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standpoint, this is not a suf¬cient reason for dismissing his theory of
categories. Not only does he make important advances in his views
of negation and assertoric force, but his logical forms of judgment
have their counterparts in today™s logics. There is no obvious falsity
in the ideas that judging requires logical or syntactic concepts, and
that these concepts have implications for our ways of conceiving
the objects of judgment. The important questions concern which
concepts are fundamental, and whether they could be derived in
any way from experience. Kant addresses the second question in the
Transcendental Deduction of the categories and the arguments for
11 Broad, Kant, 78.
The Metaphysical Deduction 93
the pure principles of the understanding. Now we can examine the
second half of Kant™s argument in the Metaphysical Deduction.

d. Step two of the Metaphysical Deduction: the real use
of pure concepts
In step one Kant argued that a complete list of pure concepts of the
understanding is provided by the logical forms of judgment. Now
he must complete his argument for categories by showing that these
pure concepts have not only a logical but also a real use. As Mel-
nick explains, Kant believes “the syntactical structure of judgments
in some sense introduces a nonsyntactical element into our knowl-
edge.”12 Showing that these syntactic concepts also have a semantic
use means showing that they function as concepts of the objects of
our judgments. As categories, Kant says at A79/B105, these concepts
would provide a “transcendental content” for knowing objects.
The key to the second stage is Kant™s claim that “The same func-
tion that gives unity to the different representations in a judgment
also gives unity to the mere synthesis of different representations in
an intuition; which, expressed generally, is called the pure concept of
the understanding” (A79/B105). Kant defends this view through his
theory of synthesis. At A76“7/B102, he reminds us that whereas gen-
eral logic puts no restrictions on the content of judgment, transcen-
dental logic is given a content in the pure forms of space and time. By
“content” Kant means reference to an existing domain. Since humans
have access to existing things only through intuition, the manifold
of spatiotemporal data restricts the domain for our judgments about
reality. Returning to his earlier view that “Thoughts without content
are empty, intuitions without concepts are blind” (A51/B75), Kant
focuses on the interdependence of concept and intuition. If pure
concepts are not to be empty “ if they are to refer to existing objects “
they must somehow relate to the data given in intuition. Correla-
tively, since space and time are the forms in which we receive all data
about existing things, they “must also always affect the concept of
these objects” (A77/B102). In short, any ¬rst-order concepts we use
to judge existing things must be interpreted spatially and temporally.

12 Melnick, Kant™s Analogies of Experience, 39.
The Metaphysical Deduction
94
Kant next argues that this spatiotemporal interpretation of pure
concepts takes place through the process of transcendental synthesis,
which takes center stage in the B edition Transcendental Deduction.
Here Kant brie¬‚y introduces the notion to support the conclusion
that pure concepts have a real use. Interpreting concepts spatiotem-
porally means applying the concepts to the data given in intuition, or
alternatively, judging that data in terms of those concepts. As Kant
explains at A77/B102“3, synthesis is the act of unifying different rep-
resentations into one complex cognition. This is true whether the
representations are data given in intuition, concepts, or even judg-
ments. To think of a manifold of intuited data as representing an
object, for example, requires apprehending the data and connecting
it in one complex representation. Although there is only one process,
it has both pure and empirical aspects. The pure aspect is the synthe-
sis of the pure manifold given in the forms of intuition. Connecting
the a posteriori data given in sensation is the empirical aspect. The
act of connecting representations is performed by the imagination,
which Kant calls “a blind though indispensable function of the soul,
without which we would have no cognition at all, but of which we are
seldom even conscious” (A78/B103). To call the imagination “blind”
is to claim that the mere act of connecting is not inherently governed
by conscious rules. As we shall see later, there are several types of
synthesis. For example, a connection according to psychological laws
of association need not take place according to rules of which one is
conscious. Kant believes this kind of synthesis is characteristic of ani-
mal perception, since animals lack intellectual capacities.13 Humans,
however, have the capacity to conceptualize, or to think according to
rules we can consciously recognize. These rules governing our objec-
tive representations are the concepts provided by the understanding.
Although we are typically not aware of the process of synthesis, we
can become conscious of it by re¬‚ecting on our representations.
At A77/B103 Kant explains that all analytic or logical processes
presuppose the synthesis of representations. He says, “Prior to all
analysis of our representations these must ¬rst be given, and no con-
cepts can arise analytically as far as the content is concerned.” This claim
is directed against the empiricist view that all thinking begins with

13 An excellent discussion of this topic is Steven Naragon™s “Kant on Descartes and the Brutes.”
The Metaphysical Deduction 95
perceptions of particular objects, from which we abstract concepts,
which we then combine in judgments. Kant™s point is this: in order
to produce empirical concepts by comparing and analyzing our intu-
itions of distinct objects, we ¬rst must discriminate those individual
objects. In the Aesthetic, Kant showed not only that existing partic-
ulars are intuited in space and time, but that their spatial-temporal
locations are necessary conditions for identifying and individuating
them. So a prerequisite for individuating objects of experience is to
identify their spatiotemporal locations. Carving out locations and
regions from the undifferentiated manifold given in pure intuition
just is the pure aspect of synthesis.
At A78/B104 Kant uses the example of counting to illustrate this
act. In counting (or measuring) one arrives at a number, which rep-
resents some plurality of units. The sum arrived at is thought as a
totality made up of the units. The implicit connection here is between
delineating spatiotemporal regions and the mathematical procedures
involved in measurement. For example, to recognize a table as a dis-
tinct object occupying a particular place at a certain time, one must
conceive the place and time as measurable regions of global space
and time. In their real use pure concepts enable us to think of the
pure manifold of space and time in terms of measurable locations
and regions that can be occupied by objects of experience. Since
this is a conceptual act, and the only use of concepts is to judge,
it is thereby an act of judging. Hence pure concepts function both
syntactically “ to combine ¬rst-order concepts (or other represen-
tations) in judgment “ and semantically “ to synthesize the pure
manifold of spatial-temporal data given in the forms of intuition. In
the latter role, pure concepts function as categorial concepts insofar as
they provide ways of conceiving necessary spatiotemporal features of
objects.
At A80/B106 Kant presents the table of categories, the semantic ver-
sions of the logical forms of judgment. He says very little about them
here, reserving details for the arguments in the Analytic of Principles.
At B110, however, he divides the four headings of categories into two
groups: he calls quantity and quality mathematical categories, and
relation and modality dynamical categories. Mathematical categories
are the pure concepts required merely to think an object of intuition.
As we shall see, these categories are used to identify individuals and
The Metaphysical Deduction
96
the properties we predicate of them. Dynamical categories enable
us to think of relations among objects. The relational categories are
concepts of temporal relations and properties of objects; the modal
categories express the ways we relate objects to the understanding.
This will become clearer as we look more closely at the categories
in later chapters. Here I plan merely to focus on their relation to
the forms of judgment, to give a sense of the plausibility of Kant™s
theory.14
The three categories under quantity are unity, plurality, and total-
ity. According to the deduction, to make judgments of universal,
particular, or singular forms, we must conceive of the objects we
are judging in quanti¬able terms, as individual members of sets and
subsets. Many commentators have noticed that Kant correlates the
concept of unity (an individual) with the universal judgment, and
totality with the singular judgment, although it seems more logical to
reverse the pairings. Despite this oddity, Kant is certainly correct that
in order to judge by quanti¬ed forms, we must identify a domain of
objects that can be individuated and divided into classes. This makes
it possible to judge about one, all, or some members of a class. As
indicated above, the conceptual scheme we use in experience typi-
cally identi¬es individuals in terms of spatial-temporal locations and
properties. We can easily recognize these features in our commonsense
ideas that every existing (physical) object must occupy some place at
any given time, and that numerically distinct objects cannot occupy
the same place at the same time. Similarly, we assume that when an
object changes its spatial location, it must traverse a continuous path
from one place to the other, and so on. Put semantically, the primary
function of the quantitative categories is to allow us to identify the
individuals to which singular terms refer.
The categorial concepts listed under quality are presupposed in
ascribing predicates to individuals in af¬rmative and negative judg-
ments. Our basis for recognizing predicates is the empirical data given
in sensation, which we represent as sensory qualities located in space
and time. In order to formulate empirical predicates we must be able
to differentiate qualities, which means we must conceive of the sensory

14 My account follows the discussions in Melnick™s Kant™s Analogies of Experience, 37“42, Allison™s
Kant™s Transcendental Idealism, chapter 6, and Falkenstein™s Kant™s Intuitionism, 241“4.
The Metaphysical Deduction 97
data in terms of reality and negation.15 The presence of a quality cor-
responds to the reality of some property, which we can predicate of
objects. Conversely, the absence of a quality corresponds to the nega-
tion of a property, which can be expressed in a negative judgment.
Kant says the third moment, limitation, “is reality combined with
negation” (B111). This is spelled out later, in the Anticipations of Per-
ception in the Analytic of Principles, where Kant analyzes the nature
of sensation. There he argues that we can know a priori that every
sensation must have some intensive magnitude or degree. Examples
of intensive qualities are the brightness of colors, sensations of hot
and cold, and the loudness of sounds. Kant believes that in order
to recognize a particular degree of intensity, we must think of the
given degree as representing a limit on the reality being sensed. Like
the quantitative categories, the qualitative categories are interdepen-
dent, with all three required to recognize the presence or absence of
a sensory quality having some degree of intensity.
The relational categories corresponding to simple and com-
plex judgment forms are the controversial metaphysical concepts
of substance“accident, cause“effect, and mutual causal interaction.
Kant himself admits at B111“12 that the correlations in the ¬rst two
cases are more obvious than in the third. The concepts of substance
and accident are real correlates of the logical notions of subject and
predicate. In a typical categorical judgment, the predicate signi¬es a
property, and the logical subject signi¬es a bearer of properties. When
these notions are interpreted temporally, they become the notions of
substance and accident. Substances are things persisting through time
(Kant will argue that they must be permanent), and accidents are their
transitory states. Now Kant is not claiming that all categorical judg-
ments in fact ascribe accidents to permanent substances. For example,
in the judgment “Red is a color,” the logical subject ˜red™ does not
designate a substance, and being a color would not be a temporary
state. What Kant is claiming, however, is that to judge existing states
of affairs by the categorical form requires us to distinguish between
transitory states and the permanent bearers of those states.

15 Kant™s claim is not that the real property is identical to the quality, but rather that the quality
provides evidence of the property. We do not literally sense gravitational or magnetic forces,
for example, but take them to be causes of the weight and motions of bodies. See A226/B273.
The Metaphysical Deduction
98
Similarly, the concepts of cause and effect are temporalized versions
of the logical notions of ground and consequent expressed in hypo-
thetical judgments. As we saw earlier, Kant thinks of the conditional
as expressing a necessary connection between the antecedent and con-
sequent. When this notion is applied to events in time, it becomes
the idea of a state that follows necessarily from another state accord-
ing to a rule. In the case of real relations among states, the rules are
causal laws. As with categorical judgments, Kant is not claiming that
all hypothetical judgments are used to make causal claims. Rather,
his point is that whenever we apply the notion of ground and conse-
quent to existing states of affairs, we must conceive of the two states
as related by causal laws.16
Finally, Kant correlates the category of causal interaction with dis-
junctive judgments. He thinks the concept of a system of substances
that mutually determine each others™ states is the real version of the
logical idea of a systematic totality of alternatives. As I remarked above,
he himself admits this is obscure. Again, we examine this view more
closely in the Analogies of Experience. Kant™s proofs of the principles
corresponding to the categories in that section demonstrate how these
categories function to order states of affairs in time.
The categories under modality are the three pairs of concepts
possibility“impossibility, existence“nonexistence, and necessity“
contingency. Since Kant says almost nothing about them here, I
shall brie¬‚y sketch his views. Just as the modal forms of judgment
are not part of the content of judgment, the modal categories do
not add content to our concepts of objects, but only concern the
ways the understanding thinks the states of affairs about which we
judge. Since the modal categories are semantic rather than syntactic
concepts, they are concepts of real (rather than logical) possibility,
actuality, and necessity. Here is what Kant has in mind. In order
to formulate a proposition that is assertible, that is, to judge prob-
lematically, one has to think the objects being judged in terms of
whether they are really possible. Really possible objects are those
that agree with the formal conditions of experience, namely the pure
16 Commentators who discuss the correlation between conditionals and causal claims include
Broad, Kant, 100, Paton, Kant™s Metaphysic of Experience, 1:299, Bird, Kant™s Theory of Knowl-
edge, 105“7, Melnick, Kant™s Analogies of Experience, 55“6, and Allison, Kant™s Transcendental
Idealism, 120“2.
The Metaphysical Deduction 99
forms of intuition and the categories of quantity, quality, and relation.
For example, whereas a three-dimensional spatial object would be a
really possible object of experience for us, a four-dimensional spatial
object would not. Corresponding to the assertoric mode of judging
are the concepts of real existence (or actuality) and nonexistence.
Thus, asserting that some state of affairs does or does not obtain pre-
supposes that we can recognize whether the objects of judgment do
or do not actually exist. We do this by means of empirical intuition.
Finally, our ability to draw conclusions according to rules of infer-
ence implies that we can discriminate between states of affairs that do
and do not follow necessarily from other states according to causal
laws.
This discussion gives us some idea of how Kant conceives the
relation between the categories and the forms of judgment. We have
seen that the concepts of the forms of judgment are logical or syntactic
concepts, whereas the categories are real or ¬rst-order concepts of
objects. One question commentators have raised concerns how many
sets of concepts there are: are these two distinct sets, or is there one set
of concepts with two different uses? As Allison points out, Kant says
explicitly at B143: “the categories are nothing other than these very
functions for judging, insofar as the manifold of a given intuition
is determined with regard to them.”17 This implies that there is one
set of concepts with two uses, logical and real. Strictly speaking, the
categories are pure concepts of the understanding in their real use. The
meaning of each category thus has two components, one logical and
one sensible. As we saw above, for example, the concepts of substance
and accident interpret the logical notions of subject and predicate
temporally as permanent bearers of transitory states. Similarly, the
concepts of cause and effect interpret the logical notions of ground
and consequent as a necessary succession of states in time. Kant calls
the sensible component the schema of the category. In the Analytic
of Principles, in the chapter on the Schematism, Kant explains why a
schema is necessary and what it consists in. From a semantic point of
view, the schema provides a criterion for applying the pure concept
to the data of intuition.

17 Allison, Kant™s Transcendental Idealism, 126“7. Other passages where Kant makes the same
point are the Prolegomena, section 39, and the MFNS, Theoretical Philosophy after 1781, 189.
The Metaphysical Deduction
100
Before we leave this exposition of the Metaphysical Deduction,
there is a last point to make about Kant™s theory of the forms of
judgment and the categories. Kant believes that it is simply a brute
fact about humans that we judge by these logical forms. At B145“6 he
says this about the unity of apperception or self-consciousness, which
is the starting point for the B edition Transcendental Deduction of
the categories:
But for the peculiarity of our understanding, that it is able to bring about
the unity of apperception a priori only by means of the categories and only
through precisely this kind and number of them, a further ground may be
offered just as little as one can be offered for why we have precisely these
and no other functions for judgment or for why space and time are the sole
forms of our possible intuition.

Just as we cannot explain why we intuit objects in three-dimensional
Euclidean space and one-dimensional time, so we cannot explain
why our judging has exactly these logical characteristics. There is no
absolute necessity attaching to either the pure forms of intuition or
the forms of judgment: there could be beings whose forms of intu-
ition and judgment are different from ours. Clearly a being who did
not intuit objects temporally could not think according to the cate-
gories of substance and cause as explained above. Such an experience
would be so removed from ours that we could not fathom it. Like
the judgments of mathematics, the synthetic a priori cognitions of
the understanding are necessary only in a relative sense, for perceivers
with our forms of sensibility and understanding. Why we have these
forms of intuition and thought is beyond explanation.


3 . conc epts a nd sing ul a r j udg m e nts
The last point concerns how to reconcile Kant™s notion of singular
judgments with the view that concepts are general representations.
One question is whether Kant™s theory of representation allows for
the notion of a singular term. As we saw above, all simple judgments
are composed of a subject and a predicate, united by the copula. In
singular judgments, the subject represents an individual rather than
a class. But this apparently contradicts Kant™s view that all concepts
are general. If there are no singular concepts, then we must ask how
The Metaphysical Deduction 101
he would analyze singular terms such as proper names and de¬nite
descriptions. Jaakko Hintikka argues that “Kant™s notion of intuition
is not very far from what we would call a singular term.”18 In response,
Manley Thompson claims that Kant™s doctrine precludes taking intu-
itions “as the subjects and as being represented by either proper names
or demonstrative pronouns.”19 Despite lacking a theory of language,
Kant makes some remarks about linguistic meaning in his lectures
on logic. These suggest an account of singular terms that tends to
support Thompson™s view.
First, despite some sloppy terminology, Kant consistently main-
tains that concepts are general representations. These remarks from
the J¨ sche Logic are characteristic:
a
A concept is opposed to intuition, for it is a universal representation . . . It is
a mere tautology to speak of universal or common concepts “ a mistake that
is grounded in an incorrect division of concepts into universal, particular,
and singular. Concepts themselves cannot be so divided, but only their use.20
Hintikka is right that Kant frequently misrepresents this position in
his writings. For example, in section 21 of the J¨ sche Logic he says
a
“in a singular judgment . . . a concept that has no sphere at all is
enclosed, merely as part then, under the sphere of another.”21 Despite
this misstatement, he more consistently maintains that although con-
cepts are general, they can have singular linguistic uses. In the Vienna
Logic he illustrates universal, particular, and singular uses of the con-
cept ˜house™: “If I say of all houses, now, that they must have a roof,
then this is the usus universalis . . . But a particular use is concerned
only with many. E.g., some houses must have a gate. Or I use the
concept only for an individual thing. E.g., this house is plastered in
this way or that.”22 And in the Dohna-Wundlacken Logic he says this
about language: “As soon as I make use of words, the representation
[Socrates] is an individual concept.”23 These passages show Kant dis-
tinguishing between representations and their linguistic expressions.
Following Thompson, we can make sense of his view.

18 Hintikka, “On Kant™s Notion of Intuition,” 43.
19 Thompson, “Singular Terms and Intuitions in Kant™s Epistemology,” 329.
20 J¨ sche Logic, Lectures on Logic, 589. See also the Blomberg Logic, 201, and the Vienna Logic,
a
349.
21 22 Lectures on Logic, 352. 23 Lectures on Logic, 487.
Lectures on Logic, 598.
The Metaphysical Deduction
102
Kant recognizes that both the name “Socrates” and the demonstra-
tive term “this house” are used to refer to individuals, even though
the latter expression contains the general term “house.” Now refer-
ence to individuals presupposes the ability to individuate objects in
experience. And according to Kant™s theory of synthesis, individuat-
ing objects requires synthesis of intuition by concepts. As Thompson
points out, language is by its nature discursive and rule-governed.24
It is a mistake to try to correlate linguistic expressions or their uses
with either concepts or intuitions. So rather than speaking of subject-
concepts in the case of singular judgments, Kant should have spoken
of subject-terms or (as we would today) referring expressions. Once we
distinguish between concepts and their linguistic expressions, there is
no dif¬culty reconciling the generality of concepts with the fact that
subject-terms in judgments may be singular linguistic expressions.

4. sum ma ry
The Metaphysical Deduction is the ¬rst stage in Kant™s argument for
the categories, in which he identi¬es the pure concepts of the under-
standing. The argument has two parts. First Kant establishes that the
understanding has one function, which is to judge. He then identi¬es
the pure concepts based on the forms of judgment, all the possible
ways in which one can judge. The concepts of these judgment forms
represent logical or syntactic features of judgment, such as subject
and predicate. Thus a list of the forms of judgment yields a complete
system of pure concepts in their logical use. In the second part Kant
argues that these pure logical concepts also have a real use, as ¬rst-
order or semantic concepts of the objects about which one judges.
This follows from his analysis of judgment as synthesis, and the claim
that the same synthetic operations that produce judgments also pro-
duce uni¬ed representations of space and time from the manifold of
pure intuition. Thus Kant concludes that the pure concepts express-
ing logical features of judgment can represent categorial features of
the objects being judged. This is the ¬rst step in arguing for synthetic
a priori knowledge of the understanding.

24 Thompson, “Singular Terms and Intuitions in Kant™s Epistemology,” 333“5.
ch ap t e r 5

The Transcendental Deduction of the categories

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