies and geometrical solids? It is merely a distinction of reason.12 Bodies are existing geometrical solids varying in size, shape, and arrangement, all moving or resting relatively to one another, and physicists regard them as such. Mathematicians regard them abstractly, apart from their existence or non-existence, and therefore simply as objects of thought.13 Other seventeenth-century natural philosophers rejected Descartes’s geometrization of everything physical. Newton maintained that matter is irreducible to extension, that corporeal nature may not be a plenum, that what Descartes called “quantity of motion” (size × speed) should be replaced by what we call “momentum” (mass × velocity), and that force be understood rather as change in momentum per unit time (or mass × acceleration). The question for him was whether “attractive” or “cohesive” forces can be understood in terms of direct impact. Strict mechanists answered in the affirmative; to explain magnetism, gravitation, or the propagation of light in “empty” space, they postulated as yet undetected vortices of very fine matter or ethereal particles having just those properties needed to save the phenomena. But Newton thought that gravitation and the cohesiveness of bodies could not be explained 12. Descartes, Meditations 3, 6 (AT 7:49, 73), Principles of Philosophy 1.62, 2.8, 2.10–12; also letter to Plempius, December 20, 1637 (AT 1:476), letter to Gibieuf, January 19, 1642 (AT 3:474–75), and letter to [?], 1645 or 1646 (AT 4:348–50). In other passages Descartes speaks as if, in cases of corporeal impact, the more Achilles-like bodies prevail over their smaller and slower neighbors. It is difficult to square such talk with his mathematization of everything corporeal. On this vexed issue, cf. A. Gabbey, “Force and Inertia in the Seventeenth Century,” and P. McLaughlin, “Force, Determination, and Impact,” both in Descartes: Philosophy, Mathematics, and Physics (ed. Gaukroger), 98, 243. 13. One may also wonder what happened to physical force. Has Descartes, in the guise of defining it mathematically, explained it away? Cf. G. Hatfield, “Force (God) in Descartes’s Physics,” Studies in the History and Philosophy of Science 10 (1979): 113–40; D. Garber, Descartes’ Metaphysical Physics (Chicago: University of Chicago Press, 1992), 297–302 with 253. In Descartes’s Meditations the term vis is used only of mental capacities; compare The World 3, 7, 13–15 (AT 11:12, 38, 40, 43, 103, 109), Dioptric 1 (AT 6:87–89), Principles of Philosophy 2.24, 2.37, 2.43, 3.56–57, 3.59, letter to Mersenne, October 28, 1640 (AT 3:213).

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in strictly mechanical terms, and denied that active forces are essential properties of matter.14 Eighteenth-century Newtonians disagreed; and Einstein, in a move Descartes would have welcomed, found a way of geometrizing both gravitational force and matter. Quantum mechanics rejects the very idea of small bits of matter having determinate sizes or shapes or locations; and it makes no sense to say of such particles that they push or pull one another directly through mutual contact.15 Yet quantum field theory, in a move Newton would have welcomed, distinguishes between elementary matter particles (fermions) and elementary force particles (bosons). So if “quantum mechanics” is not a misnomer, the term “mechanical” is more capacious than early Galile14. Newton, Principia, 2.9, 2.52 Schol (787), 2.53 Schol (789), 3.Rule 3 (795), 3.10, 39.Corol 3 (895), and General Scholium (939, 943), Newton, Opticks (New York: Dover, 1979), III.Q.28, 31 (369, 376, 388–94), with R. S. Westfall, Force in Newton’s Physics: The Science of Dynamics in the Seventeenth Century (New York: Elsevier, 1971), 89, 184, 256–68, 323–31, 359, 363–69, 377, 387–403; M. J. T. Dobbs, The Janus Face of Genius: The Role of Alchemy in Newton’s Thought (New York: Cambridge University Press, 1991), 4, 31–33, 37, 120–22, 146–50, 166–68, 185–209, 218–30, 241–43, 247–53; I. B. Cohen, Franklin and Newton (Philadelphia: American Philosophical Society, 1966), chaps. 6–7. Compare Descartes, The World (AT 11:7, 25), Reply to Sixth Objections (AT 7:440–42), Principles of Philosophy 2.4, 2.11, 4.20–27, letters to de Beaune, April 30, 1639 (AT 2:544), to Elisabeth, May 21, 1643 (AT 3:667), to Arnauld, July 29, 1648 (AT 5:222) with A. Koyré, “Newton and Descartes,” in his Newtonian Studies, 53–114, and Daniel Garber, Descartes Embodied: Reading Cartesian Philosophy through Cartesian Science (New York: Cambridge University Press, 2001), 266–70. 15. Direct contact also seems impossible on mathematical grounds. Suppose a line has been cut in two such that the two resulting lines have endpoints a and b, c and d, and that they touch each other at points b, c. Then, letting “r” range over real numbers, we have four options: {a ≤ r ≤ b}, {c ≤ r ≤ d} where b = c, {a ≤ r ≤ b}, {c ≤ r ≤ d} where b