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criterion of a priori cognitions is their necessity. But his transcendental
idealism contradicts 4.
Falkenstein argues that the pure forms of intuition are neither
innate ideas nor innate mechanisms, but a pure manifold given with
the empirical manifold in experience. The innate ideas version “ that
independently of experience we have two pure forms “lying ready in
the mind” “ violates the axiom that no representations occur prior
to experience. The pure forms are “original acquisitions” because we
“acquire” these representations only through the processed output,
namely experience. By contrast, pure concepts and principles origi-
nate in innate thinking mechanisms, the logical forms of judgment.
In terms of the input-processing-output model, they are operations
for processing the manifold of intuition. The categories express rules
governing these innate operations. But as with pure intuition, we
“acquire” our representations of these rules only through the resulting
experience.18 Although the categories are “present” before experience,
the subject can represent them only by re¬‚ecting on the process.19
Kant rejects the term “innate ideas” for a priori representations,
then, primarily because the mind can represent nothing before pro-
cessing the empirical data of intuition. Although the content of a
priori representation is not derived from empirical data, all repre-
sentation acquires its signi¬cance through its relation to empirical
intuition. In fact, this is an advantage of Kant™s theory over theories
of innate ideas. For the view that the mind has a storehouse of innate
knowledge that can be called up by reason fails utterly to connect
such knowledge to experience.

18 In Metaphysik Vigilantius of 1794“5, Kant says, “All concepts are acquired, and there cannot
be any innate idea <idea connata>. For concepts presuppose a thinking, are made or thought
through a comprehension of features.” Lectures on Metaphysics, 423.
19 Kant attributes our possession of the pure concepts to re¬‚ection in the Metaphysik Mrongovius
of 1782“3. Lectures on Metaphysics, 123“4.
The Transcendental Deduction 135
Kant™s theory of cognition differs radically from both rational-
ism and empiricism. First, he rejects the rationalist doctrine of intel-
lectual intuition. It follows that the human intellect is discursive
and can operate only on data given independently. Moreover, the
Analytic shows that all complex representations must be combined
through acts of thought. Thus rationalists are mistaken in think-
ing that humans can instantaneously “intuit” complex cognitions of
reality. Second, Kant rejects the view that sense perception is inde-
pendent of judging. Unlike sensations, sense perceptions are objec-
tive representations, produced by judging the manifold of intuition.
Perceptions, then, incorporate judgments, and perceiving cannot be
a passive process. Now although many empiricists believe complex
impressions are constructed, none of them identi¬es these construc-
tive acts with judgment. In fact, in analyzing beliefs as complex ideas,
Hume overlooks entirely the logical features of judgment.

5. su mm a ry
The Transcendental Deduction contains Kant™s central justi¬cation
for applying the categories to objects of experience. The A edi-
tion version argues that apprehending the data of intuition succes-
sively requires the imagination to reproduce previously apprehended
representations, which presupposes concepts of the understanding.
Although this version introduces Kant™s theory of synthesis and the
t.u.a., it does not link the categories to judgment. The signi¬cantly
revised B edition version corrects this defect, arguing that the cate-
gories are required to represent objects of both thought and percep-
tion. By analyzing the notion of an object in terms of judgment, Kant
links the categories to the logical forms of judgment identi¬ed earlier.
Thus he defends the application of pure concepts expressed in syn-
thetic a priori principles to the objects of experience. Because these
metaphysical concepts and principles have their seat in the subject,
they apply only to appearances and not to things in themselves. But
because they are necessary for experiencing objects, they represent
real features of appearances, and thus ground empirical knowledge.
Like the forms of intuition, they represent transcendentally ideal but
empirically real features of experience.
c h ap t e r 6

The Schematism and the Analytic
of Principles I



The ¬nal stage in justifying the categories consists in Kant™s argu-
ments for the synthetic a priori principles correlated with them. In
the Analytic of Principles, Kant defends these metaphysical principles,
including those of substance and causality that Hume attacked. As
mentioned earlier, he also added to the B edition the argument titled
the Refutation of Idealism, aimed at Descartes™s view that knowl-
edge of physical reality is less certain than self-knowledge. Thus it is
here rather than in the Transcendental Deduction that Kant responds
directly to the skeptical challenge.
The ¬rst chapter of this section, the Schematism, forms a bridge
between the Transcendental Deduction and the arguments for the
principles. It explains how pure concepts of the understanding, which
have no original connection to sensibility, can apply to objects of intu-
ition. The schema of each category is the condition relating the pure
concept to spatiotemporal objects. It provides the empirical content
that turns the syntactic concept into a real concept of an object.
Contrary to the view of many commentators, this chapter is not inci-
dental to Kant™s argument. As Allison points out, the Transcendental
Deduction shows only that the categories apply necessarily to objects
given in time. But from that argument no particular metaphysical
propositions can be derived. The Schematism speci¬es the particu-
lar temporal condition connected with each category.1 In particular,
it describes how the productive imagination mediates between the
understanding and the sensibility. Despite its importance, the discus-
sion raises two serious questions. First, does Kant need to “deduce”
the schema of each category? And second, are any concepts identical

1 Allison, Kant™s Transcendental Idealism, 175“6.

136
Schematism, Analytic of Principles I 137
with their schemata? After examining the text of the Schematism, I
shall return to these points.
This chapter then examines the introduction to the Principles and
Kant™s arguments for the principles of quantity and quality. The latter
justify applying mathematics to the spatiotemporal and qualitative
features of objects given in intuition. Chapter 7 treats the remaining
arguments for the principles of relation and modality, including the
Refutation of Idealism.

1 . th e s ch e mat i s m
The Schematism begins by distinguishing the power of judgment
from both the understanding and reason, where reason is the higher-
order intellectual faculty that produces judgments by inference from
other judgments. Here he wishes to elucidate the transcendental func-
tion of the power of judgment. At A131/B170, for the ¬rst time in the
Critique, he separates this power from the understanding as a faculty
of concepts. This distinction is required not only to set off theoreti-
cal judgment from practical and aesthetic judgment “ neither moral
judgments nor judgments of beauty are governed by concepts of the
understanding “ but also to highlight the problem of applying pure
concepts in experience. Kant characterizes the pure principles as rules
for directing the power of judgment.
At A132/B171 Kant describes judgment as the faculty “of determin-
ing whether something stands under a given rule.” This activity is a
natural talent, a product of “mother-wit” (A133/B172), and cannot be
taught, since all learning requires one to apply rules to cases. Unlike
general logic, transcendental logic supplies rules directing the power
of judgment. These principles specify not only the rule (the pure
concept), but also the a priori condition for applying the rule to an
instance. This condition is the transcendental schema. Without this
condition, the pure concepts would be “without all content, and thus
would be mere logical forms” (A136/B175).
As the Transcendental Deduction shows, this condition must link
the category to time. Thus the schema represents the temporal ele-
ment giving the pure concept signi¬cance as a ¬rst-order concept
of objects. For example, the logical relation between ground and
consequent in hypothetical judgment becomes the objective concept
Schematism, Analytic of Principles I
138
of the relation of cause and effect when interpreted as a necessary
succession of states in time. The Schematism chapter lists the schema
for each category or moment. The Principles chapter then offers tran-
scendental deductions for the synthetic a priori judgments asserting
the necessity of each schema for experiencing spatiotemporal objects.
The problem of the schematism goes back to Plato™s “third man”
dilemma: how does a general concept apply to a particular instance?
It cannot be by means of another concept, on pain of in¬nite regress.
Similarly, no particular representation can mediate the relation with-
out begging the question. Kant™s theory of the schematic function of
the imagination offers a third alternative. First, the instance must be
“homogeneous” with the concept; that is, the concept must contain
a “mark” of some feature of the object. Although the “third man”
problem also arises for empirical and mathematical concepts, it is
particularly acute for pure concepts of the understanding, because
they have no original connection to intuition.2 As Kant remarks at
A137/B176, they “can never be encountered in any intuition”; we can-
not intuit the substantiality or causal ef¬cacy of objects, although we
can think of these features.3
By contrast, both empirical and mathematical concepts contain
intuitable marks of objects. Unfortunately, Kant obscures this point
with his example of the plate: “Thus the empirical concept of a plate
has homogeneity with the pure geometrical concept of a circle, for
the roundness that is thought in the former can be intuited in the
latter” (A137/B176). Although we would expect him to claim homo-
geneity between the concept of a plate and the plate, Kant locates
the homogeneity between the empirical concept and the pure con-
cept of a circle. His real point is that the pure concept “circle” can
be exhibited in intuition. Thus we can apply the concept “plate” to
an object because the concept incorporates the intuitable roundness
derived from a pure sensible concept. Homogeneity ultimately has to
obtain between concepts and their instances. Because pure concepts
2 In Kant and the Claims of Knowledge, Paul Guyer denies that Kant is concerned generally
with concept application, since he thinks empirical and mathematical concepts include their
own rule of application. See 158“9. I discuss this point below.
3 Although we intuit spatiotemporal patterns and the intensities of sensations, Kant™s point
is that the quantitative and qualitative pure concepts apply in experience only insofar as we
conceive of appearances under the numerical systems required for extensive and intensive
measurement.
Schematism, Analytic of Principles I 139
of the understanding do not represent intuitable features, they are
“heterogeneous” with their instances.
Heterogenity concerns two distinctions: ¬rst, between concept
and instance, and second, between intellectual and sensible repre-
sentations. The transcendental schema which “mediates” between
the concept and the appearance must somehow represent all four
aspects. Kant says it “must be pure (without anything empirical),
and yet intellectual on the one hand and sensible on the other”
(A138/B177). The latter implies that it has both general and particular
features. Kant™s solution identi¬es the transcendental schema of the
category with a rule that produces a “transcendental determination
of time.”
Kant introduces this notion by distinguishing between a schema
and an image. Because both empirical and pure sensible concepts
represent intuitable features, they also have images. For example, we
can recognize images of dogs as well as of circles and triangles. Images
are produced by “the empirical faculty of productive imagination”
(A141/B181). But because they are particular, images are never ade-
quate to their concepts, never fully exhausting their content. So the
schema that connects the concept to the image must itself be gen-
eral. For concepts having images, the schema is a “representation
of a general procedure of the imagination for providing a concept
with its image” (A140/B179“80). This procedure, Kant says, can exist
only in thought, and “signi¬es a rule of the synthesis of the imagi-
nation” (A141/B180). For mathematical concepts, the schema yields
a procedure guiding the imagination in constructing an a priori spa-
tial intuition. An example would be representing a plane triangle in
Euclidean space, by beginning with a point from which one draws
a continuous straight line to a second point, and from there to a
third point, and back to the original point. For the empirical con-
cept “dog,” the schema is a rule specifying the shape of a four-footed
animal, “without being restricted to any single particular shape that
experience offers me” (A141/B180). For concepts having images, the
schema represents a procedure by which the productive imagination
creates an image for a general concept, thereby exhibiting a universal
in intuition.
Although the categories apply to individuals given in intuition, they
lack images. There is no image of totality or reality or cause as there
Schematism, Analytic of Principles I
140
is of a dog and a triangle. Consequently, the connection between the
schema and image does not apply to transcendental schemata. What
does apply is the notion of a procedure for exhibiting a universal in
intuition. Whereas schemata of empirical and mathematical concepts
are procedures for constructing images, transcendental schemata are
procedures for constructing intuitions of objects in time. Thus we
arrive at the idea that the schema is a transcendental determination
of time.
In the Transcendental Deduction Kant defended the objective real-
ity of the categories by demonstrating their necessity for intuiting
objects in global time. At A138/B177 he reminds us that to apply to
objective states of affairs, the categories must relate to the pure syn-
thesis of the temporal manifold. Allison identi¬es the transcendental
schema with the pure (formal) intuition of time, constructed by con-
ceiving of time in terms of a pure concept.4 This appears reasonable,
given Kant™s claim that “The schemata are therefore nothing but a
priori time-determinations in accordance with rules,” namely the
categories (A145/B184). More recently, however, Sarah Gibbons has
argued that Allison™s interpretation begs the question of how pure
concepts apply to the data of intuition. For identifying the schema
with the formal intuition merely presupposes that categories do apply
to the pure manifold. She thinks Kant identi¬es the schema with the
procedure for constructing the formal intuition of time.5 This read-
ing both avoids begging the question, and uni¬es the doctrine of
the schematism with Kant™s theory of mathematical construction.
In both cases the productive imagination constructs a determinate
representation of time or space, which is a pure formal intuition
exhibiting a universal rule. Gibbons argues that schemata are not
rules in the same sense as the categories. Rather they represent the
procedure “which makes possible the instantiation of the concept and
constitutes the pure formal intuition”.6 By means of this constructive
act, the productive imagination mediates between the understanding
and the sensibility. The result, as Allison explains, is to objectify time
by representing “a temporal order as an intersubjectively valid order
of events or states of affairs.” Since we cannot perceive time itself, the

4 Allison, Kant™s Transcendental Idealism, 61“79.
5 6
Gibbons, Kant™s Theory of Imagination, 56“7. Kant™s Theory of Imagination, 74.
Schematism, Analytic of Principles I 141
resulting time-determination is a “necessary characteristic of things in
time.”7 Time-determinations, then, are ways of conceiving of objec-
tive temporal properties and relations of objects.
The best way to grasp this idea is by examples. Here we shall just
focus on the correlations between schema and concept, since the Prin-
ciples arguments present a more detailed view. First, Kant correlates
each of the four headings with a temporal aspect of experience. Kant
links the categories under quantity (unity, plurality, totality) with the
generation of time itself as a uni¬ed (formal) intuition. The quantita-
tive concepts are necessary for extensive measurement; their schema
is number, which represents “the successive addition of one (homo-
geneous) unit to another” (A142/B182). In other words, to judge via
the quantitative forms, one must identify the objects being judged
as distinct individuals occupying determinate locations in time (and
space). Thus we must be able to construct measurable extents of time
(and space), by conceiving them in terms of a plurality of units.
The qualitative categories (reality, negation, limitation) are ways of
conceiving what exists in time. A being is something that ¬lls time;
nonexistence is represented by an empty time. In appearances, the
data of intuition that represent real things are sensations. Thus being
and non-being correspond to the presence and absence of sensation.
The schemata of the categories of quality are, therefore, procedures
for measuring the intensity of sensations.
The relational categories are ways of conceiving real relations
between existing states of affairs in time. Their schemata express the
three temporal features of states: duration, succession, and coexis-
tence. The schema of substance“accident is duration or permanence,
which is presupposed in distinguishing enduring things from their
temporary states. The category of cause“effect is correlated with the
existence of a necessary succession of states in time. And the category
of reciprocal causal interaction is expressed through the representation
of coexisting states.
Finally, the modality of a judgment concerns how we judge objec-
tive states in relation to the whole of time. Really possible existence
is the existence of a thing at some time or another. Actual existence
is existence at some determinate time. And necessary existence is

7 Kant™s Theory of Imagination, 183.
Schematism, Analytic of Principles I
142
existence at all times.8 Although these characterizations are sketchy,
the Principles arguments spell out the relation between categories and
schemata in more detail.
In mediating between the pure logical concepts and the data of
intuition, the schemata perform a double-edged function: they both
permit us to apply the categories to appearances and restrict their
meaning. For example, the logical concepts of subject and predicate
have no real use until they are interpreted temporally as enduring
things and their changing states. Similarly, the logical notion of a
ground and its consequent acquires objective signi¬cance only when
applied to a causally governed succession of states. Thus Kant™s theory
of schematism solves the “third man” problem for pure concepts by
appealing to procedures in the imagination for constructing temporal
features of appearances required to judge them as objective states of
affairs.
Before turning to the Principles, let us return to the two issues
raised earlier: ¬rst, whether Kant needs to “deduce” the schema cor-
related with each category, and second, whether he identi¬es any
of the three types of concepts with their schemata. Regarding the
¬rst, I think Allison and Gibbons are correct that the “deduction” of
the schema is reserved for the Principles arguments. Kant™s purpose
here is to identify the schema for each category. In the Principles he
presents transcendental deductions for the categories as applied under
their corresponding temporal condition. Thus he does not need separate
arguments for the correlations between category and schema.
The second issue is more complex, and commentators disagree
over whether Kant identi¬es concept with schema in any case. Guyer
thinks Kant correctly identi¬es them for both empirical and math-
ematical concepts. Lauchlan Chipman believes Kant identi¬es them
only for empirical concepts, but does so in error.9 On my reading,
Kant distinguishes schema from concept in all three cases. Recall that
schemata are procedures for applying concepts to their instances.
For empirical and mathematical concepts, this involves providing an
image for the concept. Now in the ¬rst place, Kant attributes the
8 As Allison points out, since a causally necessitated state need not exist at all times, we should
take the schema of necessity to be existence of a state produced causally in relation to the
whole of time. See Kant™s Transcendental Idealism, 192.
9 Chipman, “Kant™s Categories and their Schematism,” 107“9.
Schematism, Analytic of Principles I 143
schema in all cases to the imagination: “The schema is in itself always
only a product of the imagination” (A140/B179). This immediately
distinguishes the schema from concepts, which Kant attributes to the
understanding.10 Second, Kant repeatedly describes the schema as
mediating between the concept and the image. For example, he says
the schema of sensible concepts is a product of the pure imagination,
which makes images possible. But these images “must be connected
with the concept, to which they are in themselves never fully con-
gruent, always only by means of the schema that they designate”
(A141“2/B181). Now if schemata were identical with either empiri-
cal or mathematical concepts, there would be no point in describing
them as mediating between the concept and the image.11
Clearly several elements stand or fall together. If, following Gib-
bons, we take the schema to be a procedure for constructing either
images or pure intuitions of spatiotemporal features, then Kant does
respond to Plato™s dilemma. Moreover, in emphasizing the necessity
of imaginative procedures for exhibiting universals in intuition, the
Schematism doctrine is of a piece with Kant™s theory of mathematical
construction. Now let us turn to Kant™s arguments for the principles.


2. the a naly tic of princ i ple s : i n troducti on
The task of the Principles is to defend the judgments that result
when the schematized categories are applied to objects of intuition.
These judgments will be synthetic a priori, since they represent nec-
essary presuppositions of experience. The proofs offer transcendental
deductions, arguments that each principle is necessary to experience
states of affairs having objective temporal features. Kant remarks that
these arguments do not address the truth of mathematical principles,
since he believes that was established in the Transcendental Aesthetic.
Instead, arguments for the principles of quantity and quality justify
applying mathematical principles to objects given in intuition.


10 Kant de¬nes the understanding as the faculty of concepts at A51/B75, A68/B92“3, A78/B103,
and A126.
11 Chipman argues that Kant should not identify empirical concepts with their schemata, since
one can possess a concept (e.g., ˜tadpole™ and ˜bone marrow™) without being able to recognize
instances. See “Kant™s Categories and their Schematism,” 109“11.
Schematism, Analytic of Principles I
144
Kant next contrasts the supreme principles of analytic judgments
and synthetic judgments. By a “supreme principle” he means a neces-
sary condition for such judgments to be meaningful. The principle of
contradiction, “the proposition that no predicate pertains to a thing
that contradicts it” (A151/B190), serves for all judgments as a negative
criterion, that is, a necessary but not suf¬cient condition of truth. For
analytic judgments, it is also a positive criterion since it is suf¬cient
for determining their truth value. Kant also criticizes the common
expression of the principle as “It is impossible for the same thing to
be [F] and not be [F] at the same time” (A152“3/B191“2). This version
is mistaken since it illegitimately imports the sensible condition of
time into a purely logical principle.
Unlike analytic judgments, the truth value of synthetic a priori
judgments cannot be determined by the principle of contradiction
alone, since the latter are ampliative. Consequently “a third thing is
necessary in which alone the synthesis of two concepts can originate”
(A155/B194). This “third thing” can only be the “possibility of expe-
rience,” since the objects of synthetic cognition can only be given in
intuition. But experience takes place in time, and requires a synthe-
sis by the imagination in accord with the t.u.a. In other words, we
can make objectively valid synthetic judgments only by representing
objective states of affairs in one time. The pure principles are thus
rules governing the synthesis of the empirical manifold in time.
Kant begins the third section by attributing the lawlikeness of

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