secada - descartes on time and causality - 1990

Philosophical Review

Descartes on Time and CausalityAuthor(s): J. E. K. SecadaSource: The Philosophical Review, Vol. 99, No. 1 (Jan., 1990), pp. 45-72Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2185203 .

Accessed: 14/04/2014 02:56

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Duke University Press and Philosophical Review are collaborating with JSTOR to digitize, preserve and extendaccess to The Philosophical Review.

http://www.jstor.org

This content downloaded from 147.162.43.147 on Mon, 14 Apr 2014 02:56:29 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=duke

http://www.jstor.org/action/showPublisher?publisherCode=philreview

http://www.jstor.org/stable/2185203?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


The Philosophical Review, Vol. XCIX, No. 1 (January 1990)

Descartes on Time and Causality

J. E. K. Secada

H istorians of philosophy commonly believe that Descartes took time to be made up of temporal atoms.' He is thought to

have believed in the discontinuity of time; and his conception has been characterized as cinematographic. The standard view is that Cartesian temporal atoms have no duration and, hence, are indivisible. Since Descartes never explicitly set forth his supposed atomism, the support for the established interpretation comes from those passages where he holds that parts of time are mutually independent. These texts, some have argued, commit him to temporal atomism.2 Nevertheless, the standard view has not altogether lacked its critics. Jean Laporte and more recently Jean-Marie Bey- ssade have objected to it, maintaining that Descartes held a doctrine of time as continuous.3 They have argued that Descartes explicitly claimed that consciousness is not instantaneous. Further- more, some have contended that from Descartes's denial of material atomism the denial of temporal atomism follows.4

'See Jean Vigier, "Les idees de temps, de duree et d'eternite chez Des- cartes," Revue Philosophique 89 (1920), pp. 196-233 and 321-348; Jean Wahl, Du Role de l'Idge de lInstant dans la Philosophie de Descartes (Paris, France: Alcan, 1920); Norman Kemp Smith, Studies in the Cartesian Philo- sophy (New York, N.Y.: Russell & Russell, 1902), pp. 72-74 and 128-132; and New Studies in the Philosophy of Descartes (London, England: Macmillan, 1952), pp. 202-203; M. Gueroult, Descartes selon l'ordre des raisons (Paris, France: Editions Montaigne, 1953), I, pp. 272-285; and Mikio Kamiya, La The'orie Cartesienne du Temps (Tokyo, Japan: France Tosho, 1982).

2A classical example is H. Gouhier's La Pense'e Metaphysique de Descartes (Paris, France: J. Vrin, 1978), p. 135, note 79. Descartes's second axiom in the Appendix to the Second Replies ("The present time does not depend on that proximately preceding it . . .") is described as stating "la discontinuity du temps."

3Jean Laporte, Le Rationalisme de Descartes (Paris, France: Presses Uni- versitaires de France, 1945), pp. 158-160; Jean-Marie Beyssade, La Philo- sophie Premiere de Descartes (Paris, France: Flammarion, 1979), pp. 346-354 and passim.

4Bernard Williams has suggested that the texts do not warrant the attribution to Descartes of the claim that time is composed of durationless atoms; but he has not developed this suggestion (Descartes: The Project of Pure Enquiry (Harmondworth, England: Penguin, 1978), pp. 192-193,

45



J. E. K. SECADA

In this paper I will argue that, as far as we can know, Descartes had no views as to the continuity or discontinuity of time. The texts concerning the mutual independence of parts of time will be examined; and they will be shown to involve no such views. Simi- larly, I shall give reasons to reject the claim that he was committed to a view of time as continuous. Thus, contrary to the standard view and to those who affirm the continuity of Cartesian time, I will enter the discussion by opening a third front: Descartes had no views on the matter, at least as far as we can ascertain. Instead, I will argue that Descartes made a striking, though historically understandable, claim about causality; and that it is this claim which is contained in the texts that have led to the attribution of atomism. In the first part of the paper I will sketch my interpretation of the relevant passages and compare some of Descartes's causal views with those of his Scholastic predecessors. However, to present my case fully I will need to examine the Cartesian notion of continuity. This I do in the second part. There I shall argue that the Cartesian conception does not differ from that of the Aristotelians. But, contrary to the received views, I will also maintain that it is not in any direct conflict with the contemporary mathematical notion. Having thus become clearer about the concepts involved, I will be able to formulate more precisely both the defended interpretation and the matter at issue. Finally, in the third part I will address possible objections to my claims and round up the argument sketched in the first part.

I.

In the Meditations Descartes wrote that "all the duration of my life can be divided into innumerable parts such that any one of them is in no way dependent on another" (AT, VII, 48-49).5 In

note 6). More recently, Richard Arthur has criticized the standard view in "Continuous Creation, Continuous Time: A Refutation of the Alleged Discontinuity of Cartesian Time," in Journal of the History of Philosophy 26 (1988), pp. 349-375. But, with the caveat that he does "not mean to suggest that Descartes had any well elaborated theory of what constitutes a continuous duration" (p. 350), Arthur goes on to suggest that Descartes's time is continuous (p. 357).

5All references to the works of Descartes are to the Adam and Tannery edition (AT) (Paris, France: J. Vrin, 1964-1974).

46



DESCARTES ON TIME AND CAUSALITY

June 1647 he wrote to Chanut maintaining that, regarding the world, "every moment of its duration is independent from the others" (AT, V, 53). Similar passages are found in other works (see, for example, AT, V, 155 and VII, 110 and 369). I should like to draw attention to the fact that in these texts Descartes refers to parts of time or moments of duration, but not to instants or to temporal atoms. His claim may be read as applying not only or necessarily to instants but in general to segments of time. From the contexts of some of the passages where the doctrine is stated it is apparent that it was intended to be taken as asserting causal independence. Thus, what Descartes maintained is that any lapse of time, or indeed all time, can be divided into segments which are causally independent.

In order to gain in clarity I shall introduce a few definitions which borrow from set theory in what is now a common and ac- cepted fashion.

1. Segments of time A and B are separate if, and only if, there is no time which belongs to both A and B.

2. Segment of time A is causally active upon segment B if, and only if, there is something existing during A which is the cause of something existing during B. (Being causally dependent is the inverse relation of being causally active.)

3. Segment of time A is causally independent of segment B if, and only if, A is neither causally active nor causally dependent on segment B.

For Descartes causality is, at least in some sense, a relation between substances. The causal independence of parts of time is advocated when the effect in question is the existence of a substance and the cause some other substance. In the letter to Chanut, for example, the effect is the future existence of material substance and the supposed cause the past existence of matter. So the formulation in these definitions does not distort his thought.

Using these definitions, we may formulate the following Prin- ciple of the Independence of Separate Segments of Time:

All time can be divided into separate segments such that for any two such segments, one is causally independent of the other.

47



J. E. K. SECADA

The universal quantifier is intended to indicate that any time is included in some segment. I take it that it is this principle that is involved in the various texts of Descartes mentioned above. Without prejudging the issue as to the continuity of time it is clear that the divisions referred to may be, as Descartes maintains, innumerable even if time is finite at both ends. Also, the continuity or discontinuity of time is independent of the issue as to whether between two separate segments there need be a third; so the principle accommodates the text from the Second Replies, which will be examined later, where Descartes writes about the independence of a moment from that immediately preceding it. On the other hand, the expression "can be divided" (as opposed to "is divided") does point, if at all, in a direction contrary to atomism and to separate atoms of time given in reality. But it is an expression Descartes himself used (dividi potest) in the passage quoted above from the Meditations.

The principle just formulated does not entail or involve atomism. My strategy will now be to show that it was taken by Des- cartes to be established by means of considerations which are themselves also independent of temporal atomism. In the course of an argument for the existence of God in the Principles the claim that "the parts of time do not depend at all on each other" is connected with consideration of "the nature of time or the duration of things" (AT, VIII- 1, 13). Indeed, I shall maintain that Descartes took the principle to follow from "evident" features concerning the nature of time and the relation of causality. Moreover, these views concerning time and causality are akin to some views adopted by most of the Scholastic movement, by Aristotle, by Saint Thomas Aquinas, and by Francisco Suarez. Rather than being in- novative or contentious on this matter Descartes was pointing out what he took to follow from familiar and, he believed, correct doctrines.

One of the points involved is indeed evident and may be stated thus:

If A and B are separate segments of time, then no part of A is such that it is simultaneous with any part of B.

I take Descartes to be making this obvious point in the Principles where he writes that "the nature of time or the duration of things

48




is such that its parts ... never exist simultaneously," precisely when claiming their independence (AT, VIII-1, 13). It is also found in Suarez (MD, for example, XL, 1, 13; L, 9, 19-26, passim) and in Aquinas (ST, I, q.10, a.1).6 On the other hand, Descartes makes the following point about causality:

An effect can be caused only by something which exists at the time of its production.

While examining one of his arguments for the existence of God in the First Replies, again in the context of upholding the independence of parts of time, Descartes maintains that "the natural light does not dictate that the notion of an efficient cause requires it to be prior in time to its effect; on the contrary, it does not properly have the nature of a cause but when it is producing its effect, and hence is not prior to it" (AT, VII, 108). Descartes does not allow the possibility of productive activity at a temporal distance. He argues that a cause is a cause only when producing its effect; but it appears that he took it to be evident that the cause must exist at the time its effect is being produced. We should note that it is only the immediate cause, the first proximate member in the chain of causal ancestry, that need be taken into account here. But as will become apparent later this is not crucial; for according to Des- cartes any causal ancestor is simultaneous with the effect.

The demand for simultaneity between cause and effect, though less "evident," is no innovation of Descartes either. Following Aris- totle in Metaphysics V, Suarez held that "if a cause is taken in actu

secundo it is necessarily simultaneous with its effect" (MD, XXVI, 2, 14; the relevant passage in Aristotle is 1014a20-25).7 By a cause in actu secundo the Aristotelians meant a cause in act as opposed to what is only potentially a cause. The potential cause was called in actu primo or according to its vis agendi or power to act. As is

beyond dispute, Descartes is in conflict with the Aristotelians in-

6Aquinas's Summa Theologiae (ST) has been quoted from the edition by Fr. Thomas Gilby, OP (London, England: Eyre and Spotiswoode, 1963-1975). For Suarez's Metaphysical Disputations (MD), the 1621 Mo- guntiae edition of his Opera Omnia was used.

7Aristotle is quoted from the revised Oxford translation edited by Jona- than Barnes (Princeton, N.J.: Princeton University Press, 1985).

49



J. E. K. SECADA

sofar as he rejects their notion of corporeal substance as form and matter and their analysis of reality into act and potency. He has no place for the vis agendi or potentiality of efficient causes. For him a cause is such only inasmuch as it produces an effect. But it is misleading, to put it mildly, to extend this opposition to cover the matter at issue.8 Both he and the Scholastics agree with Aristotle that the cause in act is simultaneous with its effect. Descartes adds further, and here he parts company with the Aristotelians, that the nature of a cause qua cause consists solely in its acting as such and not in its potency or vis agendi; for he does not allow for the notion of a cause in actu primo. In any case the Aristotelians maintain only the possible temporal precedence of the cause in actu primo. As Suarez clearly puts it: "an efficient cause in itself may be prior in time to its effect with respect to its absolute entity or vis agenda, which Aristotle called cause in potency or in actu primo, but it is not always necessarily so; for at times the effect of such a cause can be equal in duration to it" (MD, XXVI, 2, 14).

Similarly, Aquinas writes that "a cause in act is what is actually causing a thing.... [S]peaking of causes in act, the causing and the caused must exist simultaneously.... But this is not necessary in causes which are causes only in potency."9 When he states in the Summa Theologiae that "it is not possible that something be its own efficient cause, for it would then be prior to itself, which is impossible," he should not be read as affirming that temporal precedence is a requirement of efficient causality (I, q.2, a.3). The Second Way, from which the quote above comes, is concerned with simultaneous causes. There St. Thomas should be understood as demanding not temporal priority but rather that the cause be, as Suarez put it, "most plainly and properly prior in nature" to the effect (MD, XXVI, 2, 14).10 What is being affirmed by Aquinas

8See E. Gilson, Etudes sue le Role de la Pensee Medievale dans la Formation du Systeme Cartesien (Paris, France: J. Vrin, 1975), pp. 226-227. Another late Scholastic source where the issue of the simultaneity between cause and effect is discussed in detail and where basically the same view as Suarez's is advocated is P. Fonseca, Commentariorum in Libros Metaphysi- corum Aristotelis, V, 2, q. 18 (Hildesheim, West Germany: Georg Olms, 1964 reprint of Cologne, 1615), II, pp. 230-234.

9De Principiis Naturae, V, 364, in Aquinas, Opuscula Philosophica, ed. Fr. R. Spazzi, OP (Turin, Italy: Marietti, 1973), p. 127.

'0Cf. Ferdinand Alquie's edition of Descartes's works, where he reads Aquinas in the Second Way as demanding, in contrast to Descartes, the

50




and Suarez is that the effect depends on the cause, the produced on the producer, and not vice versa. Descartes is not in conflict with the Scholastics on this point. Replying to the objections by Arnauld, he states that God is not strictly His own efficient cause because He cannot be different from Himself, He is not an effect (an effect being considered "less noble" than the cause), and He does not conserve Himself through some "positive influx" nor does He continually "reproduce" Himself (AT, VII, 242-243). Descartes, in agreement with Aquinas and Suarez, distinguishes this point from the one involving temporal precedence.

In support of the claim that cause and effect are simultaneous Descartes offers, as we have seen, the consideration that the nature of a cause consists in causing or producing an effect. He took this to be a conceptual point. But even if it is granted the matter does not appear to be settled. What the claim denies is that there can be causal or productive efficacy at a temporal distance. But it could be that something acquires the "nature of a cause" only when the effect is produced, without this on its own entailing that it must exist at that time. Something may become a cause after it has ceased being. However, the point behind Descartes's reasoning seems to be that there must be an actual entity to bring about a production. One may grant that a chain of activity gets started some time in the past which culminates in a production when the originator of the chain has passed away; but the intuition Descartes appears to advocate is that in the end there must be some existing thing which produces the effect at the moment the effect is in fact produced. This intuition is not difficult to appreciate even if it will be dis- puted by those who have a conception of causality along the lines of, for example, statistical conjunction. Descartes has little, if any- thing, to say against such conceptions. But this is not something which needs to be explored further here. It will suffice to say that the Scholastic doctrine of efficient causality, which on this point

temporal priority of the cause in relation to its effect; (Paris, France: Edi- tions Garnier Freres, 1963-1973), II, p. 527, note 1 and p. 683, note 2. On the other hand, see Gilson, op. cit., pp. 208-209 and Gouhier, op. cit., pp. 135-141. I should point out, however, that I disagree with both Gilson's and Gouhier's interpretation of Descartes's "cosmological" argument. Our differences stem, I believe, from my finding two separate Car- tesian proofs from the effects: one from the idea of God and the other from the existence of a substance that is not causa sui.

51



J. E. K. SECADA

Descartes was adopting, naturally demands that there be an existing producer to produce an effect.1'

Both of the claims about causality and the nature of time and also the principle that separate segments of time are causally independent involve no commitment to temporal atomism. Given that Descartes may quite naturally be read along the lines I have presented, that he never does explicitly advocate atomism with respect to time, and that such a doctrine generates more problems than it solves, it seems reasonable to deem the matter untouched in his works. Nevertheless more needs to be said; for the principle of the independence of separate temporal segments does not follow from the claims examined thus far. And the contrary view that Descartes believed in the continuity of time has yet to be examined. Before passing on to that, however, I will introduce some conceptual and historical clarifications of the notion of continuity. This detour, though somewhat lengthy, will prove to be necessary in order to get a better grip on the issue before us.

II.

In his Commentary on the Physics, Cardinal Francisco Toledo, wrote that those things are "continuous whose limits are one; contiguous, those whose limits are together; successive, those between which nothing of the same kind mediates" (VI, 1, 1; see also V, 3, 21-30).12 As was common in discussions of continuity in the six- teenth and early seventeenth centuries, Toledo was following Ar- istotle. So was Suarez when he defined a continuum as "that whose parts are joined by a common terminus," or when he maintained that "the species of quantity are divided according to the various modes- of divisibility, for continuous quantity . . . is divisible into parts which were united by a common terminus, while discrete

11In Descartes Against the Sceptics (Oxford, England: Basil Blackwell, 1978), Edwin Curley points out that at least some of the grounds for the simultaneity requirement can be found in Descartes's notion "that a cause must be a sufficient condition of its effect" (p. 140). That Descartes is committed to this notion is established from his implying that an effect must follow (sequitur) from its cause in AT, VII, 49.

'2Toledo's Commentaria in octo libros Aristotelis de physica auscultatione (CP) has been quoted from his Opera omnia philosophica (Hildesheim, West Ger- many: Georg Olms, 1985 reprint of Cologne 1615-1616).

52




quantity is divisible into parts that do not have a common terminus" (MD, XL, 5, 10 and XL, 4, 2). For two things to be in succession, according to Aristotle, it is necessary that they be in some order and that there be nothing of the same kind between them (Physics V, 3; 226b34-227al). When two things are in succession and, further, they have boundaries which touch, they are contiguous; if, finally, they share one common boundary, they are continuous, parts of one whole (227alO-15). This is the notion of continuity which, I believe it is safe to assume, Descartes intended when using the term continuess" and its cognates (for example, AT, VI, 36; X, 451-452; see also, VIII-1, 48; though cf. V, 164).

Consider a series of houses. It will be continuous if the houses are joined by common walls. If there are two limiting walls then the houses can at most be contiguous. As Aristotle puts it: "continuity is impossible if these extremities are two" (227al3). Consider one single continuous log of wood. We can divide it mentally at any point, but, being continuous, that point will be the common limit of the two parts of the division. If a division is entertained which, without excluding any of the matter involved, has parts which do not have a common limit, but each its own, then continuity is being denied at that division, for it involves nothing but a discrete succession between two wholes, from the limit of one to the limit of the next. Aristotle believes that bodies, time and place are continuous. Thus, in the Categories he writes: "in the case of a body one could find a common boundary-a line or a surface-at which the parts of the body join together"; "present time joins on to both past time and future time"; and, "place also is a continuous quantity, since its parts join together at one common boundary" (5a4- 14).

Consider now a continuous quantity such as a line. Wherever a division of the line is entertained a point is found that serves as common boundary to both resulting segments. "One point makes continuous the two parts of one line," as Cardinal Toledo puts it (CP, V, 3, 26). Indeed, it is never the case that two points in the line, it being continuous, are found one immediately next to the other. Between any two points in a continuous line there is always a third one. For if this were not the case, then there would be two points one next to the other and we would have, contrary to our assumption, a division with two boundaries and not a single common one. One could speak here of the "solitude" of points in a

53



J. E. K. SECADA

line. Following more common usage I will call this property the density of the line. It is the density of the line which accounts for its infinite divisibility. Since between any two points in a line there is a third, any line, being enclosed between two points, is divisible into smaller lines at such a third point. As this holds also for the resulting lines, it follows that a line is divisible in infinitum.

From Aristotle's understanding of continuity it follows that a continuous quantity is dense and Aristotle acknowledged this. In the Physics he wrote that "it is plain that everything continuous is divisible into divisibles that are always divisible" (VI, 1; 231b15- 16). And later: "everything continuous is divisible into an infinite number of parts" (VI, 8; 239a22). On these matters the late Scho- lastics were in complete agreement with Aristotle. They followed him and agreed that continuity entails density. Thus Toledo: "between the points something must mediate, namely a line; for in a continuum two points cannot be one immediately next to the other" (CP, V, 3, 29-30). And Suarez: "a continuum ... is always divisible into divisibles" (MD, XL, 5, 34). I will suppose, again un- contentiously, that on this matter Descartes also followed the established, Aristotelian, view.

Aristotle and his Scholastic followers claimed, further, that density entails continuity and, therefore, that density and continuity are equivalent. Suarez wrote that "discrete quantity . .. is not infinitely divisible, unlike continuous quantity" (MD, XLI, 5, 16; see also MD, XIII, 2, 4). Aristotle defined continuity in terms of density: "by continuous I mean that which is divisible into divisibles that are always divisible" (Physics, VI, 2; 232b24). In On the Heavens he claimed that "a continuum is that which is divisible into parts always capable of subdivision" (I, 1; 268a7). It is at this point that contemporary and early modern usages part company. Because of considerations which arise from within his own philosophy, however, Descartes must also take leave of his peripatetic companions at this juncture. Since explicitly he never takes them on as fellow travellers, I am not willing to assume he too believed that density entails continuity.

The issue is whether there can be a quantity which is dense but yet discrete, with parts not joined by a common terminus. One way in which a quantity can be discrete is by indeed having parts each with its own boundary and, hence, being also not dense. The question is whether this is the only possible way. And it seems the an-

54




swer is "no"; for a series could be divisible into parts which lack a common limit not because each has its own but rather because there is none. This is the case if one supposes a division in a line such that neither of the two adjoining parts has a first or a last member. Since at that division there is no common terminus, those parts are not continuous. Such a dense quantity would be divisible not only at its infinitely many points but also, let us suppose, at infinitely many discontinuities where the resulting parts have neither each its own terminus nor a common one.

The Aristotelians distinguished between intrinsic and extrinsic boundaries. Intrinsic limits are last or first members of a series. Extrinsic termini are not themselves members of the terminated series. Rather, all members before or after them, as the case may be, are in the series, which is thus bound by its extrinsic terminus, as it were from the outside. "Being extrinsically bound" and "being intrinsically bound" are contraries, so that if a series has an extrinsic limit, it does not also have a possible intrinsic boundary terminating it at that end. A quantity which is not dense has parts bound each by an intrinsic limit. A quantity which is continuous has parts bound both by one single point, which is indifferently intrinsic to one and extrinsic to the other (see MD, XL, 5, 4 and 55). A dense quantity with parts immediately next to each other each of which is extrinsically bound is not continuous. Such parts are limited, it is clear, by an extrinsic terminus which is not itself a part of the quantity. For the parts are assumed to be immediately next to each other; and any point in one selected to act as extrinsic limit of the other will fail to be a first or last member ex hypothesi, thereby failing also to serve as boundary for the other part. So the parts are not joined by a common limit, but separated by that discontinuity. Since each part has no last or first member around the discontinuity (again, otherwise that would be its intrinsic limit and it is supposed not to have one), density is still preserved there.

The possibility of such adjoining extrinsically bound dense parts seems to have been considered by Suarez. He pointed out that "it is not necessary that all things immediately next to each other be continuous or contiguous, if each of the two is not intrinsically bound." (See MD, XL, 5, 66; "Neque est necesse ut omnia quae sunt immediate sint continua aut contigua, nisi utrumque sit intrinsice termi- natum.") The example Suarez is discussing immediately before he makes this comment is that of two different forms which are in-

55



J. E. K. SECADA

stantiated immediately one next to the other, one having a last (or first) point while the other not. These two quantities are not continuous because one form is not instantiated in the intrinsic limit of the quantity of the other form, so the limit is not common to the quantity of both forms. Such a case is different from the one that he appears to consider in the quoted text, which may be naturally read as stating that neither one nor the other part is intrinsically finished.'3 Thus, without needing to force the text, I take Su'rez to be making a point to reinforce and round up his discussion of an otherwise different case, rather than to be restating what he had already clearly stated. The point he makes is that adjoining parts which are both extrinsically bound are also, and perhaps more clearly, neither continuous nor contiguous. Suarez did not elaborate on this matter. But he did provide the elements for an argument that such a possibility, a dense but discrete quantity, is irrelevant to discussions of continuity.

Aristotelian discussions of quantity and continuity are governed by intuitions which arise from consideration of the structure of body, space, and time. Concerning an actual division of continuous matter into two parts Suarez wrote that "the common continuative term of the matter is lost (amittatur) and two terminating or ex- treme ones result (resultant)," adding shortly thereafter that the common point is destroyed ("destruantur") since it cannot be in both parts and "there is no reason why it should be in one rather than the other" (MD, XL, 5, 55 and 56; see also XL, 5, 34; other terms used in expressing this destruction and resulting are "tol- litur" and insurgentt"). "How these terms are made is difficult to explain"; Su'arez continues, "for it is not philosophical to admit some creation or annihilation there" (MD, XL, 5, 56). He adds, hesitantly and rather obscurely, that "it appears that one should say that these material terminating indivisibles are made by resulting from the very parts of the matter (fieri per resultantiam ab ipsis partibus materia)." But one can see the kind of argument for the discontinuity of matter that Suarez might preempt here. It may be sketched as follows: matter cannot be annihilated or created; no part of matter can be extrinsically limited in re; therefore,

13To express the possibility he had just exemplified Suarez might have used "alterutrum" rather than "utrumque."

56




continuous matter cannot be divided in re. Such reasoning leads, with the addition of the premise that matter is actually divisible, to the conclusion that matter is not continuous. Succinctly, Suarez would argue that one can pass from one continuing point to two terminating ones without creating or annihilating matter.

In the case of two forms instantiated one next to the other and both limited extrinsically, the extrinsic limit is a point in the continuous quantity of the matter, but not in the discrete quantity of the forms. Suarez distinguished between things quantitative pri- marily and derivatively, or per se and per accidens. The form of quantity itself is the former, while the forms in the example are the latter. Now, while quantities per accidens can be terminated extrinsically in re, a thing quantitative per se is such that "if it is not continuous with another, it always has an intrinsic terminus, for this arises naturally and there is no contrary to stop it" (MD, XL, 5, 66). So Suarez concluded that "in these cases all quantities are either continuous or properly contiguous."

If we examine the possibility of extrinsically limited material parts in re, we can recover the considerations that led Suarez to the speculations I have just outlined. Consider a solid and dense rec- tangular body which is terminated merely extrinsically on one side. We assume, then, that there will be no surface on that side which is last. There will not be, for example, a surface of the body which could be painted or touched. For any surface we take as a pictorial or tactile candidate will have other surfaces belonging to the body coming between it and our brushes and toes. Nor could such a body, if opaque, be seen on that side. What surface will we see? Again if the surface is part of the body, then there are other surfaces which are part of the body between it and our organ. Suarez does write that "quantity is not actual extension in space, but apti- tudinal (aptitudinalis), and this the body can retain even if not actually in extended space" (MD, XL, 2, 22). Still, whatever such apti- tude for extension comes to, it was understood as involving the claim that merely extrinsically bound quantities per se are not actually given.

Contemporary discussions follow Richard Dedekind's definition of continuity in his Essays on the Theory of Numbers. A continuous straight line is such that "[i]f all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one

57



J. E. K. SECADA

point which produces this division of all points into two classes, this severing of the straight line into two portions."'4 Though Dede- kind writes of a line, it is not difficult to see how his account could be extended to terms of quantities in general. And it is clear how continuity differs from density. An account of density is obtained by using Dedekind's formulation and changing it by substituting "there do not exist two adjoining points which produce" for "there exists one and only one point which produces." A series could be dense and discrete when there is no dividing member, rather than one or two. As it happens, this is the case of the rational numbers.'5 One can divide all the rational numbers into parts that have neither a largest nor a smallest member: for example, at the square root of two. All rationals are either larger or smaller than the square root of two, the square root of two is not itself a rational number, and there are no rational numbers closest to the square root of two. Between any two rationals there is always a third, assuring the density of the series; but also, between any two rationals there is always an irrational number, assuring that the continuity of a common point will be lacking there.

The non-equivalence of density and continuity does not settle whether it follows from the density of matter that it is continuous. As suggested, it may be argued that there cannot be in re parts of matter bound by extrinsic termini. Given the Aristotelian doctrine concerning the relation between the continuity and quantity of matter, and that of space, it is not difficult to see how a Scholastic might apply this to discussions regarding the latter. Whether such arguments, and the intuitions on which they rest, are granted is a different matter. But the proper attitude, certainly, is not to ignore the distinction between the dense and the continuous nor to feign

14R. Dedekind, "Continuity and Irrational Numbers," in op. cit. (La Salle, Ill.: Open Court, 1948), p. 11. A contemporary presentation of the distinction between continuity and density is found in W. H. Newton- Smith, The Structure of Time (London, England: Routledge and Kegan Paul, 1980), pp. 112-114; Bertrand Russell, The Principles of Mathematics (New York, N.Y.: W. W. Norton, n.d.), Part IV, includes an extended discussion of continuity with a few historical references.

'5Rational or commensurable numbers are those equal to the quotient of two integers. Irrational or incommensurable numbers, such as the square root of two or the ratio of the circumference to the diameter of a circle, are not equal to the quotient of any two integers.

58




that the distinction is not possible within an Aristotelian frame- work. The distinction is expressible with the conceptual resources of Scholastic Aristotelianism, as we have seen. Further, I have argued that a case involving this distinction was explicitly mentioned by Suarez.

The issue which arises here is that concerning the relationship between mathematics, number series, and, more generally, conceptually possible orderings on the one hand and, on the other, realities such as space, material substance, and time, in particular with regards to their continuity. That the mathematical and the natural cannot always be treated together had already been noted among the Aristotelians well before Suarez. Such was the case, for example, when it was maintained that Aristotle's definitions of contiguity and continuity were not distinguishable mathematically.16 In a similar vein, one might argue that mathematical or abstract orderings which are dense but discontinuous have no rele- vance to discussions of the continuity of matter and space.

It is unclear to me how to transfer the intuitions regarding matter and space to the discussion of the continuity of time. In other words, I am not sure that in the case of time any similar moves can be made to resist considering the possibility of a dense and discrete ordering. Time, in fact, is only derivatively a quantity.

16Aristotelian contiguity requires limits that are together, touching, or in the same place. It does not appear to be possible to distinguish mathematically two points in a line except through their position or place. This might explain Descartes's impatience with the notion in the exchange with Burman (AT, V, 164). See Edith Dudley Sylla, "Infinite Indivisibles and Continuity in Fourteenth-Century Theories of Alteration," in Norman Kretzmann, ed., Infinity and Continuity in Ancient and Medieval Thought (Ithaca, N.Y.: Cornell University Press, 1982), pp. 233 and 256. Some of Aristotle's texts on continuity are conveniently collected as an appendix to this book. On the other hand, I am not persuaded by the treatment that is given to the relation between Scholastic and contemporary views on the continuum in some of the papers in this collection (for example, Sylla's and N. G. Normore, "Walter Burley on Continuity," pp. 258-269). The contrasts which are drawn are not clear to me. And late Scholastic treat- ments of these issues, like Toledo's and Sudrez's can be interpreted without involving them in any direct conflict with contemporary mathematical discussions. Richard Sorabji, Time, Creation, and the Continuum (Ithaca, N.Y.: Cornell University Press, 1983), Part V, discusses some of these topics; but it seems to me that his treatment of the relation between density and continuity and of the Aristotelian notion of continuity itself is defective (see for example p. 369 and p. 405 note 3).

59



J. E. K. SECADA

As Suarez wrote: "successive things ... are not quantitative per se, but per accident" (MD, XL, 1, 12; see also XL, 9, 4 and, in the same section, paragraphs 9 and 12).17 What is in any case clear and cer- tain is that Descartes cannot make use of the Scholastic speculations even in the case of space and the extended substance. For it is a central doctrine of his philosophy that matter can be treated purely geometrically and, furthermore, that geometry can be treated purely arithmetically. He recommends that we avoid sen- sorial intuitions and resorting to the imagination when discussing the nature of matter and space. Mathematical possibilities are, in a Cartesian treatment of these topics, natural possibilities. I take this to be well established and in need of no further documentation.

In short, though Descartes may be safely assumed to have used the Scholastic notion of continuity, it seems to me unnecessary and unjustified to suppose he also went along with the identification of continuity and density. His predecessors had ways of defending such an identification which are not open to him. And the fact that it is a common mistake to forget the Aristotelian context and take the identification to hold mathematically and purely conceptually is no good reason to attribute this error to Descartes, particularly in the light of Suarez's rather sophisticated treatment of the issue. But I am not obliged to maintain that Descartes believed density does not entail continuity. My claim is that he believed neither the one nor the other. Furthermore, even if it is argued, contrary to my views, that in the case of space and matter Descartes did, un- warrantedly though perhaps understandably, collapse continuity into density, it does not follow immediately that he must have done the same in the case of time.

Be that as it may, the issue as to the continuity or discontinuity of Cartesian time is one that, at least among some of the more prominent contributors to the discussion, has involved the view that time is dense yet discrete. Thus Gueroult wrote that Cartesian

'7There are well-known arguments by Aristotle to the effect that time, place and matter all must either be discrete or continuous (Physics, VI, 1-2; 231b18-233a20). However, these arguments do not address the possibility of a discrete time which is, nevertheless, dense. They involve only the density of time, as is clear in the quoted text. In the case of matter this would amount to its continuity. Such arguments might account for the transference of the implication from density to continuity from the case of matter and space to the case of time. But they do not necessitate it.

60




"time can . . . be conceived as indefinitely divisible without it following necessarily from this property that it is continuous."18 Hence, the issue might be cast in terms of what Descartes was committed to holding, regardless of whether he did believe it.

This leads to historiographical questions which need to be made explicit. When discussing Cartesian views of time it is necessary to be clear about the exact nature of the historical problem con- fronting us. One possibility is that we are inquiring whether Des- cartes himself held time to be continuous or discrete. Though, of course, a text can decide the question affirmatively in a straightforward manner (leaving aside issues regarding changes in his beliefs), the lack of extant texts where he professes a belief on the matter is not sufficient to decide the issue negatively. Beliefs may be inferred in a variety of ways. For example, when an inference from beliefs made explicit in writing to some other belief never explicitly acknowledged would have been immediate and obvious to the subject himself, it is wrong to deny that he explicitly believed the inferred belief solely because there is no remaining written tes- timony. Though there is here the danger of being exuberant, one should also beware of the pitfalls of excessive austerity.

A second possibility is that of inquiring not whether Descartes believed time to be continuous or discrete, but rather whether he was committed to believing one or the other. A minimal condition required for an affirmative answer to this question is that the belief in question be formulable using the conceptual baggage available to Descartes himself. It should not be claimed that somebody is committed to a belief he could not possibly understand. Evi- dently, the belief must follow from other beliefs he held. But it is not required that Descartes himself ever have recognized the implication or ever have formulated the belief.'9

'8Gueroult, op. cit., p. 275. Gueroult's own account of continuity is rather unclear: discontinuity is defined, he writes, by "la contingence, la separation et l'indgpendance re'ciproque des parties" (p. 273). But his notion of continuity is not one which can be equated with density. On the other hand, N. K. Smith, in his Studies in the Cartesian Philosophy, p. 132, exemplifies the more common practice by identifying both.

'9There is a still weaker sense in which we might enquire whether a belief merits the label "Cartesian": when Descartes neither held it nor could have understood it, yet it does follow from doctrines which he held or was committed to. I should add that I am unsure as to the claim that

61



J. E. K. SECADA

Having clarified the historical problems which we might address concerning the continuity or discreteness of Cartesian time and being clearer also about the notions of continuity and discreteness with which Descartes was operating, we can now return to our main concern. First, I hold that Descartes believed time is dense. Second, I maintain that he neither believed nor was committed to believing that time is continuous or that it is discrete. Third, I hold that the claim that time is continuous (not merely dense) is expressible using terminology available to Descartes himself.

III.

In a text I have quoted from the Meditations Descartes requires that there be innumerable parts in a finite segment of time (the duration of his life up to the point of writing that text; AT, VII, 48-49). For this to be the case there must be some stage at which time is dense, though not necessarily continuous. But if time is homogeneous, then the density must be found at all stages. This establishes that Descartes believed time is dense. Now, if this text is taken to refer to atoms, then one could not speak about a temporal atom and the one coming immediately before or after it. However, in the Second Replies Descartes wrote that "the present time has no causal dependence at all on that which has immediately preceded it" (AT, VII, 165). If this passage and that from the Meditations are interpreted atomistically, then Descartes requires both that a finite duration have infinite atoms and therefore be dense and that there be an atom immediately preceding another atom and thus that time not be dense. I have argued that he need not be interpreted atomistically in either of the two passages, or for that matter any- where. If in the Second Replies he is not taken to be referring to non-enduring instants with the phrases "the present time" and "the time immediately preceding it," then no problem arises.20

there are beliefs Descartes could not have understood: the counterfactual conditions have to be made clear. To say, loosely, that they are not expressible in the vocabulary Descartes used is not good enough, for one might argue that, ultimately, any belief will be so expressible if enough explication and circumlocution is permitted.

201n his recent alleged refutation of the view that Descartes took time to be discontinuous, Richard Arthur maintains that density is among "twen-

62




It ought to be clear that belief in temporal atomism is independent of belief in the existence of instantaneous events. Hence, Des- cartes's doctrine that the transmission of light is instantaneous and the problems that might be generated for his physics by Huyghen's discovery that the speed of light, though large, is finite are, on their own, irrelevant to the issue under examination.21

On the other hand, it should also be clear that Descartes's claims to the effect that conscious mental events take time and are not instantaneous are equally independent of views as to the continuity of time.22 In particular, it is not the case that defenders of Carte- sian temporal continuity can ground their views on such claims.

tieth-century criteria of continuity" (op. cit., p. 350) and that it is anachro- nistic to argue that Descartes believed in the discontinuity of time on the basis of his writing of neighboring instants in AT, VII, 370 and V, 193. First, Descartes writes of neighboring moments (singula momenta posse a vicinis separari; hoc momento ... momento proxime sequenti) and not of neighboring instants. In this issue the difference between divisible enduring moments and indivisible durationless instants is crucial; and whatever the general imprecision in Descartes's use of these terms, here he is clear. Arthur argues against attributing this distinction to Descartes using texts such as: "this cannot endure (durare) even for the minimum point of time, which they call an instant" (AT, VIII-1, 115) and "there is some cause which. . . creates me afresh at this moment (ad hoc momento) . . ." (AT, VII, 49; apparently, the point here is that Descartes does not say "through this moment," but "at this moment"; see also AT, VIII- 1, 159). But this is just to expect and demand the precision of technical use where it is not intended. When it matters, Descartes does not confuse enduring segments with instants. The only "textual inconsistencies" (p. 369) in these passages are those generated in the minds of some commentators. Second, if Descartes had written of neighboring instants and had thereby denied that time is dense, then he would have been committed to the claim that time is discontinuous, in a sense which is common to us and to him and his six- teenth- and seventeenth-century Scholastic contemporaries and predecessors. On the other hand, Arthur's charge of "anachronism" (p. 350) af- fords us with a striking example of conceptual confusion leading to lack of historical understanding.

2'Contrast Gueroult, op. cit., pp. 272-274. See below note 26. 22Contrast Laporte, op. cit., p. 159; and Beyssade, op. cit., pp. 135-136

and 346. In the latter passage Beyssade seems to claim a connection: "Si, comme le veut la these discontinuiste, toute intuition devait etre enfermee dans un instant...." Unfortunately, it appears that he sees this connection as evident, so he does not explain it. Though, to be fair, he might just be echoing the claim that there is such a connection which defenders of Car- tesian temporal atomism have made; see, for example, Yvon Belaval, Leibniz critique de Descartes (Paris, France: Galimard, 1960), pp. 149-150.

63



J. E. K. SECADA

One may consistently hold both that time is made up of discontinuous instants and that thinking always takes time. Indeed, without deciding on the issue of the continuity or discontinuity of time, one ought to distinguish between the specious present of consciousness and the instantaneous present involved in discussions of temporal atomism. It is this distinction which dissolves the contradiction that Beyssade finds between the claim in the Rules that intuition, while not instantaneous, is given (psychologically) "tota simul et non succesive" (AT, X, 407) and the claims that different parts of time are not simultaneous (strictly). So there is no need here to bring in a "concept cartesien de continuity" as Beyssade does.23

It might be objected that by distinguishing between the instantaneous present and the present of consciousness, I am not taking into account Descartes's doctrine that the real duration of substances and the time abstracted from it are, like extension, the es- sence of matter, and the space abstracted from it, distinct not in reality but only by reason (AT, VII, 369-370 and VIII-1, 27). This is not so. If there be instantaneous temporal atoms, still there need not be either instantaneous movement or instantaneous thought. The notion that the duration of my thought is composed of atomic instants is compatible with the claim that my thought could not exist during only one such instant; just as the claim that the duration of my bodily movement across the room is made up of durationless atoms is compatible with Descartes's assertion that no motion occurs in an instant (AT, VIII-1, 64 and XI, 45). If conscious thought and souls require a span of time in order to exist, there could still be discontinuities during their existence. It does not follow that, if there are such discontinuities, then it must be possible for the souls to exist only in the interval, which could be instantaneous, between two proximate discontinuities.24 More- over, the defender of Cartesian temporal continuity must tread

230p. cit., p. 347. 24In the Conversation with Burman, Descartes distinguishes the divisibility

of the duration of thought from the divisibility of its nature in a text which could be read as supporting my argument (AT, V, 148). However, the passage is obscure; and I would not wish to rest much on it. See also John Cottingham's commentary on the Conversation (Oxford, England: Clar- endon Press, 1976), pp. 59-60.

64




carefully here. He might end up committed to the existence of enduring indivisibles. And he would ensure that time is not dense by requiring that the specious present of consciousness be the minimum unit into which time can be divided. Anyhow, even if none of the above is granted, the undisputed claim that motionless material substance could exist for only an instant should be enough to take care of the objection and make sense of the idea of the real duration of any substance being made up of instantaneous atoms.

Descartes rejected atomism with respect to matter and some may argue that this entails a rejection of atomism with respect to time.25 Thus, the continuity of Cartesian time would be established. If this is so, at least it is not obviously so, and there are reasons to believe it is not so at all. Descartes's rejection of material atomism can be grounded on two arguments. First, he held that however small a bit of matter, if it has any dimension at all, it is divisible even further. Hence, there can be no ultimate material atoms which, having size, are indivisible. This straightforward attack is explicitly directed against classical atomistic views (AT, III, 213-214; V, 273-274; VI, 238-239; VII, 51-52).26 But -the argument does

25See Gueroult's suggestion that Laporte argued thus in op. cit., p. 272. 26Descartes held also that matter is, at least sometimes, infinitely di-

vided. In the letter to More of 5 February 1649 (AT, V, 273-274), while arguing that there can be no extended but indivisible atoms, he suggests that God could have carried out the infinite division of matter. And in Principles, II, 34 (AT, VIII- 1, 59-60) he maintains that the infinite division of matter sometimes does actually take place. On the other hand, it is important to notice that in view of these texts and the fact that Descartes apparently did not take them to commit him to material atomism, special care should be taken when claiming that belief in instants involves atomism. The doctrine of the production of movement by continual recre- ation at every instant, which helps him "deduce" the laws of motion from the nature of God and distinguish between the vectorial and the quantitative elements in movement, would only commit Descartes to atomism if he stated it so as to imply that the succession of temporal instants is not dense or not continuous. This he does not do (AT, VIII-1, 61-66; XI, 37-38 and 43-46). Suarez, who certainly was not an atomist, wrote that "between two points in a line there are infinite other points" (MD, XL, 5, 43). And dealing directly with time he stated: "time exists by means of instants, so that its indivisible parts truly and really flow and after any instant a part follows and in any part there are instants and between any instants there is a flowing part" (MD, L, 9, 22).

It is interesting to note that Descartes probably grew out of material atomism: see his early piece to Beeckman in AT, X, 68.

65



J. E. K. SECADA

not work against atomism if the ultimate atomic constituents are thought to be dimensionless. And this is precisely the case with the discontinuous view of time that has been ascribed to him, for Car- tesian temporal atoms are thought to be instantaneous. To argue against all atomism merely from the consideration of infinite divisibility is just to confuse density and continuity. This may indeed be the problem with Beyssade's claim that in solving Zeno's paradox Descartes treats both time and space as continuous.27 For though he does offer a homogeneous treatment of space and time when dealing with this paradox, the point at issue is only one of infinite divisibility, not one involving continuity or discontinuity (AT, IV, 445-447 and 499-500).

Second, one may argue against material atomism from Des- cartes's rejection of a vacuum. Classical atomism included belief in the existence of a vacuum as much as in the existence of material atoms. According to such a view, it should be noticed, the continuity of space is compatible with the discreteness of matter. Now, given that for Descartes material substance is just existing extension, no such thing as a vacuum-extension without substance-is possible (AT, V, 52, 271-273; VIII-1, 49-50; see also I, 140 and 413). It does not appear to be the case that this line of reasoning can be applied to the issue of temporal atomism.28 Hence, the Car- tesian attack on material atomism should not lead to the claim that he held that time is continuous. Moreover, it should be noticed that Descartes's criticisms of the beliefs in small but indivisible material atoms and in a vacuum can be expounded without raising questions which, in order to be properly treated, would require him to distinguish between density and continuity.

As I indicated earlier, it may be objected that the principle of the independence of separate segments of time does not follow from the considerations we have examined above. Take three segments A, B, and C. Suppose A and C are separate but B shares some times with A and some with C. B is thus not separate from A or C.

270p. Cit., pp. 350-351. 28Descartes might indeed have held that there can be no temporal

vacua. See AT, V, 343 and, for a contemporary discussion of the notion of a temporal vacuum, Newton-Smith, op. cit., Chapter II. Still, the supposed Cartesian discontinuity of time is independent of the existence of temporal vacua.

66




Now, nothing stops A from being causally active upon B and B upon C. If the transitivity of causality is upheld, then it follows that, though separate, A is causally active upon C. This objection denies the principle and produces a counterexample granting the considerations regarding time and causality from which it is sup- posedly obtained. It may go further and lend support to the atomistic interpretation of Descartes's views on time. For it could be argued that the way out of this difficulty is to restrict segments of time to simple temporal atoms so that the example cannot be formulated. But this is neither the only nor the best way out.

The counterexample proceeds by dividing time into two separate segments and then superimposing on this division a segment that spans over the two original separate ones. It then relies on the transitivity of causality to link the separate segments through the one common to both. But nothing in what has been said and ascribed to Descartes denies that for any segment its parts are themselves causally independent one from the others. Indeed the contrary is suggested by the possibility of innumerable divisions in a finite time. On the other hand, in the definitions presented above a part of time has been allowed to be causally related to another part which need not be totally simultaneous with it. That is what generates an illicit transitivity. But so long as the requirement of simultaneity is not overlooked the transitivity of causality can be preserved.

Now, it could be argued that while a cause must be simultaneous with its effect when producing it, the effect could itself produce another effect at a later date and the transitivity of causality requires the first to be a cause of the last. This is, in fact, the crux of the objection being considered. It shows how merely from the requirement of simultaneity and the obvious claim that separate segments of time are never simultaneous the principle cannot be obtained. For something could be the cause of an effect existing during a segment separate from that during which it exists simply by producing the effect at some stage and the effect continuing in existence after the cause has passed away. However, this objection ignores another item in Descartes's doctrine of causality. In the Second Replies he stated that "nothing exists concerning which the question may not be asked: 'what is the cause of its existence?'" (AT, VII, 164). Though there is a sense in which this appears reasonable enough, Descartes's understanding of it was by no means

67



J. E. K. SECADA

unproblematic. He took it to mean that it is the existence of a substance at some time that requires a simultaneous cause. In the Med- itations he held that "from the fact that I existed a short time ago it does not follow that I must exist now, unless some cause at this moment, so to say, creates me anew or conserves me" (AT, VII, 49). Shortly after he explained that "the same power and action are needed in order to conserve a substance in each moment in which it exists as would be needed, if it did not exist, to create it initially." If three substances are causally connected, they must be simultaneous. For if a substance causes a second substance to exist at some time and at a later time the second causes a third to exist, then the first substance is not the causal ancestor of the third unless it is the cause of the second at the same time as the second causes the third. If not, then the causal ancestor will be whatever is the cause of the second substance at that time.

Descartes requires the existence of a substance to have a cause satisfying the demand of simultaneity at all times during which it occurs. For him, that something is produced does not account for its continuation in being; it must be kept in existence at all times. The intuition behind the demand of simultaneity is independent of the further doctrine that substances must be produced at all times during which they exist. Descartes offers no arguments for the latter. He seems to take it to be an evident point that an enduring substance is, so to speak, made up of constituent slices, the substance at t for any time t during which it exists, and that each such slice requires a cause.29 He understands the requirement of universal causality as applying not only to the coming into existence of contingent substances, but also to their contingent existence at any other moment of their duration. Nevertheless, as I suggest below, this Cartesian intuition too is related to Medieval doctrines of causality.30

It should not be thought that atomism makes things easier at this point. If cause and effect must be simultaneous, whether there is a discontinuity in time or not is irrelevant to the capacity of past time

29Compare Anthony Kenny, Descartes (New York, N.Y.: Random House, 1968), pp. 143-144.

30This conservation requirement, together with the simultaneity one, might point in the direction of the conception of a cause as a sufficient and (disjunctively) necessary condition for its effect. See note 11 above.

68




to be causally effective on present time; for nothing short of simultaneity will do, not even infinitesimally small proximity. And if a substance requires a cause at all times during which it exists, then even if there are no discontinuities in time there must still be simultaneous causes at every moment in the existence of a substance. Descartes believed that a causal explanation was required not only of a substance's coming into existence, but of its existence at every moment. The last comeback of the atomistic interpretation is to hold that it is this belief which is grounded on temporal atomism. The argument would, briefly, run thus: if time were continuous, then the existence of a substance at some time would be assured by its having existed up to that point, though admittedly the relationship involved here would not be one of strict causal dependence; on the other hand, the defender of the atomistic interpretation continues, it is only because of his discontinuous view of time that Descartes adopts the demand for a causal account of the existence of a substance at all moments as opposed to merely so accounting for its coming into existence. This line of thought has Descartes allowing that the continued existence of a substance could be explained in non-causal terms if only time were continuous. There is, however, textual evidence against this interpretation. In the Second Replies Descartes stated: "The present time has no causal dependence at all on that which has immediately preceded it. This is why no less a cause is needed to conserve something than is needed to produce it the first time" (AT, VII, 165). It is a break in the causal chain, one which occurs whether there are discontinuities in time or not, which Descartes used to justify the requirement for a simultaneous cause at all times during the existence of something.

Descartes could have acquired this view through the influence of his Scholastic studies. It is interestingly similar to an established doctrine in the School: all creatures require a conserving cause at every moment of their existence. The Scholastics distinguished between a cause per se and a cause per accidens; and it is only the former which they had in mind with this doctrine. A series of causes per se is one where all the members are active simultaneously; where any intermediate members are dependent on the causal activity of their causes for their own efficacy; and where the members are of different kinds, ascending in perfection from the latter to the earlier. On the other hand, a series of causes per ac-

69



J. E. K. SECADA

cidens can take place in time. In it an intermediate member may be active causally when its cause is not active. And there need be no difference in the perfection of its members.

An example of a series of accidental causes of existence is that of grandparents, parents, and child; while a series that exemplifies the first two characteristics of an ordering of per se or essential causes is that of a ball, a rope, and a stick, each being held by the other. Series of essential causes of existence, however, are more difficult to exemplify. Scholastic attempts rely heavily on Aristote- lian physics; or they come to identify it with some sort of formal efficacy which involves a hierarchical conception of being and a doctrine that contingent substances exist and cause existence only insofar as they "participate in," are "given," or "receive" existence (ST, I, q.8, a.1; q.9, a.2; q.46, a.2, ad 7; q.104, a.1 and a.2; MD, XVII, 2, 2-5; XXI, 1-3).31

A Cartesian simultaneous series, on the other hand, is composed of straightforward producers. Descartes was probably sensitive to the Scholastic intuitions concerning the need for a causal account of contingent existence not only in its origin, but at any time at which it is given, so he transposed Scholastic doctrines into his own metaphysics; he found a new home for old doctrines.32 He allowed only one kind of efficient cause. If a chain of causes across time has a place within Descartes's philosophy, it is as a theoretical con- struction. The only causal relation in re he allowed for issues in a simultaneous series. Moreover, the Cartesian simultaneous series have only two members: God and a created substance. All causality within or between created substances must in the end refer to the productive activity of God as displayed through time. This is how, indeed, the laws of nature governing causal interaction between parts of the material substance issue directly from God, and how

31See also Aquinas, De Principiis Naturae, V, 362, p. 126; Aquinas, In XII Libros Metaphysicorum Aristotelis Expositio, V, 2, 773; and 3, passim, ed. Fr. M.-R. Cathala, OP (Turin, Italy: Marietti, 1964), pp. 213, 214-217; Avi- cenna, Liber de Philosophia Prima, VI, 1-3, ed. S. Van Riet (Louvain and Leiden, Belgium: E. Peeters and E.J. Brill, 1980), pp. 291-319; and John Duns Scotus, De Primo Principio, I and II, ed. A. B. Wolter (Chicago, Ill.: Forum Books, 1966), pp. 2-37. Scholastics also allowed for a simultaneous series of movers, as in Aquinas's First Way.

32See AT, VII, 370; and also AT, VII, 242 where a hierarchy of reality or perfection between cause and effect is suggested.

70




occasionalism could claim to be the true inheritor of Descartes's metaphysics.33 Still, such a Cartesian distinction between theoreti- cally constructed causes and causes in re can be seen as analogous to the Scholastic distinction between causes per se and per accident. Though such an analogy is of little help when concerned with jus- tifying Descartes's views, it does point to the degree of continuity between his metaphysics and that of his Scholastic predecessors.

Descartes believed in the following three statements:

1. time is a succession such that it has no two separate segments which are simultaneous;

2. the existence of a substance can be caused only by something that exists at the time when it is produced; and

3. the appropriate term in a causal relation is not a substance but a substance at or during some time, and all such terms require a causal account.

The texts mentioned in the discussion of Descartes's views on time can be naturally read as involving these three beliefs and from them obtaining the principle of the independence of separate segments of time. Not only is there no reason to ground any of these beliefs on an atomistic conception of time, but there is evidence in the texts against doing so. On the other hand, to argue that he held a view of time as continuous is also unwarranted; for, as I have shown, the texts do not commit him to this view either. Fur- thermore, given that there are limitations and difficulties which would inevitably hamper a discussion on Descartes's part of the question of the continuity or discontinuity of time, it seems that the correct view is that he leaves the matter untouched in his writings.

As I have suggested, the conception of causality contained in that aspect of the metaphysics of Descartes I have dealt with may indeed not exhaust the meaning of the relation of cause and effect. Descartes may have wished to allow the terms to be used in a

33The connection between Descartes and his occasionalist successors is a complex issue; and, unfortunately, this is not the place to examine it. By emphasizing that on Descartes's view God is the only true active cause I have merely pointed out one aspect of this connection.

71



manner that, for example, does not adhere to the demand of simultaneity. Such concepts could in fact be articulated within his philosophy and physics. But they would have to be distinguished from the ones I have been examining. The matter, however, falls beyond the scope of this paper. I hope to have succeeded in the rather more modest enterprise of showing that Descartes's views on time and causality, understandable within the Scholastic frame- work, are not linked to temporal atomism or, at least apparently, to any interesting views on the metaphysics of time. They do serve us, however, in drawing attention to the links between the Scho- lastic tradition and modern philosophy.34

University of Virginia

34Earlier versions of a part of this paper were read at the Anglo-French Descartes Colloquium in London, April, 1979 under the title, "Les Sources Scholastiques du Temps Cartesien"; at the Coloquio Descartes in the Universidad Catolica del Peru, July, 1980; and at the Universidad de San Marcos in Lima in August, 1986. I wish to thank commentators on those occasions, particularly Fernando Carvallo in London, and also Ber- nard Williams, Federico Camino, James Cargile, and Edwin Curley, from whose comments it has greatly benefitted.

72



secada - descartes on time and causality - 1990

Documents