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minds. As for the role he assigns to a priori forms of intuition in grounding
synthetic a priori judgments, Kant is charged with relying on a conception
of arithmetic and geometry made obsolete by the development of non-
Euclidean geometries and modern quantificational logic; he is also charged
with a misguided absolutization of a Newtonian model of natural science
made obsolete by revolutions in nineteenth- and twentieth-century physics.
In the present chapter I shall examine Kant™s claims concerning the
second of the two cornerstones mentioned above: the derivation of cate-
gories from logical functions. To do this I shall focus on one particular
case: the category of community, its relation to the logical function of
disjunctive judgment, and its application to appearances in the so-called
˜˜principle of community,™™ the Third Analogy of Experience. This case is
interesting for two main reasons. First, it is the most difficult to defend.
Kant himself was aware of this, and took great pains to explain why even
in this case, however implausible it might seem, the relation he main-
tained between logical functions and categories does in fact hold. The
general view of Kant commentators, however, is that his defense remains
utterly unconvincing. I shall argue, on the contrary, that the correspond-
ence Kant wants to establish between the logical function of disjunctive
judgment and the category of community is an important and interesting
one, although indeed it is more complex than any other. But this very
complexity is in fact my second reason for focusing on this case: what
makes the category of community difficult to grasp is that it can be under-
stood only in connection with the other two categories of relation (and
even with the previous two ˜˜titles™™ of categories, quantity and quality).
This being so, examining Kant™s argument in this case should also give us
some insight into his overall argument on the relation between logical
functions, categories, and the application of categories to appearances.
This chapter is in four parts. In the first, I shall briefly expound the
relation Kant claims to establish between logical functions of judgment
and categories.
In the second part, I shall examine Kant™s logical form of disjunctive
judgment and its relation to the category of community or universal

In the third part, I shall examine Kant™s proof of the Third Analogy of
Experience, namely his proof that necessarily, things we perceive as
simultaneously existing exist in relations of universal interaction or, in
Kant™s terms, of dynamical community.
The lesson of this examination, I shall suggest, is that neither Kant™s
general claim concerning the role of logical functions of judgment in
generating our representations of objects, nor even his more particular
claim concerning the relation between the form of disjunctive judgment
and the category of community, deserve the summary dismissal they are
often met with. Rather, Kant™s argument provides an intriguing account
of how elementary functions of minds such as ours might be responsible
for the unity of our unsophisticated, ordinary perceptual world, as well
as for the relation between this world and our more sophisticated,
scientific worldview.
Finally, in the fourth and concluding part I shall suggest that paying
close attention to the Third Analogy (the ˜˜principle of community™™) and
not just to the better-known Second Analogy (Kant™s response to Hume
on the concept of cause and its objective validity) give us important
insights into the unity of Kant™s critical system as well as its relation to
its philosophical posterity.

Logical functions and categories: the understanding
as a capacity to judge
In the Critique of Pure Reason, Kant explains that the understanding, or
intellect as a whole “ the intellectual faculty at work in forming concepts,
combining them in judgments, combining judgments in inferences, and
finally constituting systems of knowledge “ the intellect that produces all
this is essentially a Vermogen zu urteilen, a capacity to form judgments.2 In
other words, describing the features of the intellect that make it capable
of forming judgments is by itself describing just those features that also
make it capable of forming concepts, inferences, systems of thought and
knowledge. This is because, as Kant puts it in the section that precedes
his table of logical functions of judgment, if we start with the traditional
notion that the understanding is a capacity for concepts, we soon find,
upon examination, that we form concepts only for use in judgments, and
this use itself involves implicit inferential patterns and their systematic

Cf. A69/B94, A81/B106. Cf. chs. 2 and 4 in this volume.

Kant™s explanation of this point can be summarized as follows.
Concepts, as he defines them, are ˜˜universal and reflected representa-
tions.™™ They are formed by comparing individual objects, focusing on
the common features or marks of these objects and ignoring their
differences.3 A concept is thus a conjunction of common marks under
which one may recognize a class of objects as falling under the same
concept. But this means that forming concepts is forming implicit judg-
ments: for instance, forming the concept ˜˜tree™™ is forming the implicit
judgment, ˜˜everything that has a trunk, branches, and roots, is a tree™™
(and conversely, ˜˜everything that is a tree has a trunk, branches and
roots™™). On the other hand, forming such a judgment is forming the
major premise for a possible syllogistic inference, for instance, ˜˜every-
thing that has a trunk, leaves, and roots, is a tree; this tiny thing here has
a trunk, branches, roots; therefore it is a tree.™™ Judgments and syllogistic
inferences, systematically arranged, give rise to universal hierarchies of
genera and species under which individual things are classified into
natural kinds; thus they give rise to systematic knowledge.
It is by virtue of their form that judgments can thus be the source of
the systematic unity of knowledge. What Kant calls the form of a judg-
ment is the way concepts are combined in judgment.4 When we analyze
the ˜˜mere form™™ of judgment, we have to consider concepts themselves
as to their ˜˜mere form,™™ namely their universality: their being combin-
ations of marks common to a multiplicity of individual objects.5 The
˜˜form™™ of a judgment is thus the way in which concepts, as universal
representations, are combined in it. Kant™s table of logical forms of
judgment6 is a table of just those modes of combination of concepts
that are minimally necessary for the functions of intellect briefly outlined
above to emerge: subsumption of individual objects under concepts,
syllogistic inference, the systematic arrangement of knowledge and

This is true also of the categories, but does not challenge their apriority. On this point, see
above, ch. 1, pp. 26“9; also KCJ, p. 121.
Cf. Jasche Logic, x18, AAix, p. 101. Also Reflexionen 3039 and 3040, AAxvi, pp. 628“9.
Jasche Logic, x2, xx 4“8, AAix, pp. 93“6; Reflexion 2855, AAxvi, p. 547; Reflexion 2859, AAxvi,
p. 549.
On Kant™s notion of a ˜˜function™™ of judgment, see A68/B93. Cf. also A70/B95. If we rely on
Kant™s explanations in these texts, logical function and logical form of judgment seem to be
distinguished as (1) the structure of an act “ a structure that makes the act adequate to
achieving a specific purpose, that of ˜˜ordering representations under a common represen-
tation™™ “ and (2) the result of the act: the mode of combination of concepts, or the ˜˜form™™ of
the judgment resulting from the act. On this point, see above, ch. 4, pp. 92“5.

I now want briefly to review this table, with only the degree of detail
necessary to situate the particular function of disjunctive judgment
within it.
Recall that concepts, in Kant™s logic, are defined as ˜˜universal and
reflected representations™™ (that is, as universal representations formed
by comparing objects, selecting common marks, leaving aside particular
marks by which the objects thought under the same concept nevertheless
differ from each other). So considered, the kinds of combinations con-
cepts may enter into in judgment are exclusively what Kant calls ˜˜concept
subordinations,™™ where the extension of one concept (everything that falls
under the concept) is, as a whole or only in part, included in, or excluded
from, the extension of the other. The first two titles in Kant™s table
(quantity and quality, in their first two moments: universal and particular,
affirmative and negative) describe precisely the four possible cases just
mentioned: inclusion of the extension of a concept in the extension of the
other, or exclusion therefrom (affirmative or negative judgment, As are
B or As are not B), in totality or in part (universal or particular judgment,
all/no As are B, some As are/are not B).7 To these four possible combin-
ations that exhaust the possible cases of concept subordination, Kant adds,
under each of the first two titles (quantity and quality), a form of judgment
that relates concept subordination, respectively, to individual objects
(singular judgment under the title of quantity), and to the unified logical
space within which all spheres of concepts reciprocally limit each other
(˜˜infinite™™ judgment, A is not-B).
The raison d™e tre for the third title, that of ˜˜relation,™™ is more difficult to
elucidate. Kant notes that a judgment, considered according to the
forms of relation, combines two concepts (categorical judgments) or
two judgments (hypothetical judgment, where the connective is
˜˜if . . . then™™) or several judgments (disjunctive judgment, where the
connective is ˜˜either . . . or™™) (A73/B98). This is hardly any explanation
at all. We can do better if we consider the relation of judgment to
syllogistic inference mentioned above. We saw that combining concepts
in a universal categorical judgment (all As are B) was eo ipso obtaining the
premise for a syllogistic inference in which one might attribute the
predicate B to anything thought under the subject-concept A. This is

On these explanations and the privilege given to the point of view of extension in defining
the form of judgment as to its quantity and quality, cf. Jasche Logic, xx21“2. Note that
consideration of the extension of concepts, and of judgment as expressing the inclusion
or exclusion of concepts™ respective extension (Umfang), is also prominent in the explana-
tions Kant gives at A71“2/B96“8.

why Kant calls a universal categorical judgment a rule, and the subject-
concept in such a judgment the condition of a rule (for instance, the
concept ˜˜man™™ functions as a condition of the rule: ˜˜all men are mortal™™).
The term ˜˜condition™™ should here be understood as meaning ˜˜suffi-
cient™™ not ˜˜necessary™™ condition: that some entity X be a man is a
sufficient condition for its being mortal. Or, if X is a man, then X is
mortal. Since being a man is a sufficient condition for being mortal,
subsuming any individual X under the concept ˜˜man™™ provides a suffi-
cient reason for asserting of it that it is mortal.8
However, there are other kinds of conditions of a rule. One is that of
hypothetical judgment, the second title of relation in Kant™s table.
According to this form, a concept is not by itself, on its own, the condition
for attributing a certain mark to an object thought under the concept.
Instead, one can do so only under an added condition: ˜˜If C is D [added
condition], then A is B™™ (and thus any object X subsumed under the
concept A receives the predicate B under the added condition that some
relevant C is D). Kant™s example is the proposition: ˜˜If there is perfect
justice, then the obstinately wicked will be punished.™™ (Implicit possible
subsumption: any individual falling under the concept ˜˜wicked™™ is
doomed to be punished, under the added condition that the state of the
world be one of perfect justice). Or, to take up an example Kant uses in the
Prolegomena, ˜˜If the sun shines on a stone, the stone gets warm™™ (implicit
possible subsumption: any individual falling under the concept ˜˜stone™™
gets warm, under the added condition that the stone be lit by the sun).9
A third kind of condition of a rule is that expressed in a disjunctive
judgment. The proper function of this form of judgment is to recapitu-
late, as it were, the possible specifications of a concept. According to this
form, one divides a concept, say A, into mutually exclusive specifications
of this concept, say B, C, D, E: A is either B, or C, or D, or E. There are
two different ways in which one might consider it as a possible rule for
subsumption, and thus a rule by virtue of which one might attribute
some predicate to any individual thought under the condition of the
rule. One is to say that the subject of the disjunctive judgment, say A, is
the condition of the rule ˜˜A is either B, or C, or D, or E,™™ so that being
thought under A is a sufficient condition for being thought as falling

On the notion of the condition of a rule, see A322/B378; also Jasche Logic, x58, AAix, p. 120.
Reflexionen 3196“3202, AAxvi, pp. 707“10.
Cf. Prolegomena, AAiv, p. 312. And see above, ch. 6, pp. 151“3, for the difference between
Kant™s hypothetical judgment and the material conditional of modern propositional logic.

under either B, or C, or D, or E. But this is not terribly informative.
A more interesting way (corresponding to the classical inferences in
modus ponendo tollens or modus tollendo ponens) is to consider the assertion
of any one of the specifications (B, C, D, or E) of the divided concept A as
a sufficient condition for negating the others, and conversely consider-
ing the negation of all but one as a sufficient condition for asserting the
remaining one: A is B under the condition that it be neither C, nor D, nor
E; A is neither C, nor D, nor E, under the condition that it be B; and so
on.10 Note also the close connection between the forms of disjunctive
and infinite judgment: these forms jointly contribute to the constitution
of a unified logical space within which concepts delimit each other™s
sphere, and thus contribute to the determination of each other™s
About the fourth title, that of modality, Kant explains that it does not
add to the ˜˜content™™ of judgments. What Kant seems to mean is that the
modal determinations of judgment do not determine a specific difference
in the function of judging “ by contrast with quantity, according to which
one subordinates all or part of the extension of two concepts; with quality,
according to which the extension of the subject-concept is included in or
excluded from the extension of the predicate-concept; and with relation,
according to which one states that the predicate-concept can be asserted of
individual objects under the condition that the subject-concept itself be
asserted of them, or under an added condition (expressed in the ante-
cedent of a hypothetical judgment). Instead, the modality of a given
judgment expresses only ˜˜its relation to the unity of thought in general.™™
Correspondingly, Kant™s modality of judgments finds no particular lin-
guistic expression, contrary to quantity (˜˜all™™ or ˜˜some™™), quality (˜˜is™™
simpliciter or ˜˜is not™™) and relation (˜˜is,™™ ˜˜if . . . then,™™ ˜˜either . . . or™™).
Instead, in the examples Kant gives for ˜˜problematic,™™ ˜˜assertoric,™™ or
˜˜apodictic™™ judgments, modality is marked by no particular modifier
but consists, he says, merely in the ˜˜value of the copula™™ in the judgment,

Just as Kant™s hypothetical judgment is different from truth-functional material condi-
tional, so Kant™s disjunctive judgment is different from truth-functional disjunction. First
of all, as we just saw, Kant™s disjunctive judgment is a disjunction of predications: a concept
A is specified as either B, or C, or D, or E (and thus any object falling under A falls under
either B, or C, or D, or E). Second, the disjunction is exclusive, not inclusive: what is
asserted in a disjunctive judgment is that if one of the disjunct predicates belongs to the
subject, then the others do not, and conversely. Thus the meaning of the connective
˜˜either . . . or™™ grounds the forms of inference in modus ponendo tollens and tollendo ponens:
asserting one of the predicates is a sufficient reason for negating the others, negating all
but one is a sufficient reason for asserting the remaining one.

as determined by its place in a hypothetical or disjunctive judgment or in
syllogistic inferences (A74“6/B100“1).
These remarks are certainly too brief to give a full account, even less
an evaluation, of Kant™s table. My hope is that they at least shed some
light on the systematic character and, in the end, the simplicity of Kant™s
table: it displays forms (1) of concept subordination (first two moments
of quantity and quality), (2) under either an ˜˜inner™™ or an ˜˜outer™™
condition (first two moments of relation), which also takes into account
(3) the subsumption of singular objects under concepts (singular judg-
ments, third moment of quantity) and (4) the unity of concept subordin-
ation in a system of genera and species (infinite and disjunctive
judgments, third moments of quality and relation). Finally, (5) the
place of each judgment in other judgments or in inferences (its ˜˜relation
to thought in general™™) determines its modality. It is no whimsical choice
on Kant™s part to have presented these forms as a table. The tabular
presentation makes perspicuous ˜˜at one glance™™ the systematic whole of
elementary logical functions at work for the production of any of the
judgments by means of which individual objects given in sensibility are
subsumed under concepts.
Kant calls analysis the use we make of the understanding according to
the logical forms laid out in his table. By analysis here he does not mean
simply or even primarily analysis of concepts, i.e. the laying out of the
marks that constitute the content of a given concept. He means the
analysis of representations given in sensibility so as to generate concepts
from them, by means of the aforementioned operations: comparing
individual objects, focusing on common features or marks of these
objects and setting aside their differences.11 Now, such analysis presup-
poses that the objects in question are combined together in some way, in
order to be thus compared and subsumed under concepts. And not only
this: they need to be recognized as a plurality of individual things that
remain identical through time.12 For this much more than simply bring-
ing together objects for comparison is needed. What is needed is a
process of generating the representation of these objects themselves as
numerically identical individuals persisting through time. And for this,
our representation of space and time themselves need to be unified and

On this notion of analysis, cf. A76/B102. So considered, analysis consists in the operations
of ˜˜comparison, reflection, abstraction™™ described in Jasche Logic, x6, AAix, p. 94;
cf. Reflexion 2876, AAxvi , p. 555. And above, ch. 1, pp. 21“3.
On this point, see KCJ, ch. 3, pp. 44“52.

ordered. All of these operations of bringing together and ordering
(which I list here in a regressive order, from the derivative to the
primary): (1) bringing together individual things for comparison,
(2) generating the representation of these individual things as numerically
identical and persisting through time, (3) bringing together the
manifold of space and time themselves “ all of these operations Kant
calls synthesis. For any analysis leading to concepts to take place,
synthesis must already have taken place. And given that analysis
proceeds according to the logical functions of judgment, synthesis too
must take place in such a way that what is synthesized becomes
susceptible to being brought under concepts according to the logical
functions of judgment.
This relation between analysis and synthesis, finally, provides the key
to Kant™s definition of the categories. They are, he says, ˜˜universal
representations of pure synthesis™™ or, according to the more extensive
definition of the B edition, they are ˜˜concepts of an object, by means of
which the intuition of this object is taken to be determined with respect
to one of the logical functions of judgment™™ (A78/B104; B128). This
means two things: (1) categories are concepts that guide the syntheses
of spatiotemporal manifolds toward analysis according to the logical
functions of judgment, and (2) categories are, like any other concept,
˜˜universal and reflected representations.™™ What they ˜˜universally
reflect,™™ however, are not empirical features of objects, but just those
syntheses by means of which manifolds given in (pure or empirical)
intuition become susceptible to being reflected under concepts com-
bined according to logical functions of judgment.
I said a moment ago that Kant™s table of logical functions was meant to
make available ˜˜at one glance™™ the system of elementary logical functions
necessary to generate the least empirical judgment by means of which
empirical objects are subsumed under concepts. I also suggested that the
specific role of infinite and disjunctive judgments is to relate all concept
subordination to the unified logical space within which concepts reci-
procally delimit each other™s sphere and meaning. If I am right, this
means that correspondingly, the specific synthesis corresponding to
these logical forms will be a synthesis by means of which the totality of
objects belonging to a common logical sphere is reflected under con-
cepts. The logical form of disjunctive judgment, and the corresponding
category of community, thus provide the general structure, or ordering
function, for the standpoint on the whole in the context of which any
cognitive function is performed.

I now want to show what this means by considering more closely
Kant™s exposition of the relation between logical form of disjunctive
judgment and category of community.

Disjunctive judgment and the category of community
(Gemeinschaft, Wechselwirkung)
There are two ways in which Kant might choose to characterize the form
of disjunctive judgment. He could characterize it by focusing on the
relation of concepts considered in their content, and say that a concept
A is determined, that is, specified, either by the specific mark B or by the
specific mark C “ for instance, an animal is either a human being or a
beast, a rational or a non-rational animal. Or he might characterize the
form of disjunctive judgment by focusing on the extension of concepts
and say that in a disjunctive judgment, one states that a concept A,
considered in its extension or sphere, is divided into two mutually
exclusive and exactly complementary spheres, the sphere thought
under concept AB and the sphere thought under concept AC.
Kant chooses the second description of the form of disjunctive judg-
ment, focusing on the extension of concepts. This is particularly explicit
in the Jasche Logic as well as in the Reflexionen on logic from the critical
period. There Kant pictures the disjunctive judgment ˜˜A is either B, C,
D, or E™™ by the division of a rectangular area A (representing the exten-
sion of the divided concept A) into four regions B, C, D, and E (which
respectively represent the extensions of the species of A). In a disjunctive
judgment, says Kant, any ˜˜X thought under the concept A™™ belongs to
one or the other of the divisions B, C, D, or E. He prefaces this explana-
tion by a comparison between categorical and disjunctive judgment:
In categorical judgments, X, which is contained under B, is also con-
tained under A:
In disjunctive ones X, which is contained under A, is contained either
under B or C, etc.
Thus the division in disjunctive judgments indicates the coordination
not of the parts of the whole concept, but rather of all the parts of its

In the Critique of Pure Reason, Kant draws a surprising parallel between
this logical form and the category of community: just as in a disjunctive

Jasche Logic, x29, AAix, p. 108. Cf. also Reflexion 3096, AAxvi, pp. 657“8.

judgment, the sphere of a concept (its extension) is divided into its
subordinate spheres so that these subordinate spheres are in a relation
of mutual determination while at the same time excluding each other, so
in a material whole, things mutually determine each other, or even in
one material thing or body considered as a whole, the parts are in a

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