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Descartes on the Infinity of Space vs. Time: Texts and Studies in the History of Philosophy

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Abstract

In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite (or indefinite) extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes that we always imagine an earlier time in which God might have created the world if he had wanted, but insists that this imaginary earlier existence of the world is not connected to its actual duration in the way that the indefinite extension of space is connected to the actual extension of the world. This paper considers whether Descartes’s metaphysics can sustain this asymmetrical attitude towards infinite space vs. time. I first consider Descartes’s relation to the ‘imaginary’ space/time tradition that extended from the late scholastics through Gassendi and More. I next examine carefully Descartes’s main argument for the indefinite extension of space and explain why it does not apply to time. Most crucially, since duration is merely conceptually distinct from enduring substance, the end or beginning of the world entails the end or beginning of real (as opposed to imaginary or abstract) time. In contrast, extension does not depend on any enduring substance besides itself.
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6608 Ohad Nachtomy
Reed Winegar
Editors
Infinity in Early Modern
Philosophy
~
Springer
44 A.
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Chapter 4
Descartes on the Infinity of Space vs. Time
Geoffrey Gorham
Abstract In two rarely
di
s
cu
ss
ed
pas
s
age
s
-
from unpubli
s
hed
note
s
on
th
e
Prin
c
iples
of
Philo
so
ph
y
a
nd a 1647 letter to Chanut
-
Des
car
t
es
argue
s
that
th
e
que
s
tion of the
i
nfin
i
te
(o
r indefinite) extension of
s
pa
ce
i
s
importantly
diff
e
r
e
nt
fr
om the infinit
y
of time
.
In both
pa
ss
ages, he is
an
xio
u
s
to block the application
o
f
h
is
well
-
known
argum
e
nt for the indefinite extension of
spa
ce to
time
,
in
ord
e
r to
a
v
oid the theologically
p
ro
blematic implication
th
a
t
the world
ha
s
no
beginn
i
ng.
Desca
r
tes concedes that we
a
lways imagine an
ea
rl
ie
r time in which God might
h
a
ve created the world
i
f he had
w
a
nted
,
but
insist
s
that
thi
s
imaginary earlier
e
x
i
s
-
t
e
nce of
t
he world
i
s
no
t connected to its actual
du
rat
ion in the
wa
y that the
inde
fi
-
n
i
te
e
xtension
o
f space
i
s
co
nnected to the actual
ex
t
e
n
s
ion of the
world
.
This
pap
er
c
o
nsiders whether
De
scar
te
s's
metaphysic
s
can
s
u
s
tain this
asy
mmetr
i
cal
attitud
e
towards infinite
s
pace
vs.
tim
e
.
I
firs
t consider
De
sc
artes's
r
e
l
a
tion to the
'
imagi-
n
ar
y
' s
pace/time tradition
th
a
t
e
x
tended from the
l
a
te
s
chol
as
tic
s
through
Ga
ss
end
i
and More
.
I
nex
t
ex
amine carefully
Descarte
s's main argument for the
inde
fi
nit
e
ex
tension of space
an
d
e
x
plain why it does
no
t
a
pply to
tim
e
.
Most crucially,
s
i
nc
e
duration
i
s
merely conceptually distinct from
endu
r
ing
s
ub
s
tance, the end or begin-
ning of the world entail
s
the
e
nd or beginning
o
f
r
e
al (as opposed to imaginary
o
r
abs
tract) time. In
cont
ras
t
,
ex
tension doe
s
not
dep
e
nd on
an
y e
nduring
sub
s
tance
be
sides itself.
4.1 Introduction
A
lthough one prominent commentator has
d
e
clared that
th
e
i
nfinite pla
y
s
so
i
mpo
r
-
t
a
nt a part in the philo
s
ophy
o
f
De
s
cartes that
"Cartes
ia
ni
s
m may be consid
e
r
e
d
a
s
being wholly based
o
n
that idea" Koyre (1957,
106)
,
D
es
car
t
es himself
w
a
rn
s
u
s
that
"
we should never enter into arguments about the
i
nfinit
e" (AT 8A
1
4; CSM
1
G. Gorham
(
r8J
)
Philo
s
oph
y
Department
,
Ma
c
a
le
s
t
er
C
o
llege
,
Saint
Paul
,
M
N,
U
SA
e
-
m
a
il
:
ggorham
@
ma
ca
l
es
te
r
.
edu
©
S
pringer International
Publi
s
hing
AG
,
part of
Sp
r
inger
Natur
e
2
01
8
0
.
N
achtomy
,
R
.
Winegar
(
e
d
s.),
Infini
ty in
E
arl
y M
o
d
e
rn
Phil
osophy,
The
N
ew
Sy
nthese
Hi
st
o
r
ic
al
L
ib
ra
r
y 76,
h
t
tps://doi.org/10
.
1007
/978-
3
-
3
19
-
94556-9 _ 4
45
46 G. Gorham 4 Descartes on the Infinity of Space vs. Time 47
201). Descartes hoped to forestall "tiresome arguments" about the infinite by
sub
-
stituting the more modest, anthropocentric notion of the indefinite: "in the case of
anything in which, from some point of view, we are unable to discover a limit, we
shall avoid asserting that it is infinite and instead regard it as indefinite" (AT 8A
15;
CSM
1
202). But although familiar conceptual paradoxes about the infinite
-
such
as
whether the infinite is odd or even
-
are perhaps sidestepped in this way, long
-
standing cosmological problems about the extent and duration of the world are
merely
re
-
formulated: from our point of view, can we discern whether the world has
limits in space and time?
Descartes maintains that the world is spatially indefinite but temporally limited.
He therefore departs from the standard
seventeenth
-
century method of treating
space and time as analogous, with conclusions about the structure of space typically
extended, with minimal adjustments, to time.
1
For Descartes, the indefinite
exten
-
sion of space (and hence body) was a conceptual necessity (notwithstanding the
incomprehensible power of God). In the Principles
of
Philosophy (II, 21) he insists
that wherever we imagine boundaries to extension we are forced to recognize that
there must be indefinitely extended space beyond them "which we not only imagine
but also perceive to be truly imaginable, that is, real" (AT 8A 52; CSM
1
232).
Similarly, he explains to Henry More: "I think it involves a contradiction that the
world should be finite; because
I
cannot but conceive a space beyond any bounds
you assign to the universe; and on my view such a space is a genuine body" (AT
5
345:
CSMK 375). Put simply, Descartes's argument is that we find it inconceivable
that extension (hence body; hence the world) has limits.
It
might seem that we find it just as difficult to conceive temporal limits on the
world. That is, we find it hard to conceive how a motion, a body, or the world as a
whole, could begin (or end) without being preceded (or followed) by time.
If
so, it
should follow for Descartes that duration is indefinite in both temporal directions
just
as
extension is indefinite in all spatial directions. However, although he does not
raise this issue in either published versions of the Principles, it evidently occurred
to
Descartes that his reasoning about indefinite extension in Principles II, 21, men-
tioned above, would seem to make extension and duration equally indefinite. For in
his own annotations to the Principles he notes, and attempts to allay, the "fear that
in philosophizing about the indefinite extension of the World we should find its
duration likewise mounting to
infinity"
.
(AT
11
656).
2
He observes, for one thing,
that faith precludes an eternal world (at least looking backwards). Thus, in the anno
-
tation Descartes references his own admonition at the end of Part One of the
Principles, that "divine authority must be put before our own perception" (8A 39;
CSM
1
221). But he also declares it certain that our "natural reason" (ratione
naturali) cannot decide for us the question of the world's beginning. Unfortunately,
his annotation leaves the matter there, deferring to faith.
I
think it is worth inquiring
why Cartesian natural reason
-
which is so confident about the indefinite extension
of the
world-
is incapable of discerning its duration (whether indefinite or not). The
answer I will offer depends on a fundamental ontological asymmetry between
Cartesian space and
duration
.
4.2 Letter to Chanut
I:
Space
Fortunately, Descartes takes up the issue in more detail in a 1647 letter to Chanut,
who had passed on Queen Christina's concerns that Descartes might be among
those who hold the world to be infinite, and that such a doctrine was injurious to the
Christian religion (May 11, 1647; AT
5
21). In response, Descartes first puts himself
in the good company of the "Cardinal [Nicholas
]
of Cusa," who "supposed the
world to be infinite without ever being censured by the Church" (June
6,
1647; AT
5
51; CSMK 319). And he points out that we honor God to the extent we represent
his works as great. He goes on to emphasize, as in the Principles and annotations,
that he maintains only that the world is indefinite rather than infinite. In the Principles
themselves (I, 26- 7) he explains that the term 'infinite' should be reserved for God,
the sole being we understand positively to have no limits. We should say a being is
indefinite when we know only negatively that "we are unable to discover a limit"
(AT 8A
15;
CSM
1
202. See also AT
5
356; CSMK 377).
This account seems to conflate several distinct senses in which we might be
unable to discover a limit:
(i) any limit we discover could conceivably be greater.
(ii) we cannot discover any limit.
(iii) we cannot conceive (or find contradictory) any
limit.
3
Consider the examples of undiscoverable limits Descartes gives in the Principles:
the number of stars; the divisibility of quantity; the extension of the universe. The
number of stars seems to be indefinite in the weakest sense above (i). He says that
however many stars we imagine there to be, "God could have created more" (ibid.).
But this seems too weak a sense of indefinite for Descartes's conception of space,
since it would include even things with limits we might actually determine, such as
the number of humans or the size of the earth. (In fact, Descartes drops the 'number
of stars' example from all subsequent discussions of the indefinite.) The stars might
also qualify under (ii) since it may be that they are too numerous or remote for
1
See further Gorham (2012).
2
The annotations were found among papers owned by Leibniz, who titled them 'Annotations
which Descartes seems to have made on his Principles
of
Philosophy' (AT
11
545). The date is
unknown, though obviously between 1644 and 1650. On their
orig
i
n and
authenticity
,
see AT
10
207-210;
AT
11
647a and 654a. Judging by the
s
u
rrounding notes, it is plausible that Descartes is
here commenting on Principles II, 21.
3
Wilson notices this "haziness" in the characterization of indefiniteness but offers
a
slightly differ-
ent taxonomy: (i) we notice no limit; (ii) we cannot conceive a limit; (iii) a limit is repugnant or
contradictory (1999, 113). I am unsure about her distinction between (ii) and (iii) since Descartes
says to More: "It conflicts with my conceptions or, what is the same,
i
nvolves a contradiction that
the world should be finite or bounded; because I cannot but conceive a space beyond whatever
bounds you assign to the universe" (AT
5
345; CSMK
374-5)
.
For recent, illuminating discussions
of the infinite/indefinite distinction in Descartes see Ariew
(
1987), Kendrick
(
1998) and Schectman
(this volume).
48 G. Gorham 4 Descartes on the Infinity of Space vs. Time 49
beings like
us
to gauge even though we can easily conceive that there is a definite
limit. (I'll later suggest that the duration of the universe is indefinite in at most the
senses of (i) or (ii).) The divisibility of the quantity and extent of the universe seem
to be indefinite in the strongest
se
n
se of (iii) and it is this sense that is most
impor
-
tant to Descartes. Thus when it comes to his specific arguments about indefinite
divisibility and extent later in the Principles, he emphasizes that we are unable to
conceive a genuine limit to the division and extent of
matter.
4
(iii) is also the crucial sense of 'indefinite' in all the passages that address
indefi
-
nite spatial
vs.
temporal extent. Thus, returning to Descartes's response to Queen
Christina, he admits that although we lack a positive reason to know the world is
infinite, can we neither prove nor even conceive that it is finite. For "if we suppose
the world to be finite we are imagining that beyond its boundaries there are some
spaces which have three dimensions of their own and so are not purely imaginary,
as
the philosophers label them" (AT
5
52; CSMK 319). He once again reassures the
Queen (via Chanut) that he does not assert that the world is abso
l
utely infinite since
God may know it to be limited for reasons incomprehensible to us; nevertheless,
since he finds himself unable to conceive that the world has bounds he concludes
that the world is indefinite. Descartes then turns to the question whether the same
logic proves the duration of the world to be indefinite (in the future and past). Before
examining his treatment of this question, it will prove worthwhile to digress briefly
on
the historical context of Descartes
's
analysis.
negation or privation
...
this
is
also true in the example of imaginary succession,
which we conceive apart from real time" (DM 54,
IV,
7). Among non-Aristotelian
contemporaries of Descartes, Gassendi also relied on the imaginary space
/
time tra-
dition in defense of an infinite universe: "by the words 'space' and 'spatial dimen-
sions' we do not mean anything but that space which is commonly called 'imaginary'
and which the majority of sacred doctors admit exists beyond the world" (Brush
389). Gassendi is more guarded than Descartes about the ontology of space, empha-
sizing with the scholastics that it is nihil positivam since it falls outside the
sub
-
stance
/
accident dichotomy. Nevertheless, he insists that "space and time must be
considered real things, or actual entities, for although they are not the same sort of
thing as substance and accident they still exist and do not depend on the mind"
(Brush
384
-
5). Both extramundane space and premundane time are real: "the
uni
-
verse could have been created a
tho
u
sand years before the creation
...
because time
then flowed, of which the revolutions of the sun such as we now have could have
been an adequate
measure
"
(Brush
397).
7
So although Suarez and Gassendi draw
different conclusions about the ontological status of space and time, they both
assume that what goes for the one, goes for the other.
4.4 Letter to Chanut II: Time
4.3 Digression: Imaginary Space
Returning to Descartes we find, in contrast, that he resists the implication that imag-
inary time is as real and indefinite as imaginary space. In the letter to Chanut, after
rehearsing his argument for the indefinite extension of the world, he turns to the
worry (not raised by Christina) that this proves too much, namely that the world also
has no beginning or end in time. Descartes remarks that comparing the extension of
the world with its duration in this respect merely occasions the thought "that there
is no imaginable time before the creation of the world, in which God could not have
created it if he had so willed" (AT
5
52; CSMK 320). His point does not seem to be
that we cannot imagine time before creation, since we clearly can, but simply that
God
cou
l
d have created the world at any such imagined earlier time. Of course,
there is likewise no imaginable space beyond the boundaries of a putatively finite
world in which God could not have created matter. The difference is that natural
reason alone tells us that God really did create
extension
/
matter in the indefinite
space we imagine; but in the case of time Descartes insists that the always earlier
imaginable duration of the world does not entail that God "really did create it an
indefinitely long time ago" (AT
5
53; CSMK 320). He argues as follows:
For the
act
u
al or real existence of the world during the last five or
s
i
x
thousand years is not
connected to the possible
o
r imaginary existence which it might have had before then in the
way the
actua
l
spaces one conceives
surroundi
n
g a
g
l
obe (i.e. the
wor
l
d as supposed infi-
nite) are connected with the actual existence of the same
g
l
obe (ibid.).
The alleged dis-analogy in the
'connections
'
between imaginary and actual
spaces vs. imaginary and actual duration is not immediately evident. Perhaps
In an
important, late defense of the indefinite extension of the world, Descartes
explicitly contrasts his own view with those "who call this space imaginary and thus
regard the world as finite" (AT
5
345; CSMK
37
5). In both this letter to Henry
More, and
in
the letter to Chanut, Descartes is adverting to a long tradition within
late scholasticism analyzing the ontological status of the space we
'imagine
'
beyond
the limits of our finite
world.
5
The metaphysics of Suarez, for example, which was
known
to
Descartes,
6
admits an 'imaginary space
'
beyond the finite realm of the
cosmos in order to conceive the place of tile outermost sphere, the power of God to
translate the entire world, and so on. And imaginary time or succession is likewise
permitted for parallel reasons. However
,
Suarez is at pains to emphasize that imagi
-
nary space and time are mere conceptual tools or 'beings of reason' in contrast with
the real space and time of bodies and motion: "We conceive of this imaginary space
as having dimensions. But so conceived this space is a mere being of reason, a
4
AT
3
477; CSMK
3
202; AT
5
273; CSMK
363
.
5
The definitive treatments of this tradition are Duhem (1987) and Grant (1981). Des Chene (1996)
also provides an insightful discussion, giving particular
attentio
n to Descartes. On imaginary time,
especially in
S
u
arez, see Daniel (1981) and Bexley (2012).
6
AT 7
235; CSM 2
164
7
See LoLordo (1997).
50
G. Gorham 4 Descartes on the Infinity of Space vs. Time
51
Descartes's point is simply that, given the conceptual interdependence of space and
body, imaginary space entails actual body; but there is no parallel interdependence
between time and body. But this would not show that we can conceive a beginning
or end to time itself, on Descartes's
terms
.
For his proof of the indefinite extension
of the world would still.imply the indefinite extension of mere space even
if
he con-
ceded the possibility of a finite world surrounded by an extramundane vacuum. This
is most evident in the Principles version of the proof, which proceeds in two
steps
.
He first maintains that the space we inevitably imagine beyond any putative limits
to the world is not something we "merely imagine" but something "imaginable in a
true fashion, i.e. real (vere imaginabilia, hoc est realia esse)" (AT 8A 52; CSM
1
232). The next step is that "it follows that these spaces contain corporeal substance
which is indefinitely extended"
(Ibid
.
). This follows from the reality of the space
beyond limits, he points out, given the identity of space and body established a few
sections earlier (II, 11). So even someone who rejected this second step, and insisted
on a real distinction between extension and body, would have to admit an indefinite
extramundane void based on the first step. Descartes himself makes this point in
response to More, who invoked the famous Archytas thought experiment (AT
5
312)
of extending a sword at the edge of a supposedly finite
world
:
"When you imagine
a sword going through the limits
o
f
the universe, you show that you too do not con-
ceive the world as finite
.
..
though you give the name 'vacuum' to what you con-
ceive" (AT
5
345; CSMK 375). Similarly, the fact that we imagine always earlier
(later) times would entail an indefinite past (future), according to Descartes's argu
-
ment, even
if
that past (future) is empty rather than full of matter and
motion
.
4.5 Cartesian Duration and Time
But what is duration itself? Several sections earlier in the Principles, Descartes
lists duration (along with
substance
,
order and number) among the most general
categories which "extend to all classes of things" whether thinking or extended (AT
8A 23; CSM
1
208). A little later he says we can have a distinct understanding of
these universal or transcendental
catego
r
ies only if we do not assign to them the
status of
substance
.
Thus, rather than being anything separate from the thing which
endures "we should regard the duration of a thing as simply a mode
unde
r which we
conceive the thing insofar as it continues to
exist
" (AT 8A 26; CSM
1
211). His
point here is not that duration is a mere mental abstraction, or mode of thought, like
time. For he goes on to classify duration as an
unchang
i
ng
attr
i
bute: "that which
always remains unmodified
-
for example existence or duration in the thing which
exists or endures
-
should be called not
a
quality or mode but an attribute" (AT 8A
26; CSM
1
211-2)
.
As
such
,
duration and existence are not mere modes of thought
but rather ways in which anything can be conceived.
Indeed
,
he observes that "since
a substance cannot cease to endure without also ceasing to be, the distinction
between a substance and its duration is merely a conceptual one" (AT 8A 39; CSM
1
214). In the French edition of the Principles, he observes that all such attributes
"allow us to have different thoughts about a single
thing
" (AT 9B 53).
We can now see why Descartes can allow neither time nor duration before/after
creation: not time, because
i
t is a mere mode of thought, and not duration, because
it cannot be really separated from the continuance in existence of things. He makes
this explicit in the correspondence with
More
.
More suggested:
"If
God annihilated
the universe and created another one out of nothing much
later
,
this
'between-world
'
or 'world-absence' would have its own duration whose measure would be days,
years and
centuries
.
There is
the
r
efore a duration of something that does not exist"
(AT
5
302)
.
Descartes
'
s
reply is blunt:
"
it involves a contradiction to
conce
i
ve of any
duration intervening between the destruction of an earlier world and the creation of
a new one" (AT
5
343; CSMK 373). This response confirms my point that Descartes
cannot avoid a world indefinitely extended
i
n
time
,
any more than a world indefi
-
nitely extended in space, by separating time or duration from the
world
.
His dismissal of
'between-world
'
duration also reveals how similar
Descartes
'
s
reasons for rejecting empty t
i
me are to his reasons for rejecting empty space.
Extension and duration are both attributes, the latter general or transcendental and
the former peculiar to bodies. But we have already noted that attributes are merely
conceptually distinct from their substances. So to conceive an extension distinct
from corporeal substance is to conceive an extended nothing. Thus, Descartes
rejects extension without body because "it is a complete contradiction that a particu-
lar extension should belong to nothing" (AT 8A 49; CSM
1
230).
9
We can now see
that he rejects More's
speculat
i
on about a duration of
"
something that does not
exist" as
contrad
i
ctory for the same reason. It invites us to conceive duration apart
from any continuation in
ex
i
stence. But for
t
i
me to pass between worlds, with noth-
ing intervening, is no less contradictory than for the sides of a vessel to remain apart
though nothing is between them.
But perhaps this is enough for Descartes's purposes: he can allow indefinite empty
time before the creation of the world so Jong as the religiously problematic indefi-
nite pre-existence of the world is blocked. The problem is that Descartes's
meta
-
physical principles seem to preclude empty time no less than empty space. To see
why, we need to examine briefly his metaphysics of
time.
8
Contrary to the long
Aristotelian tradition that made time 'the number of motion', Descartes insists that
"
the duration which we find to be involved in movement is certainly no different
from the
durat
i
on involved in things which do not move" (AT 8A 27; CSM
1
212)
.
It
is true that in order to measure this duration common to all things, "we compare
their duration with the greatest and most regular motions, which give rise to
ye
a
rs
and days, and call this duration
'time'"
(Ibid.)
.
But Descartes insists that we must
not conflate duration itself, which is intrinsic to all things, with its temporal mea-
sure
,
which is an intellectual abstraction: "when time (tempus) is distinguished from
duration taken in the general sense (duratione generaliterv and called the measure
of movement (numerum motum), it is simply a mode of thought"
(Ibid.)
.
8
For a more detailed discussion, see Gorham (2007).
9
S
ee also AT
SA
50
;
CSM
1
231; AT
5
223; CSMK
358
.
52
G
.
Gorham
53
4.6 Creation from Eternity
So Descartes cannot allow duration to extend indefinitely backward without
admit
-
ting an eternal world, anymore than he can allow space to extend indefinitely beyond
a
limited material cosmos. Apart from falling back on faith, one way out of the
problem would be to demonstrate from natural reason that the world could not have
existed from eternity. But on this famous question, Descartes seems to adopt a quite
liberal position. In conversation with Burman, for example, he reportedly declares:
"I do not see why God should not have been able to create something from eternity"
(AT
5
155;
CB
15)
.
The topic at this point in the conversation is the second of the
Third Meditation's proofs of God
'
s
existence, which establishes that
I
would need
to be continuously created by God even
if
"I have always existed as I do now" (AT
7
78; CSM 2
33)
.
Indeed Descartes seems committed to eternal creation by his well-
known doctrine of the divine origin of the eternal truths: "from all eternity he willed
and understood them to be" (AT
1
152; CSMK 25). Descartes also makes clear that
an infinite or indefinite past is not absurd or contradictory in itself. When Burman
pushes him on the suggestion that God might have created the world from eternity
-
"but then there would have been an infinite number" (AT
5
155; CB
16)
-
Descartes
denies there is any absurdity in this. He points out that there is no less an infinite
division within any given finite
qu
antity. Indeed, Descartes seems to think the latter
sort of infinite division within matter
is
required under certain physical conditions
(AT
8A 59-60; CSM
1,
239).
10
He observes furthermore that we
believe
,
as a matter
of faith, that there is an infinite number with respect to the future, "so why shouldn't
it
be the same with respect to the past?" (AT
5
155; CB 16).
4.7
The Mereological Independence Doctrine
So
far,
the asymmetry remains unexplained: Descartes should say
-
faith
notwith
-
standing
-
that the world is indefinite
in
extension and
duration
.
But let us return
once again to the detailed letter to Chanut and consider more carefully Descartes's
insistence that the possible earlier existence of the world is not "necessarily con-
nected (necessairement jointe)" to its actual later existence in the strong way that
real extension is implicated beyond any imaginable boundary of the world. The
dis
-
analogy in these connections does not seem to arise from differences in our concep-
tions
.
For Descartes acknowledges that we find it difficult to conceive a temporal
beginning, though his expression is somewhat tortured: "il n 'y a point de temps
imaginable avant la creation du monde quel Dieu n 'eust
pule
creer,
s
'il eust voulu"
(AT
5
53;
CSMK
320). He does not explicitly say that we positively imagine earlier
times, only that there is no imaginable time unavailable for-earlier
creation
.
But his
argument doesn't seem to turn on such cautious phrasing. For he goes on to say
10
See also
AT
4 113; CSMK 232;
AT
5
274; CSMK 364; AT 7 113; CSM 2 81.
4 Descartes on the Infinity of Space vs. Time
explicitly that the world's "possible or imaginary existence" earlier does not entail
its actual indefinite existence. So we do positively imagine earlier times, just like
space beyond the world; but for some reason only the latter carries ontological
import.
Descartes does not reveal the reason until the very terse conclusion of his argu-
ment. After asserting the crucial
dis
-
analogy in the 'connections' between actual
and imagined space vs. time, he turns to a seemingly different issue: the eternal
future duration of the world (which faith teaches). He says the indefinite future pro
-
vides a more solid reason to infer its indefinite past duration than does its indefinite
extension.
Bu
t the former is not a solid reason at all: "no one infers" eternal creation
in the past from the promise of eternal life (AT
5
53; CSMK
320)
.
The relevance of
this apparent red herring to the crucial
dis
-
analogy with extension is made clear
only in the final clause of the paragraph, where he states that we cannot infer the
eternity of the world "because every moment of its duration is independent of every
other" (Ibid.).This, of course, is the
much
-
discussed premise of the second Third
Meditation proof of God's existence. In that proof, it is first restricted to the
medita
-
tor
's
own duration: "a lifespan can be divided into countless parts each completely
independent of the other" (AT
7
49: CSM 2 48). But Descartes later extends it to
bodies as well: "The separate divisions of time do not depend on one another. Hence
the fact that the body in question is supposed to have existed up until now 'from
itself,' that is, without
a
cause
,
is not sufficient to make it continue to exist in the
future" (AT
7
110; CSM
2
110)
.
11
From this he derives his version of the doctrine of
continuous creation
-
the entire universe must be
"
recreated" by God at each instant
so that "the distinction between preservation and creation is only a conceptual one
(AT
7
49; CSMK
33)-
which not only requires God's existence but also grounds the
laws of nature in the Principles
of
Philosophy (AT 8A 61; CSM
1
240).
Besides these two functions
-
proving God and the laws of nature
-
we can now
see that Descartes has a third role for the versatile doctrine of the independence of
temporal parts: blocking a seemingly Cartesian argument from natural reason for
the indefinite duration of the world. Granted that
I
always may, perhaps irresistibly,
imagine an
earlier
/
later time, it does not follow that what
I
imagine is real. For the
temporal parts of any enduring thing are not conceptually connected in such a way
that bordering parts of time guarantee one another's existence: "I regard the divi-
sions of time as being separable from each other so that the fact that
I
exist now does
not imply that
I
shall continue to exist in a little while" (AT
7
109; CSM
2
78
-
9).
While
I
can imagine that I go on living indefinitely, it is entirely up to God whether
this hope is realized. But the situation is different with extension,
I
would like to
suggest. When we consider the plenum abstractly, as geometrical res extensa, there
is
a sense in which its parts are mutually dependent. We can see this if we suppose
any part of extension persisting while a part next to it is destroyed. Either a vacuum
would then exist, which is impossible on Cartesian principles, or some other part of
''Versions of the argument and doctrine are repeated frequently. See AT 6
35
,
45; AT 8A,13; AT
7
109
,
165, 369-370; AT
5
45, 53, 155; CSM
1
128-129
,
133, 200; CSM 2
78
-
79, 116, 254-255;
CSMK 320; CB, 15-16. See Gorham (2004).
54
G
.
Gorham 4 Descartes on the Infinity of Space
vs
.
Time
55
extension would
'
move in' to fill the impossible gap (AT
5
272
-
3; CSMK 363). This
explains,
I
believe, why Descartes says in the Synopsis to the Meditations that while
individual bodies can perish since they are merely a collection of accidents, "body
in general (corpus in genere) can never perish" (unless God withdraws his
concur
-
rence) (AT
7
10;
CSM
2 14).
This mutual interdependence of parts also explains
why extension or body in general is
indefinite.
12
This does not mean that extension, unlike duration, is independent of God.
t
3
But
I think it does mean that if God creates any part of res extensa then the entire
indefi
-
nite plenum is necessitated as well, in one fell swoop. This is suggested in the
cre
-
ation story of Le Monde, which again exploits the imaginary space tradition: "a
whole new
[
world] which
I
shall bring into being before your mind in imaginary
spaces" (AT
11
31; CSM
1
90). Pre-existing imaginary space is, as it were,
presup
-
posed
.
While acknowledging that "the philosophers tell us that such spaces are infi-
nite", in order to prevent confusion Descartes asks us to confine our imagination "to
a
determinate space which is no greater, say, than the distance between the earth and
the principal stars in the heavens" (AT
11
32; CSM
1
90). It is clear that he is not
supposing that God might create a finite world, for he insists that "the matter which
God has created extends indefinitely far in all directions" (Ibid.). And we should
think of this indefinite matter as a "real perfectly solid body which uniformly fills
the entire length, breadth and depth of this vast space in the midst of which we have
brought our mind to rest" (AT
11
33; CSM
1
91). The "idea of this matter is included
to such an extent in all the ideas that our imagination can form that you must
neces
-
sarily conceive it or you never imagine anything at all" (AT
11
35; CSM
1
92)
.
Indefinite space as a whole is thus implied by the idea of any finite extended thing.
A similar point is indicated in a 1640 letter to Regius, who commented on a draft
of the Meditations. Descartes maintains that
I
could not have the positive of idea of
God's infinite perfections "unless we derived our origin from a being in which they
are actually infinite" (AT
3
64;CSMK 147). Somewhat
surprisingly
,
he extends this
reasoning to our idea of indefinite space: "Similarly I could not conceive of an
indefinite quantity by looking at a very small quantity or finite body unless the size
of the world was actually or at least possibly
indefinite
"
(Ibid
.
).
My account offers
a reason why Descartes is prepared to infer actually infinite space from the idea of
finite extension: the parts of space are all so conceptually connected that the idea of
any part requires the idea of all other parts, ad indefinitum.
The interdependence of the parts of space is also evident in Descartes's rejection
of a plurality of worlds in Principles II, 22, which immediately follows his
demon
-
stration of indefinite extension. He says the matter composing any other world
would have to be the same as composes this world, so not really a different world.
This seems to leave him open to the
plura
l
ist objection that another world might be
composed of the same kind of matter yet separate from this
one
.
But he insists that
this is impossible since "the matter whose nature consists simply in its being an
extended substance already occupies absolutely all the imaginable space in which
the alleged additional worlds would have to be located" (AT 8A; CSM
1
232). The
suggestion seems to be that any 'other' extended world is conceived as bearing a
spatial
rela
t
ion to the 'local' world, and therefore connected or interdependent in the
way that the shorelines of two continents and the ocean between them all mutually
connect.
So the parts of indefinite extension conceived as mere res extensa are mutually
dependent because the parts are nothing more than their mutual geometrical rela-
tions.
If
one of two neighboring parts had failed to exist then another would have
been in its place; but in that case the interloper would not be a distinct part from the
original. And if duration were conceived purely abstractly or geometrically, perhaps
as a line with a direction and flow, then its parts would be interdependent in a way
similar to space. Reaching the
7
th day of a week, for example, requires passing
through the first 6 days. But, as we have seen, Descartes is at pains to distinguish the
conc
r
ete duration of things (whether they move or not) from the abstract measure
'time'. The parts of duration, since they are identical to the continued existence of
enduring things, are not conceptually interdependent. My brother might endure
while
I
do not, and the world as a whole begins (or ends) when things begin (or
cease) to endure. In response to Gassen di, Descartes makes clear that the indepen-
dence of parts doctrine applies strictly to concrete duration rather than abstract time.
Thus, when Gassendi complained against the Third Meditation proof: "Can we
think of anything whose parts are more inseparable from one another than your
duration?" Descartes responded that such interdependence characterizes at most
"time considered in the abstract" but not "the duration of the thing which endures
(durantione rei durarantis)" (AT
7
369
-
70; CSM 2 255). This
exp
l
ains why he
ignores Gassendi's suggestion that the parts of a
thing
's
duration
"
are merely
exter
-
nal, they flow on without playing any active role" like
a
river flows past a rock (AT
7
301; CSM 2 209). For Descartes, such a metaphor wrongly takes duration (as
opposed to time) to be ontologically separable from enduring
things
.
But unlike the
hours of a day conceived as a measure, or extension conceived purely geometrically,
12
This
,
of course, is a version of the argument Spinoza would later champion that extended
sub
-
stance is not really divisible: "Since there can be no vacuum in nature (as I discuss elsewhere) but
all their parts must concur so there is no vacuum, it follows that they cannot be really distin-
guis
h
ed
" (Ethics I
Pl5
Schol (iv); C 96). There are many excellent discussions of
Descartes
'
s
theory of corporeal substance,
s
u
c
h as Slowik (2001).
13
Descartes
frequent
l
y asserts that corporeal
substa
n
ce is
divisib
l
e (AT
3
,
477;
CSMK
,
202-203
;
AT
8A
,
51
,
CSM 1,231), even
i
nto parts that are really distinct from one another (AT 8A, 29, CSM
1,
213). But the fact that the
d
i
fferent parts of matter are really
dist
in
ct, and hence substances as
such, does not imply that each part is an individual body. For
Descar
t
es, bodies are individuated by
relative motion so that "if the division into parts occurs simply in
ou
r thoughts there is no
resu
l
t
i
ng
change"
(AT
8A, 52; CSM
1,
2
32). Furthermore, and pace recent papers by Lennon (2007) and
Schmaltz (2009) it is unclear why the real distinction among the parts of extension should threaten
either the substantiality of extension itself or the doctrine that the parts of extension are mutually
interdependent. On the first
iss
u
e, there is no good Cartesian reason (I know of) to deny
s
u
bstanti-
ality
to
something that has really distinct or
s
ubstantial parts. On
thesecond
issue, the
part
s
of
extension seem to be mutually interdependent in the way
I
have described even granted all these
parts are really distinct. The question is not whether the parts of extension of duration are really
distinct
-
I
think they are in both cases
-
but whether these parts are mutually interdependent in
such a way that if one part exists then necessarily they all do.
56 G. Gorham 57
no part of my concrete duration is intrinsically linked to any other. And for this
reason we cannot infer from what we imagine about the world beginning earlier that
this is "truly imaginable, that is, real" (AT 8A 52; CSM
1
232).
1
4
4.8 Temporal Infinitists
To
summarize
,
Cartesian extension conceived purely abstractly or geometrically,
independently of this or that fleeting body, must be indefinite (at least relative to our
conception). In contrast, Cartesian duration is intrinsic to enduring minds and bod-
ies and no part of this duration carries any guarantee of continuance or
antecedence
,
however much we might imagine (or hope) it did. And this is the sense in which
"natural reason" aids faith in proscribing a world without a temporal beginning or
end (AT
11
656). It is worth noting that those among Descartes's contemporaries
who privilege abstract time over concrete duration
-
that is, who think time is prior
to and independent of the persistence of created things
-
tend to regard time as nec-
ess
a
rily infinite; and they do so for reasons that parallel Descartes's reasons for
denying infinity to concrete duration. For example, Gassendi insists that "time con-
sidered in itself has neither beginning nor end" (Brush 395). Gassendi is somewhat
unclear why time in itself "cannot be stilled by any force", but he is fond of the
analogy between space as mere extension in length, width and depth and time as a
"flowing extension in which it
i
s
possible to designate past, present and future"
(Brush 391). As we have seen, it is precisely this reification of time, conceived geo-
metrically, that Descartes rejects.
Newton endorses Descartes's basic argument that "we cannot imagine a limit
anywhere without imagining space beyond it" (DG 23). So he likewise agrees with
the doctrine of Le Monde that the concept
of
indefinite space is presupposed in the
idea of any finite object: "
if
any being whatsoever is posited, space is posited" (DG
25). Unlike
Descartes
,
Newton extends this analysis to duration: "we cannot think
that there is no duration even though we might suppose that no thing
endures
" (DG
26). Like
Descartes
'
s abstract time, the parts of Newton's duration depend on their
relations to all other parts: "the parts of duration are individuated by their order;
i
f
for example yesterday could change places with today, it would lose its identity and
become today" (DG 25). We can, of course, easily imagine an end to the duration of
this or that enduring thing, as Descartes points out. But it is as hard to conceive an
end to a mere ordering apart from anything else
-
such as the
Principia
'
s
"absolute,
true, and mathematical time,
[
which] of itself, and from its own nature, flows
equa
-
14
I
do not here take up the question of the infinite or indefinite divisibility of time. In my view, the
s
ame considerations in favor of-the
ind
e
finite division of space carry
ov
er to duration. Thi
s
is not
inconsistent with the independence of parts doctrine since
th
a
t concerns the relation between suc-
ces
s
ive parts of duration not the proper sub-parts of any temporal interval. The discussion of
Cartesian temporal (dis)continuity has
a
long history. Recent examples: Arthur (1988),
Garber
·
(1992
)
,
Levy
(2005)
,
and Gorham
(2008b
)
.
4 Descartes on the Infinity of Space vs. Time
bly without relation to anything
external
" (Principia 408)
-
as to conceive a limit on
geometrical space or the series of natural numbers.
Locke holds that anyone "may easily conceive in his mind the beginning of
motion but not at all duration
...
so also he
ma
y set limits to
body
,
and the extension
belonging to it, but not to space" (Essay II, xiv,
26
;
193)
.
But
,
even more than
Gassend
i and Newton, Locke recognizes the role mathematical abstraction, particu-
larly number, plays in convincing us of the necessary infinity of space and
time
:
"in
space and time, when the mind pursues the idea of infinity it there makes use of the
ide
a
s
and repetitions of number" (Essay II, xvii, 9; 215). More specifically, we think
of the infinite series of natural numbers as "like a
line
,
whereas one end terminating
with
us
,
the other is extended still forward beyond all that we can
conceive
" and "in
duration, we consider it as
if
this line of numbers were extended both ways to an
unconceivable, indeterminate and infinite length" (Essay II xvii 10;
215)
.
Gassendi, Newton and Locke all closely associate infinite space and time with
God's immensity and eternity. But Descartes strongly rejects any literal conception
of
God
's
immensity: "the alleged extension of God cannot be the subject of the true
properties which we perceive very distinctly in all space" (AT
5
271; CSMK 362). ts
But shouldn't the eternal duration of God (along with the eternal truths he decreed)
entail that time did not begin? Descartes himself suggests as much to Burman in
explaining
God
's
eternity:
since we can divide it up after the creation of the world why should it not have been pos-
sible to do the same before creation since duration remains
constant
?
Thu
s
,
eternity
ha
s
now co-existed with created things
for
,
say, five thousand years, and occupied time; so it
could have done the same before creation,
if
we had had
s
ome standard to measure it by.
(AT
5
149
;
CB 7)
However, I believe the passage can be reconciled with the letter to Chanut quite
easily. Since God is eternal (i.e. sempiternal), duration is indeed beginningless. But
this follows from the nature of God, not from our conceptions of time, whereas the
indefinite extension of the universe follows simply from our conception of space. It
is
pe
rhaps less easy to reconcile the Burman passage with
Descartes
'
s
dismissal
a
s
contradictory
More
's
speculations about a 'between-world' duration (CSMK 373).
1
6
But recall that Descartes is here responding specifically to
More
'
s
suggestion that
the
between-wor
l
d (intermundium) or
'
world-absence
'
(absentia mundi) "would
have its own
duration
" (AT
5
302). The contradiction consists in
s
upposing that the
'
world
-
absence'
it
s
elf
would have duration, any more than it would have extension,
not in supposing that God would then endure. The point to Chanut remains the
same: the universe is by its nature indefinitely extended but its duration depends on
the arbitrary will of
God
.
1
5
See also AT
5
275
;
CSMK 364
;
AT
5
342
;
CSMK
372
.
1
6
Koyre asserts that Descartes rejects
between-wo
r
ld duration because it would mean
"
introducing
time into
God
"
(I
957, 122). But why should duration between worlds make God
temporal
,
any
more than during worlds? Furthermore, there is no reason to regard a temporal God as
'contradic
-
tory
'
for Descartes and very good reasons to suppose that his God was in fact temporal. See
Gorham
(2008a)
.
58
G.
Gorham 59
4.9 Descartes and Early Spinoza
In early works of Spinoza, the influence
of
Descartes
'
s
metaphysics
of
time is very
clear.
In
the 'metaphysical
thoughts
'
(Cogitata
Metaphysica)
,
which he appended to
his 1663 'synthetic' exposition of Descartes's Principles
of
Philosophy (Descartes
Principiorum Philosophiae), Spinoza defines duration as "the
attrib
u
te under which
we conceive the existence of created things insofar as they persevere in their actual-
ity" (S 104; G
1,
244). So
conceived
,
he notes,
du
ration is distinct
on
l
y in reason
from the total existence of a thing since "as much as you take away from the duration
of th
i
ng so much necessarily you take away from its existence" (S
104
-
5; G
1
244).
As for
time
,
"
in order that duration may be determined, we compare it with other
things that have a fixed and determinate motion, and this comparison is called
time
"
(S
105;
GI
244)
.
Such 'clock
time'
,
he
emphasizes
,
"is not an affection
of
things
..
.
but rather a mode
of
thinking (modus cogitatndi) that we use to explicate
duration
"
(Ibid).
In
all of this he follows Descartes closely: the distinction between duration
and
t
i
me; the identification of the former as an attribute (continuation in existence)
that
is
merely distinct from the
end
u
ring thing; and that classification of the latter as
a conventional measure and hence a mere mode
of
thought. And so Spinoza likewise
agrees with Descartes that duration (and time) ceases "when created things cease to
exist and begin when created things begin to exist"
(
S
129;
GI
169).
But in a contemporaneous, independent letter ("On the Infinite"), Spinoza retains
the distinction between time and duration (and eternity) while seeming to hold that
duration is
infinite
.
He associates duration with the existence
of
modes, which he
suggests are infinite by the
"
force
of
the cause in which they
inhere
" (G IV
61
,
1
-
7;
C
205)
.
By this he seems to mean that the duration
of
modes is infinite insofar as
"
they flow from eternity without
whi
ch they cannot be rightly understood" (G IV
58, 2-3; C 203). What is noteworthy for our
purpose
s
is the duration
of
modes is
conceived as finite precisely because we abstractly divide it into parts: "when they
are conceived abstractly they can be divided into parts and regarded as finite" (G IV
612-3; C 205). Such division is the source
of
Zeno-like paradoxes of infinity: "when
s
omeone has conceived Duration
abstractly
,
and by confusing it with time begun to
divide it info parts, he will never be able to understand how an hour can
pass
" (G IV
58 5-7; C
203)
.
So the early Spinoza seems to split from Descartes on the question
of
infinite
duration precisely because he does not attribute parts to duration. This disagreement
is
evident in his
genera
ll
y sympathetic exposition
of
Descartes's
Princip
l
es
of
Phi
l
osophy. For instance, in his exposition
of
the second causal proof
of
God he
conspicuously omits the crucial premise about the mutual independence
of
the parts
of
time
.
Spinoza
'
s
critical exposition
of
the proof makes it instead depend entirely
on the assumption that
if
I were self-created, I would have given
myself
every
per
-
fection. Similarly, Descartes's
proof
o
f
the law of
rectilinear
motion turns crucially,
though somewhat obscurely, on the assumption that God preserves motion
"
in the
precise form in which it is occurring at the very moment he preserves it" (CSM I
242; AT 8A
64)
.
But Spinoza's puzzling reconstruction proceeds entirely from the
4
Descarte
s
on the Infinity of Space
v
s
.
Time
'
nature
of
motion
'
which supposedly
exclude
s
from consideration any "duration
that can be conceived as greater than another duration" (G I, 204;
S
65). These
amendments to
Descartes
'
s
official proofs illustrate
Spinoza
'
s
opposition to
Descartes on a metaphysical principle
-
the reality
of
temporal
part
s
-
th
a
t had
major implications for their respective
systems
.
4.10 Conclusion
Descartes is a crucial transitional figure in the revolutionary transformation
of
space
/
time concepts in the seventeenth century. Through his doctrine of res extensa,
he reified the indefinite imaginary space
of
the late scholastics: the space we
imag
-
ine beyond the world is no different from the matter we perceive in the world itself.
Although the space
of
the early Le Monde is a plenum rather than a vacuum, it
anticipates many
of
the crucial attributes
of
Newton's absolute space:
boundless
,
purely geometrical, continuous, independent
o
f
any other being, and clearly con-
ceived. Descartes's view of time was also
proto
-
absolutist insofar as he divorced
successive duration from motion and its measure. He was not, however, ready to
reify imaginary time. A time independent
of
everything else besides God, before
and after creation, for example, would qualify as a genuine
substance
.
But such a
substance would fall outside the dualism
of
mind and body: neither thinking nor
extended in three dimensions.
If
we stick to the actual world
of
minds and bodies,
duration is best regarded as a universal (transcendental) attribute;
if
we abstract time
from existing things, it is a mere mode
of
thought. His asymmetrical attitude about
indefinite space
vs
.
time therefore
seems
,
like so many Cartesian doctrines, to be a
con
s
equence
of
his strict
dualism
.
Abbreviations
AT Descartes,
R
.
1
983
.
Oeuvres De Descartes,
ll
vols. Ed. C. Adam and
P.
Tannery
.
Paris: J.
Vrin
.
Citation by volume and page.
Gassendi,
P.
1972
.
Selected Works
of
Pierre
Gassendi
.
Ed.
C.
Brush.
Johnson Reprint Co. Citation by page
Spino
z
a,
B
.
1985
.
The
Collect
e
d Works
of
Spinoza, Vol.
I.
Ed. E. Curley.
Princeton: Princeton University
Press
.
Citation by
page
.
Descartes
.
R. 1976
.
Descartes' Conversation with
Burman
.
Ed.
J
.
Cottingham
.
Oxford: Clarendon
Press
.
Citation by page.
Descartes, R. 1984
-
5
.
The Philosophical Writings
Of
Descartes, 2
vols.
,
Trans
.
J.
Cottingham
,
R. Stoothoff, and
D
.
Murdoch
.
Cambridge:
Cambridge University
Press
.
Citation by volume and page number.
Descartes,
R
.
1991. The Philosophical Writings
Of
Descartes: The
Correspond
e
nce. Trans. J. Cottingham, R. Stoothoff, D. Murdoch, and
Brush
C
CB
CSM
CSMK
60
G
.
Gorham 4
Descarte
s
on the Infinity
o
f
Space
v
s
.
Time
61
A.
Kenny
.
Cambridge:
C
a
mbridge University Press. Cit
a
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number.
DM
Suarez
,
F.
1866
.
Disputationes Metaphysicae. In Opera Omnia. Ed. by
C.
Berton.
Paris
:
Vives
.
Citation by disputation,
s
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paragraph
.
DG Newton,
I.
2004. De Gravitatione et aequipondio
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r
um
.
In
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.
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Essay Locke,
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1975
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An Essay Concerning Human Understanding. Ed. P.H.
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G
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·
S
Spinoza, B.
1998
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Th
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Ko
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(1957
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.
F
rom
t
h
e
c
l
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sed
wo
rld
t
o
t
h
e
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e uni
ve
rs
e
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Ba
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John
s
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U
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Lennon
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T.
(2007)
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T
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s.
Journ
a
l
o
f
th
e
Histor
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f
Philos
o
phy,
45
,
2
9
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Le
vy
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K.
(2005)
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I
s
De
s
carte
s
a tempora
l
atomi
s
t
?
Br
itis
h
Journ
a
l
for
th
e
Hi
s
t
o
r
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oso
phy
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1
3,
627
-
674
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.
LoLordo,
A
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(1997).
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e
Gass
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ndi and
th
e birth
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f
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nal
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E
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s
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e
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pants
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L'A analyse la distinction entre infini et indefini dans l'" Entretien avec Burman ". Examinant les diverses interpretations de cette oeuvre, et en particulier le probleme de son authencite, il montre que le Descartes de Burman ne respecte pas cette distinction, fondamentale dans sa philosophie parce qu'elle correspond a la distinction entre l'etre et le connaitre