1988-continuous creation continuous time a refutation of the alleged discontinuity of cartesian time

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C o n t in u o u s C r e a t io n

C o n t i n u o u s T i m e :

R e fu t a t io n o f th e l le g e d

D i s c o n t i n u i t y o f C a r t e s i a n T i m e

RICH A RD T . W . A RT H U R

1 I N T R O D U C T I O N

ACCORDING to Yv on Belaval, ~ eve ryo ne kno ws t hat t ime is dis con tin uou s in

Descar tes' ph i losophy , and as an assessment o f rece ived op in io n on the sub-

jec t, th i s s t a t ement can hard ly be fau l t ed . For a l l comm enta to rs on Descar tes

this century have fol lowed Kemp Smith , Vigier , and Wahl in asser t ing the

d i scon t inu i ty o f Car tes ian t ime, ' wi th the sole excep t ions o f Lapor te and ,

fol lowing him, Beyssade.3 And Laport e ' s d issen t ing view has been deal t wi th

I should like to thank several people for their encouragement and for helpful comments on

previous drafts: Howard Woodhouse, Victor Nuovo, John Nicholas, William Harper, Tom Len-

non, Brian Baigrie, and especially Michael Stack.

' Yvon Belaval, Leibniz: critique de Descartes, (Paris: Libraire Gallimard, 196o , 149: sait com-

ment Descartes a li~ indissolublemententre d'intuitionelles les trois notions de v&it~, d'instant et

d'intuition.., l'instant mesure rintuition, l'actuel mesure l'instant, c'est/~ dire que le temps est

discontinu . . .

' Norman Kemp Smith, Studies in the Cartesian Philosophy (19o2, rpt. New York: Russell &

Russell Inc., 1962), 131. Hereafter cited as Studies. Vigier, Les id&s de temps, de dur~e et

d'~ternit~ chez Descartes, Rev ue Phi losophique (192o). Jean Wahl, D u role de l id~e de l instant d am la

philosophic de Descartes (Paris: Libraire F~lix Aican, 192o .

s Jean Laporte laid out his objections to the standard interpretation promoted by Vigier and

Wahl in his/ 2 Rationalisme de D escartes (Paris: Presses Universitaires de France, 195o), especially

158-6o. Jean-Marie Beyssade's work, La Philosophie Premil, e de Descartes (Paris: Flammarion,

1979), is a re-valuation of some traditional Cartesian doctrines premised on the continuityof time

in his philosophy. See especially vii, 16-x7, 1~9-42, 346-35o. When this article was in proofs

Professor Daniel Garber drew my attention to a recent paper of his in which he arrives at much

the same conclusion (although in less detail) concerning the continuity of Cartesian time as I do

here: 'How God Causes Motion: Descartes, Divine Substance and Occasionalism, Journa l o f

Philosophy (October 1987): 566-80.

[349]



3 5 ~ J O U R N L o r T H E H I S T O R Y O F P H I L O S O P H Y 2 6 : 3 J U LY 1 9 8 8

a t l e n g t h b y M a r t ia l G u e r o u l t , w h o i n h is

D e s c a r t e s s e l o n l ' o r d r e d e s r a i s o n s 4

v i g o r o u s l y d e f e n d s t h e s t a n d a r d i n t e r p r e t a t i o n o f D e s c a r t e s ' t i m e a s

d i s c o n t i n u o u s - - - t h e c l as s ic t h e s is , a s i t is c a l le d i n t h e s t a n d a r d e d i t i o n o f

D e s c a r t e s ' w o r k s . 5

N e v e r t h e l e s s , I s ha l l a r g u e h e r e t h a t t h e c l as si c t h e s is is i n c o r r e c t , a n d t h a t

t h e r e is n o c o n v i n c i n g e v i d e n c e t h a t D e s c a r t e s d e n i e d t h e c o n t i n u it y o f t i m e ,

a n d n o c o n v i n c i n g e v i d e n c e e i t h e r f o r t h e u su a l p r e s e n t a t i o n o f D e s c a r t e s '

d o c t r i n e o f c o n t i n u o u s c r e a t i o n a s a s s e r t i n g a d i s c o n t i n u o u s s u c c e s s i o n o f d i s -

c r e t e a c ts o f d i v i n e c r e a t i o n , a s o p p o s e d t o o n e c o n t i n u o u s a ct .

I s h o u l d i m m e d i a t e l y c la r if y t h e s e r e m a r k s , f o r I d o n o t m e a n t o s u g g e s t

t h a t D e s c a r t e s h a d a n y w e l l e l a b o r a t e d t h e o r y o f w h a t c o n s t i t u te s a c o n t i n u o u s

d u r a t i o n . H e a p p e a r s t o r e g a r d t i m e a s a n a l y z a b l e i n t o a n in f in i ty o f n e i g h b o r -

i n g m o m e n t s , y e t h e d o e s n o t a t t e m p t t o s o lv e w h a t L e i b n iz r e f e r s t o a s t h e

p r o b l e m o f th e c o m p o s i t i o n o f t h e c o n t i n u u m , t h e p r o b l e m o f h o w (in t h i s

c a se ) a d u r a t i o n c o u l d b e c o m p o s e d o f a n i n fi n it y o f d u r a t i o n l e s s i n s ta n t s o r

m o m e n t s . I n f a c t D e s c a r t e s d o e s n o t e v e n b e l ie v e , I s h a ll a r g u e , t h a t t h e r e is a

p r o b l e m h e r e t h a t s h o u l d o r c o u l d b e s o l v e d b y a fi n i te m i n d . M u c h l es s d o e s

h e a d v o c a t e t h a t , i n t h e c a s e o f d u r a t i o n , t h e r e is a d e f i n i t e l i m i t t o i ts di v is ib i l-

i ty , s o t h a t a n a p p a r e n t l y c o n t i n u o u s d u r a t i o n is i n fa c t c o m p o s e d o f r e a ll y

d i s c r e t e i n d iv i s ib l e s: y e t t h i s l a t t e r v i e w is p r e c i s e l y t h e v i e w n o r m a l l y a t t r i b -

u t e d t o h i m , t h e c la s si c t h e s is , w h i c h I s h a ll e n d e a v o r t o r e f u t e .

B u t b e f o r e I b e g i n m y a r g u m e n t , l e t m e f i rs t t r y t o c l ar i fy w h a t w o u l d

c o n s t i tu t e a d i s c o n ti n u i s t t h e o r y o f t i m e i n t h e s e v e n t e e n t h - c e n t u r y c o n t e x t ,

a n d w h a t w o u l d c o u n t a s e v i d e n c e f o r it. T h e s e a r e q u e s t i o n s t h a t m u s t b e

m o o t e d n o w i f w e a r e t o a v o i d c o n s i d e r a b l e c o n f u s i o n l a t e r.

L e t m e b e g i n w i th t w o c a v ea t s . F ir st , w e m u s t b e w a r e o f a n a c h r o n i s m : w e

c a n n o t a p p l y t w e n t i e t h - c e n t u r y c r i te r i a o f c o n t i n u i t y to d e c i d e w h e t h e r D e s -

c a r t e s ' t i m e i s c o n t i n u o u s . F o r e x a m p l e , t h e f a c t t h a t D e s c a r t e s t a lk s o f n e i g h -

b o r i n g m o m e n t s ' '6 m e a n s , f r o m a m o d e r n p e r s pe c t iv e , th a t t h es e m o m e n t s

4 Martial Gueroult, Descartes selon l'ordre des raisons, vol . 1, l'dme et Dieu. (Paris: Aub ier, 1953).

The translations given are my own, although there is now a good translation by Roger Ariew:

Descartes Philosophy Interpreted According to the Order of Reasons, Voi. l , The Soul and God (Minneapo-

lis: University of Minnesota Press, 1984). From now on I shall cite references to this work in the

form : Gue r ~731193 T he second page nu m ber re fers to Ariew's translation.

5 Oeuvres de Descartes, ed. C harles Ad am an d Paul Tann ery, (Paris: Libraire Philosophique J.

Vrin, 1964-76), Tab le analytique des matii~res, Tom e 1:388 (hereafter cited as ATA with

volume and pag e number.

Descartes refers to neighboring mom ents in his controversy w ith Gassendi (AT.7:37o)

which I shall discuss in section 4 below, and also refers to next mom ents in a letter to Arnauid of

4Ju ne, 1648 (AT.5:193).



C O N ~ T I N U O U S C R E A T I O N , C O N T I N U O U S T I M E 3 5 1

cannot form a continuous sequence. This is because every continuous se-

quence (such as that o f the real numbers) is dense, which means that between

any two of its terms there is always anothe r. Thus there can be no next instant

in a properly continuous time. Yet clearly this does not count as evidence that

Descartes himself conceived the sequence o f instants as discontinuous.

Secondly, it is often supposed that the discontinuist thesis would be estab-

lished if it could be shown tha t Descartes spoke of indivisibles in time. Again,

this is not so. Descartes does of course allow indivisibles in time--instants-

.just as he allows that there are points in space. But this does not prove that

he thought time to be composed of instants, or that he denied the continuity

of time, any mor e than his acknowledgement of indivisible points proves that

he thought space discontinuous, which of course he did not. That is, he

might have regarded instants as mere endpoints of intervals of time. Then

any interval, being itself indefinitely divisible, would contain an indefinite

number of conceivable instants; but it would no t necessarily be composed of

them.

So what more would we need in order to firmly identify Descartes' time

as discontinuous? Minimally, the indivisibles would have to be

p rts

out of

which time is composed, not mere endpoints. But even granting this, there

are several distinct possibilities for a discontinuous time in the seventeenth-

century context. In the first place, there are two distinct ways in which the

parts of something could be held to be discontinuous, a strong sense and a

weak sense. In the strong sense of discontinuity, the parts could be sepa rated

by gaps; for want of a better term , I shall call this gap discontinuity. In the

weaker sense, the parts could be really separate yet touching, that is they

could be contiguous to each other.7 Now in each case the parts themselves

could be conceived as either extended or point-like, although in the case of

point-like parts it is not clear that we would have to call the resulting time

discontinuous, unless they were explicitly stated to be separated by gaps.

Extended indivisibles, finally, could be either finite or actually infinitely

small. The latter, actually infinitely small yet extended indivisibles, are the

geometric indivisibles used by Descartes' contemporaries: Fermat, Roberval,

Cavalieri, and others.

Thus we have a matrix of six main possibilities for a discontinuous and

7 L e i b n i z d i s t i n g u i s h e s e x a c t l y t h e s e t w o k i n d s o f d i s c o n t i n u i t y i n h i s e a r l y w o r k . F o r i n -

s t a n ce , in h i s l e t t e r t o J a c o b T h o m a s i u s o f A p r i l 1 6 6 9, h e s ay s d i s c o n t i n u i t y c a n b e i n t r o d u c e d

i n t o a f o r m e r l y c o n t i n u o u s m a s s i n t w o w a y s : f ir s t, i n s u c h a w a y t h a t c o n t i g u i t y is at t h e s a m e t i m e

d e s t r o y e d , w h e n t h e p a r t s a r e s o p u l l e d a p a r t f r o m e a c h o t h e r t h a t a v a c u u m i s l e ft ; o r i n s u c h a

w a y t h a t c o n t i g u i t y r e m a i n s . G . W . L e i b n iz ,

Phi losophical Papers and Let t ers

e d i t e d a n d t r a n s l at e d

b y L e r o y E . L o e m k e r , 2 d e d i t i o n ( D o r d r e c h t : D . R e i d el , 1 9 7 6 ), 9 6 .



352 JOURN AL OF THE HISTORY OF PHILOSOP HY 6:3 J ULY 1 9 8 8

d i s c r e t e C a r t e s i a n t i m e . s I t is e i t h e r g a p - d i s c o n t i n u o u s o r m e r e l y c o n t i g u o u s ,

a n d i ts p a r t s a r e e i t h e r f i n it e , a c t u a l l y i n f i n i te l y s m a l l, o r p o i n t - l i k e .

I n w h a t f o ll o w s , a l t h o u g h I s ha l l m a i n l y b e f o l l o w i n g t h e l o g ic o f t h e

a r g u m e n t s o f t h e p r o p o n e n t s o f t h e c la ss ic t h es is , I s h al l u s e t h e a b o v e m a t r i x

o f p o s s ib i li ti es a s a f r a m e w o r k f o r c l a r i f y i n g e x a c t ly w h a t m o d e l o f t im e is

b e i n g a t t r i b u t e d t o D e s c a rt e s . I n t e r m s o f t hi s f r a m e w o r k , w e s h al l s e e t h a t t h e

g a p - d i s c o n t i n u o u s m o d e l s a r e i n a d m i ss i bl e g i v e n D e s ca r te s ' c o n c r e t e i n t e r p r e -

t a t io n o f t i m e , t h u s e l i m i n a t i n g t h r e e o f t h e s ix a lt e r n a ti v e s . W e s h a l l a ls o s ee

t h a t t h e t r a d i t i o n a l d i s t i n c t i o n b e t w e e n c o n t i g u o u s a n d c o n t i n u o u s e l e m e n t s

c a n n o t b e a r e a l d i s t i n c t i o n f o r D e s c a r t e s; a n d t h a t i t is i n a n y c a s e i n a p p l i c a b l e

t o d u r a t i o n l e s s i n s ta n t s . F i n a ll y , t h e i d e a t h a t D e s c a r t e s c o u n t e n a n c e d e x -

t e n d e d t i m e i n d i v i si b l e s, w h e t h e r f i n i te o r a c t u a l l y i n f in i t e l y s m a l l, is a l so r u l e d

o u t b y h is g e n e r a l p r i n c i p l e s ; a n d , c o n t r a r y t o g e n e r a l b e l ie f , r e c e iv e s n o

s u p p o r t f r o m e i t h e r h is a d v o c a t i o n o f d i s c o n t i n u o u s c h a n g e s o f m o t i o n o r h i s

a n a ly s is o f m o t i o n i n t o i n s t a n t a n e o u s s ta te s .

B u t t hi s is q u i t e e n o u g h p r e v ie w . L e t m e n o w t u r n t o a c o n s i d e r a t i o n o f t h e

s t a n d a r d i n t e r p r e t a t i o n o f C a r te s i a n t im e .

2 THE ARGUMENT FROM CONTI N UOUS CREATI ON

E x c e p t i n G u e r o u l t ' s c as e , a n d t o a l e ss e r e x t e n t K e m p S m i t h' s, t h e a r g u m e n t

f o r t h e c la s si c t h e s i s is s e l d o m s t a t e d e x p l i c it l y . T h i s i s b e c a u s e i t is g e n e r a l l y

s u p p o s e d t h a t o n l y a d is c o n t i n u o u s t i m e w o u l d h e c o m p a t i b l e w i th D e s c a r t e s '

v e r s io n o f t h e d o c t r i n e o f C o n t i n u o u s C r e a t i o n . S o l e t u s b e g i n b y f ir st e x a m i n -

i n g t h e i m p l i c i t a r g u m e n t t h a t t h e c l as s ic t h e s is is e n t a i l e d b y t h is d o c t r i n e .

A c c o r d i n g t o D e s c a r t e s , t h e w o r l d , c r e a t e d b y G o d w i th a c e r t a i n f o r c e in

t h e f i rs t m o m e n t o f ti m e , r e q u i r e s t h e s a m e f o r c e a n d a c t io n t o k e e p i t i n

e x i s t e n c e a t a n y s u b s e q u e n t m o m e n t o f i ts e x i s t e n c e , s in c e t h e r e i s n o p r i n c i p l e

i n h e r e n t i n a n y s u b s t a n c e b y w h i c h i ts e x i s t e n c e a t a l a te r t i m e m i g h t f o l lo w

f r o m i ts e x i s t e n c e a t a n e a r l i e r t i m e . T h i s is D e s c a r t e s ' v e r si o n o f t h e t r a d i-

t io n a l S c h o l as t ic d o c t r i n e o f C o n t i n u o u s C r e a t io n . 9 I t is s t a te d c l e a rl y b y h i m

s O f course, time could be discontinuous w ithout being discrete. Leibniz, for exam ple, held

that ev ery interval of time is actually infinitely divided into con tiguous finite parts, so that for h im

no interval or par t o f time is actually infinitely small or indivisible. (See my Leibniz on Continu-

ity,

PSA

111986]: lo7 -1 15 , f or a short accoun t of Leibniz's heory o f continuity. I ho pe to publish

a fuller treatment in a forthcoming

book, The Labyrinth of the Continuum.

But since no o ne has

attributed s u c h discontinuous-but-not-discrete conception of time to Descartes, I shall not

consider i t furth er here.

9 See l~tienne Gilson's Com me ntary o n D escartes'

Discours de la M~thode

(Paris: J. Vr in, 1925),

34o -42 , fo r a discussion of th e precise similarities and differences between Descartes' version of

this doctrine an d that o f St. Thom as Aquinas.



C O N T I N U O U S C R E A T I O N , C O N T I N U O U S T I M E 3 5 3

i n se v e r a l p l ac e s , b u t i t is t h e c e l e b r a t e d p a s s a g e o n c o n t i n u o u s c r e a t i o n i n t h e

t h i r d M e d i t a t i o n t h a t is u s u a l l y c i t ed a s e n t a i l i n g a n a t o m i s t ic c o n c e p t i o n o f

t im e . I n m y t r a n s l a t i o n , t h e l a t te r r u n s a s f o l lo w s :

F o r s i n c e m y w h o l e l if e t im e c a n b e d i v i d e d i n t o i n n u m e r a b l e p a r ts , e a c h o f w h i c h i n n o

w a y d e p e n d s o n t h e r e st , i t d o e s n o t f o l lo w f r o m m y h a v i n g e x is te d a s h o r t w h il e a g o

t h a t I m u s t e x i s t n o w , u n l e s s t h e r e i s s o m e c a u s e w h i c h c r e a t e s m e a s it w e r e a g a i n a t

t h i s m o m e n t , t h a t i s , c o n s e r v e s m e . F o r i t i s q u i t e c l e a r t o a n y o n e w h o a t t e n t i v e l y

c o n s i d e r s t h e n a t u r e o f t i m e t h a t t h e s a m e f o r c e a n d a c t i o n is p l a in l y n e e d e d t o

c o n s e r v e a n y t h i n g a t e a c h m o m e n t i t e n d u r e s a s w o u l d b e n e e d e d t o cr e a te i t a n e w i f it

d i d n o t y e t e x is t. T h u s t h e f a c t th a t t h e r e is o n l y a c o n c e p t u a l d i f f e r e n c e b e t w e e n

c o n s e r v a t i o n a n d c r e a t io n is a n o t h e r o f t h o s e t h in g s w h i c h a r e m a n i f e st e d b y t h e

n a t u r a l l i g h t . ' ~

T h e s t a n d a r d i n t e r p r e t a t i o n o f t h is p a s s a g e is a s f o ll o w s. D e s c a r t e s a r g u e s t h a t

a t i m e - - - w h i c h h e r e is a c o n c r e t e t i m e o r d u r a t i o n , t h e t im e f o r w h i c h s o m e

p a r t ic u l a r t h i n g e x is ts -- -i s c o m p o s e d o f i n n u m e r a b l e m u t u a l l y i n d e p e n d e n t

p a r t s , o r m o m e n t s . S i n ce e x i s t e n c e a t e a c h o f t h e s e m o m e n t s is w h o l l y c o n t i n -

g e n t , a n d d o e s n o t a t al l f o l lo w f r o m e x i s t e n c e a t a p r i o r m o m e n t , i t is n e c e s -

s a ry f o r G o d t o r e c r e a t e e v e r y t h i n g i n ea c h s e p a r a t e m o m e n t a t w h i c h i t

e n d u r e s . T h u s t h e w o r l d is c r e a t e d i n a d i s c o n t i n u o u s s u c c es s io n o f d i s c re t e

a c ts , a n d i ts d u r a t i o n , c o r r e s p o n d i n g l y , is a d i s c o n t i n u o u s s e q u e n c e o f d i s c r e te

m o m e n t s .

T o b e ex p l ic i t, t h e r e a r e t h r e e k e y a s s u m p t i o n s i n t h is li n e o f a r g u m e n t .

F i r st , i t is a s s u m e d t h a t D e s c a r t e s r e g a r d e d t i m e a s c o m p o s e d o f m o m e n t s , a s

h is m e n t i o n o f m o m e n t s a l m o s t i n th e s a m e b r e a t h a s t h e i n n u m e r a b l e p a r t s

o f t im e a p p e a r s t o s u g g e s t . S e c o n d l y , t h e fa c t t h a t t h e s e p a r t s a re d e s c r i b e d

a s m u t u a l l y i n d e p e n d e n t is t h e n t a k e n t o m e a n t h a t th e m o m e n t s c o m p o s i n g

t i m e a r e s e p a r a t e a n d d i s t i n c t f r o m e a c h o t h e r , i n t h e w o r d s o f K e m p S m i t h

S t u d i e s ,

1 3 1) , s o t h a t t h e y f o r m a d is c r e te r a t h e r t h a n a c o n t i n u o u s w h o l e .

A n d t h i r d l y , i t is s u p p o s e d t h a t t h is i n t e r p r e t a t i o n o f D e s c a r t e s ' t i m e a s d is -

,o Meditations

3: AT , 7:48-4 9, m y t ransla tion. Th e Lat in text i s: Qu oniam enim omn e

tempus vi tae in partes innumeras dividi potest , quarum singulae a rel iquis nullo modo depen-

dent , ex co qu/ )d paulo ante fuer im, n on sequi tur m e nu nc deb ere esse , ni si al iqua causa me quasi

rursus c ree t ad hoe momentum, hoe es t me conserve t . Perspicuum enim es t a t tendent i ad

temporis n a turam , e~ldem plane vi & ac t ione op us esse ad re in quam l ibe t s inguli s mom ent i s

quibus d ura t conserv andam , quit opus esse t ad ea ndem de n ovo creandem , s i no nd um exis te ret ;

adeo ut c ons ervatio nem sol~t rat ion e /~ creat ion e d ifferre, si t et iam un um ex i is qu ae lum ine

natural i man ifesta sunt .

~ ' Cf . No rm an K em p Smi th: As Descar tes f rankly recognised, he is here com mit t ing himsel f

to yet anoth er thesis, viz. that t ime is com po sed o f durat ionless instants. New S tud ies in the

Philosophy o f Descartes

(L on do n: MacMillan, 1952), 2o2. He rea fter ci ted as

Ne w Studies.



3 5 4 J O U R N L O F T H E H I S T O R Y O F P H I L O S O P H Y 2 6 : 3 JU LY a 9 8 8

c r e te i s s u p p o r t e d b y t h e d o c t r i n e o f c o n t i n u o u s c r e at io n , i n x h a t G o d c r e a t e s

t h e w o r l d a n e w a t e a c h s e p a r a t e m o m e n t . F o r u n l es s t h e w o r l d a c tu a ll y c e a s e d

t o e x is t a t t h e e n d o f e a c h m o m e n t , t h is r e c r e a t i o n w o u l d n o t s tr ic tl y b e

n e c e ss a ry . H e n c e , a c c o r d i n g t o K e m p S m i t h , th e d o c t r i n e o f c o n t in u o u s c r e-

a t i o n e n t a il s t h e d i s c r e t e n e s s o f t im e , a n d w i t h it a c o n c e p t i o n o f e x i s t e n c e a s

b e i n g l ik e a l in e c o m p o s e d o f d o t s , a r e p e a t e d a l t e r n a t i o n b e t w e e n th e s ta t e o f

b e i n g a n d t h e s t a te o f n o n - b e i n g

( S t u d i e s , 1 3 ~ ) .

B u t al l t h r e e o f t h e s e k e y a s s u m p t i o n s a r e q u e s t i o n a b l e . I n t h e f ir s t p l ac e ,

D e s c a r te s d o e s n o t e x p li ci tl y e q u a t e m o m e n t s w i th t h e i n n u m e r a b l e p a r ts o f

t im e i n t h e a b o v e p a s s a g e . O n a n e q u a l l y p l a u s ib l e r e a d i n g o f t h e p a s s a g e , th e

m o m e n t s c o u l d b e s im p l y t h e e n d p o i n t s o f th e i n n u m e r a b l e p a r ts ( o r fi ni te

i n te r v a ls ) i n t o w h i c h a n y c o n c r e t e t im e m a y b e d i v i d e d . N o r d o e s D e s c a r t e s

e v e r s ay a n y w h e r e e ls e t h a t t i m e i s c o m p o s e d o f m o m e n t s . C e r t ai n ly h e w r i te s

o f t i m e a s i n d e f i n i t e l y d iv i s ib l e , a n d a l s o a s c o n t a i n i n g m i n i m a l p o i n t s o r

m o m e n t s . B u t h e n e v e r e x p l i c i t l y c l a i m s t h a t t h i s i n d e f i n i t e d i v i s i o n r e a c h e s a

l im i t, o r t h a t m o m e n t s a r e t h e r e s u l t i n g i n d iv i si b le p a r t s o f s u c h a li m i t e d

d i v i s i o n . A t t h e l e a s t t h i s s h o u l d p r o m p t u s t o a s k : W h a t i n d e p e n d e n t e v i -

d e n c e i s t h e r e t h a t D e s c a r t e s c o n c e i v e d t i m e a s c o m p o s e d o f i n d iv i si b le m o -

m e n t s ? A n d c o u l d h e r e a l l y h a v e p r o p o s e d t e m p o r a l i n d i v i s i b l e s a f t e r h a v i n g

s o s c a th i n g l y d i s m i s s e d t h e p o s s i b i li t y o f i n d i v is i b le s i n s p a c e ? I s h a ll r e t u r n t o

t h e s e p o i n t s i n d e t a i l i n t h e f o l l o w i n g s e c t io n s .

S e c o n d l y t h e r e i s t h e l o g i c a l s l i p p a g e , a b l y p o i n t e d o u t b y L a p o r t e a n d

B e y s s a d e , b e t w e e n t h e c l a im t h a t t h e p a r t s o f t i m e a r e se p a r a b l e , i n d e p e n d e n t ,

a n d c o n t i n g e n t , a n d t h e c l ai m t h a t t h e y a r e a ct u a ll y s e p a r a t e d , a n d t h u s d i s-

c r et e . T h e s e p a r a b i li ty o r i n d e p e n d e n c e o f t h e p a rt s o f t im e b e c o m e s p a r u n

p r e m i e r g li ss e m e n t , i n B e y s s a d e 's a p p o s i t e t u r n o f p h r a s e , t h e i n d e p e n -

d e n c e o f d i s jo i n t , s e p a r a t e d , d i s c o n t i n u o u s i n s t a n ts ( B e y s s a d e , 17 ). G u e r o u l t ,

o n t h e o t h e r h a n d , w h o s e e m s t o e q u a t e s e p a r a b i l it y w i t h s e p a r a t i o n , c l a im s

t h a t d i s c o n t i n u i t y is p r e c i s e l y d e f i n e d b y t h e s e t h r e e c h a r a c te r i s ti c s , t o w i t

c o n t i n g e n c y , s e p a r a b i l i t y , a n d m u t u a l i n d e p e n d e n c e ( G u e r . , 2 7 3 / a 9 3 ) . I d o

n o t t h i n k t h i s is a t al l o b v i o u s . B u t a g a i n I s h al l p o s t p o n e d i s c u s s i o n o f t h is

po in t t i ll a l a t e r s e c t i on .

T h e r e is a th i r d w e a k n e s s in t h e t ra d i ti o n a l a r g u m e n t , a g a in p o i n t e d o u t b y

L a p o r t e , t h a t is p e r h a p s e v e n m o r e s t ri k in g . I s n ' t i t c o n t r a r y t o l a n g u a g e a s

w e l l a s g o o d s e n s e , h e as k s , t o d e r i v e t h e d i s c o n t i n u i t y o f ti m e f r o m t h e f a c t

t h a t a f in i te b e i n g i s i n n e e d o f

c o n t i n u o u s

c rea t i on? '''~ Th a t t h i s is a s t r a in on

' Su r cette contingence Descartes fonde le besoin qu'a l '~tre fini d'une cr6ation con-

tinu6e : n'est-il pas con traire ~t la langue co m me au bon sense d'en tir er la discontinuit6 du

temps ? Laporte, 158-59




t h e n o r m a l u s a g e o f w o r d s is , I t h i n k , b e y o n d q u e s t i o n . I t is a t t e s t e d b y t h e

v a r i o u s s li ps a n d s li d e s in t e r m i n o l o g y t h a t o n e f i n d s i n p e o p l e ' s d i s c u ss i o n s o f

c o n t i n u o u s c r e a t i o n , w h i c h b e c o m e s c o n t i n u a l c r e a t io n , ,a o r c o n t i n u a l r e -

c r e a ti o n ,, 4 in o r d e r t o fi t t h e s t a n d a r d c o n c e p t i o n o f c r e a t i o n a s a c o n t i n u a l

r e p e t i t i o n o f a d i s c r e t e o r i g i n a l c r e a t i v e a c t. B u t D e s c a r te s h i m s e l f is c a r e f u l

n e v e r t o a s s e r t t h a t t h e r e is a n a c t u a l r e p e a t e d p r o d u c t i o n . H e a l w a y s q u a li f ie s

h i s d e s c r i p t i o n s w i t h a 'q u a s i ' o r a 'v e l u ti ': u n l e s s t h e r e i s s o m e c a u s e w h i c h

c r e a t e s m e a s i t w e r e a g a i n a t th i s m o m e n t , 5 ; u n l e s s t h e r e is s o m e c a u s e

w h i c h e f f e c t s m e a s

i t w e r e

a g a i n a t e v e r y s i n gl e m o m e n t ' 6 ; u n l e s s s o m e

c a u s e, n a m e l y t h e s a m e o n e t h a t p r o d u c e d u s i n t h e f ir s t p l ac e , c o n t i n u o u s l y

s o to s p e a k r e p r o d u c e s u s , t h a t i s, c o n s e r v e s u s . '17 T h i s p r a c t i c e i s e v e n f o l-

l o w e d in t h e F r e n c h t r a n s l a ti o n o f t h e

R e p l i e s

w h e r e D e s c a r t e s ' r e f e r e n c e t o

c o n t i n u a l r e p r o d u c t i o n is a g a i n c a r e f u l l y q u a l i f ie d b y a s o t o sp e a k . ' ' '8 I n

f a c t f o r D e s c a r t e s t h e r e is , f r o m t h e p o i n t o f vi ew o f G o d , o n l y o n e i n di v is i b le

a c t o f c r e a t i o n o f t h e u n i v e r s e , a s G u e r o u l t a dm i ts .~ 9

T h e p r o b l e m h e r e is t hi s. A c c o r d i n g t o D e s c ar te s , a n y t h in g h a s d u r a t i o n

o r e x i st s o n l y as lo n g a s i t is b e i n g c r e a t e d o r p r o d u c e d b y G o d . T h e r e f o r e i f

, s C f . W ah l , 2 3 : D i r e q u e i e s ch o s e s d u ren t , c ' e s t d i r e q u ' e l l e s s o n t c r (~es co n t i n u -

e l l e m e n t ; K e m p S m i t h ,

Studies

1 32 : T h i s a s s u m p t i o n o f t h e d i s c re t en es s o f t i m e D es ca r t e s

p a r t ly c o n c e a l s b y s p e a k i n g o f G o d a s con t i nua l l y co n s e rv i n g u s . ; an d G u e ro u l t ; 2 8 5 / 2 o 2 : co n -

t i n u a t io n i s n o t s y n o n y m o u s w i t h c o n t in u i t y , f o r i t c a n b e a c c o m p l i s h e d b y a r e p e t i t i o n o f t h e

d i s c o n ti n u o u s . T h e s o l e a c t o f c r e a t i o n . . , i s p r e s e n t a t e a c h in s t a n t o f c r e a t io n a s t h e c o n t in u a l

r e n e w a l o f e x i st e n ce . . .

~4 C f . A l a n G a b b e y, F o r c e a n d I n e r t i a , i n S t e p h e n G a u k r o g e r ,

Descar tes: Phi losophy M ath e-

m a t i c s andPhys i c s

(N ew J e r s ey : B a r n es an d N o b l e , 1 9 8 o ) , 3 o 2 n . 4 o . A s h e ack n o w l ed g e s , G ab b ey i s

s i m p ly f o l l o w i n g t h e i n t e r p r e t a t i o n o f D e s c a r t e s ' C o n t i n u o u s C r e a t i o n g i v e n b y G i l so n i n h i s

c o m m e n t a r y o n D e s c a r t e s '

Discourse

( c i ted ab o v e i n n o t e 9) , 3 4 ~ ~ .

~5 Medi tat ions 3 : A T , 7 : 49 : n i s i a l i qu a c a u s a m e q u a s i r u r s u s c r e e t a d h o c m o m e n t u m . S i n c e

I w r o t e t h e f i rs t d r a f t o f t h i s e ss a y a n e x c e l l e n t n e w t r a n s la t i o n o f m a n y o f D e s c a r te s ' i m p o r t a n t

w r i ti n g s h a s b e e n p r o d u c e d b y J o h n C o t t i n g h a m , R o b e r t S t o o t h o f f , a n d D u g a l d M u r d o c h : T h e

Phi losophical W ri t ing s of Descar tes

( C a m b r i d g e : C a m b r i d g e U n i v e r s i ty P r e ss , 1 9 85 ). F r o m n o w o n I

s h a ll ap p e n d r e f e r en c es to t h i s t r an s l a t i o n a s C S M a f t e r e ach o r i g i n a l l an g u a g e c it a t io n . F o r

i n s t an ce , t h i s q u o t a t i o n f ro m t h e M e d i t a ti o n s w o u l d b e c i t ed a s A T , 7 : 4 9 ; C S M .2 : 3 3 .

6 F i r s t Rep l i e s A T , 7 : 1 o 9 ; C S M , 2 : 7 9 : n i s i a l i q u a cau s a m e q u as i ru r s u s e f f i c i a t s i n g u l i s

m o m e n t i s .

7 Pr i nc i p l e s 1 , w A T , 8 :1 3 ; C S M , a : ~o o : n i s i a l i q u a cau s a , n e m p e ead em i l la q u a e n o s

p r i m u m p r o d u x i t , c o n t i n u b v e l u t i r e p r o d u c a t , h o c e st , c o n s et w e t.

s F i r s t Rep l i e s A T : 9 : 8 7 : u n l e s s t h e re w e re i n i t s o m e r ea l an d p o s i t i v e p o w e r , w h i ch , s o t o

s p eak , r ep ro d u ced i t co n t i n u a l l y [ s i c e n ' e s t q u ' i l y a i t en l u i q u e l q u e p u i s s an ce r6 e l l e e t p o s i t i v e ,

i a q u e ll e , p o u r a i n si d i r e , le r e p r o d u i r a c o n t i n u e l l e m e n t ] . T h i s c o r r e s p o n d s t o t h e L a ti n : n i si

a l i qu a p o t e n t i a i n e o s it i p s u m c o n t i n u o v e l u t i r e p r o d u c e n s ( A T , 7 : l

IO

CSM, 2:79)

,9 A n d ce r t a i n l y , t h e v a r i o u s c r ea t i o n s a r e r ea l l y o n l y o n e , s i n ce t h e c r ea t i v e ac t o f G o d i s i n

i t se l f o n e , a n d s i nc e i t w o u l d b e i n c o n c e i v a b l e f o r t h e m t o b e s e p a r a t e d b y in t e r v a ls o f d m e

(Guer . , 28o /a 99 ) .



3 5 6 J O U R N A L O F T H E H I S T O R Y O F P H I L O S O P H Y 2 6 : 3 J U L Y 1 9 8 8

God's creation or production is continuous, ~ then the duration of each cre-

ated t hing must likewise be continuous.

This creates a dilemma for those holding the discontinuist view, on one

of whose horns some authors have quite clearly become impaled. Jea n Wahl,

for instance, proposes that "creation is continuous because duration is not"

(Wahl, 18). This makes no sense at all in Descartes' philosophy, where things

endure precisely as long as they are created. Wahl tries to extricate himself

by arguing that continuous creation "is not properly speaking a veritable

continuous creation, for then there would have to be a continuous destruc-

tion. ''~ But this idea t hat a cont inuous creation would entail a continuous

dest ruct ion is precisely wrong If creation is truly continuous it will not be

interrupted at all. To say that it is continuous means that at any instant you

pick, you will find the world being created. It is only when conservation is

misunderstood as consisting in a continual reproduction, as the "repeated

alternation of being and non-being" posited by Kemp Smith and Wahl, that

there wou ld be any destruction.

In fact, we may here draw one preliminary conclusion which firmly refutes

the interpreta tion o f Wahl and Kemp Smith. This is that since duration is only

a mod e o f the existence of the universe for Descartes, it follows that there can

be no du rat ion devoid o f existence in his philosophy: there can be no tempo-

ral gaps, and thus n o "a lternation o f states of being and non-being." Descartes

is quite explicit on this point in his exchange with More: "I think it would

imply a contradic tion for us to conceive of some durati on between the destruc-

tion of a forme r world an d the creation of a new one. For, if we were to refer

this duratio n of yours to the succession of divine thoughts or something simi-

lar, this would be an error of the intellect, not a true perception of any

,o G u e r o u l t d e n i e s t h a t c o n t i n u o u s c r e a ti o n m e a n s c o n t i n u o u s p r o d u c t i o n : " C o n t i n u o u s c r e -

a t i o n is n o t a c o n t i n u a l p r o d u c t i o n :

Seipsura non comervare, sumendo creationem pro continua produc-

t ione. Fou rth Replies ( A T , 7 : ~ 4 3 , 1 . 5 " ( G u e r . , ~ 8 o / 3 1 6 n . 1 1 1) . B u t t h i s L a t i n t e x t i s m i s q u o t e d

(c rea t / onem shou ld r ead conservationem) a n d a l s o q u o t e d o u t o f c o n t e x t . D e s c a r t e s i s n o t d e n y i n g

t h a t c r ea t i o n is c o n t i n u o u s p r o d u c t i o n ; h e i s m e r e l y a g r e e i n g w i t h th e a u t h o r o f t h e Fourth

Objectiom

( A r n a u l d ) t h a t G o d c a n n o t b e s a i d to c o n s e r v e h i m s e l f in t h e s a m e s e n s e i n w h i c h h e

c o n s e r v e s t h i n g s : " G o d d o e s n o t i n f a c t c o n s e r v e h i m s e l f , i f w e t a k e c o n s e r v a t i o n t o b e t h e

c o n t i n u o u s p r o d u c t i o n o f t h e t h i n g " ( A T , 7 : 2 4 3; C S M , 2 :1 6 9 ), s in c e G o d c o u l d n o t p r o d u c e

h i m s e l f . A s h e m a k e s c l e a r i n t h e First Replies , D e s c a r t e s u n d e r s t a n d s G o d ' s c o n s e r v a t i o n o f

h i m s e l f " n o t a s w h a t h a p p e n s a s a r e s u l t o f a n y p o s i t i ve in f l u e n c e o f a n e f f i c i e n t c a u s e , b u t a s

c o n s i s t i n g so l el y in t h e f a c t t h a t t h e e s s e n c e o f G o d i s s u c h t h a t i t is i m p o s s i b le f o r h i m n o t t o e x i s t

a lw a y s [ n o n i n t e ll i g i c o n s e r v a t i o n e m q u a e f i a t p e r p o s i t i v u m u l l u m c a u s a e e f f ic i e n ti s i n f l u x u m ,

s e d t a n t ~ m q u b d D e i e s s e n t i a s i t t al is , u t n o n p o s s it n o n s e m p e r e x i s t e r e ] " (First Replies: A T , 7 : 1 o 9 ,

I I . 1 7 - 2 o ; C S M , e :7 9 ) .

9~ W a h l , 1 8: " C e n ' e s t p as u n e p e r p ~ t u e ll e r e p r o d u c t i o n , c e n ' e s t p a s ~ p r o p r e m e n t p a r l e r

u n e v * r i t a b le c r e a t i o n c o n t i n u ~ e , c a r i l f a u d r a i t a l o r s q u ' il y ai t u n e d e s t r u c t i o n c o n t i n u e . "




th in g. ~ * D e s c a r t e s ' a r g u m e n t f o r t h i s is t h e e x a c t c o r r e l a t e o f h i s r e j e c t i o n o f

v o i d s i n s p a c e . J u s t a s t h e i d e n t i fi c a ti o n o f m a t t e r a n d ( c o n c r e te ) e x t e n s i o n

r u l e s o u t t h e p o s s i b i l it y o f a v o i d s p a c e , s o t h e i d e n t i f ic a t i o n o f th e ( c o n c r e t e )

d u r a t i o n o f e a c h t h in g

as

a m e r e m o d e u n d e r w h i c h w e c o n c e iv e t hi s t h i n g

i n s o f a r a s i t s t a y s i n e x i s te n c e , 3 p r e c l u d e s t h e p o s s i b i li t y o f a n i n t e r v a l o f t i m e

d e v o i d o f e x i s te n c e . A s G u e r o u l t h i m s e l f d e c l a re s ,

In

f ac t , s i nce ex i s t ence i s

w h a t c o n s t i t u t e s d u r a t i o n , i n t e rv a l s w i t h o u t e x i s t e n c e w o u l d b e i n te r v a ls w i th -

o u t d u r a t i o n ; s o t h e r e c a n n o t b e i n te r v a ls w i th a v o i d d u r a t i o n ( G u e r . , 9 8 o /

1 9 9) . T h u s i t f o l lo w s i m m e d i a t e l y t h a t a n y c o n c e p t i o n o f C a r t e s i a n t i m e a s

c o n t a i n in g g a p s is u n t e n a b l e . T h i s u n a m b i g u o u s l y r u l es o u t t h r e e o f t h e s ix

a l te r n a t iv e s o p e n t o D e s c a r t e s f o r a t im e c o m p o s e d o f i n di v is ib l es , t h e t h r e e

g a p - d i s c o n t i n u o u s m o d e l s t h a t w e c o n s i d e r e d i n t h e fi rs t s e c t io n o f t h e

p a p e r . F o r D e s c a r te s t h e r e c a n n o t b e a n a l te r n a ti o n o f ex i s te n c e a n d n o n -

e x i s t e n c e i n t im e ; t h e r e c a n n o t b e a n y g a p s i n tim e.~ 4

B u t t h e f u r t h e r f a c t t h a t e x i s t e n c e d e p e n d s o n G o d ' s c o n t i n u o u s p r o d u c -

t io n m a k e s a n y d i s c o n t i n u i s t m o d e l o f C a r t e s i a n t im e d i f fi c u l t t o u p h o l d . I f

e x i s t e n c e is a c o n t i n u o u s e f f e c t , t h e n s o is t h e r e s u l t a n t d u r a t i o n o f t h e t h i n g s

c r e a t e d .

C o n n e c t e d w i t h t hi s is t h e e x e g e t i c a l p r o b l e m o f w h y D e s c a r t e s w o u l d i n t ro -

d u c e t h e h y p o t h e s i s o f t h e d i s c o n t i n u i t y o f t im e i n o r d e r t o e x p l a i n t h e e q u i v a -

l e n c e o f c r e a t i o n a n d c o n s e r v a t i o n . S u r e l y i f c r e a t i o n is r e a ll y d i s c o n t i n u o u s ,

t h e n i t c a n n o t b e e q u i v a l e n t t o c o n s e r v a t i o n : r e p e a t e d c r e a t i o n is, o n e w o u l d

t h in k , t h e v e r y o p p o s i t e o f c o n s e r v a t i o n . ( S u p p o s e f o r i n s ta n c e t h a t w e c o u l d

r e c r e a te m a m m o t h s b y c lo n i n g c ells o f t h e ir f r o z e n r e m a i n s, a n d t h a t w e d i d s o

e v e r y t i m e th e s p e c ie s b e c a m e e x t in c t . T o c a ll t h is a c o n s e r v a t i o n p r o g r a m

w o u l d s u r e ly b e r e g a r d e d a s a n a b u s e o f l a n g u a g e o f O r w e l li a n p r o p o r t i o n s . )

O n t h e o t h e r h a n d , i f c r e a t i o n i s t r u l y c o n t i n u o u s ( i.e ., G o d e x e r t s t h e s a m e

f o r c e c o n t in u o u s l y ) , t h e n c r e a ti o n a n d c o n s e r v a ti o n r e a ll y d o a m o u n t t o t h e

s a m e t h i n g , a n d t h e d i s t in c t i o n b e t w e e n t h e m is s o le l y o n e o f re a s o n .

22 D e s c a r t e s t o M o r e , 1 5 A p r i l 1 6 4 9 , A T , 5 : 3 4 3 , 1 1 . 1 - 7 : P u t o i m p l i c a r e c o n t r a d i c t i o n e m , u t

c o n c i p ia m u s a l i q u a m d u r a t i o n e m i n t e r c e d e r e i n t e r d e s t r u c t io n e p r i o r is m u n d i & n o v i c r e-

a t i o n e m . N a m , s i d u r a t i o n e m i s ta m a d s u c c e ss i o n em c o g i t a t io n u m d i v i n a r u m v e l q u i d s i m i le

r e f e r a m u s , e r i t e r r o r i n t e ll e c tf l s, n o n v e r a u l l iu s re i p e r c e p t i o . N o t e t h e a l m o s t i d e n t i ca l f o r m o f

t h i s w o r d i n g t o t h a t o f D e s c a r t e s ' o b j e c t i o n t o a t o m s i n h i s e a r l ie r l e t te r t o M o r e , 5 t h F e b r u a r y ,

1 6 4 9 : A T , 5 :~ ,7 3, q u o t e d b e l o w o n 3 6 7 .

s P r i n c i p l e s I , w A T , 8 : 2 6 ; C S M , 1 : 2 11 .

24 W a h l r e a li z e s t h a t h i s i n t e r p r e t a t i o n c o n t r a d i c t s D e s c a r te s ' a s s e r t i o n o f t h e s e lf -

c o n t r a d i c t o r i n e s s o f a n e m p t y t i m e , b u t n e v e r p r o p e r l y r e s o l v e s t h e d i f f i c u l t y . T h u s o n 2 4 w e

a g a i n f i n d h i m a s s e r t i n g t h a t D u r a t i o n i s t h e f a c t t h a t t h e t h i n g w h i c h e n d u r e s c e a se s t o b e a t

e v e r y m o m e n t ( 7 : 3 7 o ). W a h l ' s r e f e r e n c e h e r e i s t o D e s c a r t e s ' c o n t r o v e r s y w i t h G a s s e n d i . A s w e

s h a l l s e e b e l o w , D e s c a r t e s o n l y a r g u e s t h e r e t h a t i t is p o s s ib l e f o r a t h i n g t o c e a s e t o e x i st a t a n y

m o m e n t .



3 5 8 J O U R N A L O F T H E H I S T O R Y O P H I L O S O P H Y 2 6 : 3 J UL Y 1 9 8 8

T h u s w e se e t h a t f a r f r o m s u p p o r t i n g t h e i d e a o f a d i s c r e tc t i m e , D e s c a r t e s '

i n t e r p r e t a t i o n o f c o n t i n u o u s c r e a t i o n a c tu a l ly u n d e r m i n e s i t.

3 T H E A R G U M E N T F R O M T H E I N D I V I S I B I L I T Y O F T H E C R E A T I V E A C T

A m o r e p r o m i s i n g d e f e n c e o f t h e cl as si c t h es is is t h a t o f G u e r o u l t . H e a r g u e s

t h a t t h e c r e a t i v e a c ts o f G o d a r e n e c e s s a r il y in d iv i si b le , a n d t h a t c o n s e q u e n t l y

s o m u s t b e t h e m o m e n t s o f th e d u r a t i o n o f e ac h t h in g h e c r e a te s .

T h e a c t o f c r e a t i o n is t h e a c t o f p u t t i n g i n t o d u r a t i o n o r i n t o e x i s te n c e . . . T h i s a c t is

t h e m e a n s b y wh i ch s o m e t h i n g , o n b e i n g p r o m o t e d i n t o d u r a t i o n a n d e x i s t e n c e, a r is e s

o u t o f n o n - b e i n g i n a n i n s t a n t w h i ch i s n o t a f r a g m e n t o f t h e e n d u r i n g c r e a t e d t h i n g ,

b u t t h e m o m e n t o f t h e f r e e a n d i n d iv i si b le d e c is i o n wh i ch e s t ab l is h e s t h e t h i n g i n i ts

d u r a t i o n . . . . I n t h is i n d i vi s ib l e a c t is f o u n d t h e p r i n c i p l e o f t h e r a d i c a l a n d e s s e n ti a l

ind iv i s ib i l i ty o f t empora l ins tan t s , o f the i r d i scon t inu i ty , wh ich i s iden t i ca l to the i r

c o n t i n g e n c y a n d f o u n d e d o n it. ( Gu e r . , ~ 74 /1 94 )

B u t a g a i n t h e r e is s o m e l o g i ca l s l i p p a g e h e r e . D e s c a r t e s d o e s n o t s a y t h a t t h e

a c t o f c r e a t i o n is t e m p o r a l l y i n d i v i s ib l e . I t w i ll o f c o u r s e b e i n d i v is i b le w i t h

r e s p e c t t o it s o w n n a t u r e , j u s t a s G o d h i m s e l f is . B u t t h is is n o t t h e s a m e t h i n g ,

a s D e s c a r t e s m a k e s c l e a r i n h is Conversation with Burman. F o r i n t h e c o n t e x t o f

d i sc u s s i n g t h e i n s t a n ta n e i t y o f th o u g h t , B u r m a n a t t e m p t s t o t r a p D e s c ar t es

w i t h t h e s a m e l o g i c as G u e r o u l t . , 5 S i n c e t h o u g h t i s i n d iv i s ib l e , h e r e a s o n s , i t

m u s t b e i n s t a n t a n e o u s ; f o r i f i t is n o t i n s t a n t a n e o u s , b u t c o n t i n u o u s , i t w ill b e

d i v i s i b l e t o i n f i n i t y . T h i s i s e x a c t l y p a r a l l e l t o G u e r o u h ' s a r g u m e n t f r o m t h e

i n d iv i s ib i li t y o f G o d ' s c r e a t i v e a c t t o i t s i n s t a n t a n e i t y , s o D e s c a r t e s ' r e p l i e s w i ll

b e p a r t i c u l a r l y i n s t r u c t i v e .

B u r m a n b e g i n s h is a r g u m e n t w i t h a n a t t e m p t t o d e m o n s t r a t e a c i rc u l ar i ty

i n D e s ca r te s ' s e c o n d p r o o f o f t h e e x i s t en c e o f G o d i n th e T h i r d M e d i t a t io n ,

p o i n t i n g o u t t h a t o n e c o u l d n o t p a y a t t e n t i o n t o a ll t h e a x i o m s o f t h e p r o o f a t

o n c e , si n ce " e v e r y t h o u g h t o c c u r s in s t a n ta n e o u s l y , a n d t h e r e a r e m a n y

t h o u g h t s t h a t c o m e to m i n d i n t h e p r o o f " ( C W B , 1 1: 6 1 1 . 1 2 - 1 3 ; A T , 5 : 1 4 8 ) .

T o t h is D e s c a r t e s r e p l i e s: " i t is f a ls e th a t t h o u g h t o c c u r s i n s t a n t a n e o u s l y ; f o r

a ll m y a c ts t a k e p l a c e in t i m e , a n d I c a n b e s a id t o b e c o n t i n u i n g a n d c a r r y i n g

o n w i t h t h e s a m e t h o u g h t f o r s o m e t i m e " ( ib id ). N o w I s u g g e s t t h a t e x a c tl y t h e

s a m e is t r u e o f G o d ' s a c t o f c r e a t i o n . A l t h o u g h h e i s c r e a t in g t h e w o r l d a t e a c h

i n s ta n t , j u s t a s I a m t h i n k i n g a t e a c h i n s t a n t , t h e a c t o f c r e a t i o n i t s e lf is c o n t i n u -

o u s o v e r t im e .

B u t G u e r o u l t c a n n o t a c c e p t th is . R e m i n d i n g u s th a t " t h e p r o p e r t i e s o f t h e

c r e a t u r e a r e n o t n e c e s s ar i l y th e s a m e a s t h e p r o p e r t i e s o f th e C r e a t o r " ( G u e r . ,

9 Descartes' Conversation withBurman translated with introduction an d comm entary by Joh n

Cottingham (Oxford: C larendon Press, 1976), comm ent num ber 11, page 6. H ereafte r cited as

"CW B" with page num ber.




2 8 5 /2 O I - -2 ) , h e u r g e s u s t o a c c e p t t h a t t h e r e a r e f o r D e s c a r t es t w o f u n d a m e n -

t al ly d i f f e r e n t w a y s o f c o n s i d e r i n g t im e . T h e r e is " t h e p o i n t o f v i ew o f c r e a t e d

t h in g s , o r o f t h e a b s t r a c t " ( 2 8 o - 8 1 / 1 9 8 - 9 9 ) , w h e r e o n e s ay s t h a t a ll t h o u g h t

a n d m o t i o n o c c u p y a c o n t i n u o u s t i m e ( 2 7 5 h 9 5 & ff ) ; a n d , o n t h e o t h e r h a n d ,

t h e r e is " t h e p o i n t o f v i e w o f c r e a t i o n a n d o f t h e c o n c r e t e ," w h e r e , o n t h e

c o n t r a r y , t i m e is c o n c e i v e d a s a " r e p e t i t i o n o f in d i v is i b le a n d d i s c o n t i n u o u s

c r e a t i v e i n st a n t s" ( 2 7 5/ 1 9 5) , a n d a ll t e m p o r a l m o t i o n a r i se s f r o m " t h e r e p e t i -

t i o n o f i n s t a n t s o f m o t i o n " (2 8 1 / 1 99 ).2 6

B u t D e s c a r t e s r e l ie s o n n o s u c h d i s ti n c ti o n b e t w e e n t h e p o i n t s o f v i ew o f

c r e a t e d a n d c r e a t i o n in hi s e x c h a n g e w i th B u r m a n . F o r w h e n B u r m a n n o w

c o n f r o n t s h i m w i t h t h e o b j e c t i o n t h a t i f t h o u g h t is n o t i n s t a n t a n e o u s , b u t

c o n t i n u o u s t h r o u g h t i m e , t h e n " [ it ] w il l b e e x t e n d e d a n d d i v is i bl e ," h e r e p l ie s :

" N o t a t a ll . T h o u g h t w i ll i n d e e d b e e x t e n d e d a n d d i v is i b le w i t h r e s p e c t t o i ts

d u r a t i o n , s i n c e i ts d u r a t i o n c a n b e d i v i d e d i n t o p a r t s . B u t i t is n o t e x t e n d e d

a n d d i v is i b le w i th r e s p e c t t o i ts o w n n a t u r e , s i n ce it s n a t u r e r e m a i n s u n e x -

t e n d e d . I t is t h e s a m e w a y w i th G o d : w e c a n d i v i d e h is d u r a t i o n i n t o a n i n fi n i ty

o f p a r ts , e v e n t h o u g h G o d h i m s e l f is n o t t h e r e f o r e d i vi si b le " (C W B , i 1: 6 ; A T ,

5 : I 4 8 ) .

T h u s , f a r f r o m c o n t r a s t i n g t h e p o i n t o f v i ew o f t h e c r e a t o r w i t h th a t o f t h e

c r e a t e d , D e s c a r t e s e x p l i c i tl y p o si t s t h e i r a n a l o g y . H i s d i s ti n c t io n h e r e i s r a t h e r

b e t w e e n c o n s i d e r in g s o m e t h i n g - - a t h o u g h t , a n a ct , o r e v e n G o d h i m s e l f in

r e s p e c t o f it s o w n n a t u r e , w h e n i t is n e c e s s a r i l y o n e t h i n g , i n d iv i s ib l e ; a n d

c o n s i d e r i n g t h e s a m e t h i n g i n re s p e c t o f it s d u r a t i o n , i n w h ic h r e s p e c t i t c a n b e

r e g a r d e d a s c o n t i n u o u s , a n d t h u s i n d e f in i t e l y d i vi si bl e. T h e r e is t h e r e f o r e n o

r e a s o n w h y t h e s a m e a n a l y si s s h o u l d n o t a p p l y a ls o to G o d ' s a ct o f c r e at i o n :

t h e r e is o n l y o n e s u c h a c t , w h i c h a l t h o u g h u n e x t e n d e d a n d i n di v is ib l e w i t h

r e s p e c t t o i t s o w n n a t u r e , is n o n e t h e l e s s e x t e n d e d a n d d iv is ib le w i th r e s p e c t t o

i ts d u r a t i o n , w h i c h i s c o n t i n u o u s ( c o n t i n u o u s c r e at i on ) . T h i s m e a n s t h a t a t a n y

i n s t a n t w e p i c k , t h e r e is c r e a t i o n , a s e v i d e n c e d b y t h e i n s t a n t a n e o u s a c ti v it y o f

c o r p o r e a l t h i n g s . 2 7

9 Th is distinction o f Gueroult 's between the two "points of view" is derived from He nri

Bergson's influential interpretation o f Descartes in his Creative Evolution, transl. Arthur Mitchell

(New York: He nry H olt & Co . , 1911) . According to Bergson, the abstract world of m odern

mathematical physics "is a world that dies and is reborn at every insta nt--th e w orld which Des-

cartes was thinking of when he spoke of continued creation" (22). But this cinematographical

conception of tim e is complemented in Descartes ' thoug ht by "a time in which there is invention,

creation, true succession" (Bergson's real duration), wh ich is supp orted by "a God w ho is unceas-

ingly renewing the creative act" (345)- H ad Descartes followed out this point o f view, "creation

would have appea red n ot simply as continued, but also as continuous (346).

,7 Gue rou lt quotes Descartes' "instantaneous activity signifies creation", fro m his

Olympian

Matters, A T, lo:218; CSM , 1: 5, in the belief that it supports his claim that a cts of creation a re

instantaneous an d discontinuou s. But this confuses the instantaneous activity of bodies wi th the



36

J O U R N A L O F T H E H I S T O R Y O F P H I L O S O P H Y 2 6 : 3 J U L Y

1988

S o f a r, t h e n , m y a r g u m e n t s u p p o r t s L a p o r t e o v e r G u e r o u l t . I r o n ic a ll y ,

t h o u g h , t h e s e s a m e c o n s i d e r a t i o n s c o n c e r n i n g t h e i nd iv i si b il it y o f c r e a t io n a r e

e q u a l l y f a ta l t o L a p o r t e ' s a r g u m e n t f o r t h e c o n t i n u i t y o f t im e . F o r h a v i n g

a r g u e d a g a in s t t h e a c c e p t e d v ie w th a t t i m e is d i s c o n ti n u o u s , c o m p o s e d o f

i nd i vi si bl e m o m e n t s , L a p o r t e r e b o u n d s t o t h e o t h e r e x t r e m e : h e c la im s t h a t

D e s c a r t e s ' m o m e n t s a r e t h e m s e l v e s e x t e n d e d a n d i n d e f i n i t e l y d i v i s i b l e . T h i s

o p e n s u p h is w h o l e p o s i t io n t o r e f u t a ti o n , w h i c h G u e r o u l t d u l y p r o v i d e s w i th

s o m e d e v a s t a t i n g c r i ti ci sm s b a s e d o n D e s c a r t e s ' p h y s ic s . B e f o r e e x a m i n i n g

t h e s e , h o w e v e r , it is w o r t h n o t i n g t h a t L a p o r t e ' s m a i n a r g u m e n t f o r t h e d iv is i-

b ili ty o f m o m e n t s c o n t a i n s m u c h t h e s a m e e r r o r a s G u e r o u l t ' s a r g u m e n t f o r

thei r indivis ibi l i ty .

H i s r e a s o n i n g i s a s f o l l o w s . D e s c a r t e s e x p l i c i t l y s a y s ( i n C W B c i t e d a b o v e )

t h a t all t h o u g h t o c c u p i e s a n e x t e n d e d d u r a t i o n , s o t h e i n d iv i si b le

intui tus

p r e v io u s l y t h o u g h t t o b e i n s t an t a n e o u s , m u s t b e u n d e r s t o o d a s t a k in g p l a c e

o v e r a m o m e n t w h i c h is i ts e l f e x t e n d e d : S o l et u s n o l o n g e r s p e a k o f in s t a n ts

i n t h e a t o m i c s e n s e o f t h e t e r m . ' ', s

T h i s a r g u m e n t f o u n d e r s o n t h e s a m e r e e f a s G u e r o u h ' s , n a m e l y t h e f ai lu r e

t o p a y h e e d t o D e s c a r t e s ' d i s t in c t i o n b e t w e e n t h e i nd i vi si bi li ty o f t h e

intui tus

w i t h r e s p e c t t o it s o w n n a t u r e , a n d i ts d iv i si bi li ty a n d e x t e n d e d n e s s i n d u r a -

t i o n . O n e t h o u g h t c a n t a k e p l a c e o v e r a n e x t e n d e d t i m e w i t h o u t b e i n g d i v i s i -

b le q u a t h o u g h t . T h e f a c t t h a t o n e c a n b e i n th e a c t o f th i n k in g t h e t h o u g h t a t

a n y g i v e n i n s t a n t d o e s n o t i m p l y t h a t t h a t i n s t a n t i s e x t e n d e d .

4 C O N C R E T E D U R A T I O N V S . A B S T R A C T T I M E

A t t h is p o i n t w e s h o u l d l o o k a l it tl e m o r e c l o s e ly a t D e s c a r t e s ' d i s t in c t i o n

b e t w e e n c o n c r e t e a n d a b s t r a c t ti m e , a s p r e s e n t e d b y h i m i n h is r e p l y to

G a s s e n d i ' s c r i ti c i sm s o f t h e

Meditations.

F o r a m a j o r s o u r c e o f t h e e r r o r u n d e r -

l y in g G u e r o u l t 's a r g u m e n t f o r t h e d i s cr e te n e s s o f t im e s te m s , in m y v ie w , f r o m

t h e p e c u l i a r w a y in w h i c h h e d e p i c t s t h is d is t in c t io n b e t w e e n c o n c r e t e a n d

a b s t r a c t ti m e a s c o r r e s p o n d i n g t o a d is t in c t io n b e t w e e n t h e p o i n t s o f v ie w o f

c r e a t o r a n d c r e a t e d . A s I s e e i t, t h e d i s t i n c t io n is f a r l e ss f a n c i f u l . D e s c a r t e s

c rea t i v e ac t iv i t y o f G o d t h a t t h i s s ig n i f ie s ; an d , m o re i m p o r t an t l y , i t a l s o co n fu s e s ac t iv i t y w i t h ac t .

F o r w h i l s t t h e ac t i v i t y o f s u b s t an ces ( t h e co n a t u s o f b o d i e s an d t h e t h i n k i n g o f s ou l s) m ay b e s a i d

t o b e i n s t an t an e o u s , i n t h a t t h e s u b s t an ces a r e ac t i n g a t ev e ry i n s t an t , t h e ac t s t h em s e l v es (m o t i o n ,

t h o u g h t ) t a k e p l a c e o v e r a p e r i o d o f c o n t i n u o u s t i m e . S o G u e r o u h i s q u i t e w r o n g t o s ay th a t L i k e

l i g h t , t h o u g h t is i n s t an t an eo u s (G u e r . , 2 8 1 /1 9 9 ) .

, s N e p a r l o n s d o n c p l u s d 'i n s t an t s au s en s a t o m i q u e d u t e rm e , n i d e p en s 6 e i n st an t an 6 e .

T o u t e p e n s ~ e , d it e x p r e s s 6 m e n t D e s c a r te s , a ' f i e u d a n s l e te m p s , e t e l le o c c u p e d u t e m p s . E t

p a r t a n t , l e p r 6 s e n t d e l a p e n s ~ e n e p e u t d 6 s i g n e r . . , q u ' u n s e g m e n t tr 6 s c o u r t d e d u r 6 e .

L ' i n t u i tu s , q u i e s t I ' a c t e d e p en s 6 e co r r e s p o n d an t ~t l a p rae sens ev/ den t/ a, en v e l o p p e q u e l q u e d u r6 e

d an s s o n u n i t 6 (L ap o r t e , 1 59 ) .



C O N T I N U O U S C R E A T I O N , C O N T I N U O U S T I M E 3 61

d o e s n o t a c tu a l ly u s e t h e t e r m ' c o n c r e t e '. B u t w h a t h e o p p o s e s to a b s tr a c t ti m e

is t h e d u r a t i o n o f t h e e n d u r i n g t h in g . T h u s a c o n c r e te d u r a t i o n is s im p l y th e

s p ec if ic d u r a t i o n o f s o m e e n d u r i n g s u b s ta n c e , a s o p p o s e d t o th e i d e a o f g e -

n e r i c t i m e o r d u r a t i o n - i n - g e n e r a l . T h e l a t t e r i s a n i d e a l c o n c e p t , f o r m e d b y

a b s t r a c t io n f r o m t h e d u r a t i o n s o f a ll p a r ti c u l a r s u b s t a n c e s, j u s t a s s p a c e o r

e x t e n s i o n - i n - g e n e r a l is a n a b s t r a c t c o n c e p t f o r m e d b y a b s t r a c t in g f r o m a ll t h e

p a r t i c u l a r e x t e n s i o n s o f p i e c e s o f e x i s t in g e x t e n d e d m atte r.~ 9

T h u s i n D e s c a r t e s ' p h i l o s o p h y a n a b s t r a c t t h i n g , f a r f r o m b e i n g a c r e a t e d

t h i n g a s G u e r o u l t w o u l d h a v e i t, is n o t s o m e t h i n g w h i c h c a n e x i s t b y i ts e l f i n

t h e w o r l d ; it is s o m e t h i n g i n c o m p l e t e , l ik e a n u m b e r c o n c e i v e d a p a r t f r o m

t h i n g s n u m b e r e d , o r a s u b s t a n c e c o n c e i v e d a p a r t f r o m its a tt ri bu te s .3 o C o r r e -

s p o n d i n g l y , t h e t e r m ' c o n c r e t e ' w o u l d s i g n if y a n a c t u a ll y e x i s ti n g t h i n g a n d

t h e a t t r i b u t e s a s s o c i a t e d w i t h i t, a t h i n g k e p t in e x i s t e n c e b y G o d ' s c r e a t i v e

p o w e r . T h u s , i t is t r u e , t h e r e is s o m e c o n n e c t i o n w i t h G u e r o u l t ' s c r e a t io n o f

e x i s te n c e . B u t a c o n c r e t u m i s n e v e r t h e l e s s t h e c r e a t e d t h i n g , n o t t h e th i n g

f r o m t h e p o i n t o f v i e w o f t h e c re a t o r . G u e r o u l t ' s d i st in c t io n b e t w e e n t h e t w o

p o i n t s o f v i e w o w e s m u c h t o B e r g s o n , b u t l it tl e t o D e s c a r te s .

N e v e r t h e l e s s , e v e n c o m m e n t a t o r s w h o w o u l d f i n d li tt le o b j e c t i o n a b l e i n m y

r e n d e r i n g o f th e a b s t r a c t / c o n c r e t e d i s t in c t io n h a v e s e e n th e w o r d i n g o f D e s -

c a r t e s ' r e p l y t o G a s s e n d i a s s u p p o r t i n g t h e c la s si c t h es is .3 ' S o l e t u s l o o k a l it tl e

m o r e c l o s e l y a t D e s c a r t e s ' a p p e a l t o t h is d i s ti n c t i o n i n h i s c o n t r o v e r s y w i t h

G a s s e n d i .

G a s s e n d i o b j e c t e d to t h e p a s s a g e in t h e T h i r d M e d i t a ti o n q u o t e d a b o v e o n

t h r e e c o u n t s : f i rs t, th a t t h e p a r t s o f t im e , f a r f r o m b e i n g m u t u a l l y i n d e p e n -

d e n t o r s e p a r a b l e , f o r m a n i n v io l a b le s e ri e s a n d c o n n e c t i o n , w i t h t h e p o s t e -

r i o r p a r t s d e p e n d i n g o n t h e p r io r.a 2 S e c o n d l y , s in c e th e p a r t s o f ti m e a r e

e x t e rn a l , s uc c es s iv e a n d n o t a ct iv e , t h e ir d e p e n d e n c e o r i n d e p e n d e n c e o n

9 Descartes also acknowledges that time may be "distinguished from du ration taken in the

general sense" ( P r i n c i p l e s , 1, w AT, 8:27; CSM, 1:212); this is time in the sense of "the measu re

of motion," a mea sure which we abstract from the durati ons of certain privileged motions, such as

the day or t he year. But, as he makes clear, in distinguishing this time from duration- in-general ,

"noth ing is there by adde d to durat ion in its general sense except for a mode of thou ght" (ibid.).

This is still, even as a mathematical quantity, an ideal concept abstracted from enduring sub-

stances. It is not a "universal frame," as Beyssade calls it (Beyssade, 13~). One can not say, as he

does, that Descartes' time "is a form, empty as such, and that the durations are the different

contents that come to fill it" (ibid.). This is the "container" time o f Gassendi and Newton.

so Cf. Kemp Smith's discussion, N e w S t u d i e s , 312--13; and Descartes' letter to Clerselier,

January 12, 1646, AT, 9:i.216.

3, Cf. Ke mp Smith, N e w S t u d ie s , on th e "merely abstract," 31 ~-13; and ~o3-o4 : I t [the thesis

that Descartes uphol ds an atomic view of time] finds supp ort in the w ording of Descartes' reply to

the writer of the F i f t h O b j e c t i o n s .

~" Pierre Gassendi, F i f t h O b j e c t i o n s , AT, 7:3 ol; CSM, ~:2o 9.



36~ J O U R N L O F T H E H I S T O R Y O F P H I L O S O P H Y ~6: 3 JULY 198 8

e a c h o t h e r i s n o m o r e r e l e v a n t to th e p r o d u c t i o n o r r e p r o d u c t i o n o f t h in g s i n

t im e t ha n th e p r o d u c t i o n o r r e p r o d u c t i o n o f s o m e r o c k is a f f e c te d b y th e

f l o w o r p a s s a g e o f t h e p a r t s o f a r iv e r w h i c h f lo w s p a st it ( A T , 7 : 3 o l ;

C S M . I I . 2 o 9 - 1 o ). T h i r d l y , y o u r e x i s te n c e i s c o n t i n g e n t f r o m o n e m o m e n t t o

a n o t h e r n o t b e c a u s e a c a u s e is r e q u i r e d t o c re a t e y o u a n e w , b u t b e c a u s e t h e r e

is n o g u a r a n t e e t h a t t h e r e i s n o t s o m e c a u s e p r e s e n t w h i c h m i g h t d e s t r o y y o u ,

o r th a t y o u d o n o t h a v e s o m e i n f i rm i t y w i t h i n y o u w h i c h w o u l d f in a l ly r e su l t i n

y o u r d e m i s e ( ib i d .) .

T h i s l as t o b j e c t i o n c o n t a i n s t h e k e r n e l o f G a s s e n d i' s d i f f e r e n c e o f o p i n i o n

w i t h D e s c a r t e s . T h e g i s t o f it i s t h a t w h i l s t G a s s e n d i r e g a r d s i t a s n e c e s s a r y f o r

e v e r y e x i s t e n t t o h a v e a c a u s e w h i c h b r i n g s i t i n t o e x i s t e n c e , h e d o e s n o t s e e it

a s n e e d i n g a n y c a u s e t o k e e p it i n e x is t e n c e . O n c e a s u b s t a n c e i s c r e a t e d , t h e n

( to u s e G a s s e n d i ' s m e t a p h o r ) t h e w a t e r s o f t i m e f l o w p a s t it u n t il s o m e f u r t h e r

c a u s e t a k e s it o u t o f e x i s t e n c e T o t h i s D e s c a r t e s r e p l ie s :

When you deny that we con t inual ly need the in f luence [ influxus]3~ of the f i rs t cause fo r ou r

conservation you are den yin g a thing which all the Metaphysicians affirm as manifest,

but which the unlearned often fail to think of, because they attend only to causes of

coming to be [secundum f ier i ] but not to those of being [secundum esse] .. . God is the

cause of created things, not only se c undum f i e r i but also se c undum e s se and so he must

always influence [influere] the effect in the same way in order for it to be conserved.

And this is clearly demonstrated by what I explained about the independence of

the parts of time, which you try in vain to evade by proposing the necessi ty o f the sequence

which exists between the parts o f time cons ider ed in the abstract. It is not this that is at issue

here, b ut rat her the time or d urati on of the en dur ing thing, and you will not deny that

the individua l mom ents of this time could be separated f rom those next to them, that

is, that the en du ri ng thi ng could at an y single mo me nt cease to exist.34

In this reply Descartes does not asser t that every mom ent of concrete du rat ion

( the dura t ion o f the endur i ng th ing ) is ac tua l ly separa ted f rom the nex t , as

ss The term

inf luxus

literally means 'inflow', and is echoed later in this passage by the verb

influere 'to flow into'. According to Alan Gabbey, in an erudite discussion in his Force and

Inertia (3Ol-3O2 nn. 3 l, 38) Descartes' puzzling introduction of this term into his paraphrase of

Gassendi's objection evokes not only the inf luxus divinus of Aquinas and Thomist theologians, but

possibly also the inf luxus astrorum of the astrologers. Gabbey concludes that no English term is rich

enough to convey all these senses. But in the Chambers Tw entieth Century Dictionary 'spiritual influx'

and 'power of producing an effect' are both given as senses of the word 'influence',along with the

astrological sense, so I have translated it accordingly.

s4 AT, 7:369-7o, reading definiri for AT's impossible definere in the last phrase. Note that my

translation differs in many respects from Cottingham's here. In particular, I demur from his

translation ofpartes as divisions, of conservare as keeps in existence (thus masking the origin of

the conservation laws of modern physics in Descartes' philosophy), and of inf luxus as continual

action (CSM, 2:254-5). Ariew's translation of Gueroult's render ing of this passage likewise needs

amending here: his could not deny that the movements cannot be separated should read could

not deny that the moments could be separated (Guer., chap. 6, p. 316 n. lO5). Movements

should also be corrected to moments in the corresponding text (Guer., 279/198).



C O N T I N U O U S C R E A T I O N , C O N T I N U O U S T IM E 3 6 3

G u e r o u l t a l l e ge s. a s T h e e m p h a s i s is r a t h e r o n t h e c o n t i n g e n c y o f th e i r c o n n e c -

t io n , o n t h e f a c t t h a t t h e y c o u l d b e s e p a r a t e d , t h a t th e e n d u r i n g t h i n g c o u l d a t

a n y m o m e n t c e a s e t o e x i s t. E v e n i n t h e f u r t h e r q u o t a t i o n G u e r o u l t c i t e s i n

s u p p o r t o f h i s c l a i m , D e s c a r t e s ' e m p h a s i s is o n t h e p o s s ib i li ty o f s e p a r a t i o n o f

t h e p a r ts o f t i m e : I c o n s i d e r t h e p a r t s o f t i m e to b e s e p a r a b l e f r o m o n e

a n o t h e r . a ~ F o r w h a t D e s c a r t e s is c o n c e r n e d t o r e f u t e is n o t t h a t th e d u r a t i o n s

o f t h i n g s a r e c o n t i n u o u s , b u t t h e i d e a t h a t t h e i r c o n t i n u o u s e x i s t en c e d o e s n o t

r e q u i r e a c au s e. a7 I t is a g r e e d t h a t a n e n d u r i n g t h i n g h a s a d e f i n i t e e x i s t e n c e a t

a n y g i v e n m o m e n t o f it s d u r a t i o n . Y e t s in c e t h is e x is t en c e d e p e n d s o n G o d ' s

c o n t i n u o u s a c t io n , a n d a t h i n g h a s d u r a t i o n o n l y a s l o n g a s i t e x is ts , t h e r e is n o

m o m e n t t h a t is n o t c o n t i n g e n t : w i t h o u t G o d ' s a c t io n t h e r e w o u l d b e n o l i nk b e -

t w e e n o n e m o m e n t a n d t h o s e t h a t fo l lo w it. B u t p r o v i d e d G o d a c t s c o n t i n u -

o u s l y o v e r a n e x t e n d e d t im e , a b o d y w il l h a v e a c o n t i n u o u s d u r a t i o n . I n t h e

w o r d s o f B e y s s a d e , T h e c o n t i n u i t y o f a n u n d i v i d e d p a r t , e i t h e r o f b o d y o r

d u r a t i o n , a lw a y s d e p e n d s o n a f re e a c t o f G o d ; t o c o n t i n u o u s c r e a t io n t h e r e

c o r r e s p o n d s t h e a c t b y w h i c h G o d k e e p s u n i t e d r e a l ly d is t i n c t p a r t s t h a t h e

c o u l d d i v i d e. a a

5 . C O N T I G U I T Y

W e h a v e s e e n t h a t n o n e o f th e s t a n d a r d a r g u m e n t s f o r t h e c la ss ic t he s i s

s u c c e e d s i n p r o v i n g C a r t e s i a n t i m e d i s c o n t i n u o u s . B u t m i g h t i t n o t s ti l l b e so ,

n o n e t h e l e s s ? I f i t is , t h e n g i v e n t h e u n t e n a b i l i t y o f t h e g a p - d i s c o n t i n u o u s

m o d e l s d i sc u s s e d a b o v e , t h e o n l y r e m a i n i n g m o d e l s f o r a d i s c o n t i n u o u s t im e

a r e t h o s e i n v o l v i n g c o n t i g u o u s i n d i v i s ib l e s , t h e s e in d i v i s ib l e s b e i n g e i t h e r f i-

35 Th e creative mo m en t of each end ur ing thin g is . . . enclosed within itself, radical ly sepa-

ra ted f ro m a l l o t he rs [Le mom ent c r6a teur de chaque chose duran t e e s t . . , enfe rm~ en l u i m&ne ,

radica lement s~par6 de tous les aut res] (Guer. , ~74h94 ) .

36 Co nside ro tem por is partes a se m utu o sejungi posse,

Reply to the Fir s t Objec t ions

A T ,

7:1 o 9, 11 .9 - t o; CS M, 2: 7 8; c i ted by Gu eroui t on 274/315, n. 81.

37 This is no idle bo ne o f con tention. It reflects a deep differen ce in theological doctrine, an d

a corresp ond ing deep di fference in physics . Th e key issue is whe ther c rea ted things n eed G od's

ac tion on them cont inuously, as a m at te r of course , o r w hether hi s act ion o n them need only be

intermittent. In this contex t Descartes w ould be k een to prov e that God 's action is necessary at any

single mo m en t of t ime; b ut n ot tha t his act ion is really discontinuous. But since in th e seventeenth

cen tury causes w ere always closely associated w ith forces, this also makes fo r a crucial d ifferenc e

in the res ultant physics of the two rival metaphysical viewpoints. Descartes bel ieved that a force

was always necessary to conserve a given thing in existence, and in this Leibniz endorsed him

fully; whereas N ew ton, fol lowing Bar row and Gassendi in maintaining the ind epe nd enc e of

du rat ion fro m existence, rejected the idea o f a c a u s a s e c u n d u m e s s e especially in its Leibnizian

manifestation as v i s v i v a o r action cr~atrice.

38 Beyssade, 35o : La continuit6 d'u ne part ie indivise, corp s ou dur6e, d6p end to ujou rs d'u n

acte l ibre d e Dieu, ~t la cr6at ion co ntin u& cor resp on d l 'acte par lequel Dieu, maintient unies des

parties r& llem en t distinctes qu ' i l po urra i t diviser.



364

JOURN L OF THE HISTORY OF PHILOSOPHY

26:3

JULY

988

nite or actually infinitely small, or perhaps points. In this section I want to

discuss whe the r a mode l based on such a contiguity/continuity distinction is a

real option for Descartes. The n in the following sections I shall turn to the

question of time atoms, and whether there exists any additional textual evi-

dence for Descartes' having coun tenanced them.

According to the traditional Aristotelian distinction, two parts o f a whole

are contiguous if their extremities are together, but continuous if they have

an extremity in common. T ha t is, the parts of a continuous whole are the parts

into which it could be divided (i.e., merely potential parts), whilst the parts o f

an aggregate of con tiguous indivisibles would be these indivisibles themselves,

the actual parts into which it is divided. A time divided into such contiguous

indivisible parts appears to be what Guerouh has in mind when he writes of

discontinuity being synonymous with the characteristics of separateness, con-

tingency, and mutual in dependence.

Might Cartesian time be discontinuous in this sense? I shall argue that this

is most unlikely. In the first place, Descartes had little patience with the tradi-

tional distinction between contiguity and con tinuit y--a nd for good reason, as

we shall see, since the distinction is not even applicable in its Aristotelian form,

given Descartes' equation of matter with space, and time with concrete dura-

tion. But secondly, even supposing some sort o f distinction between contigu-

ous Cartesian durations and continuous ones could be made, it would be

inapplicable to point-like indivisibles, since these have no endpoints. The im-

portance of this is that these are the only type o f indivisibles countenanced by

Descartes, as I shall argue in the next section.

Descartes nowhere explicitly discusses contiguity in connection with time.

But he does allude to bodies being contiguous in the sixth of the Repl ies , and in

the Conver s a ti on w i t h Bu r m an . Burman uses this text to initiate a discussion of

Descartes' atti tude to the t radit ional distinction.

In the text in question Six th R eply , AT, 7:433), Descartes claims that when

one body contains another in such a way that they possess a surface in com-

mon, this surface can equally well be rega rded as the extremity of one body as

the oth er in the sense in which those bodies are said to be contiguous whose

extremities are together. Bur man rightly criticizes him on this claim, pointing

out that calling the contain ing and contained contiguous is in accordance

with the co mmon way of talking, where in the Schools they call bodies contigu-

ous if their extremities are together, but not with the truth of the matter at

hand, for in this case there is only one extremity common to both. s9 Thus

according to the Aristotelian distinction, Descartes' two bodies, the containing

39 CWB,47; AT, 5:164: Haec non dicuntur secundum rei veritatem, nam sic una solhm est

extremitas, quae utriusque est communis,sed secundhmvulgarem dicendi modum, quo in Sco|is



C O N T I N U O U S C R E A T I O N , C O N T I N U O U S T IM E 3 6 5

a n d t h e c o n t a in e d , w o u l d b e c o n t i n u o u s r a t h e r t h a n c o n t i g u o u s , s in c e t h e

f a c t t h a t t w o b o d i e s h a v e a n i d e n t ic a l e x t r e m i t y s e e m s q u i t e s u f f i c ie n t f o r

c o n t i n u i t y ( ib id .) . B u t in t hi s c a se , B u r m a n a sk s , w h a t a r e c o n t i g u o u s b o d i e s

g o i n g t o l o o k li ke ? D e s c a r t e s ' r e p l y is c u r t , b u t t o t h e p o i n t : H o w o t h e r p e o p l e

w o u l d d e f i n e t h e s e t h i n g s i s a l l t h e s a m e t o m e ; I c a l l t w o b o d i e s c o n t i n u o u s

w h e n t h e i r s u r fa c e s a r e j o i n e d t o e a c h o t h e r s o i m m e d i a t e l y t h at t h e y b o t h

m o v e w i th o n e a n d t h e s a m e m o t i o n o r b o t h c o m e to r es t t o g e t h e r ; a n d t h o se

t h a t b e h a v e o t h e r w i s e a r e c o n t i g u o u s ( ib id .) .

I m p l i c i t in t h is p a r t i c u l a r e x c h a n g e i s t h e r e a l iz a t io n b y b o t h m e n t h a t t h e

A r i s t o t e li a n d i s t i n c t i o n b e t w e e n c o n t i g u i t y a n d c o n t i n u i t y i s i m p o s s i b le t o

m a i n t a i n w i th i n t h e C a r t e s ia n f r a m e w o r k . F o r t hi s w o u l d r e q u i r e o n e t o b e

a b le t o d i s t i n g u i s h b e t w e e n t h e e n d p o i n t s o f tw o b o d i e s b e i n g t o g e t h e r a t t h e

s a m e p o i n t i n sp a c e , a n d t h e i r b e i n g t h e s a m e p o i n t . B u t D e s c a r t e s d e n i e s t h a t

t h e r e i s a r e a l d i s t i n c t i o n b e t w e e n b o d y a n d s p a c e : a s h e s a y s i n t h e

P r i n c i p l e s ,

T h e r e i s n o r e al d i f f e r e n c e b e t w e e n s p a c e . . , a n d t h e c o r p o r e a l s u b s ta n c e

c o n t a i n e d i n it , b u t o n l y a d i f f e r e n c e i n t h e w a y w e a r e a c c u s t o m e d t o c o n c e i v e

o f t h e m (w o ; A T , 8 : 4 5 ). B u t t h is m e a n s t h a t t h e r e i s l ik e w is e o n l y a c o n c e p -

t ua l d i f f e r e n c e b e t w e e n t h e e x t r e m i t y o f a b o d y a n d t h e p o i n ts o f s p a c e it

o c c u p i e s. T h u s t h e A r i s t o te l i a n d i s t i n c ti o n f a il s t o r e p r e s e n t a r ea l d i f f e r e n c e :

t h e e x t e n s i o n o f t h e w h o l e u n i v e r s e is c o n t i n u o u s , e v e n i f s o m e b o d i e s i n it a r e

c o n c e i v e d as m e r e l y c o n t i g u o u s w i th o n e a n o t h e r .

B u t p r e c i s e l y a n a l o g o u s c o n s i d e r a t i o n s a p p l y t o ti m e , s i n ce j u s t a s s p a c e o r

e x t e n s i o n is o n l y c o n c e p t u a l l y d is t in c t f r o m e x t e n d e d s u b s t a n c e , s o ti m e o r

d u r a t i o n is o n l y c o n c e p t u a l ly d i s t in c t f r o m e n d u r i n g s u b s ta n c e

P r i n c i p l e s , I ,

w A T , 8 A : u 6 ) . C o n s e q u e n t l y , t h e r e is n o r e a l d i s ti n c t io n b e t w e e n t h e m o -

m e n t s t h a t b o u n d c o n s e c u t i v e d u r a t i o n s w h i c h a r e t o g e t h e r ( c on t ig u i t y ) a n d

t h e i r o c c u r e n c e a t t h e s am e m o m e n t ( c o n ti n u it y ). T h u s i t w o u l d a p p e a r m o s t

u n l i k e l y t h a t D e s c a r t e s w o u l d e q u a t e c o n t i g u i t y w i th a d i s c o n ti n u i ty , a s L e i b -

n i z d i d .

O f c o u r s e , t h e s e c o n s i d e r a t i o n s d o n o t m a k e i t a n y le ss u s e fu l t o h a v e a

c o n c e p t u a l d i s t i n c t io n o f c o n t i g u i t y , w h i c h is w h y D e s c a r t e s p r o v i d e s a c ri te -

r i o n f o r t h e c o n t ig u i t y o f b o d i es in r e s p o n s e t o B u r m a n ' s p r o m p t i n g . S o th e

q u e s t i o n a ri se s w h e t h e r a n y s u c h c r i te r i o n c a n b e f o u n d f o r c o n t ig u o u s d u r a -

t io n s , p e r h a p s o n e a n a l o g o u s t o D e s c a r te s ' o n e f o r b o d ie s .

A n a r g u m e n t a l o n g t h e s e l i n e s m i g h t g o a s f o l l o w s . A c c o r d i n g t o D e s -

c a r t es , tw o b o d i e s a r e c o n t i g u o u s i f t h e y c an m o v e w i th i n d e p e n d e n t m o t i o n s

w h i l e st il l t o u c h i n g , a s in t h e c a s e o f a b al l r o l l i n g in a b o w l . T h u s t h e c r i t e r i o n

ea dicuntur co ntigua, qu oru m extrem itates sunt simul. No te that Cottingham 's translation of the

second half of this sentence need s am ending, since it does not convey the fact that B urman is

criticizing Descartes for an inappropriate appeal to the com mo n, Aristotelian sense of contiguity.



66 JOURNAL OF THE HISTORY OF PHILOSOPHY 26 :3 JULY 98 8

f o r sp a t ia l c o n t i g u i t y d e p e n d s o n i n d e p e n d e n t m o v a b i l it y , a f a c t w h i c h m a k e s

i t h a r d t o a p p l y t o t im e , s i n c e i t is n o t o b v i o u s h o w d u r a t i o n s c o u l d b e s a id t o

c h a n g e t h e i r r e l a t i v e l o c a t i o n i n t i m e . O n e s u g g e s t i o n , h o w e v e r , w o u l d b e t o

f o ll o w t h e i m p l ic i t lo g i c o f G u e r o u h ' s p o s i t io n , a n d e q u a t e m o v a b i l it y w i t h

s e p a r a b il it y . F o r i f a ll t h e m o m e n t s o f a g i v e n d u r a t i o n w e r e c o n t i n u o u s , t h e n

o n e m o m e n t c o u l d n o t b e m o v e d i n t h e s e n se o f s e p a r a t e d w i t h o u t its

n e i g h b o r s b e i n g m o v e d a ls o . B u t t h is D e s c a r t e s d e n i e s : a ll m o m e n t s a r e

i n d e p e n d e n t a n d s e p a r a b le . S o t h e y m u s t b e m e r e l y c o n ti g u o u s .

B u t t h is a n a l o g y i s f l aw e d . S e p a r a b i l i ty c a n n o t s t a n d i n f o r m o v a b i li ty . T h i s

c a n b e s e e n b y r e f e r e n c e t o t h e c a s e o f s p a c e . F o r t h e ( a r b i tr a r il y t a k e n ) p a r t s

o f e v e n a c o n t i n u o u s m a t e r ia l b o d y a r e s e p a r a b le , s in c e a n y e x t e n d e d b o d y is

d i vi si b le . T h e y a r e n o t f o r t h a t r e a s o n m e r e l y c o n t i g u o u s . S im i la r ly , th e s e p a r a -

b i li ty o f a ll th e p a r t s o f a d u r a t i o n c e r t a in l y m a k e s t h e i r c o n n e c t i o n c o n t i n -

g e n t , b u t it d o e s n o t n e c e s s a r il y m a k e t h e m d i s c o n t i n u o u s .

S o G u e r o u l t ' s e q u a t i o n o f d i s c o n t i n u i t y w i t h s e p a r a b i l i t y is i n c o r r e c t (a l-

t h o u g h t h is is o b s c u r e d b y h is a p p a r e n t f a i lu r e t o d i s t in g u i s h s e p a r a b i li ty f r o m

s e p a r a t io n ) . I f t w o C a r t e s i a n d u r a t i o n s a r e t o b e c o n t i g u o u s a n d n o t c o n t i n u -

o u s , t h e y m u s t b e a c t u a l l y s e p a r a t e d , n o t j u s t s e p a r a b l e . A n a c t u a l d iv i s io n

m u s t o c c u r b e t w e e n t h e m . N o w a c t u a l d iv i si o ns in s p a ce a r e e n g e n d e r e d b y

t h e d i f f e r i n g m o t i o n s o f t h e v a r i o u s p a r t s o f m a t t e r. B u t a s D e s c a r t e s m a k e s

c l e a r i n h i s r e p l y t o G a s s e n d i , a c t u a l d i v i s i o n s o r s e p a r a t i o n s i n t i m e a r e e f -

f e c t e d b y s u b s t a n c e s c e a s i n g t o ex i st : f o r a m o m e n t t o b e a c tu a l ly d i v i d e d f r o m

o r s e p a r a t e d f r o m s u c c e e d i n g o n e s i s f o r t h e e n d u r i n g t h i n g t o c e a s e t o e x i st a t

t h a t m o m e n t ( A T , 7 : 3 7 o) . T h u s g i v en t h e e q u iv a l e n c e o f d u r a t i o n w i th t h e

c o n t i n u e d e x i s te n c e o f a s u b st a n c e , t h e m o m e n t s o f c re a t io n a n d e x t in c t io n

s e e m t o b e t h e o n l y e x t re m i t ie s a d u r a t i o n c o u l d p o s s es s .

B u t j u s t a s t h e e x i s t e n c e o f c o n t i g u o u s w h o l e s is n o t e n o u g h t o m a k e t h e

e x t e n s i o n o f t h e u n i v e r s e d i s c o n t i n u o u s , s o t h e e x i s t e n c e o f is o l a te d c o n t i g u -

o u s d u r a t i o n s - - s a y t h e c o n t i g u o u s d u r a t i o n s o f m y l iv in g b o d y a n d m y

c o r p s e - - i s n o t s u f f i c i e n t fo r a d i s c o n t i n u i ty i n t h e d u r a t i o n o f all c r e a t e d

e x is te n c e . T h e o n l y w a y th a t t h is c o u l d h a p p e n w o u l d b e i f e v e r y t h i n g i n t h e

u n i v e r s e w e r e a n n i h i l a te d o r c r e a t e d t o g e t h e r. A n d t h e o n l y w a y t h a t s u c h

d i s c o n t in u i t ie s w o u l d c o m p r i s e a d i s c o n t i n u o u s o r d e r w o u l d b e i f a ll s u b -

s t a n c e s w e r e c r e a t e d f o r a c e r t a in d u r a t i o n , t h e n a n n i h i l a te d , a n d a d is t in c t se t

o f s u b s t a n c e s w e r e i m m e d i a t e l y c r e a t e d i n th e i r p l a c e . B u t th i s ta k e s u s b a c k t o

t h e t h e o r y o f r e p e a t e d a n n i h il a ti o n a n d c r e a ti o n w e a l re a d y r e j e c t e d a b o v e as

i n c o m p a t i b l e w i t h D e s c a r t e s' d o c t r i n e o f c o n t i n u o u s c r e a ti o n .

T h u s , i n c o n c lu s i o n , t h e r e s e e m s to b e n o b a si s i n D e s c a rt e s ' p h i l o s o p h y f o r

a r e a l d i s t i n c t i o n b e t w e e n c o n t i n u i t y a n d c o n t i g u i t y . A n d t h e o n l y b a s i s f o r

c o n c e p t u a l ly d i s ti n g u i sh i n g a m e r e l y c o n t i g u o u s t e m p o r a l o r d e r w o u l d b e i f

t h e e n d p o i n t s o f c o n s e c u t iv e d u r a t io n s w e r e t h e m o m e n t s o f t h e d e s tr u c t io n




a n d c r e a t i o n o f s e p a r a t e u n i v e r s e s . T h e s e u n i v er s es , m o r e o v e r , w o u l d h a v e t o

e n d u r e l o n g e n o u g h t o h a v e di s ti n c t e n d p o i n t s . A s u c c es s i o n o f i n s ta n t a n e o u s

u n i v e r se s c o u l d n o t e v e n b e d i s t in g u i s h e d c o n c e p t u a l ly f r o m a c o n t in u o u s l y

e x i s ti n g u n i v e r s e .

T h u s i f t h e c l as si c t h e si s is c o r r e c t i n s u p p o s i n g C a r t e s i a n t i m e t o b e a

s e q u e n c e o f d i s c o n t i n u o u s i n d iv i s ib l e m o m e n t s , t h e s e i nd i vi si bl es m u s t b e e x -

t e n d e d t i m e a t o m s . S o le t u s n o w t u r n t o t h e q u e s t i o n o f w h a t f u r t h e r e v i d e n c e

t h e r e i s f o r t h e i d e a t h a t t i m e is c o m p o s e d o f e x t e n d e d e l e m e n ts .

6 . M O M E N T S A N D I N S T A N T A N E I T Y

I n h i s

Principles

D e s c a r t e s o n o n e o c c a s i o n r e f e r s t o t h e u n e x p e c t e d a p p e a r -

a n c e o f a s t a r o c c u r r i n g i n a n e x t r e m e l y s h o r t t im e , a s i f i n a m o m e n t 4 o ; a n d

i n h i s

Repl ies to the Firs t Object ions

h e s p ea k s o f th e r e b e i n g n o p o w e r w i t h in

a n y o n e o f u s w h i c h w o u l d s u ff ic e to c o n s e r v e h i m through e v e n a m o m e n t o f

t i m e . 4 , T h e s e l o c u t i o n s s e e m t o s u p p o r t t h e i d e a t h a t a m o m e n t o r i n s t a n t i s

n o t a f t e r a ll a m e r e p o i n t i n t im e , b u t a t r u e p a r t o f e x t r e m e l y s h o r t d u r a t i o n .

S o c o u l d D e s c a r t e s h a v e c o u n t e n a n c e d t e m p o r a l i n d iv i si b le s , e i t h e r f i n it e o n e s

o r o n e s w h o s e q u a n t i t y i s n o n - z e r o b u t v a n i s h i n g l y s m a ll ?

T h e a n s w e r t o t h i s q u e s t io n , I c o n t e n d , is a f i rm n o . F o r e v e n t h o u g h

D e s c a r t e s n e v e r e x p l i c i t ly d i s c u s se s t i m e a t o m s , h e e x p l i c i tl y r e j e c t s s p a t i al

i n di v is ib le s , a n d , I m a i n t a i n , h i s a r g u m e n t s a g a i n s t t h e m s h o u l d a p p l y e q u a l l y

w e l l t o ti m e . O f s p a t i a l a t o m s h e s a ys : I sa y t h a t it w o u l d i m p l y a c o n t r a d i c t i o n

f o r t h e r e t o b e a t o m s w h i c h a r e c o n c e i v e d o f as e x t e n d e d a n d a t t h e s a m e t i m e

i n d i v i s i b l e , s i n c e a l t h o u g h G o d c o u l d h a v e m a d e t h i n g s w h i c h a r e s u c h t h a t

t h e y a r e n o t d i v i d e d b y a n y c r e a t e d b e in g , w e c e rt a i n ly c a n n o t u n d e r s t a n d h i m

a s h a v i n g b e e n a b l e t o d e p r i v e h i m s e l f o f h is o w n f a c u l ty o f d i v i d i n g t h em . 4 *

T h u s i t is n o t t h e i n d e f i n i t e d i v is ib i li ty o f m a t t e r t h a t r u l e s o u t t h e e x i s t e n c e o f

a t o m s , s in c e t h e r e w o u l d b e n o t h i n g c o n t r a d i c t o r y a b o u t t h e e x is t e n ce o f

p a r t ic l e s o f m a t t e r t h a t h a d n o t i n f a c t b e e n d i v i d e d . B u t i t is c o n t r a d i c t o r y t o

s u p p o s e t h a t s u c h p a r t i c l e s a r e i n d i v i s i b l e i n p r i n c i p l e , f o r t h i s w o u l d b e t o s e t

l im i ts o n G o d ' s c r e a t i v e o m n i p o t e n c e , a n d t h u s t o li m i t t h e u n l i m i t a b l e .

4 0 P r in c ip l e s

I I I , wa I 1 A T , 8 : 1 5 9 , l 1 . 1 4 - 1 5 : i d e o q u e b r e v i s s i m o t e m p o r e , a c t a n q u a m i n

m o m e n t o .

4~ Firs t Rep l ies:

A T , 7 : x 1 1 ; C S M , ~ : 8 0: c / l m q u e n u l l a m i n s e i n v e n i t p o t e n t i a m , q u a e s u f fi c ia t

a d i p s u m v e l p e r m o m e n t u m t e m p o r i s c o n s e r v a n d u m , m e r i t o c o n cl u d it s e e ss e a b al io ( m y

e m p h a s i s ) .

4 , L e t t e r t o M o r e , 5 t h F e b r u a r y 1 6 4 9 ; A T , 5 : u 7 3 : D i c o i m p l i c a t e c o n t r a d i c t i o n e m , u t

a l i q u a e d e n t u r a t o m i , q u a e c o n c i p i a n t u r e x t e n s a e a c s i m u l i n di v is i b il e s; q u i a , q u a m v i s D e u s e a s

t a l e s e f f i c e r e p o t u e r i t , u t ~ n u l l a c r e a t u r ~ d i v i d a n t u r , c e r t ~ n o n p o s s u m u s i n t e l l e g e r e i p s u m s e

f a c u l t a te e a s d i v i d e n d i p r i v a r e p o t u i s s e . C f . t h e a l m o s t i d e n ti c a l w o r d i n g i n h i s l e t t e r t o G i b i e u f ,

1 9 t h J a n u a r y 1 6 4 ~ , A T , 3 : 4 7 7 , q u o t e d b y L a p o r t e , u 5 9 , a s w e ll a s t h e m o r e p o n d e r o u s p a s s a g e i n

t h e P r i n c i p le s

I I , w A T , 8 : 5 1 - 5 ~ ; C S M , 1 : u 3 1 - 3 2 .



368 JOURN L OF THE HISTORY OF PHILOSOPHY 26:3 JULY 1988

Here Gueroult thinks he sees a loophole. For, he argues, if it is not indefi-

nite indivisibility tha t forms the basis of Descartes' rejection o f spatial indivisi-

bles, but the unlimitability of divine creative omnipotence, then this arg ume nt

against indivisibles is evidently not valid for durat ion , since dur ati on is not a

reality, a substance distinct from creative omnipotence, but is this omnipo-

tence itself insofar as it creates existence (Guer., ~76/195 ). Consequently,

according to Gueroult, the creative instant can be, and in fact is, indivisible.

Its indivisibility derives from tha t of the creative act itself, and the refore has

noth ing in common with the indivisibility of the atom of extension rejected

by Descartes (ibid.).

But this line of argumen t has already been un de rmi ned by our conclusions

in section 4 above where we saw that Gueroult's reading of the abstract/

concrete distinction as one between created and creative is untenable. Con-

crete dura tion is the du rati on o f the created thing, just as concrete extension is

the extension of the created thing. Thus Gueroult's attempt to exempt in-

stants f rom Cartesian anti-atomism is unsuccessful. Although God could have

created things which, as a matte r o f contingent fact, always exist for some very

short duration ('moment'), we cannot understand him as having been able to

deprive himself of his own faculty of creating them for some lesser time, i.e.,

of being able to divide such moment s into smaller parts. Th ere for e moments

cannot be ext ended indivisibles, no matter how small their extension.

But this still leaves us with the problem of how to account for the passages

quoted above, where Descartes writes of moments as if they were ext ended , as

in his talk of conservation throu gh a momen t of time, and so forth. Given the

untenability of time atoms, perhaps Laport e is right after all in his claim that

moments are true parts of time, extremely small but nonetheless divisible

durations? It would appear not. Such a reading is flatly contradicted by other

passages in the same works where Descartes speaks of the instant as a mere

point of time, totally devoid of dura tion. Thu s a few pages before the above

quoted reference to a momen t as

brevissimum tempus

in the

Principia,

Descartes

alludes to a min imu m point of time, which they call an instant minimum

temporispunctum, quo d instans vocant; III, art. 63; AT, 8:115, 1.8-9). And in the

Regulae, discussing privations of positive qualities, Descartes says: The cogni-

tion through which I intuit what nothing is, or an instant, or rest, is no less

true than that through which I understand what existence is, or duration, or

motion Rules fo r the Direction o f the Mind, Rule 12, AT, lo:42o, U. ~-8; CSM,

45). Here again Descartes seems to regard an instant as a mere limit, a priva-

tion o f duration.

How should we deal with these inconsistencies? An ingenious solution is

that offered by Beyssade. He proposes that there are two distinct technical

terms here: There is the moment, defined as brevissimum tempus, which is a




t r u e d i v i si b le p a r t o f d u r a t i o n , a s L a p o r t e s u g g e s t e d . B u t w e m u s t c l e a rl y

d i s t i n g u i s h t h i s f r o m t h e t e r m i n s t a n t

( i n s t a n s

i n t h e L a t i n ) , w h i c h , B e y s s a d e

c la im s , D e s c a r t e s a l w a y s u s e s . . , i n t h e s tr ic t s e n s e o f li m i t, f o r a p r i v a t i o n o r

n e g a t i o n o f d u r a t i o n , w h i c h e x c l u d e s p r i o r i t y in t im e , w h i c h c a n n o t b e d i m i n -

i sh e d . 4 a T h i s d i s t i n c t i o n , a c c o r d i n g t o B e y s s a d e , i s i m p l i c i t i n D e s c a r t e s ' u s a g e

o f th e L a t in w o r d s m o m e n t u m a n d i n s t a n s , a l t h o u g h i t is n o t a l w a y s f o l l o w e d i n

t h e F r e n c h t r a n s l a t i o n s :

I f

a p a r t c o n t a i n s n o t h i n g o t h e r t h a n p o i n t s, a p o i n t

is i n al l r i g o r n e v e r a p a r t . S i m i l a r ly f o r d u r a t i o n : t h e i n s t a n t is i ts e x t r e m i t y ,

t h e m o m e n t i s a p a r t . . . . O n e c a n t h u s s p ea k o f c o n s e r v a t i o n t h r o u g h a

m o m e n t o f t i m e

( D i s c o u r s e

4 : A T , 6 : 3 6 , 11. 2 - 3 , a n d

R e p l i e s t o F i r s t O b j e c t i o n s ,

AT, 7 :111 , 11 . 1o - 1 1 , 9 .8 8) , o f n e i g h b o r i n g m o m e n t s

( R e p l i e s t o F i f t h O b j e c t i o n s ,

A T , 7 : 3 7 o , 1 .4 ), o r o f s u m m i n g m o m e n t s t o c o m p o s e t h e d u r a t i o n o f a m o t i o n

( P r i n c i p l e s , I I I , 5 9 : t h e t r a n s l a t o r h a s m i x e d t h e w o r d s i n s t a n t a n d m o m e n t ,

t h e L a t in o n l y u s e s m o m e n t u m ; B e y s s a d e, 3 4 9 - 5 o ) .

T h i s i n t e r p r e t a t i o n h a s t h e v i r t u e o f n e a t n e s s . I t a p p e a r s t o r e s o l v e t h e

i n c o n s is t e n c ie s i n D e s c a r t e s ' u s a g e w i t h o u t c o n f l i c t in g w i th h i s o p p o s i t i o n t o

e x t e n d e d i n di v is ib l es , s in c e i t m a k e s m o m e n t s e x t e n d e d b u t d iv is ib le , a n d

i n s ta n t s in d i v is i b le b u t u n e x t e n d e d .

N e v e r t h e l e s s , d e s p i t e i ts in g e n u i t y , B e y s s a d e 's i n t e r p r e t a t i o n is f a c e d w i t h

t w o m a j o r s e t s o f d i f f i c u lt i e s . T h e f i rs t is t h a t i t s i m p l y d o e s n ' t r e s o l v e t h e

t e x t u a l i n c o n s i s t e n c i e s . I f it d i d , D e s c a r t e s w o u l d a l w a y s w r i t e ( in t h e L a t i n ) o f

t h in g s b e i n g a t i n st a nt s , a n d e n d u r i n g t h r o u g h m o m e n t s . Y e t i n t h e p a s sa g e

i n v o lv i n g t h e l o c u t io n m i n i m u m t e m p o r i s p u n c t u m , q u o d i n s t an s v o c a n t ,

D e s c a r t e s w r i te s o f e n d u r i n g t h r o u g h t h is in sta nt; ~4 a n d w h e n h e r e f e r s t o

m o m e n t s i n t h e

M e d i t a t i o n s ,

h e s p e a k s o f a su b s t a n c e' s b e i n g c o n s e r v e d a t ( n o t

t h r o u g h ) e v e r y m o m e n t o f its d u r a t i o n . W o r s e , i n th e p a s sa g e w h e r e h e

a l le g e d ly d e f i n e s a m o m e n t a s b r e v is s im u m t e m p o r u m , w h a t h e a c t u a l l y w r i t e s

is a n d t h e r e f o r e i t is d i f f u s e d o v e r t h e w h o l e o f th is s u r fa c e i n a n e x t r e m e l y

s h o r t t i m e , a s i f i n a m o m e n t . 4 5 T h i s is h a r d l y t o d e f i n e a m o m e n t a s a n

e x t r e m e l y s h o r t t im e . I t w o u l d b e m o r e p l au s ib l e to i n t e r p r e t t h e

a s

i f i n a

m o m e n t a s m e a n i n g

a s

i f i n n o t i m e a t a ll . T h u s i t a p p e a r s t h a t D e s c a r t e s '

u s a g e is t o o i n c o n s t a n t t o s u p p o r t B e y s s a d e ' s i n t e r p r e t a t i o n .

S e c o n d l y , a n d m o r e d a m n i n g l y , t h is v ie w is o p e n t o t h e s a m e o b j e c t i o n s

4s Beyssade, 348: Sau f err eu r de n otre part , D escartes pren d toujours le mot, et son original

Latin

instans,

au s ens stricte de iim ite, po ur u ne privation ou n~gation de dur~e, qui exclut toute

priorit~ de temps, qui n e saurait diminuer.

Principles,

III , w AT, 8:115, i i . 5-9 :

h o c

non nisi per m inimum temporis puoctum,

quod instans vocant, du rar e potest, & ide6 continuitatem e arum mo rris non interrum pit.

4s Principles,

I I I, w 11: AT, 8:159 , i I. 14-15: idebque brevissimo tempore, ac tanquam in

mo me nto, supra totam istam superficiem se diffundet.



3 7 ~ J O U R N L O F T H E H I S T O R Y O F P H I L O S O P H Y 2 6 : 3 J UL Y 1 9 8 8

t h a t G u e r o u l t a l r e a d y r a i se d a g a i n st L a p o r t e ' s p r o p o s a l t h a t m o m e n t s a r e

e x t e n d e d . A r g u i n g t h a t t h e q u e s t i o n o f t i m e ' s d i s c o n t in u i t y c a n n o t i n a n y c as e

b e re s o l v e d m e r e l y b y a p p e a l t o s c a t t e r e d q u o ta t i o n s , b u t o n ly b y r e f e r e n c e t o

t h e w h o l e C a r t e s i a n c o n c e p t i o n o f m o t i o n (2 7 4 / 1 94 ), G u e r o u l t p o i n t s o u t t h a t

t h e p r o p o s e d e x t e n d e d n e s s o f th e C a r t e s i a n m o m e n t is i n f la t c o n t r a d i c t io n t o

D e s c a r t e s ' a n a l y s is o f m o t i o n a s a s u c c e ss i o n o f i n s t a n t a n e o u s s t at e s, a s w e l l a s

t o t h e i n s t a n t a n e i t y o f l ig h t . F o r D e s c a r t e s a l w a y s t r e a t s m o t i o n s t a ti c al ly : h e

a n a l y z e s i t a s c o n s i s t i n g i n a c e r t a i n c o n a t u s - - a n e n d e a v o r , o r t e n d e n c y t o

m o v e - - a t a n y i n s t a n t o f th e m o t i o n . A n d h e r e D e s c a r t e s is e x p li c it t h a t t h e

i n s ta n t s a r e u n e x t e n d e d , t h e y a r e m e r e p o i n t s o f t i m e i n w h i c h n o r e a l m o t i o n

c a n o c c u r , b u t o n l y a t a n g e n t i a l t e n d e n c y . T h i s i s t h e b a s is o f hi s f a r - r e a c h i n g

c o n c l u s i o n t h a t i n e r t i a l m o t i o n m u s t b e r e c t il i n e a r , m o t i o n i n a s t r a i g h t l in e :

A n d a l t h o u g h i t is t r u e t h a t n o m o t i o n o c c u r s in a n i n s t an t , i t is h o w e v e r

o b v i o u s t h a t e v e r y t h i n g t h a t m o v e s , i n e v e r y s i n gl e i n s ta n t t h a t c a n b e s p e c i -

f i ed w h i l e it is i n m o t i o n , h a s a d e t e r m i n a t i o n t o c o n t i n u e i ts m o t i o n i n a g i v e n

d i r e c t i o n i n a s t r a i g h t l i n e , b u t n e v e r i n a c u r v e d l in e. 4 6

B e y s s a d e , o f c o u r s e , a c k n o w l e d g e s t h a t t h e r e i s n o m o t i o n i n a n i n s ta n t .

Y e t h e s t il l a r g u e s t h a t t h e

c o n a t u s

a c c r u e d . . . in t h e m i n i m a l d u r a t i o n o f a

m o m e n t c a n b e a t t r i b u t e d t o t h e m o v i n g th i n g t a k e n a t a n in s t an t , w h e n i t

b e c o m e s , a c c o r d i n g t o h i m , t h e t h i n g ' s d e t e r m i n a t i o n t o m ov e.4 7 B u t f r o m t h i s

i t f o l l o w s t h a t t h e c o n a t u s (a s o p p o s e d t o t h e m e r e d e t e r m i n a t i o n t o m o v e )

e n d u r e s f o r a m o m e n t , w h e r e a m o m e n t i s a t r u e p a r t o f d u r a t io n . A n d s in ce

l i g h t i s i d e n t i f i e d b y D e s c a r t e s a s a

c o n a t u s

i t i s t h e r e f o r e s ti ll t h e c a s e t h a t , a s

o n L a p o r t e ' s v ie w , t h e p a s s a g e o f l i g ht w o u l d t a k e a f in i te a m o u n t o f t i m e : i t

w o u l d h a v e a t e m p o r a l m o t i o n a n d a r e a l s p e e d ( G u e r . 2 7 3 ). B u t a s G u e r o u l t

o b s e r v e s , D e s c a r t e s e x p l i c i t ly d e n i e s t h a t t h e p a s s a g e o f l i g h t is a n a c t u a l

m o t i o n , t h a t i t t a k e s t i m e ; i t i s, l i k e a l l c o n a t u s s t ri c tl y i n s t a n t a n e o u s . T h u s t h e

a l l eg e d e x t e n d e d n e s s o f th e m o m e n t c o n t r a d i c t s C a r t e s i a n p h y s i cs a t i ts v e r y

c o r e .

M u s t w e t h e n j u s t a c c e p t t h a t D e s c a r te s w a s r a t h e r c a r e l e ss in h i s r e f e r -

e n c e s to m o m e n t s o r i n s t a n ts a s i f t h e y w e r e e x t e n d e d ? I n t r y i n g t o a v o i d t hi s

c o n c l us i o n , o n e t e m p t a t i o n i s t o r e a d h is m o m e n t s a n d c o n a t u s e s a s e l e m e n t s

o f d u r a t i o n o r m o t i o n o f v a n i s h i n g q u a n t i t y , a s i n fi n it e si m a ls . T h i s i n t e r p r e t a -

46

Principles

II, w AT , 8:64/CSM, 1:242: Ac quamvis nullus motus fiat in instanti, mani-

festum tam en est om ne id quod movetur, in singulis instantibus quae po ssum designari dum

movetur , determ inatum esse ad m otum suum continuandum versus a l iquam partem, secund~m

lineam rectam, no n autem u nqu am secundhm ullam lineam curvam.

47 Be yssad e, 141 n. 5: M ais le conatus ains i acquis et accru dans la dur6e, au m oins dans la

dur~e m inimale d 'un mo m ent, peu t ~tre attribu6 au m obile pris ~ un instant de son mo uvem ent et

en u n point de sa trajectoire; il est alors sa

d~termination ~

tel mouvem ent (Principles, II, w AT ,

8:64 11 .4- 5 & l~--13)-



C O N T I N U O U S C R E A T I O N C O N T I N U O U S T I M E

37

t io n h a s b e e n e x a m i n e d a t l e n g t h b y G u e r o u l t , w h o I t h i n k r i g h t ly r e j e c ts it,

b u t hi s e x a m i n a t i o n is w o r t h a b r i e f c o n s i d e r a t i o n .

G u e r o u l t h i m s e l f c an a c c o u n t f o r t h e a m b i g u it y o f D e s ca r te s ' p h r a s in g i n

t e r m s o f h is a b s t r a c t / c o n c r e t e d i s ti n c ti o n . F r o m t h e ab s t ra c t , c r e a t e d p o i n t o f

v i e w , h e s a ys , i n s ta n t s n o l o n g e r a p p e a r a s r i g o r o u s l y i n d iv i si b le , n o t h i n g -

n e s se s o f d u r a t i o n , b u t a s f r a g m e n t s o f d u r a t i o n s . . , t h a t a r e a s s m a ll a s

poss ib l e , b r e v i s s i m a t e m p o r a . . . i n f in i t e ly s m a l l a c t u a l s ( G u e r . , 2 7 5 / 1 9 5 ) . B u t

s in c e D e s c a r t e s ' p h y s i c s c o u l d n o t b e c o n s t i tu t e d w i t h o u t b e i n g r e f e r r e d t o a

c o n c r e t e p o i n t o f v ie w , m e a n i n g t o t h e a b s o l u t e i n d iv is ib i li ty o f t h e i n s t a n t

( G u e r . , ~ 7 9 / 1 9 8 ), s o m e u n i o n o f t h e t w o p o i n t s o f v ie w is n e c e s sa r y f o r t h e

p h y s ic a l e x p l a n a t i o n o f c h a n g e . N o w t h e s e t w o p o i n ts o f v ie w c o u l d b e u n i -

f ie d , a n d t h e c o n c o m i t a n t i n c o n s i s t en c i e s r e s o l v e d , if w e w e r e t o r e g a r d D e s -

c a r t e s ' i n s t a n t s a s a n t i c i p a t i o n s o f L e i b n i z ' s d i f f e r e n t i a l s , a s i n fi n i te l y s m a l l y e t

d i v is ib l e a c tu a l s. B u t a s G u e r o u l t h a s s t r e ss e d , h o w e v e r e n t i c in g a n i n t e r p r e t a -

t io n t h is m a y b e , t h e f a c t r e m a i n s t h a t D e s c a r t e s h i m s e l f n e v e r d o e s a c h i e v e

s u c h a re s o l u t i o n . I n f a c t i t i s f l at ly c o n t r a d i c t e d b y hi s t h e o r y o f t h e i n s t a n t o f

l ig h t a s a b s o l u t e i n t e m p o r a l i t y , a n d b y h is r e d u c t i o n o f m o t i o n t o a s u c c es -

s io n o f d i f f e r e n t s t a te s ( G u e r . , ~ 7 4 / a9 4 ) . T h u s t h e L a p o r t e a n d e f i n it i o n o f

a n i n s t a n t a s a n e x t r e m e l y s h o r t t im e t h a t c o u l d l e a d to t h e i n fi n it e si m a l a s a

v a n i s h i n g m i n i m u m , d o e s n o t a c t u a ll y l e a d t o i t a n d is o n l y a n i m p e r f e c t

m a n n e r o f s p e a k i n g - - t h e i n s t a n t is e s s e n ti a ll y a ra d i c al n e g a t i o n o f all d u r a -

t i o n ( G u e r . , ~ 7 4 / 1 9 4 ) .

Q u i t e s o . B u t t h is c o n c l u s i o n m i l it a te s e q u a l l y a g a in s t G u e r o u l t ' s o w n i d e a

t h a t t h e r e c o u l d b e s u c h L a p o r t e a n m o m e n t s e v e n f r o m t h e ab s tr a ct , c r e a t e d

p o i n t o f v i ew . I n f i n it e l y sm a l l, d iv i si b le m o m e n t s a r e s i m p l y in c o m p a t i b l e w i t h

C a r t e s i a n p h y s i c s, e v e n a t i ts m o s t a b s t ra c t . F o r c o n f i r m a t i o n o f t hi s o n e n e e d

o n l y r e f e r t o D e s c a r t e s ' r e l e n t le s s h o s t i l i ty to t h e i n f in i t e s im a l t e c h n i q u e s i n b u r -

g e o n i n g u s e a m o n g h is p e e r s , e sp e c ia ll y F e r m a t a n d R o b e r v a l. W e m u s t t h e r e -

f o r e c o n c l u d e w i th G u e r o u l t t h a t D e s c a r te s ' r e fe r e n c e s t o m o m e n t s a s i f t h e y

a r e e x t r e m e l y s h o r t ti m e s is i n d e e d o n l y a n i m p e r f e c t m a n n e r o f s p e a k in g .

7 . D I S C O N T I N U I T Y A N D M O T I O N

B u t b e f o r e c o n c l u d i n g , t h e r e is o n e f u r t h e r a r g u m e n t f o r t h e cl as si c t h es is I

f e e l o b l i g e d t o c o n s i d e r , i f o n l y o n a c c o u n t o f its w i d e s p r e a d i n f lu e n c e . T h i s i s

t h e a r g u m e n t f r o m d i s c o n t i n u o u s m o t i o n .

S i m p l y s t a t e d , i t r u n s a s f o l l o w s . A s i s w e l l k n o w n , D e s c a r t e s d e n i e d t h a t a

d e c e l e r a t in g b o d y h a d t o g o t h r o u g h a ll t h e i n te r m e d i a t e d e g r e e s o f s p e e d .

T h a t is , h e d e n i e d ( in t h is s e n s e , a t l e as t ) t h e c o n t i n u i t y o f m o t i o n . Y e t h e

u p h e l d t h e c o n t i n u i t y o f m a t t e r o r e x t e n s io n . B u t , so t h e a r g u m e n t g o e s, if

m o t i o n is d i s c o n t i n u o u s a n d s p a c e is c o n t i n u o u s , it f o ll o w s t h a t t i m e m u s t b e

d i s c o n t i n u o u s .



372

J O U R N A L O F T H E H I S T O R Y O F P H I L O S O P H Y

26:3

J U L Y

~988

Gueroult gives what appears to be an inverted form of this argument:

Whereas Galileo justifies the infinite dimin ishmen t of speed by the infinite

divisibility of time, which implies that of the instant itself, Descartes, consider-

ing that the instant cannot be diminished and is an indivisible in all rigor,

concludes from this that the elementary speed is also an absolute indivisible

and that real (temporal) motion is made up of the repetition o f these indivisi-

bles (Guer. 282/199 ).

Thu s, fo r Gueroul t, Descartes' static analysis of motion is evidence for a

radical temporal atomism. Motion is analyzed in terms of a succession of

discrete states because time is discontinuous. The ref ore motion, like duration,

is composed of a discontinuous succession of actual indivisibles.

But despite appearances, and whichever way round it is proposed, this

argument is invalid. For it is perfectly possible for motion to be discontinuous

while space and time are both continuous. Such motion would be represent ed

on a gra ph of (continuous) space against (continuous) time by a discontinuous

line. But this kind of discontinuity has n othing to do with any composition out

of indivisibles. And far from deriving the discontinuity of motion f rom that of

time, as Gueroult suggests, Descartes was rather bound to assert it as a conse-

quence of his laws of collision. For his natural philosophy, unlike that of

Leibniz, could make no sense of the elasticity of matter; so colliding bodies

had to change their speed instantaneously, and thus discontinuously. It was of

course for the disharmonies attendant on these discontinuous changes of

motion that Leibniz took him to task,48 but not fo r any supposed d iscontinuity

in time. Indeed, nowhere in his writings does Leibniz attribute such a

discontinuous time to Descartes.49 The bottom line here is that a body unde r-

going a discontinuous change in its motion in a collision does not thereby

cease to exist at that time, but rather remains in existence continuously

throughout the process. It therefore has a continuous duration despite the

discontinuity of its motion.

To conclude, there is no doubt that Gueroult is right to draw attention to

the static charac ter o f motion in Cartesian physics, and with it the difficulty of

deriving duration from an instant that denies it, motion from a state (274/

193 ) . Descartes never comes to terms with time as an independen t variable or

geometric quantity. And Gueroult and Koyr6 are certainly correct to see this

48 H i s c r i t i q u e i s c o n t a i n e d i n h i s Crit ica l Thoughts on the General P art o f the Princip les o f Descartes

o f 1 6 9 2 , G . 4 : 3 5 4 - 9 2 , t r a n s l a te d b y L o e m k e r i n Leibniz Philosophical Papers and Letters 3 8 3 - 4 1 z .

49 I n f a c t, L e i b n i z s o b j e c t i o n t o D e s c a r t e s m e a s u r e o f c o n s e r v e d f o r c e p r e s u p p o s e s t h a t

C a r t e s i a n t i m e i s c o n t i n u o u s . A c c o r d i n g t o L e i b n iz , i f G o d e x e r t s a f o r c e o f m v a t e v e r y s in g l e

i n s t a n t a s D e s c a r t e s p r o p o s e s , t h e n , a s s u m i n g t i m e i s c o n t i n u o u s , t h e t o t a l f o r c e a c c r u i n g w o u l d

b e g i v e n b y t h e t i m e i n t e g r a l o f m v , w h i c h i s p r o p o r t i o n a l t o m y . S e e L e i b n iz s Specimen Dy-

namicum

i n L o e m k e r , e s p e c ia l ly 4 51 n . 7 , a n d r e f e r e n c e s g i v e n th e r e .




q u a s i - e li m i n a t io n o f t i m e a s o n e o f th e c h i e f d e f e c t s o f C a r t e s i a n p h y s ic s , a

s h o r t c o m i n g t h a t b o t h N e w t o n a n d L e i b n i z w e r e s o o n t o r e d r e s s . B u t t h i s i s

n o t a t a ll t h e s a m e a s h is h a v i n g a d v o c a t e d a c o n c e p t i o n o f t im e a s d is c o n t i n u -

o u s , a s c o m p o s e d o f i n d iv i si b le s , a s I h o p e m y a r g u m e n t h a s s h o w n . R a t h e r , I

c o n t e n d , t h is w a s s i m p l y t h e o n l y w a y D e s c a r t e s c o u l d f i n d t o g iv e a c o n s i s t e n t

a n al ys is o f c o n t i n u o u s m o t i o n a n d d u r a t i o n w i t h o u t t h e c o n c e p t s o f th e c a l cu -

l us : t h e r e m u s t b e a t e n d e n c y t o m o v e a t a n y p o i n t in t im e i n o r d e r f o r t h e

m o t i o n t o b e tr u l y c o n t i n u o u s ; c o r r e s p o n d i n g l y , t h e r e m u s t b e c r ea t io n a t a n y

i n st a n t in o r d e r f o r t h e r e t o b e c o n t i n u o u s e x i s te n c e a n d d u r a t i o n .

T h i s is i n fa c t t h e s e n s e o f th e p a s s a g e c o n c e r n i n g t h e m i n i m u m p o i n t o f

t i m e

minimum temporis puncture)

a l l u d e d t o a b o v e : f o r s i n ce t h e y a r e in p e r -

p e t u a l m o t i o n , a l t h o u g h it c a n s o m e t i m e s h a p p e n t h a t t h e y ar e a r r a n g e d i n

p r e c i se l y t h e s a m e w a y a s t h e l e a d e n b a ll s d e p i c t e d i n t h e f i g u r e , th i s c a n o n l y

l as t f o r t h e m i n i m u m p o i n t o f ti m e w h i c h t h e y c all a n i n s ta n t , a n d f o r t hi s

r e a s o n d o e s n o t i n t e r r u p t t h e c o n t i n u i t y o f t h e i r m o ti on . 5 o

C O N C L U S I O N

I h a v e a r g u e d t h a t t h e c la s si c t h e s i s is a m i s t a k e , t h a t a n a n a ly s i s o f t h e

p a s sa g e s w h e r e D e s c a r te s p u r p o r t e d l y a r g u e s f o r t h e d i s cr e te n e s s o f t im e r e -

v e al s o n l y a r g u m e n t s f o r t h e c o n t i n g e n c y o f all th e i n n u m e r a b l e p a r ts i n to

w h i c h ti m e c a n b e d i v id e d , t h e d e p e n d e n c y o f th e i r c o n n e c t io n o n G o d ' s c o n -

t i n u o u s a c t i o n . I h a v e a r g u e d t h a t G o d ' s a c t o f c r e a t io n , a l t h o u g h i n i ts e l f

i n d i v is i b le , is c o n t i n u o u s a n d i n d e f i n i t e l y d i v is i b le i n r e s p e c t o f i ts d u r a t i o n , a n d

t h a t o n l y s u c h a t r u l y c o n t i n u o u s c r e a t i o n w o u l d b e e q u i v a l e n t t o c o n s e r v a t i o n .

A n d I h a v e a r g u e d t h a t D e s c a r t e s ' c h a r a c te r i st i c w a y o f a n a l y z in g t e m p o r a l

a c t iv i ty i n ' t e r m s o f i n s t a n t a n e o u s t e n d e n c i e s t o a c t a t e a c h i n s t a n t is p e r f e c t l y

c o m p a t i b le w i th h i s h o l d i n g t h a t t h o u g h t s a n d m o t i o n s a r e c o n t i n u o u s in t im e ,

d e s p i t e h is a v o w a l o f t h e e x i s te n c e o f d i s c o n t in u o u s c h a n g e s o f m o t io n .

B u t I h a v e n o t a r g u e d t h a t D e s c a r t e s p r e s e n t s u s w it h a c o h e r e n t o r s a ti sf a c-

t o r y a c c o u n t o f t h e c o n t i n u it y o f t im e , o f h o w a c o n t i n u o u s d u r a t i o n c o u l d b e

c o m p o s e d o f a n i n fi n it e o r i n d e f in i te n u m b e r o f d u r a t io n l e s s i n st an ts . N o r

s h o u l d I h a v e , a s I s h a l l n o w a r g u e , s i n c e D e s c a r t e s d o e s n o t r e g a r d t h e

p r o v i s i o n o f a t h e o r y o f c o n t i n u i t y a s a l e g it i m a t e e n d e a v o r .

T o s e e th i s, o n e n e e d o n l y s u r v e y D e s c a r t e s ' r e a c t io n s t o G a l il e o' s a t t e m p t

t o p r o v i d e s u c h a t h e o r y i n h i s Two N ew Sciences . G a li le o h a d p r o p o s e d t h a t t h e

c o n t i n u u m , t h o u g h i n f in i te l y d i v is i b le i n t o q u a n t i f i e d p a r t s ( th e i n n u m e r a -

5 0 P r i n c i p l e s

I I I , w A T , 8 A : 1 1 5 , a l . 5 - 1 o : c / ir a e n i m i n p e r p e t u o si n t m o t u , q u a m v i s

a l i q u an d o p o s s i t co n t i n g e re , u t eo d em p l an ~ : m o d o t i n t d i s p o s i t i a c g i o b i p l u m b e i i n h ac f i g u rh

d e p i c ti , h o c n o n n i si p e r m i n i m u m t e m p o r i s p u n c t u m , q u o d i n st a n s v o ca n t , d u r a r e p o te s t, & i d e 6

c o n t i n u i t a t e m e a r u m m o t O s n o n i n t e r r u m p i t .



3 7 4 J O U R N L O F T H E H I ST O R Y O F PH I L O SO P H Y 6:3 JULY 1 9 8 8

b l e f in i t e p a r t s i n t o w h i c h D e s c a r t e s ' l i fe c o u l d b e d i v i d e d ) , w a s a l s o d i v is i b le

i n t o a n in f i n it y o f u n q u a n t i f i a b l e p a r t s o r in d iv is ib l es , t h e m s e l v e s s e p a r a t e d

b y i n di vi s i bl e vo i ds , w h i c h h e s u p p o s e d h e l d m a t t e r t o g e t h e r b y s u c t io n . T h e s e

i n di v is ib l es t h e n b e c a m e t h e b a s is f o r t h e p i o n e e r i n g w o r k o f hi s p u p il s C a v a -

l ie r i a n d T o r r i c e l l i in t h e I n t e g r a l C a l c u l u s ( m o r e a c c u r a t e ly , t h e G e o m e t r y o f

I n d iv i si b le s ), w h e r e a li n e w as u n d e r s t o o d a s c o m p o s e d o u t o f a n i n f in i t y o f

i n d i v is i b le p o i n t s , a s u r f a c e o u t o f a n i n f i n i t y o f i n d iv i s ib l e li n e s, a n d s o f o r t h .

D e s c a r t e s ' r e a c t i o n t o a ll th i s is s c a t h i n g , t o s a y t h e l e as t. T h e b a s is f o r t h i s

h o s ti li ty , a s w e s h o u l d h a v e e x p e c t e d f r o m h is d i sc u s s io n s i n t h e

P r i n c i p i a

a n d

e l s e w h e r e , is t h a t t o g i v e a n a c c o u n t o f c o n t i n u i t y i n v o lv e s r e a s o n i n g a b o u t

i n fi n it y , a n d t h is i s n e c e s s a r il y b e y o n d o u r r e s o u r c e s a s f in i te c r e a t u r e s . T h e f a c t

t h a t G a l i l e o a c k n o w l e d g e s t h is a n d s ti l l g o es a h e a d w i t h h is a c c o u n t o f c o n t i n u -

it y, a p p e a r s t o D e s c a r t e s a s o v e r w h e l m i n g h u b r i s . I n r e p l y t o M e r s e n n e , w h o

s e n t h i m a c o p y o f G a l il e o 's b o o k f o r h i s c o m m e n t s , h e w r i te s : H e is l a c k i n g i n

e v e r y t h i n g h e s a y s a b o u t i n f i n it y , i n th a t , n o t w i t h s t a n d i n g h is a d m i s s i o n t h a t

t h e h u m a n s p ir it , b e i n g f in i te , is n o t c a p a b l e o f u n d e r s t a n d i n g i n fi n it y , h e d o e s

n o t s t o p d i s c u s s in g e v e r y t h i n g a s i f h e u n d e r s t o o d it j u s t t h e s am e . s x

A s f o r t h e d e t a i ls o f G a l i le o 's t r e a t m e n t o f t h e c o n t i n u u m , D e s c a r t e s r e je c t s

t h e t h e o r y o f i n di vi s i bl e b u t e x p a n d a b l e v o i ds w i th t h e r e m a r k : T h e w h o l e o f

w h a t h e s a y s a b o u t r a r e f a c t i o n a n d c o n d e n s a t i o n is n o t h i n g b u t a s o p h is m . ~ ,

S i m i la r ly , G a l il e o 's p r o o f t h a t a s t r a ig h t l i n e is c o m p o s e d o f a n i n f i n it y o f

a c t u a l p o i n t s is d i s m i s s e d b y h i m a s o n l y a n i m a g i n a t i o n , p u r e a n d s im p l e. 5 3

T h i s j u d g m e n t a l o n e , i n c i d e n ta l l y , s e e m s t o m e s u f f i c i e n t t o d i s p o s e o f

G u e r o u l t ' s c o n t e n t i o n t h a t D e s c a r t e s c o n c e i v e d i n s ta n t s f r o m t h e a b s t r a c t a n d

i m p e r f e c t p o i n t o f v i ew o f c r e a t e d e x i s t e n c e a s i n f in i te l y s m a ll a c t u al th i n g s

( G u e r . , 2 7 5 / 1 9 5 ) .

T h i s d is m i s sa l o f G a l i le o 's p r o o f t h a t t h e l in e is c o m p o s e d o f a c t u a l

i n d iv i s ib l e s a s a n i m a g i n a t i o n is i t s e lf s i g n i f ic a n t i n t h e l i g h t o f D e s c a r t e s '

c o n t r a s t b e t w e e n b e i n g a b le m e r e l y to i m a g i n e s o m e t h i n g , a n d b e i n g a b le t o

p r o p e r l y u n d e r s t a n d it . T h u s , w e m a y t h i n k ( w it h G a l i le o ) t h a t w e c an i m a g i n e

a l a s t e l e m e n t i n a n i n f i n i t e d i v i s i o n , a n a c t u a l i n d i v i s i b l e ; b u t n o m a t t e r h o w

s m a l l w e i m a g i n e s u c h i n d i v is i bl e s to b e, w e n e c e s sa r i ly r e p r e s e n t t h e m i n o u r

i m a g i n a t i o n a s e x t e n d e d , a n d c a n t h u s c l e a r l y a n d d i s ti n c tl y c o n c e i v e t h e i r

d i vi si b il it y . T h u s o u r i m a g i n a t i o n d e c e i v e s u s : i n d i vi s ib l e s a n d t h e a c t u a l l y

i n f i n it e l y s m a l l a r e n o t d i s t i n c t ly c o n c e i v a b l e .

5, Descartes to M ersenne, l 1 October 1638,Correspondance CXL VI: 383: II manque en tout

ce qu'il dit de l 'infini, en ce que, n onobstant qu'il confesse que l'esprit hum ain, estant fini, n'est pas

capable de le com prend re, i l ne laisse pas d 'en discourir tout de m esm e que s ' il le comprenoit.

5, To ut ce qu'il dit de la rarefaction & condensation n'est qu'vn sophisme (ibid., 384).

53 II fait considerer vne ligne droite, descrite par le mo uuem ent d'vn cercle, po ur pr ou ue r

qu'eUe est com pos~e d'vne infinit~ de poins actu ce qu'il n'est qu'vne imagination toute pure

(ibid., 384).




There is a similar failure of imagination with respect to infinite division,

which, as Beyssade observes (350), Descartes appeals to in his explanation of

the "catch" in Zeno's Achilles Paradox. The paradox, as Descartes himself

expounds it, is as follows: a tortoise, which has ten leagues' start on a horse

going ten times as fast as it, can never be overtaken by the horse, because while

the horse covers ten leagues the tortoise covers one more, and while the horse

covers this league the tortoise advances anoth er tenth o f a league further , and

so on to infinity."~4 Descartes has already set up a correct solution to the

paradox, by showing how a geometrically decreasing infinite series of finite

parts, such as r + v%o + r + . . . nevertheless adds up to a finite whole, in

this case r This he does entirely geometrically, without recourse to the idea of

a limit, by an ingenious application of the Method of Exhaustion. He consid-

ers a line AB, and subtracts 88 from the left side, and SAoths from the right

side. He then subtracts a fu rthe r iAoothfrom the left, and S/,ooths fro m the right,

and so on till the length of the line is exhausted "and one will have arrived

from both sides precisely at the point G" (446). But the ratio of 1:8 having

been preserved for all the lines subtracted, this must be the ratio of their

aggregata, AG:GB. So AG:AB = 1:9, and it follows that at the end of a nin th of

a league, the horse begins to overtake the tortoise. He then concludes: "And

the catch lies in that one imagines that this ninth part of a league is an infinite

quantity, because one divides it in one's imagination into an infinity of parts"

(ibid.). Thu s the paradox arises thro ugh a limitation of the imagination. One

can imagine an infinite division only by picturing an infinite collection of parts

in one's mind. But this seems to entail an infinite quantity, hence the catch.

However, by applying the methods of geometry, and without any appeal to

what happens a t infinity," one may und ers tand that when the division is

"done an actually infinite nu mber of times" (ibid., 446), the aggregate o f terms

will be '/9.

This example shows very nicely, I believe, how Descartes thought one

should tackle problems having to do with the actual infinite without subjecting

oneself in any way to the limitations of the imagination, or committing oneself

to the "last elements" o f an actually infinite division.

Thus, in conclusion, I maintain that Descartes not only did not hold that

durations were composed of an infinity of really discrete actual indivisibles,

but this is a view he could not have held.

M iddlebury College

L e t t e r t o C l e r s e li e r , J u n e / J u l y 1 6 4 6, A T . 4 : 4 4 5 - 4 7 . S h o w i n g a n ic e t o u c h o f h u m o r , D e s -

c a r t es s i g n s t h i s l e t t e r I a m i n f in i t e ly y o u r s , R e n &

1988-continuous creation continuous time a refutation of the alleged discontinuity of cartesian time

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