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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

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