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relation of mutual attraction and repulsion:
In order to be assured of this agreement [between the category of
community and the form of a disjunctive judgment], one must note
that in all disjunctive judgments the sphere (the multitude [Menge] of
everything that is contained under it) is represented as a whole divided
into parts (the subordinated concepts), and, since none of these can be
contained under any other, they are thought of as coordinated with one
another, not subordinated, so that they do not determine each other
unilaterally, as in a series, but reciprocally, as in an aggregate (if one member
of the division is posited, all the rest are excluded, and vice-versa). Now a
similar connection is thought of in a whole of things, since one thing is not
subordinated, as effect, to another, as the cause of its existence, but
is rather coordinated with the other simultaneously and reciprocally
as cause with respect to the determination of the other things (e.g., in
a body, the parts of which reciprocally attract and also repel each other).
(B 112, translation modified)14

What is surprising here is that Kant appears to assimilate a logical
relation between concepts and a material relation between things: the
mutual exclusion and complementarity of spheres or extensions of con-
cepts is assimilated to the mutual determination, by attraction and repul-
sion, of material bodies or parts of material bodies.
But this cannot possibly be right. Assimilating in this way the relation
of mutually exclusive concepts in a disjunctive judgment and the
relation of things belonging to one world-whole, or of parts making up
one material thing, is prima facie precisely the kind of move Kant
rejects throughout the Critique. As he insists in the appendix to the
Transcendental Analytic, On the Amphiboly of Concepts of Reflection,
this rejection is the core of his opposition to Leibnizian rationalist meta-
physics. Leibniz™s major metaphysical mistake, according to Kant, is to
have thought that things could be distinguished and determined by
concepts alone, specified all the way down to individuals, so that the

When Kant talks about ˜˜the multitude . . . contained under a judgment™™ he presumably
means: the multitude thought under each sub-species of the divided concept (for instance,
the multitude thought under AB, and the multitude thought under AC).

latter are completely determined as infimae species, lowest specifications
of concepts. Against this view Kant maintains, in the Amphiboly, that two
drops of water, for instance, may be identical as to their concepts, namely
as to the discursive representation of their internal determinations of
shape, size, and quality, and nevertheless be numerically distinct, solely
by virtue of their position in space (A264/B320).15 Similarly, any two
surfaces may be identical to one another as to their concept, namely their
internal determinations of size and shape, and nevertheless be numeric-
ally distinguished by their position in space as a whole. Now, it seems that
the parallel Kant draws, in the Metaphysical Deduction of the
Categories, between the logical relation of mutually exclusive and com-
plementary concepts in disjunctive judgment on the one hand, and the
relation of things expressed in the category of community on the other
hand, is just the Leibnizian error Kant denounced in the Amphiboly
chapter. This impression is only enhanced by the fact that in the text
quoted earlier, Kant describes the reciprocal action between parts of
things in terms of attraction and repulsion, namely in terms of precisely
the kind of external relation that he insists is quite distinct from the
relation of internal determinations expressed in a logical disjunction of
completely determined concepts, as Leibniz would have it (cf. A265“6/
B321, A274/B330).16 This being so, the skepticism or even derision
frequently directed at Kant™s claim concerning the parallel between the
logical form of disjunctive judgment and the category of community
seems to be a very healthy one indeed by the terms of Kant™s own
doctrine. For if this parallel displays the very confusion Kant himself

Cf. Leibniz, Nouveaux essais sur l™entendement humain, ii, ch. 27, x3. Engl. trans. and ed. Peter
Remnant and Jonathan Bennett New Essays on Human Understanding (New York:
Cambridge University Press, 1981).
One may argue on Kant™s behalf that he explains the form of disjunctive judgment in terms
of the division of the sphere or extension of a concept into its subspheres, which is the
division of a whole into its parts and thus grounds the parallelism with the division of a
whole of physical things into its parts, or even the division of one physical thing into its
parts (category of community). This is correct as far as it goes, but it is not sufficient to
alleviate the charge of amphiboly. First, it remains that if things are represented as the
ultimate parts of the sphere of a concept, then they are individualized as ultimae species,
lowest specification of a concept, instead of being, as Kant claims they should be, individ-
uated (represented as numerically distinct) by virtue of their position in space and time as
forms of sensible intuition. Second, Kant invariably presents the category of community as
a concept of the universal interaction of empirical things. We need more than a consid-
eration of concepts according to their extension to explain how such an interaction might
relate to the community of concepts under a higher concept, and thus clear Kant of the
suspicion of amphiboly. And indeed, Kant does provide us with more justification than
this, as I show below. See also KCJ, pp. 436“53.

denounces in the Amphiboly, there is every reason for discounting this
particular correspondence between logical form and category.
However, I want to argue that this suspicion, despite its seeming
plausibility, is unwarranted. Kant™s point is not that relations of things
in space (the a priori form of external sense) are essentially the same as
relations of concepts in logical space. If we follow the general thrust of his
metaphysical deduction of the categories, we should understand his
point as being, rather, that the same act of the mind which, by means
of analysis, generates the form of disjunctive judgment and eventually,
the form of a unified system of such judgments, also generates, by means
of the synthesis of spatiotemporal manifolds, the representation of a
community of interacting things or parts of things “ ˜˜for instance™™
(B112 quoted above) the relations of reciprocal attraction and repulsion
of parts in a material body. And indeed, this is what Kant writes:
The same procedure of the understanding when it represents to itself the
sphere of a divided concept, it also observes in thinking of a thing as
divisible; and just as in the first case the members of the division exclude
each other, and yet are connected in one sphere, so in the latter case the
understanding represents to itself the parts of the latter as being such
that existence pertains to each of them (as substances) exclusively of the
others, even while they are combined together in one whole. (B113,
emphasis mine; translation modified)

Note here how systematic the correspondence is. Just as the under-
standing represents to itself the subspheres (the extensions of the sub-
concepts) of a divided concept as excluding one another (if one of the
specifications is asserted of the divided concept, the others are
excluded), so it represents to itself the existence of an individual sub-
stance as excluding the existence of all others (where one exists, no other
can exist at the same time). Just as the subconcepts are represented as
combined together in one whole, so the things or parts of things are
represented as constituting one material whole.17 However, this simi-
larity in the relations represented by the understanding should not lead
us to forget “ on pain of amphiboly “ the dissimilarity between the two
cases: the individuation of things in space cannot be represented by way
of the specification of concepts. What we want to know, then, is how this
individuation is represented by the understanding. Kant™s answer,

I am grateful to Steve Engstrom for pressing me on this point and bringing to my attention
the full measure of the structural similarities Kant underlines here.

according to the Metaphysical Deduction of the Categories cited in the
first section of this chapter, is that individuation of things in space is
represented by way of the acts of synthesis that are necessary if any
analysis of the sensible given into concepts is to be possible.
I intend to show that Kant™s argument in the Third Analogy is meant
to lay out just those acts of synthesis by way of which things are indivi-
duated in space and time. According to Kant, those acts of synthesis are
acts by means of which things are represented as being in relations of
universal causal interaction. Only insofar as they are so individuated can
they also be thought under concepts of natural kinds (namely, under a
universal scale of genera and species) ordered according to the form of
disjunctive judgment and a system of such judgments.
If this is correct, one can perhaps complete Kant™s elliptic statement in
the passages just cited by saying the following. For a Leibnizian, the
similarity between the understanding™s representation of the mutual
relation of disjunctive spheres of a divided concept on the one hand,
and the mutual relation of things or parts of things in space on the other
hand, goes all the way down: individual things just are ultimate specifi-
cation of concepts. For Kant, by contrast, although there is indeed the
systematic similarity described above between the understanding™s
representation of the two relations (between concepts, between empiri-
cally given things in space), one of them (the relation of concepts)
is thought by way of analysis (of the sensible given into concepts; and
of concepts into higher concepts); the other (the relation of things)
is represented by way of synthesis of manifolds in space and time, a
synthesis that results in presenting things as individuated in space by
their relations of universal interaction.
Here again the Amphiboly chapter may help us clarify Kant™s view, no
longer as a warning against possible amphibological interpretations of
his point, but rather as a confirmation of the positive account I just gave
of the correspondence between the logical disjunction of concepts and
the category of community. Kant explains, in the Amphiboly, his oppos-
ition to Leibniz™s view according to which substances are individuated
by their intrinsic determinations (determinations they have on their
own, independently of any external relation to other substances).
According to Kant, on the contrary, substances, i.e. material things
whose essential properties persist while their accidental properties
change,18 are recognized under concepts of external relations (mutual

On Kant™s concept of substance, see ch. 2 in this volume, pp. 53“4.

causal determination). This means, then, that the move from recogniz-
ing things as individuated in space and time, to thinking them under
concepts of natural kinds, is a move from representing them in relations
of universal mutual interaction, to thinking them under concepts of
relational properties (cf. A274“5/B330“1, A283“4/B339“40).
Let me summarize my argument so far: it might seem that in relating
the category of community, or universal interaction, to the logical form
of disjunctive judgment, Kant is guilty of the very amphiboly that he
denounces in Leibniz (confusion between the relation of mutual deter-
mination between spheres of concepts, and the relation of mutual causal
determination between things). However, I argue that Kant is not guilty
of this confusion. Rather, Kant™s point is that the concepts of natural
kinds under which we know material things in nature (and thus, classify
them under hierarchies of genera and species according to the form of
disjunctive judgment) are concepts of relational properties “ univer-
sal causal interaction. This being so, the category of community
(Gemeinschaft), by virtue of which things are thought as belonging
under one logical space of concepts, is also a category of universal causal
interaction (durchgangige Wechselwirkung), by way of which they are
thought as universally related in one empirical space (and time).
To examine Kant™s argument for this point, I now turn to the Third
Analogy of Experience.

Kant™s proof of the Third Analogy: simultaneity
and universal interaction
In the Third Analogy of Experience, Kant argues that our experiencing
the simultaneous existence of appearances is sufficient to attest that
these appearances are in relations of thoroughgoing community
(Gemeinschaft) or interaction (Wechselwirkung). This is because, Kant
argues, representing the simultaneous existence of appearances is our
doing, and this representation is possible only if we represent appear-
ances as being, with respect to one another, in relations of universal
interaction. Thus the statement of the Analogy: ˜˜All substances, insofar
as they can be perceived in space as simultaneous, are in thoroughgoing
interaction [in durchgangiger Wechselwirkung]™™ (B256).19

In the first edition, the Analogy is stated as follows: ˜˜Principle of community. All sub-
stances, insofar as they are simultaneous, stand in thoroughgoing community (i.e. inter-
action with one another).™™ The formulation in B is superior in that it makes clearer that
˜˜simultaneous™™ means: ˜˜something we represent, or perceive, as simultaneous.™™ Similarly,

As any careful reader of Kant™s Analogies of Experience knows, the
three Analogies should be read together as one argument, which concerns
the conditions of our representation of objective time-determinations.
Kant™s question is: how do we come to have any representation at all of
objective temporal determinations of appearances, since our apprehen-
sion of them is always successive, and since we have no given temporal
framework that might allow us to locate events and states of affairs in
time? In the Second Analogy, Kant explains how the subjective succession
of perceptions in apprehension can be the experience of an objective
succession of states of things; in the Third Analogy, he explains how
the subjective succession of perceptions in apprehension can be the
experience of an objective simultaneity of things in particular states.
Prior to this, in the First Analogy he has argued that any representation
of objective temporal order (succession or simultaneity) rests on the
presupposition of something permanent, as the substrate of objective
temporal determinations. I do not propose here to evaluate Kant™s over-
all argument in the Analogies of Experience.20 What I am mainly
concerned with is how discursive forms (forms of analysis or reflection)
and forms of sensible synthesis relate, according to Kant, in the particular
case of the Third Analogy.
Kant™s reasoning proceeds, roughly, according to the following

the argument in B is more clearly laid out as an argument about the conditions for our
experiencing things as simultaneous. One may wonder how such conditions put any
constraint at all on how things actually are. But the Transcendental Deduction is supposed
to have established just this point: the conditions of possibility of experience are the
conditions of possibility of the objects of experience. Evaluating the argument of the
Deduction is of course beyond the scope of this chapter. One should at least remember
one essential aspect of its conclusion: the objects we are talking about here are objects as
appearances “ as individuated in space and in time, the forms of our sensible intuition.
For an analysis and evaluation of Kant™s Analogies of Experience, see KCJ, ch. 11. On the
Second Analogy, see ch. 6 in this volume.
There are two expositions of the argument in the Third Analogy. The first in A, remain-
ing unchanged in B: A211/B258“A213/B260. The second added in B: B256“8. In my
view, the exposition in B is the clearer of the two, for reasons similar to the ones
I advocated in the previous footnote: the argument in B, just as the formulation of the
Analogy itself, makes it clearer that what Kant is talking about are the conditions for our
experience of objective simultaneity (which is also the only context in which the very
notion of simultaneity has any meaning at all). In my reconstruction of the argument
I will thus follow the order of the B edition. In an effort to limit the length of the
footnotes, I shall indicate the textual support for each step simply by the reference in B
(i.e. the 1787 version) and A/B (when the 1781 version provides useful additional textual
support). I shall not quote the texts themselves.

1 The synthesis of our apprehension in imagination is always
2 We nevertheless experience a subjective succession in apprehension
as an objective simultaneity of things in particular states if, and only
if, we experience the subjective succession as being order-indifferent.
For example, we are conscious that we could direct our gaze indif-
ferently from the moon to the earth or from the earth to the moon;
it is in this way that, even though we might never perceive at the
very same time the moon at its zenith and the surface of the earth,
we do experience these objects as simultaneously existing (B257;
3 We have no perception of time itself that would allow us to derive from
the simultaneity of objective states of things the order-indifference of
the subjective succession in our apprehension of these states
4 Nor would the mere subjective succession of perceptions in our
apprehension suffice to generate either the representation of its own
order-indifference or the interpretation (experience) of this order-
indifference as objective simultaneity. Subjective succession in appre-
hension would, by itself, give us only: one perception, then the other,
and reciprocally, the latter, then the former. It would give us no access
to the simultaneity of things as the necessary condition for the order-
indifference of the perceptions (B257).
5 We are conscious of the subjective succession as order-indifferent, and
thus as a representation of objective simultaneity if, and only if, in
relating the subjective succession of perceptions in apprehension to
objects, we form judgments such as: if object X (recognized under
concept A) exists at time t at point p1, then object Y (recognized under
concept B) exists at that same time at point p2, and reciprocally, if the
latter exists, then the former exists at the same time. We thus think X
and Y as being in themselves determined with respect to the logical
form of a hypothetical judgment whose reciprocal converse is also
thought to be true (if X, recognized under A, exists at p1 at t, then Y,
recognized under B, exists at p2 at t; and conversely if Y recognized
under B at p2 at t, then X under A at p1 at t). Thus a pure concept of

This premise is not explicitly stated in the argument of the B edition, but it is common to all
three Analogies, and explicitly stated in the first and second: see A182/B225 (First
Analogy), A189/B234, A198/B242 (Second Analogy); in the Third Analogy, this premise
is implicit at B257.

the understanding is applied whenever we experience objective
simultaneity (B257).23
6 This concept is that of mutual conditioning, i.e. interaction. Thus the
coexistence of things in space can be experienced only under the
presupposition that they are in relations of universal interaction or
community (B257“58; also A212“13/B259“60).
7 So, all appearances, insofar as we perceive (experience) them as
coexisting, exist in relations of thoroughgoing reciprocal influence
(B258; also A213/B259“60).24

In what I present as step (5), I am making explicit that the ˜˜pure concept of the under-
standing™™ needed to represent the reciprocal sequence as objective is the ˜˜concept of an
object, by means of which its intuition is regarded as determined with regard to one of the
logical functions for judgment™™ (cf. B128), in this case the function of a hypothetical
judgment together with its reciprocal converse. Here again, as in the case of the Second
Analogy, I hope to show why it is helpful to stress this relation between the pure concept of
the understanding and the corresponding logical function of judgment. Note already that
the logical function at work here is not that of a disjunctive judgment, but that of
a hypothetical judgment (and its reciprocal converse). This is quite explicit in Kant™s
presentation of his example, that of perceiving the earth and the moon to exist
˜The synthesis of imagination in apprehension would only present each of these
perceptions as one that is present in the subject when the other is not, and conversely,
but not that the objects are simultaneous, i.e., that if the one is then the other is also at the
same time, and that this is necessary in order for the perceptions to be able to succeed
each other reciprocally (B257, emphasis mine).
Of course a disjunctive judgment might itself be translated into hypothetical judg-
ments, such as: ˜˜if the one is at a given point, then the other is not,™™ where each of the
two simultaneously existing things excludes the other from the point in space which it,
itself, occupies, just as each of the two concepts B and C dividing a higher concept A in
the disjunctive judgment: ˜˜A is either B or C™™ each exclude the other™s extension from
their own. But it is important to note that it is not this negative form that Kant
mentions in expounding his argument: what he says is that ˜˜If the one is then the
other is also at the same time.™™ This, it seems to me, expresses the relation of mutual
conditioning that would be captured by two reciprocal hypothetical judgments. Each of
the two coexisting things is thus individuated as to its existence in space by its relation
to the other (and in fact, each of the indefinitely many coexisting things is thus
individuated by its relation to all the others) and eventually reflected under concepts
that can be combined according to the form of disjunctive judgments, say for instance:
˜˜this is either outside the solar system or a satellite of the sun or a satellite of another
body within the solar system.™™
Note that here we find the same move as in the Second Analogy, from what we presuppose,
to what is true of objects (as appearances). I suggest that the move is (implicitly) justified
here in the same way as it was there: by referring back to the argument of the
Transcendental Deduction to the effect that ˜˜the conditions of possibility of experience
are the conditions of possibility of the object of experience™™ (cf. above, ch. 6, p. 159).
I will not dwell on this point. What interests me about the third Analogy is more specifically

Now, this conclusion is prima facie completely implausible.It is simply
not true, one might object, that I perceive my desk and my chair as
simultaneously existing only if I suppose a relation of interaction
between them, and it is also not true that I perceive the earth and the
moon as coexisting only if I suppose reciprocal influence between them.
The objection seems only too obvious. However, it might be overcome if
we remember that there is originally nothing more to the pure concept
of cause than ˜˜the concept of an object, by means of which its intuition is
regarded as determined with regard to . . . the logical function of a
hypothetical judgment™™ (B128). Thus by ˜˜interaction™™ (namely recipro-
cal causal action), Kant means nothing other than the relation between
the states of one (relatively permanent) substance and the states
of another, such that they can be regarded as determined with regard
to the logical function of a hypothetical judgment whose reciprocal
converse (the consequent taking the place of the antecedent, and conver-
sely) is also taken to be true. What Kant is saying is that interpreting two
successively apprehended states, say A and B, as simultaneously existing
states of objects, is thinking something like this: ˜˜If X (recognized under
concept A) is part of the present whole of my experience, then Y (recog-
nized under concept B) is part of the same whole. And if Y (recognized
under concept A) is part of the whole of my present experience, then X
(recognized under concept B) is part of the same whole.™™ What we
represent to ourselves as the simultaneity of things in space is then
nothing other than the sensible (temporal) form, that is, the mode of
ordering individuals in time, resulting from a synthesis guided by the
capacity to analyze according to the discursive form of a hypothetical
judgment whose reciprocal converse is also believed to be true. In
accordance with this discursive form, asserting the presence (existence,
Dasein) of one of the objects perceived is represented as a sufficient
condition for asserting the presence of the other, and conversely the
presence of the latter is reflected as a sufficient condition for asserting
the presence of the former. Which specific determinations condition one
another (i.e. specifically what conditions what), we do not know. We shall
acquire such determinate cognition only by means of the indefinite,
never completed process of corrections and specifications of our discur-
sive judgments in actual experience. Nevertheless, Kant™s point is that

the relation, in Kant™s argument, between the respective roles of the logical form of
disjunctive judgment and that of hypothetical judgment, both of which, I maintain, play
a role (the latter more directly than the former) in our ordering appearances in such a way

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