Coexistence, Community, and Communio Spatii:
Kant Contra Newton and Leibniz
James Messina (SUU)
In the Third Analogy of the Critique of Pure Reason, Kant argues for the so-called
“principle of community”: the claim that all substances whose states we can experience as
coexisting must be in thoroughgoing mutual interaction. Though for many years the Third
Analogy was widely regarded as a gratuitous and confusing addendum to the Second
Analogy, tacked on for architectonic reasons as opposed to serious philosophical ones,
there has been growing recognition of its fundamental importance for Kant’s Critical
Project. For one thing, proof of the principle of community is required to establish the
applicability of the category of community to objects of experience, a category that Kant
regards as distinct from and irreducible to the category of cause and effect.1 In this respect,
the Third Analogy is essential for one of the main goals of the Analytic of Principles: to
show that and how all the categories are necessary for the possibility of objective
experience. For another thing, versions of the principle of community underlie both
Newtonian and Leibnizian natural philosophy. Newton’s law of universal gravitation, for
instance, is a specific instance of the claim that all corporeal substances constantly act on
one another, while Leibniz’s thesis of the relativity of motion can be seen as a corollary of
Leibniz’s own version of the principle of community: every change in a monad (including
changes in the motions of its corresponding body) is mirrored by a change in every other.
Anyone during Kant’s time who wished to provide a metaphysical foundation for physics
would have needed to provide a proof of some version or other of this principle. Kant’s
For a good discussion of this point, see Eric Watkins, “Making Sense of Mutual Interaction,” in Kant and
the Concept of Community (Rochester: University of Rochester Press, 2011), 41-62 (42-46).
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1
proof of the principle occurs in the Third Analogy. The principle of community plays a
crucial role in the Metaphysical Foundations of Natural Science, where Kant invokes it to
demonstrate his third law of mechanics (the equality of action and reaction) (Ak. 4:544545).
Of late, considerable progress has been made in reconstructing the argument of the
Third Analogy. However, an important aspect of the argument has not yet received
satisfying treatment: Kant’s account of the relationship between existence in space,
coexistence2, and community. Kant commits himself to two substantive claims in
particular that need to be explained. First, (SCE): in order to cognize that the states of a set
of substances are coexistent, it is necessary to have outer intuitions of those substances,
that is, intuitions that have space as their form. Second, (SCM): in order to cognize that a
set of substances have definite spatial locations relative to one another at a given moment,
it is necessary that those substances be in thoroughgoing mutual interaction. A proper
understanding of Kant’s justification for these claims is not only necessary for an
understanding of the overall argument of the Third Analogy. It is also necessary for
understanding Kant’s stance on two related questions that are answered very differently in
the context of the Newtonian and Leibnizian systems: the question of whether substances
need to coexist in space in order to be able to interact with one another, and the question of
whether space or a community of substances is ontologically prior.
In this paper, I will argue for two points. First, even though (SCE) and (SCM) are,
at least on their face, epistemic claims, they rest in part on metaphysical considerations
regarding space. This may come as a surprise, since on many interpretations of the Third
As I am using the terms here, ‘coexistence’ and ‘simultaneity’ are synonyms. Coexistence is thus to be
understood as a specifically temporal notion as opposed to a more general metaphysical one.
2
2
Analogy, Kant’s arguments turn exclusively on epistemic considerations regarding a
particular type of temporal relation, namely, coexistence, i.e. simultaneity. By contrast, I
will show that the Third Analogy involves a surprisingly sophisticated metaphysics of
location, modality, and causal interaction, one which does not itself depend on
Transcendental Idealism, though it is very much consistent with it.
Second, (SCE) and (SCM), along with the considerations that support them,
represent an attempt to carve out a middle position between the Leibnizian and Newtonian
accounts of space and community, at least as Kant understands those accounts. Contra the
Leibnizian position, Kant holds that we cannot cognize any sort of coexistence among
substances (including mental substances) unless those substances are given within a spatial
framework that grounds the possibility of their mutual interaction. But contra the
Newtonian position, Kant does not deny the possibility of mutual interaction in such a case
tout court. He merely denies that we could cognize a non-spatial community. Moreover,
whereas Newton and his followers take the thoroughgoing mutual interaction of substances
to rest on the brute fact that substances have locations in space, Kant holds that the
grounding relation goes in the other direction. For Kant, whether a substance has a definite
location in space at a given moment depends on whether it is interacting with other
substances at that moment, while its specific location is determined by how much force it is
exerting and having exerted on it at that moment. While this position may suggest
agreement with the Leibnizian view, there is a key difference. Unlike Leibniz and his
followers, at least as Kant interprets them, Kant does not try to explain space itself,
understood as a repository for all possible spatial properties, in terms of mutual interaction.
Instead, Kant regards space as something that ontologically precedes and makes possible
3
the mutual interaction of substances, while at the same time taking the latter to be required
for there to be any definite spatial locations. In this respect, the Third Analogy is an
attempt to argue for a principle that is central to both Newtonian and Leibnizian natural
philosophy, by means of assumptions that are profoundly anti-Newtonian and antiLeibnizian.
In §2, I lay out the argumentative goals of the Third Analogy and introduce (SCE)
and (SCM). In §3, I situate (SCE) and (SCM) in the context of two questions concerning
space and community that were answered very differently by the Newtonians and
Leibnizians. In §4, I explore Kant’s reasons for endorsing (SCE) and explain how they
bear on the first question at issue between the Newtonians and Leibnizians. In §5, I
investigate Kant’s reasons for endorsing (SCM) and explain how they bear on the second
question at issue between the Newtonians and Leibnizians. In §6, I conclude.
II. The Third Analogy and the Relationship between Space, Coexistence, and Community
As formulated in the B-edition of the Third Analogy, the principle of community
states that: “All substances, insofar as they can be perceived in space as coexistent, are in
thoroughgoing mutual interaction” (B256).3 By mutual interaction, or community as it is
also called, Kant means a state of affairs in which substances reciprocally act on one
another, such that each is the causal ground of a determination in the other.4 For a set of
substances to be in thoroughgoing mutual interaction, each must act, either immediately or
Cf. the first edition formulation of the principle of community: “All substances, insofar as they are
coexistent, stand in thoroughgoing community (i.e. interaction with one another)” (A211). Here no mention
is made of space.
4
For a fuller discussion of this point, see Watkins, “Making Sense of Mutual Interaction.”
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mediately, on every other.5 In contrast to many of his contemporaries, who hold that all
substances without exception are in community with one another, Kant self-consciously
restricts his version of the principle of community to a specific class of substances: all
those of which we can perceive (i.e. cognize) that their states coexist. Kant’s principle says
nothing about substances (if there be any such) whose states we cannot cognize as
coexisting.
It is generally agreed that the Third Analogy is a kind of transcendental argument
(or perhaps, set of arguments). Throughout the Analogies Chapter of the Critique, Kant
proceeds by reflecting on the conditions of the possibility of a particular type of
experience: namely, temporal experience. In the Third Analogy, Kant focuses, in
particular, on the conditions of the possibility of cognizing that substances have coexistent
(i.e. simultaneous) states. Kant argues, inter alia, for the following closely related claims:
(Conc1) If we are to cognize that the states of substances coexist, we must apply the
category of community to them6; (Conc2) If we are to cognize that the states of substances
coexist, those substances must be in thoroughgoing mutual interaction. (Conc2) is one
formulation of the principle of community. It is a statement to the effect that a certain set
Some commentators endorse a “strong” interpretation of “thoroughgoing mutual interaction” such that
substances in thoroughgoing mutual interaction must act immediately on one another (as opposed to either
immediately or mediately). I tentatively offer the weak interpretation above (to avoid begging any questions
in advance), but my points in this paper are consistent with both interpretations.
6
Kant draws what I am calling (Conc1) at B257: “Consequently, a concept of the understanding of the
reciprocal sequence of the determinations of these things simultaneously existing externally to each other is
required in order to say that the reciprocal sequence of perceptions is grounded in the object, and thereby to
represent the coexistence as objective.” One reason that Kant goes through the trouble of establishing Conc1
is so that he can build an argument showing that we are entitled to apply the category of community to
objects. The other premises of this argument are as follows: If application of the category of community is a
necessary condition of our cognition of the coexistence of objects, then it is a condition of the possibility of
the experience of those objects. If application of the category of community is a condition of the possibility
of experiencing objects, then the application of the category of community to those objects is legitimate. As
we will see, (Conc1) also figures as a premise in an argument designed to establish the claim that cognition
of coexistence requires not just intuition, but outer intuition.
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5
of substances (namely, all those that we cognize as coexisting) are such that they must be
in a community. By contrast, (Conc1) is a more straightforwardly epistemic claim; it is a
claim to the effect that we must apply the category of community to substances in order to
cognize that they coexist.7
In recent years, commentators have made considerable progress in their efforts to
understand Kant’s argument for (Conc1) and (Conc2). One particularly noteworthy
advance, in my opinion, is the recognition that it is possible for the argument of the Third
Analogy to be both transcendental – insofar as it results from reflection on the conditions
of a certain type of experience – and to rest on metaphysical considerations. Watkins, for
instance, has recently provided a compelling reconstruction of Kant’s argument for the
principle of community, whereby the fundamental premises are taken to be claims about
the manner in which simultaneity relations are (ontologically) constituted.8
In what follows, I attempt to apply this insight to a key aspect of the Third Analogy
that remains poorly understood: the relationship between existence in space, coexistence,
and community. In the course of the Third Analogy, Kant commits himself to two
substantive claims whose justification has not yet been adequately illuminated. The first
7
(Conc1) and (Conc2) are often not distinguished, though they are clearly not identical. However, on a
certain understanding of transcendental idealism – one according to which our application of the category of
community to objects of intuition is partly constitutive of those objects being in a community – the truth of
(Conc1) is a necessary condition for the truth of (Conc2).
8
See Eric Watkins, Kant and the Metaphysics of Causality (Cambridge: Cambridge University Press, 2005),
219-227. Aspects of Watkins’ interpretation have recently been criticized by Andrew Chignell and Derk
Pereboom in “Kant’s Theory of Causation and its Eighteenth-Century German Background,” Philosophical
Review, Vol. 119, No. 4 (2010): 563-591. One of their objections is that, if Kant were to hold that temporal
properties (like simultaneity) are ontologically constituted by the categories, then (given the similarities
between time and space), Kant ought to hold that spatial properties (in particular, locations) are likewise
ontologically constituted by the categories. But, they claim, there is insufficient evidence that Kant holds the
latter view; absent some plausible explanation for the dis-analogy between time and space, Watkins’
interpretation loses credibility (580-581). One of my goals in this paper is to defend Watkins against this
criticism by showing that Kant does hold that spatial properties are ontologically constituted in the same
manner that temporally properties are, so Watkins has no dis-analogy to explain.
6
claim concerns the relationship between space and coexistence: (SCE) if we are to be able
to cognize that the states of a set of substances are coexistent, we need to have outer
intuitions of those substances. Kant’s commitment to (SCE) is reflected in the B-edition
formulation of the principle of community: “All substances, insofar as they can be
perceived in space as coexistent, are in thoroughgoing mutual interaction” (B256; my
emphasis). In formulating the principle in this manner, Kant implies that the only
substances whose states we can cognize as coexistent are those that are given to us in outer
intuition. Indeed, throughout the Third Analogy, Kant tends to speak of cognition of the
“coexistence of substances in space” rather than merely of the “coexistence of substances.”
In this manner, Kant commits himself to (SCE), which is by no means a trivial claim.
(SCE) is incompatible with the Cartesian view that, although the mind is a non-spatial
substance, we can have knowledge of the coexistence of its states with those of corporeal
substances (in particular, those of the body). In order to consistently accept (SCE), Kant
must either deny (a) that we can cognize that our mental states coexist with states of
corporeal substances, and/or (b) that our mental states are states of a radically non-spatial
substance.9 The substantive nature of (SCE) makes the question of its justification all the
more pressing. Surprisingly, there has been relatively little discussion of it.10
Here it’s necessary to distinguish between the coexistence of the states of my phenomenal mind and
phenomenal bodies, and the coexistence of the states of the noumenal substances corresponding,
respectively, to my phenomenal mind and phenomenal bodies. Given that noumenal substances are neither
spatial nor temporal, there is a straightforward answer to the question of whether we can cognize their
coexistence: we cannot, because absent time there is no coexistence. As we will see, Kant’s explanation for
why we cannot cognize that those substances interact is different: here we cannot say definitely that the
substances do not interact. What we can say, though, is that we could never comprehend, and thus cognize,
their interaction because they are not in space. As for whether I can cognize the coexistence of the states of
my phenomenal mind and phenomenal bodies, though I cannot argue for this point here, my view is that Kant
thinks that I can cognize their coexistence and that I can do so precisely because my phenomenal mind has a
“virtual presence” in space (which is to be contrasted with its having a definite location in space in the
manner that material substances do). Kant seems to think my phenomenal mind is virtually in space in virtue
of the interaction of the noumenal substance corresponding to it and the noumenal substance corresponding
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7
The second claim concerns the relationship between space and community. In an
intriguing remark towards the end of the Third Analogy, Kant writes:
The word ‘community’ is ambiguous in our language and can mean either
communio or commercium. We use it here in the latter sense, as a dynamical
community, without which even the local community (communio spatii) could
never be empirically cognized. (A213/B260)
By a local community, or communio spatii, Kant means a set of substances that have
definite locations relative to one another at a given moment; each is a determinate distance
from the others. In this passage, Kant commits himself to (SCM): if we are to be able to
cognize that substances have definite spatial locations, these substances must be in
thoroughgoing mutual interaction. (SCM) can be thought of as a spatial version of the
principle of community, a formulation that makes no reference to time, unlike the version
that I call (Conc2). Like (SCE), (SCM) is a substantive principle. It is by no means obvious
why substances must act causally on one another in order for one to be able to cognize that
they have definite locations.11
to my body. The former is virtually present wherever in space its effects on the latter appear to me (namely,
in the movement of my body). Given that the noumenal substances corresponding to my mind and body are
not themselves in space, their interaction is inexplicable. See, e.g., 28:756-758.
10
For two exceptions, see Margaret Morrison, “Community and Coexistence: Kant’s Third Analogy of
Experience” [“Community and Coexistence”], Kant-Studien 89/3 (1998): 257-277 (266-268) and Friedman,
Kant and the Exact Sciences (Cambridge, Massachusetts: Harvard University Press, 1992), 38-39. Though
Morrison and Friedman do not discuss (SCE) per se, they do try to make sense of Kant’s reasons for claiming
that “it is not possible to have insight into the objective reality of [the concept of community] without
intuition, and indeed outer intuition in space” (B292). As will become clear, this claim is a crucial premise in
Kant’s argument for (SCE).
11
Morrison’s interpretation of the Third Analogy does not seem to allow for the substantive character of
(SCM). According to Morrison, “mutual interaction means, for Kant, a mutual determination of position”
(269). For Morrison, the mutual interaction of substances is not what determines their spatial positions; to say
that substances mutually interact just is to say that they have determinate positions relative to one another.
Thus, it would seem that, for Morrison, (SCM) is a tautology. That Kant himself does not view it as a
tautology is clear from the wording of A213/B260. Morrison’s reading also has two other serious problems.
One is that it would leave Kant unable to explain spatial position through the interaction of substances (since
these things would amount to the same thing). Another is that it would leave Kant without any way to talk
about the mutual interaction of non-spatial substances. Indeed, such interaction would be a contradiction in
terms. But, as I will argue, Kant does not rule out mutual interaction of non-spatial substances; a fortiori, he
doesn’t regard it as a contradiction in terms.
8
Unlike (SCE), (SCM) has received a fair amount of attention in the literature. But
there is no consensus about what reasons Kant has for endorsing it. Some commentators
take it to be the result of a sophism, an illegitimate slide between two very different senses
of ‘mutual determination’.12 Other, more charitable commentators have attempted to find a
reputable argument on its behalf.13 But so far, to my knowledge, no commentator has
succeeded in providing a rationale for (SCM) that is at once reputable, consistent with the
text of the Third Analogy, and compatible with Kant’s other commitments. In later
sections, I attempt to provide justifications for (SCE) and (SCM) that fulfill these
desiderata. As I will show, the arguments for both claims rest on an interesting mixture of
epistemological and metaphysical considerations regarding space.
III. The Historical Context of (SCE) and (SCM)
(SCE) and (SCM) are not only significant because of their intrinsic philosophical
interest and their role in the overall argument of the Third Analogy. They are also of
broader historical interest, insofar as they bear on two related questions that were tackled
very differently by the main natural philosophical systems of Kant’s day: the Newtonian
and Leibnizian. The first question can be formulated as follows: must substances
(including thinking substances) coexist in space in order to be able to interact? The second
question can be formulated as follows: which is ontologically prior, space or a community
12
For example, P.F. Strawson, The Bounds of Sense (London: Methuen, 1966), 140.
See, e.g. Paul Guyer, Kant and the Claims of Knowledge (Cambridge: Cambridge University Press, 1987),
274-275. As Guyer understands Kant’s argument for (SCM), Kant is claiming that judgments about the
spatial positions of substances depend for their justification on judgments about the mutual interaction of
those substances. One problem with Guyer’s reading is that he fails to adequately explain why the one sort of
judgment depends on the other sort of judgment. Another problem is that he fails to explain why there isn’t a
circularity problem here, since it seems that judgments about mutual interaction must themselves depend on
judgments about spatial position.
13
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among substances? That Kant saw a connection between the Third Analogy and questions
like these is evident from an intriguing and cryptic remark that he inserted into his personal
(first-edition copy) of the Critique:
Space makes community possible. Now since the thinking being with all its
faculties, whose effects belong merely to inner sense, is not a relation of space, the
commercium of the soul with the body is therefore not comprehensible. The
community of things in themselves must either have a third substance, in which
they exist as accidentia and are in relation to one another – Spinozism – or, since
this won’t do, it remains incomprehensible. Space is itself the phaenomenon of
possible community. (Ak. 23:31-32)
A proper understanding of (SCE) and (SCM) promises to shed light on the relationship
between Kant’s natural philosophy and those of Newton and Leibniz, at least insofar as
those systems bear on these questions. In turn, viewing the Third Analogy in the context of
these questions promises to shed light on (SCE) and (SCM).
It is reasonably clear how an orthodox Newtonian would (or should) answer the
first question: substances are unable to interact without coexisting in space. For Newton,
space is a condition of existence; a substance cannot exist without existing in space. A
fortiori, substances cannot coexist – that is, exist at the same time – without existing in
space. As Newton puts the point in De Gravitatione, “Space is an affection of being just as
being. No being exists or can exist which is not related to space in some way.”14 This claim
entails the falsity of the Cartesian view that minds (conceived of as un-extended, thinking
substances) do not exist in space.15 It also entails that God exists in space (at least in some
fashion), a conclusion that Newton notoriously draws in the General Scholium of the
14
Isaac Newton, Philosophical Writings (Cambridge: Cambridge University Press, 2004) , ed. Andrew
Janiak, 25.
15
For an explicit statement to this effect, see Newton, Philosophical Writings, 31.
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Principia.16 For our purposes, what is especially noteworthy is that when one puts the
claim that substances cannot coexist without existing in space, together with (1) Newton’s
view that time is also a condition of existence, and (2) the (seemingly self-evident)
assumption that substances are unable to interact unless they exist, it follows that
substances need to coexist in space in order to be able to interact.17
Even clearer than how the Newtonians would answer the first question is how Kant
thinks they would answer it. In the Inaugural Dissertation, Kant likely has in mind both
Newton and Crusius, who defends a broadly Newtonian account of space,18 when he
writes:
They treat them [i.e. space and time] as primitive conditions which are already
given in themselves, and, in virtue of which to be sure, and independently of any
other principle, it would not only be possible but also necessary that a number of
things should be mutually related to one another…. (Ak. 2:391)
Kant here ascribes to Newton and Crusius the view that space is a condition of the
possibility of “a number of things being mutually related” (that is, substances being in
mutual interaction). As Kant understands their position, the Newtonians would answer the
first question with a resounding ‘yes’.
But in the passage just quoted, Kant also ascribes a further view to the Newtonians,
one that has implications for the second question mentioned above: in addition to making it
possible for substances to interact, space actually makes it necessary for the substances that
16
Isaac Newton, Philosophiae Naturalis Principia Mathematica, Volume 2 (Cambridge, MA: Harvard
University Press, 1972), ed. Alexandre Koyré and I. Bernard Cohen, with Anne Whitman, 762. For a fuller
discussion of Newton’s disagreement with Descartes on these points, see Andrew Janiak, “Substance and
Action in Descartes and Newton,” The Monist, vol 93, no. 4: 657-677.
17
It is interesting to note that a version of this (Newtonian) claim has recently been defended by Jaegwon
Kim and brought to bear in an attack on Cartesian dualism. See Jaegwon Kim, Physicalism, or Something
Near Enough (Princeton: Princeton University Press, 2005), 78-85.
18
Like Newton, Crusius regards space as a condition of existence and believes that things have absolute as
well as relative locations. See Christian Crusius, Entwurf der nothwendigen Vernunft-Wahrheiten [Sketch of
the Necessary Truths of Reason] (Leipzig,1745), §48, and § 51-52.
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coexist in it to interact with one another. Being together in space forces substances into
reciprocal causal connection. Moreover, it fixes the nature of this mutual interaction, the
laws according to which it operates. Kant uses the word ‘determine’ in this context:
For, since whatever things exist are, in their opinion, necessarily somewhere, it
appears superfluous to them to enquire why these same things are present to
one another in a fixed manner. For this, it seems to them, would be determined
in itself by the entirety of space, which includes all things. (Ak. 2:406–407)
As Kant understands the Newtonian view of space, space alone determines that and how
substances are “present to” – that is, act causally on – one another. In virtue of existing
within the “entirety of space” spatial substances are forced to interact with one another and
to do so in a “fixed manner,” such that each exerts a definite amount of force on every
other at every moment, according to definite laws.
In ascribing to the Newtonians the view that space is a “primitive condition” that
determines that and how substances interact, Kant is clearly alluding to the Newtonian
view of space as an all-encompassing structure containing infinitely many absolute places.
Part of what Newton means in calling these places absolute is that each place endures over
time, and is, as a matter of brute fact, a definite distance from every other at every moment.
These distances are what they are, independent of whether the places are occupied. All
substances that exist at a given time automatically inherit the distance relationships that
obtain among the absolute places that they occupy at that time.19 Moreover, according to
Newton’s account of gravitation, all existing substances exert a definite amount of
attractive force on one another at every moment, merely in virtue of being some definite
distance apart at every moment. Newton’s famous inverse square law dictates that the
19
For discussion of this point, see John Earman, World Enough and Space-Time (Cambridge, Massachusetts:
MIT Press, 1989), 11.
12
amount of attractive force exerted by two substances at a time is inversely proportional to
the amount of distance between them.
It is in this manner that space, on the Newtonian view, can be said to determine that
and how existing substances interact. Facts about the mutual interaction of substances (in
particular, facts about whether they exert attractive force on another at a given time and
how much force they exert) are grounded in facts about space (in particular, facts about
whether they exist in space at a given time and how far apart they are at that time). Space is
a “primitive” condition because there is no deeper ground for the fact that the places
substances occupy at a particular instant are such-and-such distance apart. Thus, at least for
Kant, the Newtonian answer to the second question is as clear as the first: space is
ontologically prior to mutual interaction.
A Leibnizian would answer the foregoing questions in a completely different
fashion. According to a standard reading of Leibniz’s philosophy, one which Kant himself
subscribes to, at least at certain points in his career, the fundamental structure of reality
consists of un-extended, windowless, mind-like, simple substances: monads. Though
monads do not really act on one another, in the sense of really bringing about changes in
one another’s states, they exercise a kind of ideal causal influence insofar as every change
in the state of a monad is lawfully coordinated with changes in the states of every other
monad. This lawful coordination of coexisting monads, which is described by Leibniz,
Wolff, and even Kant as a community of substances, is the result of a divine decree. Rather
than having ultimate ontological status, bodies as well as the spatial framework in which
they are related, are phenomena grounded in the thoroughgoing community of monads.
13
This is what Kant means when he says that “Leibniz thought of space as a certain order in
the community of substances” (A275/B331).
On this reading of the Leibnizian philosophy, it has fairly clear implications for the
two questions above. With regard to the second question, community (in particular, a
community among monads) is ontologically prior to space, since the latter supervenes on
the former. With regard to the first question, the coexistence of substances in space is not a
condition of the possibility of those substances standing in a community, since it is only in
virtue of the thoroughgoing community of monads that it is possible for bodies (and the
monads associated with them) to exist at spatial locations relative to one another. God,
rather than space, is a condition of the possibility of the community of substances. In this
regard, Kant asserts, “[Leibniz’s] principle of the possible community of substances among
themselves had … to be predetermined harmony” (A274/B331).
The Newtonian and Leibnizian systems, as Kant understands them, thus offer very
different answers to the questions posed above. In the next two sections, I will show how
Kant’s arguments for (SCE) and (SCM) bear on these questions. Though one might think
that the Newtonian and Leibnizian views exhaust the logical space on these topics, I will
argue that in both cases Kant manages to steer a middle course between them.
IV. Kant’s Justification for (SCE)
The task of this section is to get clear on Kant’s justification for (SCE): why does
Kant think that, in order to cognize that the states of two substances are coexistent, it is
necessary to have outer intuitions of those substances? Why must we intuit the substances
in space? As we will see, the search for a satisfying answer to this question quickly leads
14
off the beaten path of Kant’s theory of cognition and into the thickets of Kant’s
surprisingly sophisticated metaphysics of location, modality, and causal interaction. From
this vantage point, the differences between Kant’s account of space and community and
those of Leibniz and Newton will emerge more clearly.
Suppose we grant a central tenet of Kant’s theory of cognition: that all cognition
requires the application of some category to an object or objects of intuition. It is still not
obvious why it would not suffice to intuit objects (in particular, substances) in time alone
in order to cognize that their states coexist. Nothing that Kant says in the Schematism
Chapter of the Critique helps us to answer this question. Even if we grant that the
categories must be schematized – that is, given meaning – before they can be used to
cognize objects of intuition, the puzzle does not dissolve. In fact, it is worsened, since it is
Kant’s view that the categories can be schematized by time alone.
At least the beginning of a solution to this puzzle lies in an easy-to-overlook aspect
of Kant’s theory of cognition. Cognition, for Kant, does not merely require the application
of a schematized category to an object given in intuition; it further requires the application
of a category whose objective reality is ensured. According to Kant, a category has
objective reality if and only if it is possible for it to be instantiated by the object (or
objects) of cognition (see, e.g., A223/B270 and B291).20 Apparently, the mere fact that a
The possibility at issue here is metaphysical possibility – in particular, what Kant calls real possibility. For
a helpful discussion of Kant’s distinction between real and logical possibility, see Andrew Chignell, “Kant,
Modality, and the Most Real Being,” Archiv fuer Geschichte der Philosophie, 91 (2009): 157-192. According
to Chignell, the real possibility of a thing or proposition requires not just that the positive predicates
associated with it be logically consistent, but also that they be “given” in “logical space” and that they be
really harmonious (171-176). I agree with this general characterization of real possibility. I also agree with
Chignell that Kant (both pre-Critical and Critical) thinks that real possibility requires explanation. However,
I disagree with Chignell’s claim that, for the pre-Critical and Critical Kant, the explanation of the real
possibility of the fundamental predicates is that they are instantiated to a maximal degree by an actual being:
namely, God. I reject this idea, because I think that, for the Critical Kant, there are certain fundamental,
really possible predicates that God doesn’t instantiate, like community and location. What’s special about
20
15
category has been schematized (that is, given some sort of meaning) does not guarantee
even the possibility that anything in the world answers to it, let alone the possibility that
the particular objects one is applying it to instantiate it. But without having some sort of
guarantee that the category could be instantiated, Kant thinks, even efforts to apply a
schematized category to an object given in empirical intuition would fall short of cognition
– since, for all one knew, there might be some metaphysical (if not conceptual)
impossibility in the object’s instantiation of the category. If our cognition is to be justified,
then we need some guarantee that it is metaphysically possible for the objects to which we
are applying it to instantiate it.
But what could provide the requisite guarantee? Surely it could not be any of the
categories, since it is these whose possible instantiation is in question. Instead, the
guarantee must come from some intuition, which provides us with insight into the
possibility of the category’s being instantiated. But what sort of intuition? According to
Kant, for cognitive agents like us such insight is only afforded by outer intuitions –
intuitions whose form is space:
[I]n order to understand the possibility of things in accordance with the categories,
and thus to establish the objective reality of the latter, we do not need merely
intuitions, but always outer intuitions. (B291)
What is particularly interesting for our purposes is Kant’s claim that the intuition of space
is what guarantees for us the objective reality of the category of community. Kant asserts:
these sorts of predicates is that they are formal and a priori. The Critical Kant might well hold that the real
possibility of all fundamental, material and a posteriori predicates is ultimately to be explained by the fact
that they are instantiated to a maximal degree by God, but the real possibility of the categories as well as the
fundamental predicates of pure sensibility (whose a priori, formal character didn’t become fully clear to Kant
until the Critical period) requires a different sort of explanation entirely. Since Kant thinks we need some
assurance of the real possibility of the instantiation of such predicates if we are to be justified in using them,
one constraint on the explanation is that it should appeal to something that not only grounds possibility but
also serves as a readily accessible epistemic indicator of it. As I argue, this is why Kant appeals to space to
account for the real possibility of the instantiation of community by objects of cognition.
16
…[T]he possibility of the category of community is not to be comprehended at all
through mere reason, and thus it is not possible to have insight into the objective
reality of this concept without intuition, and indeed outer intuition in space. (B292)
Drawing on the claim that outer intuition is required to ensure the objective reality
of the category of community, it is easy to build an argument for (SCE): cognition that the
states of substances are coexistent requires that the substances be objects of outer intuition.
We merely need to put the former claim together with what I called (Conc1), which says
that the specific category that must be applied for cognition of coexistence is the category
of community – as well as the further claim that cognition requires the application of a
category whose objective reality is ensured. We obtain an argument of the following form:
(1) Cognition of the coexistence of the states of substances requires application of the
category of community. (Conc1)
(2) Cognition requires application of a category whose objective reality is guaranteed.
(Tenet of Kant’s theory of cognition)
(3) Cognition of the coexistence of the states of substances requires that the objective
reality of the category of community is guaranteed. (From 1 and 2)
(4) In order for cognitive agents like us to have a guarantee of the objective reality of the
category of community (the possibility of its instantiation by the objects we are applying it
to) the objects it is applied to must be given in outer intuition.
Conc: For cognitive agents like us, cognition of the coexistence of the states of substances
requires that those substances be given in outer intuition.
The premise of this argument that we have yet to account for is (4). It is not immediately
obvious why we need to have outer intuitions, in particular, in order to have a guarantee of
the objective reality of the category of community. It is natural to wonder why inner
intuitions (intuition that simply have time as their form) do not suffice.
The answer, I think, lies in the note (already mentioned above) that Kant inserted in
his copy of the Critique in the Third Analogy section. There Kant says that “space makes
17
community possible” and that “space is the phaenomenon of possible community” (Ak.
23:31-32).21 As I understand these remarks, Kant believes that it is in the nature of a
spatial (as opposed to temporal) framework that it both indicates,22 and opens up, the
possibility of reciprocal causal relation for whatever things are given in it. If this is correct,
then to have an outer intuition of an object (that is, an intuition of an object given within a
spatial framework) is ipso facto to have insight into the possibility of that object’s
instantiation of the category of community.
Our task now is to make sense of why Kant thinks that space can play this role. My
suggestion is that space, as Kant understands it, is able to do this in virtue of the special
nature of spatial location.23 For Kant, spatial locations are (1) determinations that are (2)
relational, (3) possible or actual, depending on whether or not they are instantiated by
substances, and (4) action-dependent: that is, only instantiated by substances that act
causally on other substances and are acted on by them in turn.
These features of location need to be unpacked, starting with (1). In contrast to
Newton, who takes locations in absolute space to be individuals, endowed with various
properties (like magnitude and distance), Kant takes locations, at least in the primary sense
of the term, to be determinations,24 i.e. properties, of certain substances: namely, those that
Cf. Ak. 28:325: “Space is possibility of community.”
Consider Ak. 29:1007 in this regard:“…[I]f one thinks of space as symbol, i.e., in the place of all relations
and reciprocal action itself, then one thinks under this the summation [Inbegriff[] of all phenomena, and
indeed as co-presences, i.e, as present to one another, and reciprocally acting on each other, and the being
which contains them, as symbol.”
23
As I am using the term ‘location’ [Ort] here it is synonymous with ‘position’. This is Kant’s primary sense
of the term ‘Ort’ (see, e.g. Ak. 29:839-840). But Kant sometimes also uses the term to refer, not to a property
of things in space, but to an extended part of space, one which is itself infinitely divisible into further parts.
‘Ort’ in this secondary sense is perhaps best translated as ‘place’. Places have sizes, shapes, and locations,
corresponding to the sizes, shapes, and locations of the objects that inhabit them.
24
See, e.g., A274/ B330: “But that which is inner [in the state of a simple substance] cannot consist in
location [Orte], shape, contact, or motion (which determinations are all outer relations)” (A274/B330). See
also the Metaphysical Foundations of Natural Science: “[E]verything real in the objects of the outer senses,
21
22
18
are objects of our outer intuition. That Kant thinks of all spatial determinations, including
locations, as determinations of (material) substances is clear from claims like the
following: “Matter, as mere object of the outer senses, has no other determinations except
those of external relations in space, and therefore undergoes no change except by motion”
(Ak. 4:543).25 In the case of location, we might call the properties in question locationproperties. For Kant, there are infinitely many such properties and each is unique, insofar
as it can only be instantiated by one material substance at a given time. (In this respect,
location-properties are very different from “universals” like color, size, weight, etc.). The
uniqueness of location-properties allows them to play an individuating role with respect to
material substances in space. As Kant writes in the Amphiboly Chapter, “Thus, in the case
of two drops of water, one can completely abstract from all internal difference (quantity
and quality) and it is enough that they be intuited in different locations at the same time in
order for them to be held to be numerically distinct” (A263-264/B319-320).
Turning now to (2), locations, for Kant, are not just any properties of substances;
they are relational properties.26 In the Metaphysik Mrongovius, transcripts of the lectures
on metaphysics that Kant gave in the 1780’s, Kant defines location [Ort] as “determinate
position, i.e., relation to other things in space” (Ak. 29:839-840). Here we can usefully
distinguish between (what we might call) the neighborhood location of a substance – its
position relative to some (arbitrarily-chosen) nearby substance or set of substances – and
which is not merely a determination of space (location, extension, and figure)…” (Ak. 4:523). In describing
location, extension, and figure as determinations of space, Kant is not denying that they are also
determinations of substances. Indeed, I think Kant’s view is that the various extended parts of space (what I
call ‘places’ in the previous footnote) inherit their determinations from the determinations of the objects that
occupy them. A place is, for example, a cube with such and such area and location if and only if it contains
an object with those properties. If it contains no such object, or if the object is itself indeterminate, then it is
indeterminate with regard to these properties. See B137-B138, A429/B457, and A431/B459 in this regard.
25
See also Ak. 4:289, where Kant describes extension and location as primary qualities of bodies (i.e.
material substances).
26
Indeed, all spatial properties are relational, for Kant. See, e.g. B66-B67, A274/ B330, and A284/B340.
19
its global location – its position relative to all other spatial substances. There are two
senses in which both types of location-properties are relational. First, a substance cannot be
assigned either type of location-property unless at least one other substance is as well: a
lone substance would not have any location, since location is always location relative to
some other substance. Second, if a substance undergoes a change in either type of locationproperty during some interval of time, its change entails a change in the location-properties
of a certain set of other substances. The neighborhood location-property assigned to a
substance at a given time varies along with the neighborhood location-properties of the
other substances in its neighborhood, such that if substance A has a neighborhood location
relative to substance B, and substance A changes its neighborhood location between t1 and
t2, substance B undergoes a corresponding shift in its neighborhood location during that
time.27 Similarly, the global location of a substance varies along with the global locations
of all others, such that if any substance alters its global location between t1and t2, all other
substances undergo a corresponding shift during that time. It is in this respect that spatial
location is reciprocal. In having this character, spatial location differs importantly from
temporal location. To the extent that we can even make sense of a substance changing its
temporal location – it exists at t1 in state A, at t2 in state B, etc. – these changes do not
seem to entail any corresponding changes of temporal location in other substances. It is
27
For evidence that Kant views (what I am calling) neighborhood location-properties in this way, see his
proof of the Third Law of Mechanics in the Metaphysical Foundations of Natural Science (Ak. 4:454-457),
as well as Kant’s 1791 letter to Christoph Friedrich Hellwagin in which he comments on this proof. There, he
writes that this law “rests on the overall relation of the efficacious powers in space. This relation is
necessarily one of reciprocal opposition and must always be equal (action is equal to reaction), because space
does not make possible one-sided, but rather always reciprocal relations; thus, the alteration of these
relations, that is, the motion and the action of bodies on another that brings forth motion, makes possible
purely reciprocal and equal and opposite motions” (Ak. 11:244).
20
this fact that Kant has in mind when he says that space “does not make possible one-sided
relations, but rather always reciprocal ones” (Ak. 11:244).
With regard to (3), a location-property is either actual or merely possible at t1,
depending on whether or not it is instantiated by a substance at that moment. As we’ve
seen, locations for Kant are relational properties of substances. Kant thinks that there can
be empty locations – locations that are uninhabited by substances. Indeed, Kant thinks that
(i) space is ontologically prior to the substances that populate it, and (ii) in a space devoid
of substances, there would still be locations, and indeed, infinitely many of them. As he
asserts in the Metaphysik Mrongovius, “[Space] precedes all things, it is viewed as an allencompassing receptacle, containing nothing except locations of things” (Ak. 29:830).28
Since Kant thinks of locations as properties of substances, to say that space contains
infinitely many empty locations is to say that space contains infinitely many uninstantiated location-properties. As I interpret Kant, location-properties differ in their
modal status, depending on whether or not they are instantiated by substances: instantiated
location-properties (i.e. non-empty locations) are actual properties, whereas un-instantiated
location-properties are merely possible properties. This interpretation makes philosophical
sense, and is supported by passages like the following: “Thus things, as appearances, do
determine space, i.e., among all its possible predicates (magnitude and relation) they make
it the case that this or that one belongs to reality” (A431/B459).29 What is especially
striking here is the talk of possible predicates of space. The ascription to Kant of the view
that empty locations are merely possible relational properties fits well with this passage. It
28
Cf. A24-25/B38-39
At the end of this section, I will explain what Kant means when he says that the things in space
“determine” it.
29
21
also fits well with various remarks that Kant makes throughout his career to the effect that
a totally empty space is not an actual thing but rather a possibility.30 As I understand these
passages, empty space is a mere possibility in the sense that it comprises various merely
possible (that is, un-instantiated) spatial properties.
Finally, turning to (4), location-properties are action-dependent, by which I mean
that a substance cannot instantiate a given location-property, and thus that locationproperty cannot be actual, unless the substance acts causally on others. Kant commits
himself to such a view in his earliest published work, True Estimation of Living Forces:
“For when we analyze the concept of what we call location, we find that it suggests the
actions of substances on each other” (Ak. 1:20-21). The doctrine recurs in Kant’s first
wholly philosophical work, the New Elucidation.31 Kant’s continued commitment to this
doctrine during the time that he was writing the Inaugural Dissertation is evident in a
reflection written between 1769 and 1770: “The being of a thing in a location can be so
expressed: location is the ground of something, which means as much as: to be in a
location is to act externally [äußerlich] in certain relations” (Ak. 17:453).32 Given the
resiliency of this understanding of location, and the light it sheds on Kant’s mature views
about space and community, there can be little doubt that Kant continued to hold it
throughout his career. I will have more to say in the next section about what Kant’s reasons
might be for thinking that a substance needs to act in order to instantiate a locationConsider the following examples: “Space, prior to all things determining (filling or bounding) it, or which,
rather give an empirical intuition as to its form, is, under the name of absolute space, nothing other than the
mere possibility of external appearances....” (A429/B457). “Space is nothing actual, but rather a possibility
which has its ground in something actual” (Ak. 17:404). “Pure space is merely potential relation and is
represented before things but not as something actual” (Ak. 17:578).
31
See, e.g., Ak. 1:414.
32
This is not to say that there are not important changes in his account of spatial location. I would suggest
that one key alteration is that, unlike the Kant of the True Estimation, the later Kant believes in uninstantiated (that is, merely possible) location-properties and views space as a repository of such properties.
30
22
property. For now, it suffices to note that Kant’s doctrines of the relationality and actiondependence of location-properties entail, in the case of global location-properties, that a
substance cannot instantiate such a property (that is, have a location) unless it acts on, and
is in turn acted on, by all the others. For Kant, such thoroughgoing mutual interaction is a
matter of each substance’s exercising its force on the others and having the forces of all the
others exercised on it.33
Understanding the reciprocity and action-dependence of global location-properties
is crucial for understanding Kant’s (metaphysical) claim that space makes possible
community. Space, for Kant, makes possible a thoroughgoing mutual interaction of spatial
substances by making possible the instantiation of global location-properties. Kant’s view
of space as a condition of the possibility of substances having global locations is evident in
Some Remarks on L. H. Jakob's Examination of Mendelssohn's Morgenstunden [1786],
where Kant writes, “[space] is something not yet existing [noch gar nichts Existierendes]
but merely the condition for locations outside of one another, thus for purely outer
relations” (Ak. 8:153). By making possible the instantiation of global location-properties,
which are reciprocal and action-dependent in the senses explained above, space makes
possible a thoroughgoing mutual interaction of the substances given in it. This is what
Kant means when he says that space “contains in itself a priori formal outer relations as
33
Morrison argues that the notion of mutual interaction at issue in the Third Analogy has to be separated
from the notion of a substance’s exercising a force, since otherwise the Third Analogy would infringe on the
proper job of the Metaphysical Foundations of Natural Science. According to Morrison, it is the job of the
Metaphysical Foundations to deal with the notion of a mutual exercise of force; in the Third Analogy, by
contrast, the mutual interaction of substances is simply a matter of their having positions in space. See
Morrison, “Community and Coexistence,” 269-274. In footnote 11 I argued that this characterization of
mutual interaction is untenable. I would now add that there is a perfectly natural way of making sense of the
division of labor between the Metaphysical Foundations of Natural Science and the Third Analogy without
having to say that Kant completely abstracts from the notion of force in the latter. The task of the
Metaphysical Foundations of Natural Science is to state the specific forces at issue in cases of mutual
interaction and the specific laws governing them, while in the Third Analogy Kant merely shows that there is
a thoroughgoing reciprocal exercise of some forces or other according to some laws or other.
23
conditions of the possibility of the real (in effect and countereffect, thus in community)”
(B293).
But this only leads to a new question: how is space able to make possible the
instantiation of global location-properties? Space is able to do this because it comprises
infinitely many extended parts,34 each of which is the host of various merely possible
spatial properties, such as size, shape, and location (both global and neighborhood). In this
respect, space is a subset of what Kant calls in the Transcendental Ideal “the whole of
possibility” (A572/B600). The latter comprises all possible predicates by means of which a
substance could be determined, whereas space comprises all possible spatial predicates by
means of which a substance could be determined. On Kant’s view, the only way that
substances can be determined with regard to a set of predicates is if those predicates are
stored somewhere as possible predicates. The same holds with regard to spatial properties,
like location. In order for substances to be determined with regard to their spatial
properties, all possible spatial properties that could be ascribed to them must be given
along with the different parts of space. Space, conceived in this sense, makes possible the
determination of the substances in space by hosting all possible spatial properties. At this
point, we’ve reached explanatory bedrock, at least insofar as Kant’s rationale for (SCE) is
concerned.
It is important to recognize that space, understood in the above way, is not given as
determinate,35 nor does it determine which, if any, spatial properties are actual as opposed
to merely possible. The various extended parts that space comprises are only determined
34
As noted earlier, Kant uses the same word to refer both to these and to the location-properties that have
been the focus here: ‘Ort’.
35
Kant says in the Prolegomena that space is “indeterminate with respect to all specific properties” (Ak.
4:322). I will have more to say about the meaning of this remark (and others like it) in the next section.
24
with regard to their locations – that is, they only have an actual location – insofar as they
are filled with substances that instantiate location-properties. In this respect, space is
determined by the substances in it. These substances determine, out of a range of possible
properties, what actual properties the different parts of space have. This point will be
important for understanding (SCM).
In §5, I will return to the assumption that a substance’s having a location at a given
instant requires that it act, that is, exercise its force, on other substances. For now, the
important points are the following. First, Kant has principled reasons for thinking that
space makes possible a thoroughgoing community among objects of intuition in a manner
that time cannot. In particular, Kant thinks that space, in virtue of being a storehouse of all
possible spatial-properties, makes it possible for substances to have global locations (that
is, to instantiate global location-properties). Since substances cannot have locations unless
they act on one another, if space makes it possible for the substances given in it to have
locations then it makes it possible for them to act on one another. Second, Kant’s claim
that we need to avail ourselves of outer intuition in order to guarantee the objective reality
of the category of community rests on a particular metaphysics of space – in particular, the
view that space makes possible a community among the substances given within it. Third,
the considerations that lead Kant to endorse (SCE) do not commit him to either the
Newtonian or Leibnizian answers to the question of whether substances must be in space
in order to be in community.
It should be obvious how Kant’s assumption that space makes possible a
community among whatever substances are given in it puts him at odds with the
25
Leibnizian answer to the above question. Kant writes in the General Note on the System of
Principles:
Hence Leibniz, who ascribed a community to the substances of the world only as
conceived by the understanding [and not as given in outer intuition], needed a
divinity for mediation; for from their existence along this community rightly
seemed to him incomprehensible. (B293)
In contrast to Kant, for the Leibnizian it is always God rather than space that opens up the
possibility of community.
Though one might initially think that this assumption commits Kant to the
Newtonian view that substances must coexist in space in order to be able to interact, in
fact, it does not. The claim that space makes it possible for the substances given in it to be
in community is compatible with there being instances of community in which both relata
do not coexist in space. Indeed, Kant is careful to leave open this possibility in the
Critique, since his practical philosophy presupposes a community of non-spatio-temporal,
mental substances (the kingdom of ends). Moreover, even though Kant explicitly denies
that we could have theoretical cognition of such a community (since, as we saw, such
cognition requires the application of a category whose objective reality is ensured by outer
intuition) he nowhere denies that we can coherently think it. For Kant, we are free to apply
the categories to whatever objects we please, whether or not they can be given in outer
intuition. It is just that we can have no insight into the objective reality of the categories
vis-à-vis the objects we are applying them to when those objects are not given in outer
intuition. Thus, Kant would agree with Newton that we could not cognize interaction
among any substances (like Cartesian minds) that do not coexist in space, while
nevertheless rejecting the Newtonian position that such interaction is metaphysically (and
conceptually) impossible.
26
V. Kant’s Justification for (SCM)
At this point, we have explained why Kant thinks that, for us, cognition that the
states of substances are coexistent requires that we intuit those substances in space. We
still need to explain Kant’s justification for (SCM): why is thoroughgoing mutual
interaction required for cognition of a communio spatii, an order of spatial substances in
which each has a definite spatial location relative to the others at a given moment?
The first step towards an explanation is to recognize that, when Kant uses the term
‘cognition’ in the Third Analogy, he has in mind a propositional attitude that is both
justified and veridical.36 What this means is that a subject cannot cognize that a given
manifold of spatial substances have definite spatial locations relative to one another at a
given moment, unless this is in fact the case. Since truth for Kant is a condition of
cognition, if a further condition must be met in order for it to be the case that substances
have definite locations, the latter would itself be a condition on cognizing that a manifold
of substances are in a communio spatii.37 As I interpret Kant, he holds that mutual
interaction is a condition of substances having definite locations in space at some time t1 –
that is, as instantiating location-properties. From this, it follows straightforwardly that
cognition of a communio spatii requires mutual interaction.
But it is not immediately obvious why substances need to interact in order to have
locations. As we saw in §4, the thoroughgoing mutual interaction of substances follows
36
I am not claiming that he always uses the term in this way. Indeed, sometimes Kant seems to allow for
false cognition. All that’s required for my purposes is that he uses the term in a stricter sense in the Third
Analogy.
37
Cf. Watkins, Kant and the Metaphysics of Causality, 200: “…[T]he Analogies are arguing that something
ontological or metaphysical is required as a condition to ground something epistemological, and that the one
can thus be said to make the other possible.”
27
from the fact that location is reciprocal and action-dependent. However, we have yet to say
why Kant regards location-properties as action-dependent. My suggestion is that this
requirement stems from Kant’s understanding of substances as inherently active, a doctrine
that Kant shares with the Leibnizians. This doctrine seems to entail that all properties
(even relational ones) instantiated by a substance are at least in part grounded in its causal
activity, the exercise of its characteristic forces. Otherwise, there is no basis for saying that
a given property is an actual property of this substance, as opposed to a merely potential
property of it, or an actual property of some other substance.38 (Indeed, one could also
argue that a property is not actualized unless there is some activity in virtue of which it is
actualized.) Kant, of course, disagrees with the Leibnizians about whether the sort of
causal activity that (at least in part) grounds a substance’s instantiating different properties
at different times entails real causal influence. Kant, as various commentators have pointed
out, has principled reasons for maintaining that it does: for a substance to exercise its
forces is for it to act on other substances.39 Locations, as we have seen, are reciprocal
properties. As such, substances can only instantiate location-properties through reciprocal
causal activity: by really acting on others and by being acted on by them in turn.
It is the fact that spatial substances stand in reciprocal causal relations at t1 that is
responsible for their having global locations with respect to one another at t1, and not viceversa. Moreover, the specific manner in which substances interact at t1 – the amount of
Lucas Thorpe calls this the “principle of active inherence.” For further explanation and discussion, see
Lucas Thorpe, “Kant on the Relationship between Autonomy and Community,” in Kant and the Concept of
Community (Rochester: University of Rochester Press, 2011), ed. Charlton Payne and Lucas Thorpe, 63-87
(75ff.).
39
For a helpful discussion of the pre-Critical Kant’s reasons for rejecting pre-established harmony, see
Watkins, Kant and the Metaphysics of Causality, 23-100.
38
28
force they exert on one another – in part40 determines the distance between those
substances at that moment, and thus their specific locations. We can illustrate this last
claim more concretely by considering the particular case of attractive and repulsive forces.
Though in the Third Analogy Kant does not specify the sort of causal activity that he takes
to be necessary for determining spatial location, it is clear from the Metaphysical
Foundations of Natural Science that he thinks these specific forces are at work. According
to the account presented in the dynamics chapter of the Metaphysical Foundations, at
every moment, every material substance exercises its attractive and repulsive forces on
every other, in a manner inversely proportional to the square and cube of their distances,
respectively. My suggestion is that, for Kant, when substances exercise a given amount of
attractive and repulsive force at t1, they do not do so because of their locations (and the
distance between those locations) at that moment. Rather, substances have these specific
locations at t1, and are this particular distance apart, because they exercise this amount of
attractive force and this amount of repulsive force at t1.41 In this way, the global location of
substance A at a given time, as well as its distance from any given substance B, is
determined by the amount of attractive and repulsive force that A exercises on B at that
time and by the (equivalent) amount of attractive and repulsive force that B exercises on it.
This is compatible, of course, with our having to use the amount of distance between
substances to calculate the amount of attractive and repulsive forces that they are
exercising. Priority in the order of being does not entail priority in the order of knowing.
Moreover, the sort of synchronic determination at issue here does not preclude diachronic
I say “in part” because their mass is also relevant for determining their distance.
I think this interpretation helps to explain why Kant appears unbothered by a construal of universal
gravitation as involving action at a distance. For Kant, substances are only a specific distance apart in virtue
of interacting. Problems with action at a distance only arise if one thinks that the specific distance between
substances is (ontologically) prior to their acting on one another.
40
41
29
determination: the amount of force exerted by a given substance at t1 is diachronically
determined by the state of the universe at previous moments (in particular, by facts about
the masses and amounts of force exerted by substances at previous moments) and the laws
of nature.
Kant’s account of the synchronic determination of distance through the exercise of
force is one that Newton, at least as Kant understands him, implicitly denies. For Newton,
it is not the causal activity of spatial substances that determines why a given substance A
has the global location that it does at t1 and (relatedly) why it is precisely D distance from a
given substance B. On Newton’s view, as Kant understands it, there is nothing that
determines facts about location and distance beyond the nature of space itself; in this sense,
they are “primitively given”. Instead of explaining the distances between substances at a
given time through the amount of force exerted by substances, for Newton, the quantity of
attractive force exerted by one substance on another at that moment is determined in part
by their distance. Kant explicitly rejects such a view. As he writes in the L1 lectures,
written between 1773 and 1774, “space would laugh at us” if we were to ask it to do what
Newton claims it does (Ak. 28:213).
But apart from its risibility, what reasons might Kant have for rejecting the
Newtonian position? Why not think that the fact that substances are located at t1 is what
grounds the fact that they stand in reciprocal causal relations at t1? Similarly, why not think
that the amount of force exerted by each substance on the others at t1 is explained (at least
in part) by the distances between their locations at that moment? One reason Kant has for
rejecting the Newtonian view is that he takes it to be incompatible with the transcendental
ideality of space. Kant writes in the Antinomy Chapter:
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Thus things, as appearances, do determine space, i.e., among all its possible
predicates (magnitude and relation) they make it the case that this or that one
belongs to reality; but space, as something subsisting in itself, cannot conversely
determine the reality of things in regard to magnitude and shape, because it is
nothing real in itself. (A431/B459)42
For Kant, the ideality of space implies that it cannot impose determinate relationships on
the substances given within it, such as a distribution of location-properties in accordance
with the inverse square law. Considered on its own, apart from the empirical objects given
within it, space is, as Kant says in the Prolegomena, “so indeterminate with respect to all
specific properties, that certainly no one will look for a stock of natural laws within it”
(Ak. 4:322). Rather than imposing determinate spatial and causal relationships on the
empirical objects in it, it is the forces of the latter and the laws governing those forces that
determine space by determining what locations are actual.
So one reason Kant rejects the Newtonian view about spatial location and force is
that it is incompatible with the transcendental ideality of space, which Kant takes to imply
that it is in need of “determination” by empirical objects. But Kant also has other reasons
that are independent of his contentious doctrine of the ideality of space. These reasons
stem from his understanding of locations as relational and action-dependent, as well as his
understanding of space as a repository of possible spatial properties. These doctrines do
not presuppose the ideality of space. Start with the first. Kant takes it to be analytic that
...to be in a location is to act externally [äußerlich] in certain relations. Because in
absolute space no relation of one thing to another can be met with (without the
relation of acting on another), a thing cannot be met with in absolute space. (Ak.
17:453)43
42
For one of the few discussions of this passage in the secondary literature, see Gerd Buchdahl, Metaphysics
and the Philosophy of Science. The Classical Origins: Descartes to Kant (Cambridge, Massachusetts: MIT
Press, 1969), 577.
43
Kant makes a remark in a very similar vein at Ak. 17:578 (written between 1772 and 1773): “Absolute
space, against which [wogegen] created things stand in actual relations, is impossible. For no substance is
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Kant suggests here that the Newtonian position rests on a faulty understanding of what it
means for a thing to be in a location. According to Kant, a thing has a location in space
only if it stands in a “certain” causal relation with other things. But locations in absolute
space, at least as Newton conceives it, are not like this: they do not entail the existence of
any definite causal relationships, since space could be wholly empty, or could be inhabited
by a single object that does not act on anything else. Since locations in absolute space do
not entail definite causal relationships, but a thing’s being located entails its being in a
definite causal relationship, a thing cannot have a location (or, as Kant says, “be met with”)
in absolute space.
Admittedly, this argument rests on a contentious understanding of what it means for
a thing to be at a location. It would be open to a proponent of absolute space to distinguish
between absolute and relative locations, maintaining that the former are neither relational
nor action-independent. And indeed, one can find Newton and other advocates of absolute
space (such as Crusius) making precisely such a distinction. However, Kant does not need
to insist on his particular notion of location in order to make the point that there is a crucial
gap in the Newtonian account. Recall that, for Newton, the fact that substances act on one
another in a definite way at t1 is supposed to be grounded in the fact that they are definitely
located in absolute space. But, as Newton conceives of absolute space, a thing can be in it
without standing in any relations to anything else. Thus, the mere fact that two substances
have definite locations in absolute space is not, all on its own, sufficient to account for their
having any relations to one another (let alone causal relations). Given this insufficiency,
present somewhere without acting, and indeed outwardly [äußerlich]; in absolute space, however, there are
no correlates [Correlate].”
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Kant could argue, we have reason to think that the grounding relation goes in the opposite
direction: substances are definitely located with respect to one another because they act on
one another in a definite way – that is, they exert a definite amount of force in accordance
with definite laws.
Just as Kant’s conception of location entails the falsity of the Newtonian view, so
does his conception of space as a storehouse of possible location-properties. If this is
indeed what space is, it is obvious that it cannot itself determine why specific substances
instantiate the location-properties that they do. This view of space immediately entails the
“indeterminacy of space”. As with Kant’s view of location, this particular view of space
does not presuppose transcendental idealism. One could, at least in principle, maintain both
doctrines while maintaining that location-properties are properties of things in themselves
(and thus denying that they are merely subjective). This is significant because it means that
Kant’s reasons for rejecting the Newtonian position go deeper than his doctrine of
transcendental idealism.
It is important to note that this view is fully compatible with the view I attributed to
Kant in the previous section: namely, that space makes it possible for the substances given
in it to interact with one another. Kant, unlike the Leibnizians does not try to explain space
in terms of causal (or quasi-causal) relations. Instead, he regards space as a relational
framework that exists in some sense prior to the substances given in it, and that makes it
possible for them to interact with one another.
But as we also saw, Kant holds that this space, when considered apart from the
substances in it, is indeterminate. Qua indeterminate, space merely makes possible the
mutual interaction of the substances in it; it does not itself impose any specific way of
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acting on them. Rather, by exerting a definite amount of force on each other in accordance
with laws, substances make it the case that they have definite locations and are definite
distances apart. In this way, the existence (and thus the cognition) of a communio spatii
depends on there being a thoroughgoing mutual interaction among substances.
VI. Conclusion
In this essay, I have tried to shed light on an underexplored aspect of Kant’s Third
Analogy: his account of the relationship between space, coexistence, and community. In
particular, I tried to get at Kant’s justification for (SCE) – if we are to cognize that the
states of substances are coexistent, these substances must be objects of outer intuition –
and (SCM) – if we are to cognize that substances have definite spatial locations relative to
one another, it is necessary that those substances be in thoroughgoing mutual interaction.
As I argued, the considerations that lead Kant to (SCE) and (SCM) are both
epistemological and metaphysical. (SCE), for instance, rests most crucially on the
epistemological claim that cognition requires the application of a category whose objective
reality is ensured, and on the metaphysical claim that space makes possible the community
of the substances in it (i.e. provides the category of community with objective reality).
(SCM), in turn, rests most crucially on the epistemological claim that cognition of a state
of affairs requires that the state of affairs actually obtain, and on the metaphysical claim
that a substance’s being a definite distance away from another substance at a given time is
grounded in its exercising a definite amount of force on that substance at that time. In
taking Kant’s arguments for (SCE) and (SCM) to rest in part on metaphysical
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considerations, my interpretation complements Watkins’ recent reconstruction of Kant’s
argument for (Conc2).
I also tried to explain how (SCE) and (SCM) bear on two questions that are
answered very differently in the context of Newtonian and Leibnizian natural philosophy:
(1) must substances coexist in space in order to be able to interact with one another, and (2)
is space or community ontologically prior? As I argued, the considerations that lead Kant
to (SCE) and (SCM) allow him to navigate between the Newtonian and Leibnizian answers
to these questions. With regard to the first question, Kant holds, contra the Leibnizian
position, that at least for a certain class of substances (namely, all those whose states we
can cognize as coexistent) space is a condition of the possibility of their mutual interaction.
Yet, contra the Newtonian position, Kant is careful to avoid claiming that it is
metaphysically impossible for there to be substances that do not coexist in space and yet
interact with one another. He merely denies that we could have cognition that such
substances mutually interact, because we could have no guarantee of the objective reality
of our concept of community when applied to them. With regard to the second question,
Kant holds, contra the Newtonian position, that mutual interaction is ontologically prior to
a communio spatio: substances only have definite locations in space in virtue of acting on
one another in a definite way. At the same time, Kant is careful to avoid claiming that
space itself is grounded in the mutual interaction of substances. On its own, apart from the
things in it, space is something indeterminate that makes possible mutual interaction.
There is an irony to all of this. The Third Analogy is designed to legitimate a
version of a principle that figures crucially into both Newtonian and Leibnizian natural
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philosophy: the principle of community. Yet Kant argues for this principle by means of
assumptions that are (at least in his mind) profoundly anti-Newtonian and anti-Leibnizian.
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