1 I thank Alan Nelson, Paul Hoffman, and Patricia Easton for working with me as I developed the views presented here, and also Nick Jolley and Larry Nolan, who commented on earlier drafts of this paper. I have benefited from audiences present at professional meetings where I presented earlier versions of this paper, and also from the comments of those who responded to these papers: Alison Simmons, at the 1998 Pacific American Philosophical Association, and Jeremy Hyman, at the 1997 Descartes, Cartesianism, and Anti-Cartesianism Conference at University of California, Irvine. I am also grateful for the discussions at meetings of the Southern California Cartesian Circle, and to the referees for the Canadian Journal of Philosophy for their very helpful comments. The abbreviations to editions of Descartes's works are as follows: AT: Oeuvres de Descartes, Vols. I-XII and Supplement, ed. Charles Adam and Paul Tannery (Paris: Leopold Cerf, 1897-1913). CSM: The Philosophical Writings of Descartes, Vols. I and II, trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch (Cambridge: Cambridge University Press 1985). CSMK: The Philosophical Writings of Descartes, Vol. Ill, trans. John Cottingham, Robert Stoothoff, Dugald Murdoch, and Anthony Kenny (Cambridge: Cambridge University Press 1991).

2 As one of the anonymous reviewers points out, perhaps here Descartes is giving criteria for identifying a body, and not for defining ‘a body.’ There is, however, a long tradition of taking this passage as a definition; see Daniel Garber, Descartes’ Metaphysical Physics (Chicago: University of Chicago Press 1992), 157-72.

3 Garber, Descartes’ Metaphysical Physics, 168-9.

4 Garber, Descartes’ Metaphysical Physics, 179-81.

5 Leibniz, Gottfreid Philosophical Essays, Ariew, Roger and Garber, Daniel ed. and trans. (Indianapolis: Hackett 1989), 163.Google Scholar

6 Kenny, Anthony Descartes: A Study of His Philosophy (New York: Random House 1968), 214.Google Scholar

7 Kenny, Descartes, 214-15.

8 There is another collection of closely related puzzles that concern the circular definitions of ‘motion’ and ‘a body’ tensions between Descartes's characterization of motion as relative and motion's status as a mode, and the relation between the local motion of bodies and the quantity of motion in the universe that God creates. Some of the classical treatments of these issues are by Leyden, W. Von Seventeenth-Century Metaphysics (London: Garden City Press 1968), 271;Google Scholar Dugas, René Mechanics in the Seventeenth Century (Neuchatel: Editions de Griffon 1958), 172–3;Google Scholar Westfall, R.S. Force in Newton's Physics: The Science of Dynamics in the Seventeenth Century (New York: Neale Watson Academic Publications 1971), 57–8,Google Scholar 151; Prendergast, Thomas L. ‘Descartes and the Relativity of Motion,’ Modern Schoolman 49 (1972), 67;Google Scholar Gaukroger, Stephen Descartes: An Intellectual Biography (Oxford: Clarendon Press 1995), 373;Google Scholar Wilson, Margaret Descartes (New York: Routledge 1978), 77;Google Scholar and Garber, Descartes’ Metaphysical Physics, 168-9.

9 Hoffman, Paul ‘The Unity of Descartes's Man,’ Philosophical Review 95 (1986), 347–9,CrossRefGoogle Scholar argues that this is the case.

10 Jeremy Hyman made this point in conversation.

11 See Nelson, Alan ‘Micro-Chaos and Idealization in Cartesian Physics’ Philosophical Studies 77 (1995), 5–11,CrossRefGoogle Scholar for a discussion of these passages.

12 There are also implications for Descartes's accounts of the individuation of minds, dualism, the mind-body union, and God's creation. See Lennon, Thomas ‘The Problem of Individuation among the Cartesians,’ in Individuation in Early Modern Philosophy: Descartes to Kant, Barber, Kenneth F. and Garcia, Jorge J.E. eds. (Albany: State University of New York Press 1994)Google Scholar for the connection between the individuation of bodies and minds.

13 Garber, Descartes’ Metaphysical Physics, 181.Google Scholar

15 There are several senses of the term ‘independences’ at least two of which are captured by the terms ‘causal independence’ and ‘ontological independences.’ As is apparent below, according to the reading I present in this paper, referents of both of these terms are attributes, ; therefore the causal independences and the ontological independences of extended substances are only conceptually distinct from it and from each other; the analogous point holds for mental substance, and its attributess. Descartes also defines ‘substance’ in the Second Replies (AT VII162; CSM 1114). There he focuses on the relation between substances and attributes. For a discussion of this relation as a criterion for substantiality, see Paul Hoffman, ‘Descartes's Theory of Distinction,’ Philosophy and Phenomenological Research 94 (2001), 58ff., and Matthew Stuart, ‘Descartes's Extended Substances,’ in New Essays on the Rationalists, Rocco J. Gennaro and Charles Huenemann, eds. (Oxford: Oxford University Press 1999), 82-83.

14 See Bennett, Jonathan ‘Space and Subtle Matter in Descartes's Metaphysics’ in New Essays on the Rationalists, Gennaro, Rocco J. and Huenemann, Charles eds. (Oxford: Oxford University Press 1999), 16–17,Google Scholar who also dismisses Descartes on this account.

16 Though there are important differences among their accounts, some commentators who roughly fall into this camp are Bennett, ‘Space and Subtle Matter,’ 10-11; Brown, Gregory ‘Math, Physics, and Corporeal Substance in Descartes,’ Pacific Philosophical Quarterly 70 (1989), 291;CrossRefGoogle Scholar Chene, Dennis Des Physiological Natural Philosophy in Late Aristotelian and Cartesian Thought (Ithaca: Cornell University Press 1996), 367–75;Google Scholar Rocca, Michael Delia ‘If a Body Meet a Body: Descartes on Body-Body Causation’ in New Essays on the Rationalists, Gennaro, Rocco J. and Huenemann, Charles eds. (Oxford: Oxford University Press 1999), 48–9;Google Scholar Garber, Descartes’ Metaphysical Physics, 181;Google Scholar Hoffman, ‘Unity’ 347-9; Jeremy Hyman, ‘Is There a Special Problem for Descartes about the Real Distinction of the Parts of Matter?’ (unpublished manuscript); Kenny, Descartes, 214-15; Eric Palmer, ‘Descartes on Nothing in Particular’ in New Essays on the Rationalists, Gennaro, Rocco J. and Huenemann, Charles eds. (Oxford: Oxford University Press 1999), 26–9;Google Scholar Prendergast, ‘Descartes and the Relativity of Motion’ 67ff.; Edward Slowik, ‘Descartes and Individual Corporeal Substance’ British Journal for the History of Philosophy 9 (2001);CrossRefGoogle Scholar and Wilson, Margaret Descartes (New York: Routledge 1978), 87–8.Google Scholar

17 Though there are important differences among their accounts, some commentators who roughly fall into this camp are Cottingham, John Descartes (Oxford: Basil Blackwell 1986), 84–8,Google Scholar 212-17; Grosholz, Emily ‘Descartes and the Individuation of Physical Objects’ in Individuation in Early Modern Philosophy: Descartes to Kant, Barber, Kenneth F. and Garcia, Jorge J.E. eds. (Albany: State University of New York Press 1994), 48,Google Scholar 54; Gueroult, Martial Descartes’ Philosophy Interpreted according to the Order of Reasons, Vol. 1, trans. Ariew, Roger (Minneapolis: University of Minnesota Press 1983), 63–74;Google Scholar Keeling, S.V. Descartes (Oxford: Oxford University Press 1968), 129–30;Google Scholar Lennon, Thomas ‘The Eleatic Descartes’ (forthcoming); Thomas Lennon, ‘Descartes's Idealism’ in Vol. 4 of Philosophy and Culture, Proceedings of the XVII World Congress of Philosophy (Montreal: Editions Montmorency 1988);Google Scholar Lennon, Thomas The Battle of the Gods and Giants: The Legacy of Descartes and Gassendi (Princeton: Princeton University Press 1993), 191–210;CrossRefGoogle Scholar Lewis, Geneviève Rodis L'individualité selon Descartes (Paris: J. Vrin 1950), 46,Google Scholar 51, 60; and Williams, Bernard Descartes: The Project of Pure Enquiry (London: Penguin 1978), 126–9.Google Scholar The most developed accounts are by Lennon and Gueroult. Lennon argues that the whole extended universe is the only secondary extended substance (my terminology), and that it is a kind of motionless Platonic form. According to this account, the ideal extended substance appears to us as if it were divided into individual bodies, themselves merely phenomenally individuated modes of the extended substance. While I find the spirit of this interpretation appealing for reasons discussed below, I resist the following claims involved in Lennon's thesis: extended substance is a kind of Platonic form, all motion is fully ideal, and bodies are merely modes and are not substances at all. Gueroult also argues that bodies are modes of the one secondary extended substance (my terminology), but he understands this modal status in yet another way. Gueroult holds that things such as sticks, stones, pieces of wood, iron, etc. are aggregates of corpuscles; he also holds that, whereas bodies change their shapes, corpuscles do not (Gueroult, Descartes’ Philosophy, 297–8, n. 165Google Scholar). He discusses the sense in which bodies have a kind of substantiality, albeit in a ‘third-order’ sense according to which they imitate secondary substances by being really distinct from each other in a way that roughly corresponds to how secondary substances are really distinct from each other (63-74). In another work, Gueroult says that bodies are held together by cohesion, a kind of force established by God ('The Metaphysics and Physics of Force in Descartes,’ in Descartes: Philosophy, Mathematics and Physics, Gaukroger, Stephen ed. (Sussex: Harvester Press 1980), 212.Google Scholar While I find Gueroult's interpretation appealing, I resist the claim that bodies are composed of a determinate quantity of corpuscles that do not change their shapes. Descartes explicitly argues in Principles, Part II, sections 33-35 that there are no such atoms, and also that all bodies are in continual division (AT VIII58-60; CSM I 237-9). Gueroult, too, finds this endpoint to the division problematic (Gueroult, Descartes’ Philosophy, 225, n. 53Google Scholar).

18 It may be objected that in this passage Descartes uses the term ‘body’ as a mass noun rather than a count noun. However, insofar as Descartes explains that what ‘body taken generally’ refers to has a different criterion of corruptibility than what ‘a body’ refers to, this passage commits him to two entities, each with its own ontological status.

19 In ‘The Unity of Descartes's Man,’ Paul Hoffman criticizes Gueroult for using this passage to support the thesis that individual bodies are modes of the indefinitely extended corporeal substance. Hoffman states: ‘First, it is not at all clear that Descartes is referring to the extended universe taken as a whole when he says that body, at least taken generally, is a substance (“corpus quidem in genere sumptum esse substantiam“). Second, he falls short of saying that individual bodies are modes’ (Hoffman, ‘Unity,’ 348). On the first point, I agree with Hoffman that the passage is indecisive in this way. However, here and elsewhere Descartes does make a distinction between an incorruptible extended substance and corruptible ones. One way to account for that distinction is to understand incorruptible and corruptible substances as substances at two different ontological levels; further, the substance in the weaker, tertiary sense can also be understood as a mode of the secondary substance. On the second point, I agree that Descartes never writes about bodies as modes. However, as I argue below, bodies simply are their sizes, and Descartes does hold that sizes are modes. For some examples of texts that imply that sizes are modes, see Principles, Part I, section 48 (AT VIIIA, 23; CSM1208) and section 69 (AT VIIIA 33; CSM I 217) where he includes ‘size’ in a list with ‘shape,’ ‘motion,’ and ‘position.’ Also see Optics (AT IV 138-140; CSM 1172).

20 Note that my discussion of tertiary substances differs significantly from John Cottingham's discussion of trialism, in ‘Cartesian Trialism,’ Mind 94 (1985): 118-130, according to which minds, bodies, and men (qua embodied beings) have different ‘features’ particular to them.

21 Nolan, Lawrence in ‘Reductionism and Nominalism in Descartes's Theory of Attributes’ Topoi 16 (1997) 129–40,CrossRefGoogle Scholar and ‘Theory of Universals,’ Philosophical Studies 89 (1988) 161-80 develops an interpretation along these lines.

22 See Principles, Part I, section 56: ‘We do not, strictly speaking, say that there are modes or qualities in God, but simply attributes, since in the case of God, any variation is unintelligible’ (AT VIIIA 26; CSM I 211).

23 I read the Cartesian meditator's realization that God is not a deceiver (AT VII69-70; CSM II48) as an implicit realization that God is supremely goodp. Notice that God's goodnesSp can be discovered by regarding God as immutablep in that when one understands God as immutablep, one also understands God as perfectp, and that deception — the negation of goodnessp — involves imperfection.

24 See Principles, Part I, section 56: ‘[In] the case of created things, that which always remains unmodified — for example existence and duration in a thing which exists and endures — should be called not a quality or a mode but an attribute’ (AT VIIIA 26; CSM I 211-212).

25 Extensions also plays the unique role of being a principal attribute, , . See Principles, Part I, section 26 (AT VIIIA 15; CSM I 202) for Descartes's account of the indefinite extension, of the universe. See Principles, Part I, section 23 (AT VIIIA 14; CSM 1201) for an account of God's creation.

26 Though many commentators have noted the role that quantity of motion plays in Descartes's physics, no one has understood it as an attributes of secondary extended substance.

27 Cottingham, Stoothoff, and Murdoch (see CSM I is) use diamond brackets to indicate a translation that involves the addition of a term or phrase from an early translation approved by Descartes.

28 Consider the passages where Descartes writes about the following as modes: shapes and motions (AT VIIIA 25; CSM I 210-211), positions and sizes (AT VIIIA 48; CSM I 229), surfaces and shapes (AT IV 163-164; CSMK 241), surfaces and motions (AT IV 187; CSMK 248), sizes, shapes, motions, and positions (AT VIIIA 23; CSM I 209), and shapes, positions, and motions (AT VIIIA 32; CSM I 216).

29 In Principles, Part II, section 13 Descartes explains that all positions are relations among bodies (AT VIIIA 47; CSM1228). In Principles, Part II, section 25, he explains that a body is in motion when it changes in relation to its neighborhood (AT VIIIA 53-54; CSM I 233). He defines ‘surface’ as a boundary in Principles, Part II, section 13 (AT VIIIA 48; CSM I 229) and also in the Fourth Replies (AT VII 250-251; CSM I 174).

30 In the section below on Cartesian physics, I discuss this view in light of Principles Part II, section 23; I argue that on the correct reading of this passage, it does not conflict with the reading given in this paper.

31 Another way of putting this point about mind-dependence and mind-independence is in terms of what is subjective and objective. Put in such language, my point is this: bodies are objective in that they are dependent on secondary extended substance for their extension; they are subjective in that they are dependent on perceivers for their precise delimitations.

32 In Principles, Part I, section 60 (AT VIIIA 28; CSM1213), Descartes explains that the real distinction is discovered by exclusion. Descartes sometimes uses the Latin and French cognates of ‘exclude’ and ‘deny’ as synonyms. For example, in Rule 14 (AT X 445; CSM 161) Descartes uses the Latin terms excludere and negate synonymously; also see the letter to Gibieuf (AT III 475; CSMK 202) where he uses the French term nier when explaining how one can perform a faulty abstraction by denying an attribute of a substance although the attribute is rightly associated with that substance.

33 See the famous passage in the Sixth Meditation where Descartes perceives the real distinction, between mental and extended substances (AT VII 78; CSM II54).

34 I follow Wells, Norman J. in ‘Descartes on Distinction’ in Quest for the Absolute, ed. Adelmann, Frederich (Chestnut Hill: Boston College 1966), 112,Google Scholar in using the term ‘mutual exclusion.’

35 Descartes also discusses a second kind of modal distinction (AT VIIIA 29-30; CSM I 214).

36 The attributes cannot be reduced to modes of our mind, because then they would be modes and so modally distinct (AT VI 350; CSMK 280). They cannot be two different parts of the substance because Descartes says that substances don't have parts; he makes this point when he explains that the essence and existence of a substance are ‘in no way distinct’ in substances (AT VI 350; CSMK 280).

37 This view is similar in spirit to Nolan's in ‘Reductionism and Nominalism.’ For a quite different interpretation of Descartes's theory of distinctions, see Hoffman, Paul ‘Descartes's Theory of Distinction,’ Philosophy and Phenomenological Research 94 (2002) 57–78.CrossRefGoogle Scholar

38 Garber, Descartes's Metaphysical Physics, 163.Google Scholar

39 I thank one of the anonymous reviewers for this point about the translation.

40 This view runs parallel to that developed by Alan Nelson in his discussion of the relation between the Cartesian laws of physics and the innate ideas of rational beings (Nelson, ‘Micro-Chaos’ 10).