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the judgmental function of the intellect. Kant™s critical theory offers
a radically new analysis of the understanding, to remedy the defects
of both traditions.

b. Skepticism and objective knowledge
The second signi¬cant issue is skepticism or the justi¬cation of knowl-
edge. Greek philosophy included two schools of skeptics, the Aca-
demics and the Pyrrhonians. The Academics argued that although it
was impossible to justify any claim to know conclusively, some beliefs
were more likely to be true than others. By contrast, the Pyrrhonians
argued that even claims to probable knowledge could not be jus-
ti¬ed, since attempts to establish a criterion of justi¬cation led to
either circular reasoning or an in¬nite regress. Historically, skepti-
cism has taken many forms. Greek skeptics such as Sextus Empiricus
raised doubts about both sense perception and reason. In the modern
period, the rationalists tended to mistrust the senses, but claimed a
privileged status for knowledge derived from reason. Empiricists such
as Locke and Hume recognized that sense experience could not justify
claims to necessary knowledge of reality. In Hume™s works these argu-
ments turned into the most thorough and devastating attack on the
certainty of scienti¬c, metaphysical, and commonsense beliefs con-
cerning mind-independent reality. Moreover, for Hume, knowledge
of the self was just as unattainable as knowledge of the external world.
As one might expect, commentators disagree in interpreting Kant™s
response to skepticism. Because the Analytic contains several argu-
ments for pure concepts and principles of the understanding, it is not
always obvious what assumptions about knowledge Kant™s arguments
depend on.2 Certain passages, however, are clearly aimed against some

2 Guyer makes this point forcefully in Kant and the Claims of Knowledge, chapters 3“5.
The Metaphysical Deduction
76
forms of skepticism mentioned above. In the Analogies of Experience
in the Analytic of Principles, Kant evidently intends to defend the
metaphysical principles of substance and causality against Hume™s
attack. The Refutation of Idealism, added to the B edition Analytic
of Principles, is explicitly directed against Descartes™s view that self-
knowledge is more certain than knowledge of the external world. In
chapter 7 we shall assess Kant™s response to the challenges posed by
skepticism.

c. The notion of categorial concepts
There is no question that Kant intends his theory of pure concepts to
replace Aristotle™s theory of the categories. In his Categories, Aristo-
tle identi¬ed ten classes as the fundamental ontological types under
which all things fall: substance, quantity, quality, relation, place, time,
posture, state, action, and passion. Although these are metaphysi-
cal classi¬cations, the theory is based on semantics, since Aristotle
derived these classes from types of predicates, and the distinction
between essential and accidental predication. Every descriptive term
denotes things falling under at least one of these ten classes. Nouns
like “animal” and “plant” signify substances; adjectives such as “red”
and “hot” signify qualities; others like “is next to” signify relations,
and so on. Aristotle thought that things falling under all categories
could be the subject of essential predications, but only substances
could be the subject of accidental predications, since substances can
retain their identity while undergoing change in time. In general, the
categories express metaphysical principles that set limits on mean-
ingful discourse. With the development of modern logic, Frege and
Russell radically revised Aristotle™s conceptual scheme, and twentieth-
century philosophers debated whether there is any necessary con-
ceptual scheme. Kant, however, remains squarely in the Aristotelian
tradition in claiming that an exhaustive list of necessary ontological
concepts can be derived from logical concepts. Let us now examine
the ¬rst step in his argument for this position.

2 . t he meta ph ys ic a l d ed uc ti on: d iscoveri n g t h e
p ure concepts in th e f orm s of j udg m e nt
Kant™s discussion falls into four parts. From A50 to A66/B74 to B79 he
explains transcendental logic as a science of the pure understanding.
The Metaphysical Deduction 77
The second part contains the ¬rst step of the deduction at A66“
9/B91“94, where Kant analyzes the logical use of the understanding.
Following this passage is the third part, from A70 to A76/B95 to B101,
which discusses the logical forms of judgment. The fourth part, where
Kant argues that the concepts of these forms of judgment have a real
use as categories, begins at A76/B102 and continues to the end of the
chapter.

a. Introduction to transcendental logic (A50“66/B74“91)
Kant describes transcendental logic as the science of the rules of
the pure understanding required for cognition. This conception pre-
supposes two distinctions: ¬rst, between the understanding and the
sensibility; and second, between the real as opposed to logical uses of
the understanding. Kant ¬rst reminds us that understanding and sen-
sibility play distinct roles in knowledge. Sensibility is a merely passive
capacity for receiving impressions through the senses. The under-
standing, by contrast, is a spontaneous power to think of objects
through concepts. Thus each capacity has a distinct function and
produces a characteristic type of representation. Sensations given in
intuition and the concepts that depend on them are empirical rep-
resentations known a posteriori. The pure forms of intuition and the
pure concepts arising solely from the activity of the understanding (if
there are any) are a priori representations. Just as pure intuition rep-
resents only formal features of sensible objects, pure concepts would
represent only the most general features thought in any idea of an
object.
Kant next points out that these two capacities provide comple-
mentary and indispensable aspects of knowledge. At A51“2/B75“6
he sharply contrasts sensible affection with the power of thought.
Human intuition is sensible and gives us access to existing states of
affairs. But sensibility yields an undifferentiated manifold of data,
which is only the material for representing objects. To take this data
to represent objects requires classifying and organizing it in terms of
some conceptual scheme. This is the role of the understanding. The
senses do not think; the understanding does not sense: “Without
sensibility no object would be given to us, and without understand-
ing none would be thought. Thoughts without content are empty,
intuitions without concepts are blind” (A51/B75).
The Metaphysical Deduction
78
This memorable passage expressing the “blindness thesis” neatly
captures the essential contributions of sensing and thinking. When
Kant says thoughts without content are empty, he means that think-
ing alone cannot give us access to existence. A mere concept neither
informs us about what exists, nor guarantees its applicability to exist-
ing objects. Concepts are “empty” if they have no reference to the
world, since we cannot know whether they are true or false of any-
thing. On the other hand, until the data of intuition is thought, it
is “blind.” The sensory manifold as received is an undifferentiated
array, not discriminated into particular objects or states of affairs.
Now Kant argued in the Aesthetic that this manifold contains a pure
part, the forms of space and time. It is important to understand, how-
ever, that the pure forms of intuition supply only one aspect of the
undifferentiated manifold. They make object identi¬cation possible
by providing the material for identifying spatial and temporal loca-
tions of objects. But no intuitive data, pure or empirical, is given as
organized into recognizable patterns. Just as sense impressions must
be bundled to relate to distinct objects, the spatiotemporal manifold
must be conceived in certain ways to represent spatial and temporal
locations. On Kant™s view, the essential function of the understanding
is to organize the sensible data, both pure and empirical, to make it
intelligible, by thinking it in terms of some conceptual scheme.
Kant next distinguishes between general and transcendental logic.
General logic is the science of the fundamental rules of all thought;
Kant says it contains “the absolutely necessary rules of thinking, with-
out which no use of the understanding takes place” (A52/B76). By
general logic he means both the syntactic rules for forming judg-
ments and the rules specifying valid inferences. This logic is “general”
because it applies necessarily to any object, regardless of its nature.
Any logic whose rules are restricted to a certain kind of object is a
“special” logic.
At A53“5/B77“9 Kant remarks that the Critique concerns pure
rather than applied logic. Pure logic is a formal science rather than
a study of the way people in fact think. The latter is a branch of
empirical psychology, which examines thinking processes “under the
contingent conditions of the subject . . . which can all be given only
empirically” (A54/B78“9). Thus it “can never yield a true and proven
science” (A55/B79), which must begin with necessary principles. In
The Metaphysical Deduction 79
his writings on logic Kant also characterizes pure logic as a prescriptive
or normative science as opposed to the descriptive science of empirical
psychology.3
Transcendental logic is a special logic falling under pure general
logic, for it is the science of necessary rules of thought about objects
given in space and time. Whereas general logic “abstracts from all
content of cognition” (A55/B79), transcendental logic has a content,
namely the pure forms of intuition identi¬ed in the Transcendental
Aesthetic. It abstracts only from the empirical features of spatiotem-
poral objects. This is a logic of the real use of the understanding, and
Kant will argue that its principles are synthetic a priori rather than
analytic, as are the principles of general logic. Despite the fact that
transcendental logic is restricted to objects given in intuition, its con-
cepts and principles nevertheless originate in pure understanding. A
science of these pure concepts would demonstrate their origin (in the
Metaphysical Deduction), as well as their scope and objective validity
(in the Transcendental Deduction). In other words, this science will
identify and justify the privileged conceptual scheme by which the
understanding organizes the data of intuition into representations of
objects.
Before beginning the Metaphysical Deduction, Kant makes some
general remarks about the nature of truth, and explains his division
of Transcendental Logic into an Analytic and a Dialectic. At A58/B82
he offers a nominal de¬nition of truth as “the agreement of cognition
with its object.” This de¬nition is only nominal because it does not
provide a criterion for recognizing cases. In fact, Kant argues, there
can be no general criterion suf¬cient for all true judgments. A general
criterion would apply without regard to differences in the objects,
but the distinction between true and false judgments implies that
objects differ. Thus Transcendental Logic can supply only a necessary
condition for truth, “the conditio sine qua non, and thus the negative
condition of all truth” (A59“60/B84). The Transcendental Analytic
will argue that the pure concepts and principles of the understand-
ing are necessarily true of objects of experience. Since there is no
suf¬cient criterion of truth, however, it is possible to misuse these
concepts and principles. The Transcendental Dialectic examines this

3 See section II of the J¨ sche Logic, Lectures on Logic, 531.
a
The Metaphysical Deduction
80
misuse of the understanding, showing that the traditional metaphys-
ical debates result from applying the categories beyond the limits of
experience.

b. Step one of the Metaphysical Deduction: the logical function
of the understanding
At A64/B89 Kant states that a successful demonstration of categories
must show that the concepts are pure rather than empirical, and that
they originate in the understanding rather than the sensibility. This
latter point separates categories from mathematical concepts which,
although a priori, are derived from the forms of intuition. In addition,
the list must include only fundamental concepts, and it must be sys-
tematic to ensure completeness. Kant believes it is possible to obtain
a complete list because pure concepts express functions of the under-
standing, which is “a unity that subsists on its own” (A65/B89“90).
Thus the key to a complete list is to assume that the understanding
has one function.4 This method is an improvement over Aristotle™s,
who merely conducted an empirical (Kant says “mechanical”) survey
of concepts, which can never guarantee the systematic completeness
of the list. In the ¬rst stage of the Metaphysical Deduction, then,
Kant analyzes this uni¬ed function of the understanding to identify
a complete list of pure concepts.
At A68/B93 Kant remarks that up to now he has characterized
the understanding by contrast with the sensibility, and he reiterates
that cognition contains only two elemental representations, intuition
and concept. Since the understanding does not yield intuitions, it
must produce concepts, which Kant describes as “discursive” rather
than intuitive. This is explained in a key passage: “All intuitions,
as sensible, rest on affections, concepts therefore on functions. By a
function I understand the unity of the action of ordering different
representations under a common one” (A68/B93). There are several
important points here. First, intuitions arise from the way the sub-
ject is passively affected by objects. Intuiting is not an activity, but
a state the subject undergoes. (This is why Kant labels sensibility

4 Bernd D¨ r¬‚inger argues eloquently that Kant™s table of categories is based on a teleological
o
analysis, in “The Underlying Teleology of the First Critique.”
The Metaphysical Deduction 81
a capacity rather than a faculty.) By contrast, the understanding is
a spontaneous faculty that acts to perform a function. In describing
these acts as “discursive,” Kant recalls the Latin discursus, which means
“running through.” The understanding functions, he says, to unify
different representations by bringing them under a general represen-
tation, namely a concept. Thus it operates by “running through”
diverse representations and classifying them in terms of a concept.
Consider the unifying role of the concept ˜green.™ When one classi¬es
diverse objects (an apple, a leaf ) as green, one unites them into the
class of things falling under the concept. Now the German for “con-
cept” is Begriff, which comes from the verb begreifen, meaning “to
grasp.” A concept, then, represents the unity grasped at once in the
diverse things to which it applies. The function of concepts is to unify
diverse representations by representing a characteristic common to
them.
In the next step Kant identi¬es conceiving with judging: “Now
the understanding can make no other use of these concepts than that
of judging by means of them” (A68/B93). Here he departs from the
classical view that conceiving is logically prior to judging. His point
is that concepts have no use other than to think of something, an x,
as a thing of a certain kind F. But this act of conceiving an x as an F is
equivalent to thinking the proposition that x is F, which is an act of
judging. (We shall see below in the discussion of modality that not
all judgments make assertions; in a “problematic” judgment one may
only consider the proposition that x is F.) The key to deriving a list
of pure concepts, then, is the analysis of judgment.
Judgment, according to Kant, is “the mediate cognition of an
object, hence the representation of a representation of it” (A68/B93).
Considered most abstractly, a judgment is a way of representing an
object or objective state of affairs. It yields knowledge indirectly,
through its component concepts, which are also mediate represen-
tations of objects:
In every judgment there is a concept that holds of many, and that among
this many also comprehends a given representation, which is then related
immediately to the object. So in the judgment, e.g., “All bodies are divisi-
ble,” the concept of the divisible is related to various other concepts; among
these, however, it is here particularly related to the concept of body, and this
in turn is related to certain appearances that come before us. (A68“9/B93)
The Metaphysical Deduction
82
Here Kant points out that to predicate something of one or more
objects requires a predicate-concept, which is by its nature general,
and can apply to many things. But the objects of the predication
must themselves be picked out or represented by the subject-term. In
the sentence “All bodies are divisible,” the subject-term is “bodies”,
also a general representation. Concepts can be applied to existing
things only when connected to the data given in intuition. Thus
both the subject-concept ˜bodies™ and the predicate-concept ˜divisible™
represent objects indirectly, through sensible intuition. The entire
judgment, then, is a complex representation of objects by concepts.
Kant regards judgments as syntactic structures that (in the simplest
case) combine or unify subject- and predicate-concepts, which we
shall call ¬rst-order concepts.
Kant next establishes the priority of judgment over concept by
claiming that the only function of the understanding is to judge, and
by analyzing concepts as predicates of possible judgment:
We can, however, trace all actions of the understanding back to judgments,
so that the understanding in general can be represented as a faculty for
judging. For according to what has been said above, it is a faculty for
thinking. Thinking is cognition through concepts. Concepts, however, as
predicates of possible judgments, are related to some representation of a still
undetermined object. (A69/B94)
If the only use of concepts is to judge, and if the understanding is
essentially the power to think by means of concepts, it follows that the
only function of the understanding is to judge. Now Kant does not
deny that the mind produces concepts from other representations by
comparison and abstraction. But on his view creating concepts in this
way makes sense only because the concepts are used in judging. More-
over, he attributes concept formation to the faculty of judgment in its
re¬‚ective mode, rather than the determinative mode involved in mak-
ing cognitive claims. For Kant the primary activity of the understand-
ing is to make determinative judgments concerning objective states
of affairs; all other functions are derivative and presuppose this role.5
The second signi¬cant implication of this passage is to analyze both
concept and object in terms of judgment. When Kant says a concept
is a “predicate of a possible judgment,” he means that the essential

5 The only treatment of re¬‚ective judgment in the First Critique occurs in the Amphiboly of
Concepts of Re¬‚ection. See chapter 8 below.
The Metaphysical Deduction 83
function of a concept is to serve as a predicate in judgment. As we saw
above, concepts can also be used as subject-terms in judgments, but
from the logical standpoint, what separates general from particular
representations is that they signify predicates rather than the things of
which they are predicated. Now by virtue of the fact that they are the
means of judging objects, concepts are inherently objective represen-
tations. This distinguishes them from sensations, for example, which
are merely subjective states. When Kant says concepts are “related to
some representation of a still undetermined object,” he means that
as predicates, concepts are ways of classifying objects into kinds. The
things being classi¬ed are the objects of judgment. A representation
of an undetermined object would be some data given in intuition,
which has not yet been classi¬ed as of a certain kind. The connec-
tion between concept, object, and judgment is only sketched here,
but becomes central to the B edition Transcendental Deduction. For
now we can say that in this analysis, Kant establishes that the notion
of judgment is fundamental, and that the notions of concept and
object are to be analyzed in terms of it.
In concluding this ¬rst half of the Metaphysical Deduction, Kant
says, “The functions of the understanding can therefore all be found
together if one can exhaustively exhibit the functions of unity in
judgments” (A69/B94). In short, a complete list of pure concepts
produced by the activity of the understanding can be derived from a
list of the forms of judgment. What Kant does not say, which only
becomes apparent in the next section, is that these are syntactic or
second-order concepts expressing the logical properties of judgments.
To see why this must be so, let us review his argument so far.
Kant™s main premises are these:
1. All acts of the understanding are judgments.
2. Judgments are acts in which the understanding uni¬es diverse
representations into a single, more complex, representation of an
object.
What is needed here is an expansion on premise 2, concerning
the nature of judgment. As we saw above, judgments are complex
representations of objects by means of concepts. In the simplest case,
a judgment has a subject-concept and a predicate-concept, which
function as ¬rst-order concepts of objects. Now concepts are gen-
eral representations that unify (other) diverse representations in a
The Metaphysical Deduction
84
judgment. Since the ¬rst-order concepts are diverse representations,
in order to combine them into a judgment, the understanding must
employ second-order concepts. These higher-order concepts express
the various ways to combine ¬rst-order concepts (and other repre-
sentations, including judgments) to produce judgments of any form.
Thus the pure concepts identi¬ed here are second-order concepts
of the syntactical properties of judgments, which express the logi-
cal operations of the understanding. So to complete this part of the
argument, we can add the following premise:

3. The function of a concept is to unify other representations in
making judgments.
From premises 1“3 Kant can draw the conclusion:
4. All judgments presuppose second-order, syntactical concepts
expressing the forms for combining ¬rst-order concepts (or other
representations) in judgment.
From 4 and the following de¬nition of a pure concept in 5:
5. Pure concepts express the logical operations of the understanding,
Kant is then entitled to conclude:
6. Therefore, a complete list of forms for unifying representations
in judgment will produce a complete list of pure concepts of the
understanding.

Here Kant has argued that the understanding must produce a set
of pure concepts from its own logical activities in judging. Clearly
these concepts cannot be derived from experience, because they are
presupposed in the act of recognizing objective states of affairs. At this
point Kant has achieved his ¬rst goal in the Metaphysical Deduction,
namely to demonstrate that there is a determinate set of pure concepts
of the understanding, and that an exhaustive list is provided in the
table of the forms of judgment. The method of derivation shows these
concepts to be a priori in the weak sense that they are not derived
from experience. In the next section Kant discusses these forms of
judgment.

c. Interlude: the table of the forms of judgment (A70“1/B95“6)
Kant™s table expresses his logical theory. As we saw, Kant™s logic is
an extension of Aristotelian syllogistic logic, which Kant thinks is
The Metaphysical Deduction 85
complete and not capable of revision. We also noted that quanti¬ca-
tion theory, developed by Frege and Russell from the late nineteenth
century, thoroughly revolutionized modern logic. This advance poses
a problem for Kant, because he claims to derive a complete list of
a priori concepts from judgment forms regarded today as hopelessly
outdated. Even if one accepts the idea of a privileged set of categorial
concepts, it seems likely that Kant has not identi¬ed the correct set.
As one might expect, this is a standard verdict among commentators.
Despite the shortcomings of Kant™s logic, his assumption that the
activity of judging presupposes a set of non-empirical concepts is
plausible. Moreover, there are signi¬cant overlaps between Kant™s
logical forms and those recognized in contemporary theory. Here
I shall present an overview of Kant™s theory and its relation to
contemporary logic.
At A70/B95 Kant notes that judgment forms are logical features
that remain when one abstracts from the content (¬rst-order concepts)
of a judgment. Every judgment has four logical characteristics, which
he calls “heads” (Titel ): quantity, quality, relation, and modality.
Under each head he identi¬es three “moments” which jointly express
all possible forms under that head. The completeness of the table
depends on this type of organization. In particular, the fact that there
are three moments under each head indicates that the list is derived
from a functional or teleological analysis of the understanding, rather
than a purely mechanical procedure.6 The organic nature of the table
becomes apparent when one considers the interdependence of the
three moments under each head.
As we shall see, Kant sets modality apart from quantity, quality,
and relation, since only the latter three features concern the content
(the logical syntax) of judgments. By modality Kant means the way
in which the judgment is “held in the mind,” that is, whether it is
asserted or not. Today this aspect is called the illocutionary force of
an utterance, and is classi¬ed under the pragmatics of judgment (or
speech acts), rather than syntax. So Kant is on the right track in
separating modality from the other three heads. The underlying ¬‚aw
in the entire table is the view that quantity, quality, and relation are
independent of one another. In modern logic all three aspects would

6 See D¨ r¬‚inger, “The Underlying Teleology of the First Critique,” 820“2.
o
The Metaphysical Deduction
86
be subsumed under the heading of logical operators. Kant™s table,
then, re¬‚ects the classical tradition, which, as we shall see, did not
have a suf¬ciently general theory of logical syntax.
Let us begin with quantity. Here Kant endorses the classical view
that every judgment is either universal, particular, or singular, de¬ned
by the scope of the subject. The subjects of universal judgments are
an entire class (e.g., “All humans are mortal”); subjects of particular
judgments are part of a class (e.g., “Some philosophers are Greek”).
Subjects of singular judgments such as “Socrates is Greek” are indi-
viduals, typically referred to by proper names or de¬nite descriptions.
On this view, the quanti¬ers “all” and “some” operate on the subject-
concept, identifying the extension of the class to which the predicate
applies. Kant also follows tradition in claiming that in inference, sin-
gular judgments can be treated like universals because “they have no
domain at all” (A71/B96). They are similar to universal judgments
inasmuch as the predicate is valid of the entire subject concept. Never-
theless, singular judgments are “essentially different” from universals
as cognitions, since the singular stands to the universal “as unity to
in¬nity”; that is, singular judgments ascribe a predicate to a distinct
individual rather than to a set of individuals. Modern logic classi¬es
singular judgments as atomic, and quanti¬ed judgments as complex
because they include logical operators.
Although every judgment properly falls under one and only one
moment, the moments are interdependent because the notions of class
and individual are correlative or mutually imply one another. This is
because a concept de¬ning a class represents features of individuals,
and individuals are recognizable in terms of their features. Hence if
one can think of individuals as members of classes or sets, one can also
subsume subsets under sets. In other words, the ability to judge by
any one of these forms also entails the ability to judge by the others.
This helps ¬‚esh out the idea that the understanding has a uni¬ed
function, despite the variety of judgment forms.
Although he recognizes the distinction between quanti¬ed and
unquanti¬ed judgments, Kant lacks our notion of a quanti¬er. Today,
a singular sentence like “Socrates is Greek” is classi¬ed as an atomic
sentence because it contains no logical operators, including quanti-
¬ers. It is expressed by a symbol such as ˜Fa™, where ˜F™ stands for
the predicate “is Greek,” and ˜a™ is an individual constant referring
The Metaphysical Deduction 87
to Socrates. Universal sentences have a universal quanti¬er for the
main logical operator and are symbolized as quanti¬ed conditionals.
The judgment “All humans are mortal,” for example, is symbolized
(∀x)(Hx ⊃ Mx), read as “For everything, if it is human, then it is
mortal.” The particular judgment “Some philosophers are Greek” is
today symbolized by a formula whose main operator is the existen-
tial quanti¬er: (∃x)(Px & Gx), which is read as “There is something
which is both a philosopher and Greek.” One problem is that these
three forms are not exhaustive. Kant overlooks unquanti¬ed complex
judgments whose main operator is a truth-functional operator such as
“if-then.” For example, in the sentence “If Plato is a teacher, then Aris-
totle is a student,” the main operator is the conditional. The sentence
could be symbolized as follows: Tp ⊃ Sa. Although each component
judgment is singular, the entire conditional does not fall under any
of Kant™s three moments of quantity. This illustrates one problem in
Kant™s treatment of quantity and relation as independent features.
The second head classi¬es judgments under quality into af¬rma-
tive, negative, and in¬nite. Most commentators view Kant™s notion of
in¬nite judgments as rather tortured, and more for the sake of sym-
metry than any logical reason. The real focus of this heading is the
theory of negation, where we see the same lack of generality as above,
despite a clear advance over the classical view. In classical accounts,
the negative particle “not” was viewed as attached to the copula “is”
connecting the subject and predicate, and thus as extending to the
entire judgment. But many thinkers treated negative judgments as
denials, or actions opposed to af¬rmations. Since in af¬rming one
unites the predicate and the subject, in denying one must “separate”
the subject from the predicate.7 Accordingly, negation characterizes
the action rather than the content being judged. Since denying means
separating the component concepts, however, there is no unity to the
judgment, which is required for it to have a truth value. A more gen-
eral problem is that it is not always clear how to classify judgments as
af¬rmative or negative. Since the propositions “God is just” and “God
is not unjust” are logically equivalent, it seems pointless to classify the
¬rst as af¬rmative and the second as negative. Although Kant takes

7 This is true of the Port-Royal Logic. See Arnauld and Nicole, Logic or the Art of Thinking,
part II, chapter 3.
The Metaphysical Deduction
88
the classical position in separating negation from the other logical
operators, he rejects the view of negation as denial, placing it in the
content of the judgment.
The moments under quality are af¬rmative, negative, and in¬nite.
Examples of each are “The soul is mortal,” “The soul is not mortal,”
and “The soul is non-mortal.” Now Kant admits that the in¬nite
judgment is an af¬rmation in logical form. The negation in the in¬-
nite form falls on the predicate (“non-mortal”) rather than on the
copula “is.” From the standpoint of general logic there are really only
two qualitative modes, af¬rmative and negative. Kant thinks the in¬-
nite form must be recognized, however, because transcendental logic
“also considers the value or content of the logical af¬rmation made
in a judgment by means of a merely negative predicate” (A72/B97).
And he goes on to state that in¬nite judgments are “merely limiting,”
which will be signi¬cant in terms of the a priori knowledge provided
in transcendental logic. If Kant™s identi¬cation of in¬nite judgments
as a distinct moment depends on transcendental logic, then this looks
like the tail wagging the dog. In any case, two aspects stand out from
the logical point of view. First, in spite of Kant™s three moments, log-
ically speaking the only distinction is between judgments in which
negation is the main operator and those in which it is not. Second,
and more important, Kant correctly locates negation in the content
of the proposition rather than the action of judging. We shall return
to this point in discussing modality.
The remainder of Kant™s analysis of content falls under relation,
where he explicitly indicates the forms of simple and complex judg-
ments. The three forms are subject-predicate, hypothetical (or condi-
tional), and disjunctive judgments. Subject-predicate judgments are
the simplest or atomic form, since they have no judgment as a part.
Hypotheticals and disjunctions are complex forms, which express dif-
ferent ways of relating judgments. Today we are struck by the absence
of conjunction, so in this respect Kant™s table seems incomplete. This
threefold division of relational forms stems from Kant™s view that
there are only three ways in which two concepts can relate to one
another. The ¬rst, found in the categorical form, is the inherence
of a predicate in a subject. The second is the relation of ground
to consequent as expressed in hypothetical judgments. And ¬nally,
The Metaphysical Deduction 89
disjunctive judgments express the relation of opposition among the
members of a division. Let me comment brie¬‚y on each of these
forms.
It was traditional to analyze simple judgments as composed of
a subject, a predicate, and a copula connecting the two. Some logi-
cians recognized that subjects and predicates could themselves contain
embedded judgments, as in the sentence “God who is invisible made
the world which is visible.”8 But given the overall subject-predicate
structure, all embedded judgments had to be located in the subject or
the predicate. There were many dif¬culties with this theory. For one
thing, the grammatical subject of a sentence was not always the logical
subject, and it was often not obvious how to distinguish the subject
from the predicate of a sentence. This analysis also could not account
for immediate inferences, such as from “All horses are animals” to
“All heads of horses are heads of animals.” Frege replaced the subject-
copula-predicate analysis with the distinction between singular terms
(constants and variables) and functions, including predicates and logi-
cal operators (truth-functional connectives and quanti¬ers). He elim-
inated the copula by analyzing predicates as incomplete expressions
naming functions (e.g., “is Greek”) and singular terms as complete
expressions naming objects (e.g., “Socrates”). Thus the unity of the
proposition was achieved by the ¬t between incomplete and complete
expressions. Although Kant accepts the subject-copula-predicate anal-
ysis for atomic judgments, he did not force complex judgments into
the subject-predicate mold.
The two logical operators under relation are the conditional (if-
then) and disjunction (either-or). Kant™s views of both are traditional,
differing from the truth-functional treatment today. At A73/B98“9
Kant says:
The hypothetical proposition, “If there is perfect justice, then obstinate evil
will be punished” really contains the relation of two propositions, “There is
a perfect justice” and “Obstinate evil is punished.” Whether both of these
propositions in themselves are true, remains unsettled here. It is only the
implication that is thought by means of this judgment.
8 This example is from the Port-Royal Logic. Arnauld and Nicole™s analysis of restrictive and
non-restrictive subordinate clauses made an important contribution to semantics. See Logic
or the Art of Thinking, part I, chapter 8, and part II, chapter 6.
The Metaphysical Deduction
90
Here Kant recognizes that asserting a conditional does not commit
one to asserting either the antecedent or the consequent, but only a
relation between them. In characterizing this relation as implication,
however, Kant takes the conditional as non-material rather than the
weaker material conditional of truth-functional logic.9 In the material
conditional the “if-then” expresses the weak truth-functional relation
that whenever the antecedent is true, the consequent is true. This
interpretation does not capture stronger relations such as logical and
causal relations between the antecedent and consequent. Kant™s view
of the conditional as non-material was actually standard for his time.
The noteworthy feature of Kant™s view of disjunctive judgments is
his exclusive interpretation. This is clear from A73/B98“9:
the disjunctive judgment contains the relations of two or more propositions
to one another, though not the relation of sequence, but rather that of logical
opposition, insofar as the sphere of one judgment excludes that of the other,
yet at the same time the relation of community, insofar as the judgments
together exhaust the sphere of cognition proper.
After stating his example, “The world exists either through blind
chance, or through inner necessity, or through an external cause,” he
says, “To remove the cognition from one of these spheres means to
place it in one of the others,” and vice versa, since the alternatives
“mutually exclude each other, yet thereby determine the true cogni-
tion in its entirety” (A74/B99). In other words, for Kant disjunctions
express a (potentially) complete inventory of mutually exclusive alter-
natives. In contemporary logic this is called an exclusive interpreta-
tion, in which the entire disjunction is true just in case exactly one
disjunct is true. Typically, however, the wedge ˜∨™ is used today to
symbolize ˜or™ in the weaker, inclusive sense, in which the disjunction
is true if at least one disjunct, and possibly both, are true.
Kant™s treatment of modality is undoubtedly the most interesting
part of his theory of judgment, for he is the ¬rst philosopher to sepa-
rate entirely the content of the proposition from the act of asserting it.
Descartes came close to this view when he distinguished perceptions
of the understanding, which included propositional thoughts, from
the act of the will involved in judging. It was essential to Descartes™s

9 Melnick makes this point in Kant™s Analogies of Experience, 52“6.
The Metaphysical Deduction 91
method that one be able to apprehend a proposition without com-
mitting oneself to its truth value. In explaining modality Kant also
separates thinking a proposition from asserting it. At A74/B99“100
he says the modality of judgment “is distinctive in that it contributes
nothing to the content of the judgment (for besides quantity, qual-
ity, and relation there is nothing more that constitutes the content
of a judgment), but rather concerns only the value of the copula in
relation to thinking in general.” The modality is the way the subject
thinks the proposition rather than a feature of its content. In current
speech act theory this aspect of an utterance is called the illocution-
ary force, and its recognition is commonly traced to Frege™s notion
of assertoric force. In his 1918 essay “The Thought,” Frege explicitly
separated the force of an utterance from its propositional content,
because he recognized that it is possible to use declarative sentences
non-assertorically.10 After Frege, philosophers of language developed
a general theory of illocutionary force, the pragmatic signi¬cance of
an utterance, characterizing the effect the speaker hopes to produce
in the listener.
As usual, Kant lists three moments under modality: problematic,
assertoric, and apodictic. Problematic judgments are those in which
a proposition is not asserted, but, as Kant says, “one regards the asser-
tion or denial as merely possible (arbitrary).” In the assertoric mode,
“assertion or denial is considered actual (true). Apodictic judgments
are those in which it is seen as necessary” (A74“5/B100). Here, as
with quantity, it seems there are really two modes, for the main dis-
tinction is between assertoric and non-assertoric uses. In problematic
judgments one thinks or apprehends the judgment without making
a commitment to a truth value. This is clear from Kant™s statement
that component judgments in conditionals and disjunctions are held
only problematically. Both assertoric and apodictic judgments involve
assertions; in the latter the action is additionally thought as necessary.
Since Kant thinks of modality as a logical aspect of judging, he char-
acterizes these modes as expressing logical possibility, logical actuality,
and logical necessity. But it is not clear how he relates those concepts
to the notion of assertoric force. C. D. Broad suggests Kant thinks
the three modes represent secondary judgments (in the simplest case)

10 “The Thought,” in Frege, Logical Investigations.
The Metaphysical Deduction
92
of the forms “˜S is P™ is possible,” “˜S is P™ is true but not necessary,”
and “˜S is P™ is necessary.”11 Unfortunately this misses Kant™s insight
that assertoric force is not part of the syntax of a judgment, ¬rst-
order or otherwise. In contemporary modal logic the possibility and
necessity operators are part of the content of the proposition, just like
the other logical operators. Thus one can formulate claims about the
logical possibility or necessity of sentences without asserting them.
A second difference between Kant and modern logic concerns the
notion of logical necessity. At A76/B101 Kant says that in a modus
ponens syllogism:
the antecedent in the major premise is problematic, but that in the minor
premise assertoric, and indicates that the proposition is already bound to the
understanding according to its laws; the apodictic proposition thinks of the
assertoric one as determined through these laws of the understanding itself,
and as thus asserting a priori; and in this way expresses logical necessity.
In this inference, where one asserts the premises and conclusion, in
the major premise (“If P, then Q”) both P and Q are held only prob-
lematically. The minor premise asserts P, and the conclusion asserts Q.
Kant thinks that when one accepts Q as following deductively from
the premises, then one thinks its assertion is necessary. This necessity
attaches to the act of drawing the inference, and thus seems to be
based on the idea of validity. This is not equivalent to our notion of a
logically necessary truth, however, since there is no restriction on the
content of the conclusion of a valid argument. Our notion of logical
necessity is closer to Kant™s notion of analyticity.
Although Kant™s theory of judgment forms is outmoded from our
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




The Transcendental Deduction of the categories is the heart of the
Critique of Pure Reason. Here Kant argues that we are justi¬ed in apply-
ing pure concepts of the understanding to objects of experience. His
strategy is to show that the categories are necessary conditions for
experiencing objects given in intuition. Kant completely revised this
section in the B edition; here we shall examine both the A and B edi-
tion versions, to understand what was lacking in the 1781 version. As
many readers are disappointed to discover, both deductions treat the
categories as a group. Not until the Principles of Pure Understanding
does Kant defend individual categories.
In the A edition Preface to the Critique, Kant says the deduction
of the categories “has two sides,” one objective, the other subjective.
The objective side must “demonstrate and make comprehensible the
objective validity of its concepts a priori” and thus is essential to his
project. The subjective side is less essential and concerns “the powers
of cognition on which [the understanding] rests” (Axvi“xvii). Many
commentators have assumed that Kant is referring to two distinct
proofs, one concerning conditions for experiencing objects, the other
the subjective sources of experience. As we shall see, there is reason
to reject this reading.
This chapter proceeds as follows. Section 1 treats the introduction,
common to both editions, and then considers the question of the
objective and subjective deductions. The A edition argument and
its weaknesses are the subject of section 2. Section 3 then discusses
the complex B edition argument. Finally, in section 4 I highlight the
revolutionary nature of Kant™s theory of judgment.



103
The Transcendental Deduction
104

1 . t he id ea of a t ra ns ce nd e nta l deduction
The introduction is undoubtedly the most comprehensible part of
the Transcendental Deduction. The ¬rst paragraph explains that a
transcendental deduction is a normative argument justifying the use
of a concept, as opposed to a factual argument concerning its actual
use. Empirical concepts do not require such a deduction because
experience can “prove their objective reality” (A84/B116“17), or their
application to objects of experience. There are also “usurpatory con-
cepts,” such as fortune and fate, whose validity is subject to question.
But the deduction concerns the pure concepts of the understanding,
which are not derived from experience, and therefore require a special
proof to justify their use in experience.
Kant next explains the particular dif¬culty in justifying these con-
cepts. First, transcendental deductions differ from empirical deduc-
tions, which can show only how a concept is acquired through
experience, and thus cannot justify a priori concepts. There are actu-
ally two types of a priori concepts: those originating in the forms of
sensibility, space and time, and those originating in the understand-
ing (A85/B118). His reference to “concepts” of space and time is not
accidental; all mathematical concepts as well as concepts of spatial
and temporal features are also pure despite their basis in the forms
of intuition. From A88 to A90/B120 to B122 Kant explains why it is
more dif¬cult to justify pure concepts produced by the understand-
ing. First, despite their a priori origin, mathematical concepts (e.g., a
triangular shape) can be displayed in intuition, but this is not true of
concepts such as substance“accident and cause“effect. Second, Kant
believes the Aesthetic proofs that space and time are forms of intuition
establish the validity of spatiotemporal and mathematical concepts for
objects given to the senses. By contrast, pure concepts of the under-
standing have no original connection to the sensibility, and so their
application to appearances demands an additional argument. As he
says at A90/B122“3, objects given in intuition must accord with the
pure forms of sensibility since “otherwise they would not be objects
for us”; but that they must also accord with the conditions of thought
“is a conclusion that is not so easily seen.” And just below: “Appear-
ances would nonetheless offer objects to our intuition, for intuition
by no means requires the functions of thinking” (A90“1/B123).
The Transcendental Deduction 105
Now it is important not to misunderstand this point. Kant will
in fact argue that for any intuition to represent an object, it must be
subject to the categories. All he is claiming here is that the indepen-
dence of the sensibility from the intellect entails the logical possibility
that we receive sensory data to which pure concepts do not apply. For
example, appearances might be so haphazard that no causal con-
nections can be discerned. The problem is precisely how subjective
forms of thought can apply necessarily to the data given through the
senses.
At section 14 Kant details his strategy. He reiterates the alternatives
previously outlined: either the object makes the representation possi-
ble, or the representation makes the object possible. In the ¬rst case,
the representation depends on the nature of the object, and so only
a posteriori representations can arise. By implication, the only way
a representation can apply necessarily to an object is if it makes the
object possible. Kant is careful to specify at A92/B125, however, that
only the nature and not the existence of the object depends on the
representation. Thus by “making the object possible” Kant means
the representation presents as an object whatever is given to us as exist-
ing. Clearly he rejects the phenomenalist view that particular acts of
representing bring objects into existence.
Following this analysis, the issue is whether pure concepts are nec-
essary conditions under which anything can be “thought as object in
general” (A93/B125“6). If so, then these concepts are presupposed in
all experience of objects. The Transcendental Deduction must show
that pure concepts of the understanding relate “a priori to objects of
experience, since only by means of them can any object of experience
be thought at all” (A93/B126). In closing the A edition Introduction,
Kant lists the three subjective sources of experience: sense, imagina-
tion, and apperception or self-consciousness, which is the ultimate
basis of the understanding. He also remarks that each of these capac-
ities has both empirical and transcendental functions. By contrast,
the B edition emphasizes the failures of the empiricists to account for
such concepts as substance and causality. Unlike Locke, Hume recog-
nized the impossibility of a straightforward empirical deduction. But
since he did not think the mind could produce ideas independent of
impressions, Hume traced metaphysical concepts to the psychological
process of association, thus offering an indirect empirical deduction.
The Transcendental Deduction
106
As Kant sees it, Hume mistakes the objective necessity of pure con-
cepts for a merely subjective necessity based on experience.
Before proceeding, let us return to Kant™s distinction between an
objective and a subjective deduction. Taken literally, the objective
proof should proceed without any reference to subjective capacities.
But since this is not possible, commentators have gone to interesting
lengths to identify the two sides.1 In Kant and the Mind, however,
Andrew Brook sensibly remarks that both editions base the objective
validity of the categories on the theory of synthesis, an account of the
subjective sources of experience. Thus the distinction cannot mark
out two different proofs.2 In fact, Kant makes the same point at A97.
Since the objective validity of the categories depends on their necessity
for thinking of objects, “we must ¬rst assess not the empirical but the
transcendental constitution of the subjective sources that comprise
the a priori foundations for the possibility of experience” (A96“7).
Clearly the distinction between “objective” and “subjective” sides of
the deduction marks two aspects of one argument. In fact, Kant
drops the distinction in the B edition, where the argument is clearly
continuous.

2 . th e a ed ition d e du cti on
Everyone agrees that the 1781 proof fails miserably. Nevertheless, the
argument introduces the key notions of the synthesis of imagination,
the transcendental unity of apperception, and the correlation between
objectivity and subjectivity. Moreover, independently of Kant™s larger
project, it soundly refutes the empiricist doctrine that all ideas are
derived from experience. Finally, the contrast between the A and B
edition deductions brings into relief the key elements of the more
successful proof. Thus there are good reasons to examine the ¬rst
edition proof.
Kant begins by claiming that it is impossible for an a priori concept
to represent an object independently of intuition, for only intuition
can give objective reality or content to the concept. Otherwise it
1 Whereas Kemp Smith claims the B edition ignores the subjective side, Paton thinks both
sides appear in both editions. See Kemp Smith, Commentary, xliv, 235“48 passim; and Paton,
Kant™s Metaphysic of Experience, 1:350“3, 499ff, 526ff.
2 Brook, Kant and the Mind, 120.
The Transcendental Deduction 107
would “be only the logical form for a concept,” and not a concept
through which one thinks an object. Since the “objective reality”
of a concept is its application to whatever exists, his point is that
the content of any meaningful concept must relate in some way to
spatiotemporal appearances. If it failed to do so, the concept might
have the logical form of a predicate, namely generality, but would
lack any feature allowing us to recognize instances in experience.
At A96 Kant says establishing the validity of pure concepts requires
demonstrating their necessity for experience of objects.
Kant next makes a point essential to the deduction, that to qualify
as a cognition, a representation must be inherently complex. Perhaps
because of its intuitive plausibility, he offers no support for it here,
remarking only that cognition “is a whole of compared and connected
representations” (A97). At A99 he implicitly links this claim to the
fact that all representations occur in one time. According to this view,
a simple, unanalyzable impression could not by itself represent an
object. In the B edition Kant justi¬es the complexity of cognition
more systematically.
Although most commentators take the four numbered sections
detailing the threefold synthesis to constitute the A edition deduction,
the Preliminary Remark claims that this discussion is only prepara-
tory to the systematic exposition, located in section 3. In fact, that
later discussion contains many points that assume prominence in the
B edition deduction. Despite Kant™s description of that exposition as
systematic, his failure to present a uni¬ed argument clearly necessi-
tated the complete reworking of the deduction.
To understand the A edition strategy we need to recognize his
peculiar treatment of the threefold synthesis. As Paton points out, the
three “parts” are not separate stages but different ways of describing
the same process. The parts are related in Chinese box fashion, so
that each subsequently described synthesis is contained in the stage
previously described.3 Thus the ¬rst description, of the synthesis of
apprehension in intuition, gives the most general characterization.
Kant then argues that that process must include the second “part,” the
synthesis of reproduction in the imagination. The third step similarly
argues that the synthesis of reproduction presupposes the synthesis

3 See Paton, Kant™s Metaphysic of Experience, 1:354“5.
The Transcendental Deduction
108
of recognition in the concept. Finally Kant introduces the ultimate
necessary condition of the entire complex process, the transcendental
unity of apperception or “I think.”
Kant begins the three-step argument by claiming that all repre-
sentations are subject to time, and therefore bear temporal relations
to every other representation (A98“9). Consequently “they must all
be ordered, connected, and brought into relations” in time. He next
returns to his characterization of cognition as complex, pointing out
that as a cognition of an object, every intuition contains a manifold.
In order to recognize this complexity, we must apprehend the parts
successively, at distinct times. The process of unifying the successively
apprehended parts into one representation is the synthesis of appre-
hension in intuition. Kant says that although the intuition provides
a manifold, it cannot be “contained in one representation, without the
occurrence of such a synthesis” (A99). Not until the next step does
he attribute this activity to the imagination.
This ¬rst step assumes that we in fact have empirical intuitions
that we recognize as complex. A complex representation is a repre-
sentation of a single, uni¬ed thing made up of parts. Recognizing the
complexity means being aware of both the parts and their unity. To
intuit an apple, for example, as red, hard, juicy, in a certain space, and
existing through a certain time, means representing it as one object
having these diverse characteristics. Now because the sensibility pas-
sively receives the intuitive data, our recognition of both complexity
and unity requires us actively to discriminate the parts before unify-
ing them. As Kant says, “for as contained in one moment no rep-
resentation can ever be anything other than absolute unity” (A99).
In other words, any data apprehended only instantaneously or non-
successively cannot be recognized as having parts. Now this view has
an interesting implication, namely that the manifold of intuition is
not composed of absolute or “simple” parts. Because space and time
are in¬nitely divisible, any intuited manifold can be discriminated
into parts of any degree of complexity (e.g., spatial and temporal
parts). In consequence, the degree of complexity is relative, depend-
ing on the ¬neness with which one discriminates parts. Kant™s point
is that producing a uni¬ed complex representation presupposes two
distinct capacities: apprehending the parts successively and unifying
them into a whole.
The Transcendental Deduction 109
At A99“100 Kant remarks in passing that synthesis must also be
performed on the a priori manifold given in intuition. Space and
time, too, are represented as wholes divisible into parts. Just as sense
impressions must be connected to represent uni¬ed objects, so the
spatial and temporal data must be connected to represent one space
and one time. This hints at the dual role of pure intuition: as forms
of sensibility, space and time provide frameworks for receiving the
empirical data; as pure manifolds, they provide a content for pure
concepts of the understanding. The A edition focus on empirical
intuition obscures the crucial second role, a defect remedied in 1787.
Here Kant merely asserts that there is a pure as well as an empirical
synthesis of apprehension. He should say, of course, that the synthesis
of apprehension has both pure and empirical aspects.
The next step argues that for the synthesis of apprehension to occur,
the imagination must reproduce representations. Unfortunately the
order of presentation muddles the argument, which has two steps.
The main point, located in the second half of the second paragraph, is
that apprehending identi¬able objects requires reproducing in imag-
ination the previously apprehended parts. Kant then argues that this
process is a transcendental act of the imagination, presupposed in
all empirical association. The entire argument assumes that when
we have a single complex representation, we are aware of both the
discriminated parts and the unity binding them into a whole. Now
previously Kant stated that the parts must be discriminated in suc-
cessive moments. So to end up with a uni¬ed representation, the
imagination must reproduce the parts previously apprehended. Con-
sider the example of counting. The resulting number is a complex
whole composed of units. Kant points out that if one did not repro-
duce the previously apprehended units as one progresses, “no whole
representation . . . could ever arise” (A102). When counting to two,
for example, one must think of the second unit as distinct from the
¬rst unit. Otherwise one would merely apprehend one unit twice.
But in order to represent this relation between the two units, the
imagination must actually reproduce the thought of the ¬rst unit.
The same is true in drawing a line or thinking of some period of
time. Each succeeding part must be thought in its relation to the
already apprehended parts to represent the entire line or time period.
As Michael Young points out, this does not mean “reliving” the
The Transcendental Deduction
110
experience, but rather incorporating the thought of the previous parts
into the thought of each successively represented part.4 These exam-
ples are noteworthy because they involve the synthesis of parts of space
and time: even our a priori intuitions provide cognition only on the
condition that they contain a thoroughgoing synthesis of reproduc-
tion. Consequently the synthesis of imagination is grounded “on a
priori principles, and one must assume a pure transcendental synthe-
sis of this power, which grounds even the possibility of all experience”
(A101).
Kant reinforces this conclusion at A100“1, by criticizing attempts
to derive ideas of objects from associations based on experience. Here
he argues that the psychological process of association presupposes
the a priori synthesis of the manifolds of space and time. Suppose,
for example, that smelling a certain odor evokes a certain childhood
memory. In this empirical association, the imagination must con-
nect not only the qualitative aspects but also the times and places of
the two experiences. But the ground that permits identifying times
and spaces cannot be derived from the association, since spatiotemp-
oral regions are presupposed in discriminating experiences. Thus
Kant concludes that the imagination must perform a transcenden-
tal function, presupposed by experience, enabling us to “call up” the
previously apprehended parts of the manifold. Reproducibility is a
necessary condition for representing not only empirical objects but
also space and time themselves as complex wholes.
The third section is the most complex, for here Kant introduces
both the relation between concepts and the transcendental unity of
apperception, and the correlation between objectivity and subjec-
tivity. In this way he relates pure concepts to both the necessity of
self-consciousness and the idea of objectivity. Unfortunately, the argu-
ment is completely done in by its unsystematic presentation. Kant
¬rst argues that the synthesis of reproduction requires the synthesis
of recognition in a concept: “Without consciousness that that which
we think is the very same as what we thought a moment before, all
reproduction in the series of representations would be in vain” (A103).
This requires the use of concepts because recognizing something as
the same thing previously apprehended requires conceiving that thing
under some predicate F. In counting, for example, one can reproduce

4 Young, “Kant™s View of Imagination,” especially 147ff.
The Transcendental Deduction 111
previously apprehended units only if one recognizes the reproduced
parts as the same units previously apprehended. Ultimately, to repre-
sent the resulting integer, we must conceive the units as parts related
by the addition operation: Kant says the concept of number “consists
solely in the consciousness of this unity of the synthesis” (A103). In
other words, to generate representations of uni¬ed things composed
of parts, we must employ concepts of both the whole towards which
one is progressing, as well as the parts composing it. Although Kant
has not yet connected these concepts to the categories, he has shown
that a system for conceiving part“whole relations is presupposed in
experience of complex particulars.
The remainder of this passage links pure concepts to the experience
of objectivity and the necessity of self-consciousness. Kant™s presen-
tation is so badly organized, however, that it is not easy to see the
connections between these ideas. From A103 to A111 he appears to
make this argument:
1. Consciousness of conceptual unity presupposes a unitary con-
sciousness. (A103“4)
2. The notion of an object of representation includes the idea of a
necessary unity. (A104“6; A108“9)
3. Consciousness of objective unity requires a transcendental self-
consciousness (as opposed to an empirical self-consciousness).
Awareness of this identical self makes possible the notion of a
transcendental object. (A106“7; A108)
4. A transcendental self-consciousness is consciousness of unity of
synthesis by means of pure concepts. (A107“8)
5. Thus the pure concepts are presupposed in all objective awareness.
(A109“11)
One can see from this summary why the A edition deduction is
deemed a failure. Nevertheless, let us examine the main points, to
prepare for the B edition proof.
At A103“4 Kant connects the unity thought through concepts with
a unitary consciousness. We saw that in counting, the concept of the
number represents the whole resulting from a successive addition of
units. Like the concept of number, all concepts represent the unity
of a manifold, insofar as they are ways of thinking part“whole rela-
tions. Now Kant argues that consciousness of conceptual unity pre-
supposes a unitary consciousness. To end up with a single complex
The Transcendental Deduction
112
representation, the manifold being uni¬ed must be united in a single
consciousness. William James revisited this point in the nineteenth
century by arguing that giving each of twelve persons one word of
a twelve-word sentence does not result in any consciousness of the
entire sentence.5 Despite its necessity, however, Kant says we may not
always be aware of this unity of consciousness:
This consciousness may often only be weak, so that we connect it with
the generation of the representation only in the effect, but not in the act
itself, i.e., immediately; but regardless of these differences one consciousness
must always be found, even if it lacks conspicuous clarity, and without that
concepts, and with them cognition of objects, would be entirely impossible.
(A103“4)

Although it is not apparent, Kant is getting at more than the point
that “it takes one to know one,” as Allison puts it.6 For from A107
on, Kant wants to connect concepts not just to numerically identical
consciousness, but to awareness of the identity of consciousness, that
is, identical self-consciousness. His term for this self-consciousness is
the transcendental unity of apperception (henceforth t.u.a.). This slide
from a unitary consciousness to a necessary self-consciousness is one
weakness in the A edition argument.
Kant actually introduces the necessity of self-consciousness
through an analysis of objectivity, which he then connects to pure
concepts. At A104“5 he notes that the object of a representation is
thought of as something “corresponding to and therefore also distinct
from the cognition.” That is, in taking a mental state to represent an
object, I at least implicitly distinguish the object from my awareness
of it. Although I may think that my awareness corresponds to the
object, I must also recognize that the object is independent of it. This
leads to the second aspect, the necessity implied by objectivity. Kant
says the object is that which prevents “cognitions being determined
at pleasure or arbitrarily rather than being determined a priori, since
insofar as they are to relate to an object our cognitions must also
necessarily agree with each other in relation to it” (A104). Represen-
tations of an object must conform to the rules governing it, and hence
they must possess a necessary unity. At A109 Kant labels the object of
5 Cited by Kemp Smith, Commentary, 459.
6 Allison, Kant™s Transcendental Idealism, 139.
The Transcendental Deduction 113
a representation the “transcendental object = X.” This notion of the
transcendental object is merely formal and has no particular content;
it is common to every representation of an objective state of affairs.
Kant says it “cannot contain any determinate intuition at all,” and
thus represents only the unity of a “manifold of cognition insofar as
it stands in relation to an object” (A109).
The next stage connects the necessary unity of the transcendental
object to the t.u.a. Recall that the Aesthetic argues that we are directly
acquainted only with appearances, which, from the transcendental

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