Cartesian Temporal Atomism: A New Defence, A New Refutation¹

¹My title is intended to evoke Richard Arthur's influential article: ‘Continuous Creation, Continuous Time: A Refutation of the Alleged Discontinuity of Cartesian Time’ (Arthur, 1988).

Click to increase image sizeClick to decrease image size

Notes

¹My title is intended to evoke Richard Arthur's influential article: ‘Continuous Creation, Continuous Time: A Refutation of the Alleged Discontinuity of Cartesian Time’ (Arthur, 1988).

²The most important texts are the Third Meditation (AT 7: 48–9, CSM 2: 33), Fifth Replies (AT 7: 369–70, CSM 2: 254–5), Principles of Philosophy 1, 48–69 (AT 8A: 22–34, CSM 1: 208–17), conversation with Burman (AT 5: 148–9; CSMK: 335), letters to Arnauld (AT 5: 193, CSMK: 355; AT 5: 221–3, CSMK: 357–8), and letter to More (AT 5: 343, CSMK: 373). In what follows ‘AT’ refers to Descartes (1996); ‘CSM’ refers to Descartes (1985); ‘CSMK’ refers to Descartes (1991).

³For the most detailed formulation and defence of these laws, see Principles of Philosophy 2, 36–42 (AT 8A: 61–6, CSM 1: 240–3). Similar formulations and proofs are given in le Monde, Chapter 7 (AT 11: 37–47, CSM 1: 92–7).

⁴Defenders of the traditional view include Wahl (1920), Gilson (1925: 420), Gueroult (1984: 193–202), Kemp Smith (1952: 202–5), Bonnen and Flage (2000). Recent critics include Beyssade (1979: Ch. III), Arthur (1988), Secada (1990), Garber (1992: 266–73), Des Chene (1996: 325, n88), Frankfurt (1999), Bennett (2001: Vol. 1, p. 98), Gorham (2004: 392, n18). For additional defenders and critics, see Levy (2005: 627, n2 and n3).

⁵In what follows, references to Levy (2005) will be simply by page number.

⁶Descartes says that there is a conceptual distinction between things that are not really distinct, such as substances and their attributes, when we are unable to ‘form a clear and distinct idea of the substance if we exclude from it the attribute in question’ (AT 8A: 30, CSM 1: 214). In the French translation of this passage he emphasizes that the attributes of a body, such as its extension and divisibility, do not differ at all from one another ‘except in so far as we sometimes think confusedly of one without thinking of the other’ (AT 9B: 53, CSM 1: 215 n1; See also AT 4: 349–51, CSMK: 280–1). In the case of duration, he explicitly warns against separating it from the enduring thing: ‘We shall also have a very distinct understanding of duration, order and number, provided we do not tack onto them any concept of substance’ (AT 8A: 26, CSM 1: 211). It is worth noting that although Arthur is the source for Levy's notion of strong discontinuity, Arthur himself recognizes that from Descartes's identification of duration and existing things ‘it follows immediately that any conception of Cartesian time as containing gaps is untenable’ (1988: 357).

⁷See also AT 2: 482, CSMK: 132; AT 5: 273, CSMK: 363.

⁹See also AT 11: 656.

⁸See also AT 5: 52, CSMK: 320; AT 5: 224, CSMK: 359; AT 5: 346, CSMK: 375.

¹⁰As Levy concedes, given that Descartes's acceptance of strong temporal discontinuity would amount to a ‘glaring mistake’ on his part, this ‘raises the burden of proof against my interpretation’ (628).

¹¹See also Bonnen and Flage (2000: 4) and Gorham (2004: 394).

¹²Secada (1990: 49–51, 66–71). See also Curley (1978: 139–40), Gaukroger (2002: 77–8) and Gorham (2004: 396–400).

¹³See also AT 7: 240, CSM 2: 167.

¹⁴On the historical pedigree of the principle of causal simultaneity, see Secada (1990: 49–51). Other explanations besides causal simultaneity have been offered for the causal independence thesis. For example, Descartes may have simply held that such things as ‘parts of my existence’ are not powerful enough to be the efficient causes of their successors, as suggested by Bennett (2001: vol. 1, pp. 97–8), Garber (1992: 264) and Frankfurt (1999: 62–3). For criticism of this explanation, see Gorham (2004: 394–6).

¹⁵Secada (1990: 48–52).

¹⁶In a footnote, Levy levels an additional objection against Secada's causal simultaneity reading. According to Levy, Descartes's position is that causes cannot act at a temporal distance, not that they must ‘fully coincide’ in time. So understood, Levy maintains, the doctrine does not explain why an earlier part of my existence cannot cause a later part as the former may ‘touch’ the latter without acting at a temporal distance (649, n49). Descartes is much clearer than Levy:

The natural light does not establish that the concept of an efficient cause requires that it be prior in time to its effect. On the contrary, the concept of a cause is strictly speaking applicable only for so long as the cause is producing the effect, and so it is not prior to it.

(AT 7: 108; CSM 2: 78)

The cause is not earlier at all, not even so recent as it ‘touches’ the effect.

¹⁷AT 8A: 64, CSM 1: 242; AT 11: 45, CSM 1: 97.

¹⁸See also AT 11: 332, CSM 1: 330; AT 6: 84, CSM 1: 153.

¹⁹This problem is also discussed by Secada (1990: 66–9).

²⁰See also AT 7: 165, CSM 2: 116.

²¹There is an additional, purely theological, explanation for the Counterfactual Assumption. As Descartes explains to Gassendi, if a created thing could exist on its own until something prevented it, ‘the creator would have to tend towards non-being by performing a positive action whenever he wished to bring our existence to an end’ (AT 7: 371, CSM 2: 255). The same point is made in a letter to ‘Hyperaspistes’ (AT 3: 429, CSMK: 194).

²²See also AT 7: 370, CSM 2: 255; AT 5: 53, CSMK: 320.

²³This is mentioned by Bonnen and Flage (2000: 4) and Bennett (2001: vol. 1, p. 98). The real distinction between parts of my duration need not imply that the duration of my soul is a mere ‘pseudo-substance’, as Bennett suggests (ibid.), as Descartes allows substances to have substantial parts. I discuss this in detail elsewhere (Gorham, forthcoming).

²⁴See also AT 8A: 62, CSM 1: 240; AT 6: 45, CSM 1: 133; AT 7: 369, CSM 2: 254–5.

²⁵Levy says Descartes's response to Gassendi ‘directly contradicts’ his statement of the proof of continuous creation at Principles 1, 21 (659). On the contrary, Principles 1, 21 incorporates the elaboration in the response to Gassendi. Whereas in the Third Meditation the conclusion is said to follow simply from the ‘nature of time’ (AT 7: 49, CSM 2: 33) in the Principles Descartes says it follows from ‘the nature of time or duration of things’ (AT 8A: 13, CSM 1 200). Descartes clearly wants the reader to understand that the issue is not time abstracted from the duration of concrete things. See also Principles 1, 57 where he says that ‘when time is distinguished from duration taken in the general sense, and called the measure of movement, it is merely a mode of thought’ (AT 8A: 27, CSM 1: 212). ‘In the same way’ as he explains further in the next section, ‘number, when it is considered in the abstract or in general, and not in any created things, is simply a mode of thought’ (ibid.) This reinforces the point he makes to Gassendi that the continuous creation argument concerns duration in the things, not time in the abstract. For discussion of the distinction between time and duration in Descartes, including its late scholastic background, see Solère (1997).

²⁶As Levy correctly observes (664), this problem should not be confused with the question of duration without substance (‘empty time’), as both Arthur (1988: 356–7) and Secada (1990: 66 n28) seem to do. It follows from the merely conceptual distinction between substance and duration that there can be no duration with substance, as Descartes says explicitly in a letter to More (AT 5: 543, CSMK: 373). The more serious problem for Levy is that the same doctrine about substance and duration implies that nothing can separate temporal atoms.

²⁷I do not say, of course, that the connection is always clear in Descartes. In particular, there is the vexed issue of whether God could have made the eternal truths otherwise, despite the inconceivability of this to us. For a good recent discussion, see Kaufman (2002). My point is simply that Descartes certainly thinks we can learn a good deal about what is possible or not from our conceptions. For an interesting discussion, see Bennett (1994).

²⁸See also AT 7: 20, CSM 2: 14; AT 10: 419, CSM 1: 45.

²⁹The reference to the ‘countless (innumeras)’ parts of time in the proof of continuous creation is problematic for those versions of discontinuity which are opposed to infinite divisibility. (As Secada points out (1990: 55), one can conceivably hold that time is both infinitely divisible and discontinuous.) In response to this Levy writes that when Descartes says the parts of time are innumeras he ‘could just mean many or too many to count’ (657). This is too quick. First, there are other contexts in which Descartes uses ‘innumeras’ to mean infinitely (or at least indefinitely) many. For example, in Principles 2, 34, he argues that motion in the plenum requires an ‘infinite, or indefinite [infinitum, sive indefinitam], division of the various particles of matter’. For in order for one part of matter to move into continuously smaller spaces in the plenum, ‘it is necessary that all the imaginable particles, which are in fact innumerable [innumerae], should shift their relative positions to some tiny extent. This minute shifting of positions is a true case of division’ (AT 8A: 60, CSM 1: 239). Clearly, he is using ‘innumerable’ to mean ‘infinite or indefinite’. Furthermore there are additional passages which indirectly indicate that Cartesian time is infinitely divisible. In a letter of 11 March 1640 to Mersenne, he says ‘there is no quantity which is not divisible into an infinite number of parts, and force, motion and impact are all species of quantity’ (AT 3: 36). But motion cannot be infinitely divisible unless time is. Similarly, in his discussion of Zeno's paradox of Achilles and the Tortoise, Descartes seems to allow that the time required in order for a horse to catch up to a tortoise can be divided infinitely:

The answer is that it is true that the horse will never overtake it while traveling that league and that tenth of a league and that hundredth and thousand of a league and so on; but it does not follow that it will never overtake it because the tenth and hundredth and thousandth only add up to a ninth of a league at the end of which the horse will start to be in the lead.

(AT 4: 447, CSMK: 291–2)

Finally, in the conversation with Burman, he says about God: ‘we can divide his duration into an infinite number of parts’ (AT 5: 148, CSMK: 335), although it is possible that his point here is simply that God's duration is everlasting.

³⁰When Descartes says in Principles 1, 55 that duration is ‘simply a mode under which we conceive the thing in so far as it continues to exist’ (AT 8A: 26, CSM 1: 211) he cannot mean that it is a modification of thinking substance, such as judgement or perception. Otherwise, given that there is no real distinction between substances and their duration (Principles 1, 62), Descartes would be Berkeley. Lawrence Nolan has pointed out that Descartes frequently uses ‘mode of thought’ in roughly the sense of ‘way of thinking about’, as in ‘Aristotle provides us with a way of thinking about virtue’ (Nolan, 1997: 132). It is this sense intended in Principles 1, 55, as he makes clear in the very next section: ‘in the case of created things, what always remains unmodified – for example, existence or duration in a thing which exists and endures – should not be called a quality or mode but an attribute’ (AT 8A: 26, CSM 1: 211–12). The distinction between the two senses of ‘mode of thought’ is explained in a letter to an unknown correspondent in 1645 or 1646 (AT 4: 348–9, CSMK: 279–80).

³¹‘It is a manifest contradiction for them [bodies] to be apart, or to have a distance between them, when the distance in question is nothing’ (AT 8A: 51, CSM 1: 231).

³²For recent discussion of such issues, see Solère (1997) and Gorham (2007).