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standpoint, are our own representations. Whatever the appearances
stand for “ the thing in itself “ is a cipher (X) to us. Since we can-
not get “behind” the appearance, our awareness of unity cannot be
derived from the thing itself. By elimination, the only source of this
necessary unity is the subject, the unity of consciousness: “the unity
that the object makes necessary can be nothing other than the for-
mal unity of the consciousness in the synthesis of the manifold of
representations” (A105). In short, the data of intuition acquires its
representative relation to an object only when it is brought to the
t.u.a. The thought that what appears in intuition is an object existing
independently of one™s awareness of it, is produced in the process
of uniting the manifold in an identical consciousness. At A108 Kant
reiterates that pure apperception is simply consciousness of the act of
synthesis: for the mind could not think its own identity a priori in the
manifold of representations “if it did not have before its eyes the iden-
tity of its action, which subjects all synthesis of apprehension (which
is empirical) to a transcendental unity.” As we saw above, this entails
only the possibility of recognizing the identity of self-consciousness,
rather than its actual recognition.
Kant next distinguishes this transcendental self-consciousness from
empirical self-consciousness. He agrees with Hume that consciousness
of the self given in intuition is empirical and constantly changing: “it
can provide no standing or abiding self in this stream of inner appear-
ances . . . That which should necessarily be represented as numerically
identical cannot be thought of as such through empirical data” (A107).
Empirical apperception is awareness of oneself as a particular subject.
As Hume puts it, it is awareness of one™s own “bundle of percep-
tions,” which has a constantly changing content. In representing our
empirical selves, we take ourselves as objects of experience, distinct
The Transcendental Deduction
114
from other objects, including other subjects. Thus the concept of the
empirical self differs for each consciousness. By contrast, the t.u.a. is
a merely formal consciousness, and not the awareness of an object.
It is simply the thought of the numerically identical subject of any
mental state. Because it does not pick out a particular subject, it is
the same thought for each thinker. Kant agrees with Hume that a ¬‚ux
of perceptions cannot provide the notion of a numerically identical
consciousness. Hume failed to see, however, that such a consciousness
is required to represent the necessary unity of any object, including
oneself as an empirical consciousness. This is why Kant describes the
t.u.a. as original:
This pure, original unchanging consciousness I will now name transcendental
apperception . . . even the purest objective unity, namely that of the a priori
concepts (space and time) is possible only through relation of the intuitions
to it. The numerical unity of this apperception therefore grounds all concepts
a priori. (A107)

The t.u.a. is a primitive fact of our mental life, and cannot be derived
from any other features of consciousness. On the contrary, all uni-
¬ed representations, pure or empirical, of physical or mental objects,
presuppose it.
Kant™s theory that the objectivity of representation originates in
synthesis has a second important implication, namely that the ideas
of the transcendental object and of the necessary unity of appercep-
tion are correlates. At A123 Kant says, “For the standing and lasting
I (of pure apperception) constitutes the correlate of all our represen-
tations so far as it is merely possible to become conscious of them”
as representations. To say they are correlates means that the ideas
mutually imply one another: to be aware of an object of my represen-
tation is (at least implicitly) to distinguish objective from subjective
states, and vice versa. This point becomes prominent in the B edition
deduction.
The ¬nal step of the argument identi¬es the synthetic functions
required to produce the idea of objectivity with pure concepts. The
necessary unity essential to the idea of objectivity “is impossible if
the intuition could not have been produced through a function of
synthesis in accordance with a rule that makes the reproduction of
The Transcendental Deduction 115
the manifold necessary a priori” (A105). That is, the rules governing
the synthetic operations that produce the idea of an object in general
are contained in the categories. When we represent a triangle, for
example, the relations among the sides of the triangle must conform
to certain rules (e.g., that they enclose angles totaling 180—¦ ). These
rules governing the ways the manifold is connected “ the functions
of synthesis “ are contained in the concept of the triangle. Not until
A110“11 does Kant argue explicitly that these concepts must be pure or
a priori. Merely empirical concepts could not represent the necessity
and universality required for objectivity. Thus Kant concludes that the
categories “are fundamental concepts for thinking objects in general
for the appearances, and they therefore have a priori objective validity”
(A111). In sum, the categories contain the rules required to think the
data given in intuition as representing objects or objective states of
affairs. Consequently they apply necessarily to anything represented
as an object.
In section 3, from A115 to A119, Kant presents the same ideas again,
in an order closer to that of the B edition deduction. At A120 he then
states that he will demonstrate the relation between the categories
and appearances by starting from the opposite point, namely from the
empirical data. In what follows he rehearses the argument concerning
the threefold synthesis, from empirical unity to transcendental unity.
It is understandable if the reader feels that Kant is rehashing the same
material, without a clear sense of progress.
Although it foreshadows many of the ideas of the B edition deduc-
tion, the A edition version has several crucial defects. First, Kant
fails to establish the necessity of transcendental self-consciousness
for all thinking. Although awareness of objects requires a numeri-
cally identical consciousness, Kant does not explain the connection
to self-consciousness. Second, Kant does not support his claim that
this self-consciousness can occur only through synthetic acts. Finally,
the notion of judgment is completely lacking in the A edition discus-
sion. This is especially egregious, since Kant derived the pure con-
cepts in the Metaphysical Deduction from the forms of judgment,
and also claimed that the only function of the understanding is to
judge. We shall see how his strategy in the B edition addresses these
problems.
The Transcendental Deduction
116

3. t h e b ed it ion de d uc ti on

a. Preliminary remarks
Commentators generally agree that the B edition proof divides into
two parts, the ¬rst located in sections 15“20, and the second in sections
21“6. As stated in the title of section 20, the ¬rst part concludes that
“All sensible intuitions stand under the categories, as conditions under
which alone their manifold can come together in one consciousness”
(B143). Kant™s ¬nal conclusion, located at the end of section 26, is this:
“all synthesis, through which even perception itself becomes possible,
stands under the categories, and since experience is cognition through
connected perceptions, the categories are conditions of the possibility
of experience, and are thus valid a priori of all objects of experience”
(B161). The dif¬culty is explaining the relation of the two parts.
Dieter Henrich made the ¬rst plausible argument that the two
proofs are separate, yet both required to show that the categories are
necessary conditions for experience of objects given in intuition. In
the ¬rst step Kant assumes that the intuitions already “contain” unity,
and he argues that wherever there is unity, it must be thought by
means of the categories. But this does not yet guarantee that what-
ever we intuit will be subject to the categories. Kant needs the second
argument to bring spatiotemporal intuitions under the range of intu-
itions containing unity, to prove that whatever we intuit spatially and
temporally must thereby be thought by the categories.7
Henry Allison agrees that the two arguments are two steps in a
single proof, but disagrees about the relation between them.8 He
maintains that the two steps use different notions of an object, draw-
ing different conclusions about the categories. In the ¬rst step, Kant
argues that the categories necessarily apply to any object of judgment
for a discursive intelligence, one that thinks about objects given inde-
pendently in an “intuition in general.”9 The notion of the object here
7 Henrich, “The Proof-Structure of Kant™s Transcendental Deduction,” 642.
8 See chapter 7 of Kant™s Transcendental Idealism, 133“72. Allison criticizes Henrich™s interpre-
tation at 351n6.
9 Kant classi¬es intelligences into intuitive and discursive. An intuitive intellect can, through the
mere act of thinking, provide its own data for judgment (B135). Human intellect is discursive,
since the sensibility provides our data for thought. The term “intuition in general” refers to
any data given to a discursive intellect, regardless of its form.
The Transcendental Deduction 117
is the object of thought, denoted by the German Object. This step
attempts to demonstrate the objective validity of the categories, to
show that they are required for thinking about objects. The second
step argues that the categories apply necessarily to objects of expe-
rience, and thus have objective reality. The German word for object
here is Gegenstand, which denotes the object given in intuition. Only
in the second stage does Kant connect the categories to our form
of spatiotemporal intuition. In this discussion I shall follow Allison™s
interpretation, since it provides a more coherent reading of the text.

b. Stage one: sections 15“20
Section 15: general characterization of synthesis
Section 15 establishes a claim crucial to Kant™s theory of cognition,
that for a discursive intellect, the manifold of intuition is not given
as uni¬ed. Instead, (complex) representations are uni¬ed by means
of thinking. This act of combining is a spontaneous act of the under-
standing (B130). Kant calls it synthesis,
to draw attention to the fact that we can represent nothing as combined in
the object without having previously combined it ourselves, and that among
all representations combination is the only one that is not given through
objects but can be executed only by the subject itself, since it is an act of its
self-activity. (B130)
This is an important corrective to theories that overlook the role of
the understanding in unifying sense impressions. Because sensibility
is passive, it cannot combine the data given in intuition. Furthermore,
even sense impressions given as spatially or temporally contiguous are
not thereby uni¬ed into impressions of an object. Kant™s point is that
any combination recognized in a uni¬ed representation must be a
thought combination. This is true even of the pure forms of space and
time, which provide only a priori manifolds. This data can represent
one space and time only insofar as we think of it as belonging to
one space and time. At the end of this ¬rst paragraph Kant points
out that such combinatory synthetic acts are always presupposed by
analysis, acts which divide representations into parts. In order for us
to separate out the parts of a complex representation, they must ¬rst
have been combined. He will say more about this in section 16.
The Transcendental Deduction
118
The ¬nal point of section 15 concerns the unity of consciousness
required for synthetic acts of the understanding. Uni¬ed representa-
tions are those in which one is conscious both of the manifold parts
and also of the their interconnection. In such a combination, the
unity is thought by means of a concept. (This is important since there
are forms of connection, such as association, which do not arise by
means of concepts.) At B131 Kant points out that conceptual unity
cannot result from the act of combining, since the former makes the
combinatory act possible. Moreover, the fundamental unity of con-
sciousness precedes even the category of unity correlated with the
quantitative form of judgment, since all use of concepts in judgment
presupposes unity of thought. Kant says this unity must be sought
“someplace higher, namely in that which itself contains the ground
of the unity of different concepts in judgments, and hence of the
possibility of the understanding, even in its logical use” (B131). This
is Kant™s beginning point for his deduction in section 16.

Section 16: the original synthetic unity of apperception
The deduction of¬cially begins here, where the ¬rst sentence states
the ¬rst premise: “The I think must be able to accompany all my
representations; for otherwise something would be represented in me
that could not be thought at all, which is as much as to say that the
representation would either be impossible or else at least would be
nothing for me” (B131“2). This sentence includes several claims. First,
it is necessarily true of me, as a discursive intellect, that I can attach
the “I think” to any state that represents something to me. Kant is
not saying that in fact I always do this, only that it must be possible
for me. If I could not, he says, the representation would be “nothing
for me.” This means that states that represent something to me have
two features: ¬rst, I can recognize them as my own states; and second,
they have an intentional object of which I can be conscious. In other
words, states that are representations for me have both subjective and
objective aspects, which I can distinguish.10
Now the act of attaching the “I think” is the act of apperception
or self-consciousness. Insofar as I recognize a representation as mine, I
10 Allison says that the claim that such representations would be “nothing for me” does not
imply that they would not exist, but rather that I would not be conscious of them as my
representations. He believes Kant thinks we could have unconscious representations. See
Kant™s Transcendental Idealism, 137 and 353n18.
The Transcendental Deduction 119
ascribe it to myself, and thus must be conscious of myself as the sub-
ject of the state. As in the A edition, Kant calls this self-consciousness
the transcendental unity of apperception (t.u.a.), and he distinguishes
it from empirical self-consciousness. The t.u.a. is original because it
is not derived from any other representation, but is a primitive fact of
consciousness. It is pure rather than empirical because it has no dis-
tinguishing content of its own. Kant says it is in all consciousness “one
and the same, [and] cannot be accompanied by any further represen-
tation” (B132). Recall that empirical self-consciousness is awareness of
oneself as a particular subject. In addition to the “I think” it includes
the speci¬c content of inner sense. By contrast, “through the I, as a
simple representation, nothing manifold is given” (B135). In a later
section in the Dialectic, Kant calls the I of apperception “a single
thing that cannot be resolved into a plurality of subjects, and hence a
logically simple subject” (B407). Thus the t.u.a. is the bare thought
of the numerical identity of the self as the thinking subject.
In several passages Kant says this ¬rst premise is analytic: “this
principle of the necessary unity of apperception is, to be sure, itself
identical, thus an analytic proposition” (B135; also B138 and B407).
Now it is important to understand exactly what claim is analytic,
since from this premise Kant wants to derive the synthetic conclu-
sion that the categories apply necessarily to any object of thought.
The key is the scope of the statement, “The I think must be able to
accompany all my representations.” Kant is claiming not that this
statement is analytically true of all conscious beings, but rather that
it is analytically true for any consciousness that can recognize its own
representations. There are two relevant contrasts here. At B138“9 Kant
distinguishes human consciousness from an intuitive intellect which
generates its own manifold through its thinking. For such an intel-
lect, there is no distinction between subjective and objective states,
and so such an intellect would not be capable of this original self-
consciousness. The second contrast is with animal perceivers, which
lack intellectual capacities altogether and thus cannot recognize their
representations as such. They might have a uni¬ed consciousness,
but they would lack a uni¬ed self-consciousness. In other words, it is
a brute fact (and therefore a synthetic truth) that human perceivers
are discursive intellects who can recognize their own representations.
But it is an analytic truth that any consciousness that can recognize
its own representations can attach the “I think” to any of them.
The Transcendental Deduction
120
The second premise occurs at B133: “this thoroughgoing identity of
the apperception of a manifold given in intuition contains a synthesis
of the representations, and is possible only through the conscious-
ness of this synthesis.” To say that the t.u.a. “contains” a synthesis
means that in order to think the identity of the “I” one must con-
nect a manifold of representations in thought. To recognize that it
is the same “I” in “I think a” and in “I think b” one must connect
the thoughts so that one thinks “I think a + b.” Kant™s strong claim
here is that performing such a synthesis is a necessary condition for
recognizing the identity of self-consciousness. In thinking one™s self-
identity by ascribing representations to oneself, one both connects
the representations and (at least implicitly) recognizes this connec-
tion. At B133“4 Kant repeats his A edition claim that consciousness
of one™s numerical identity cannot be derived from empirical self-
consciousness. Instead, to recognize the empirical self requires one to
unite the empirical manifold in a numerically identical consciousness.
Thus empirical self-consciousness presupposes the t.u.a.
The ¬nal point in section 16 concerns Kant™s claim at B133“4 that
the apperception, like concepts, has both an analytical and a syn-
thetic unity. This is easier to grasp if we begin with his discussion
of concepts in the footnote. Here Kant argues that although both
kinds of unity are essential to general representations, the synthetic
unity provided by concepts is more fundamental than their analytical
unity. The analytical unity of a concept is the unity it provides as a
common characteristic of things. In thinking the concept “solidity,”
we recognize it as a feature that belongs to potentially many things. In
representing a feature common to its instances, the concept provides
analytic unity. But these instances are complex things, which have
many different properties. For example, they must also be spatially
extended and have other physical properties. Kant says the objects
analytically united under the concept “also have something different
in themselves” (B134). And he concludes: “therefore only by means
of an antecedently conceived possible synthetic unity can I represent
to myself the analytical unity.” That is, to represent the objects that
possess common characteristics, one must ¬rst represent the unity
of the complex object. In its synthetic function, a concept uni¬es
diverse features of the object. For example, the concept “chair” uni-
¬es the diverse properties such as shape, size, weight, and location
that belong to a chair. Kant™s point is that although concepts contain
The Transcendental Deduction 121
both kinds of unity, synthetic unity is more fundamental because it
is presupposed by analytical unity.
At B133“4 he makes the same claim about the t.u.a.: “the analyt-
ical unity of apperception is only possible under the presupposition
of some synthetic one.” In other words, the “I think” as attached to
each representation functions on one hand as a common character-
istic. Abstracted from all content of representation, it has an analytic
unity. But since this identical self-consciousness requires a synthesis
of representations, the “I think” also produces a synthetic unity. In
this respect it functions as the form of any thought in which one uni-
¬es different representations. For this reason Kant calls it “the highest
point to which one must af¬x all use of the understanding . . . indeed
this faculty is the understanding itself” (B134n). In short, the t.u.a. is
the very basis, and thus the form, of all thinking.

Section 17: the relation between the t.u.a. and the notion of an object
In section 17 Kant establishes what Allison calls the “reciprocity the-
sis,” namely that the t.u.a. is both necessary and suf¬cient for repre-
senting objects.11 This is equivalent to showing both that whenever
one performs the “I think” one thereby represents an object (or objec-
tive state of affairs), and that whenever one represents an object one
thereby connects representations in the synthetic unity of appercep-
tion. It does not become clear until section 19 that this act is judgment.
Once we put these points together we can get a better idea of what
Kant means by the objective validity of representation.
Kant™s entire argument in section 17 is contained in the second
paragraph:
Understanding is, generally speaking, the faculty of cognitions. These con-
sist in the determinate relation of given representations to an object. An
object, however, is that in the concept of which the manifold of a given
intuition is united. Now, however, all uni¬cation of representations requires
unity of consciousness in the synthesis of them. Consequently the unity
of consciousness is that which alone constitutes the relation of represen-
tations to an object, thus their objective validity, and consequently is that
which makes them into cognitions and on which even the possibility of the
understanding rests. (B137)
Let us take this argument point by point.
11 See Kant™s Transcendental Idealism, 144“8.
The Transcendental Deduction
122
First Kant describes the understanding as the faculty of cogni-
tion, which implies that the mere data given in intuition are not in
themselves cognitions. Next he de¬nes a cognition as a “determinate
relation of given representation to an object,” which simply means a
representation of a determinate object. His point is that the function
of the understanding is to know objects. Implicit is the idea that at
the ¬rst order, the representations are those given in the manifold
of intuition. Next comes the key to this section, Kant™s de¬nition of
an object as “that in the concept of which the manifold of a given
intuition is united.” This tortured sentence in effect de¬nes an object
as whatever is thought as a uni¬ed manifold by means of a concept.
The object here is the object of thought; the de¬nition establishes
that it must be a complex whose parts (the manifold) are uni¬ed
by a concept. Drawing on section 15, the next sentence states that
all uni¬ed representations contain consciousness of unity. From sec-
tion 16 we know that consciousness of unity is based on the t.u.a.
Thus, Kant concludes, it is the t.u.a. that confers objective valid-
ity on representations. That is, the act of bringing representations
to the “I think” is necessary and suf¬cient for making them into
representations of an object. Put less technically, Kant has argued
that when one uni¬es some manifold by means of a concept, one
thereby renders the manifold thinkable as an object or gives it objective
validity.
At B137“8 Kant emphasizes that the mere manifold given in intu-
ition does not by itself represent an object, but provides only the data
for cognition: “the mere form of outer sensible intuition, space, is not
yet cognition at all; it only gives the manifold of intuition a priori for
a possible cognition.” To cognize some spatial region requires con-
necting the spatial manifold in some determinate way by means of a
concept. Thus to represent a line in space one must delineate the part
of space making up the line by means of the concept of a line. Kant
concludes that this consciousness of synthetic unity is required of all
cognitions, and thus applies to any manifold given in intuition “in
order to become an object for me.” It is important to notice the subtle
shift in this last sentence, which claims that the object is the (mani-
fold of ) intuition itself. In other words, this analysis has taken place
on the second-order level, where the objects (of thought) are one™s
representations (the manifold given to one in intuition). At the end
The Transcendental Deduction 123
of this chapter we shall see the signi¬cance of this aspect for Kant™s
response to skepticism.
For now, let us summarize the steps of the argument in sections 16
and 17:
1. It is necessarily true of humans as discursive intellects that they can
attach the “I think” to any of their representations, and, by doing
so, express the numerical identity of self-consciousness.
2. Attaching the “I think” is possible only insofar as one connects
one™s self-ascribed representations by means of synthetic acts.
3. Any synthetic unity of representations requires uni¬cation under
a concept.
4. Any manifold uni¬ed under a concept counts as a thought of an
object.
5. Therefore, thinking of an object is necessary for the t.u.a.
6. Therefore, the t.u.a. is a suf¬cient condition for representing an
object.

Section 18: objective vs. subjective unity
Here Kant distinguishes an objectively valid unity of representations
from a unity that has only subjective validity, as a way to introduce
the notion of judgment in section 19. The ¬rst kind is the unity con-
tained in the thought of an object; the second kind is characteristic
of a mere association of representations. Unfortunately Kant con-
fuses two different notions of subjective validity. He begins section
18 by contrasting the objective unity of the t.u.a. with “the subjec-
tive unity of consciousness, which is a determination of inner sense”
(B139). By the latter he means a mere association of representations in
consciousness: “One person combines the representation of a certain
word with one thing, another with something else; and the unity of
consciousness in that which is empirical is not, with regard to that
which is given, necessarily and universally valid” (B140).12 The point
is that although a mere association of representations has a kind of
unity in consciousness, it is not a thought unity. Association occurs
12 The process of association has historical signi¬cance because Hume took it to be the source
of all metaphysical concepts, including personal identity. But Kant takes association as the
paradigm example of a subjective unity since it connects representations in time without
thereby representing an object.
The Transcendental Deduction
124
when one representation immediately triggers another in time. It
depends on memory and psychological processes arising from what
Hume called the “customary conjunction” of representations. For
this reason Kant assigns it to the reproductive imagination at B141.
To say that an association is only subjectively valid means that it does
not produce a representation of an object. (It is also subjective in
the secondary sense that the association of representations depends
on contingent facts about the subject.) When Kant calls this type of
connection “a determination of inner sense” he means that it represents
a temporal ordering of the actual contents of consciousness. But the
connection is not conceptual; a mere association does not represent
an object, and hence lacks objective validity. Associated perceptions
are united temporally in consciousness, but do not produce a unity
of self-consciousness. Now one can of course take an association as
an object of thought by re¬‚ecting on it. In recognizing the sequence
as one in which one representation triggers another, one thereby con-
fers objective unity on it. This is equivalent to taking a unity in
consciousness as a unity for consciousness. Clearly, however, the abil-
ity to associate representations does not entail the ability to represent
the association as such. Kant thinks that animals possess the former
ability but lack the intellectual capacities for the latter.
Unfortunately, in this passage Kant confuses the subjectivity of an
association of perceptions with that of the empirical unity of apper-
ception. The latter, as we have seen, is awareness of oneself as a
particular subject. Empirical self-consciousness includes the content
of inner sense, but is not a mere association of perceptions, since
it represents the self as an object. Although empirical apperception
varies in content by subject, and thus is subjective in the secondary
sense, it nevertheless contains an objective unity of representations.
Thus Kant is mistaken to use empirical apperception to exemplify a
non-objective unity, which is the kind of subjectivity relevant to the
deduction here.

Section 19: objective unity and judgment
In section 19 Kant argues that representing an object is equivalent
to judging. He begins by complaining that the standard de¬nition
of a judgment as a relation between two concepts fails to specify the
nature of the relation. At B141“2 he says that in judgment one brings
The Transcendental Deduction 125
a manifold to the objective unity of consciousness. In the simplest
case of a categorical judgment, this objective relation is represented
by the copula “is” connecting the subject- and predicate-concepts.13
Now to say that judgment possesses a necessary unity is not to deny
that there are empirical or contingent judgments. The objective unity
of the judgment, even if empirical, resides in the fact that judgments
represent assertible thoughts about objects or objective states of affairs.
Even if it is only a contingent truth that my cat is orange, the judgment
“Buroker™s cat is orange” uni¬es diverse representations to produce
an assertible claim about an object. Unfortunately Kant™s examples at
the end of the section obscure this point, since he tries to express an
association of perceptions by the conditional judgment “If I carry a
body, I feel a pressure of weight.” By his own argument, however, once
one judges an association, one has thereby uni¬ed the representations
in the objective unity of apperception.14 As Allison points out, Kant™s
theory of synthesis entails that all judgments confer objective validity
on representations, even if the objects of judgment are “subjective”
states.
This step clari¬es the notion of objective validity, for unlike asso-
ciations of representations, judgments are true or false. For a repre-
sentation to have objective validity is for it to be capable of having
a truth value. What Kant has shown, then, is that subjects who can
recognize their own representations must be able to ascribe them to
themselves by the “I think.” This act is synthesis, which connects
a given manifold of representations in the (objective) unity of self-
consciousness. But synthesis is equivalent to judging; in judging one
conceives a manifold as related in a way that can be asserted to obtain.
Since assertions are true or false, Kant has argued that the t.u.a. is
both necessary and suf¬cient for producing representations that have
objective validity, that are assertible. The objects here are objects of
13 For hypothetical and disjunctive judgments the objective unity of two judgments is effected
by the logical operators “if-then” and “or.”
14 This is reminiscent of Kant™s discussion of judgments of perception and judgments of
experience in the Prolegomena. The former merely report perceptions, whereas the latter
make objective claims. Kant™s examples of the ¬rst are “The room is warm, sugar sweet,
wormwood nasty” (see section 19). In this case he claims two sensations are referred to
the same subject, but not to an object. Only when a judgment makes a claim about an
object does it have objective validity. This view apparently contradicts Kant™s position in
the Critique that every judgment contains objective unity. Allison explains this and other
dif¬culties with the Prolegomena account in Kant™s Transcendental Idealism, 149“52. I am also
indebted to his discussion at 152“8.
The Transcendental Deduction
126
judgment or thought. There is as yet no reference to spatiotemporal
objects of human intuition.

Section 20: the categories necessarily apply to all objects of judgment
The ¬nal step of this ¬rst stage relates judgment to the categories.
Kant does this in the last three sentences of section 20:
Therefore all manifold, insofar as it is given in one empirical intuition,
is determined in regard to one of the logical functions for judgment, by
means of which, namely, it is brought to a consciousness in general. But
now 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 (§13). Thus the manifold in a given intuition also necessarily stands
under categories. (B143)
Section 19 shows that insofar as a manifold is ascribed to oneself in
the t.u.a., it must be judged. To judge a manifold is to think it as
an object under the logical forms of judgment. As the Metaphysical
Deduction shows, the logical forms of judgment are “functions of
synthesis,” or the particular ways one connects the representations
making up a judgment in consciousness. Here Kant points out that
the categories are these same logical functions in their real use. They
are the pure concepts of the understanding as applied to whatever
objects one judges.
To make the point clearer, consider that whenever I take several
representations to be my representations, I judge that they belong to
me. In so judging them I make them objects of thought. To judge
them to belong to me requires conceiving of them in ways suitable
for judging under the logical forms of judgment. For example, to
judge them under the quanti¬cational forms presupposes that I am
able to identify and individuate them. This requires conceiving them
under the concepts of unity, plurality, and totality. Thus I can make
judgments about one representation, some representations, and all my
representations. The same would presumably be true for the categories
correlated with the logical forms of quality, relation, and modality.
There are two further points to mention here. First, Kant™s refer-
ence to empirical intuition implies only that the manifold is given
independently of the understanding, regardless of the forms of intu-
ition. When the objects of thought just are one™s representations, of
The Transcendental Deduction 127
course, the manifold is that given in inner sense. The second point
concerns Kant™s statement that the manifold must be determined by
one of the logical functions for judgment. This is a clear mistake. First,
Kant wants to argue that all the categories are necessary for judging
objects. Moreover, as I argued in chapter 4, the three forms under
each heading are interdependent. What Kant should say is that all
the categories apply necessarily to the objects of judgment.

c. Stage two: sections 21“6
Sections 21“3: preliminary remarks to the second stage
At B144 Kant summarizes the argument so far, pointing out that
it abstracts “from the way in which the manifold for an empirical
intuition is given,” attending only to the unity produced in intuition
by means of the category. The second paragraph speci¬es that the
argument assumes only that the manifold of intuition is given inde-
pendently of the understanding. Thus the ¬rst part of the deduction
establishes that any discursive intelligence, regardless of its particu-
lar mode of intuition, must employ categories to think about objects.
The second stage of the deduction, by contrast, concerns the necessity
of the categories for experiencing objects given in our spatiotempo-
ral forms of intuition. Thus it attempts to show that the categories
apply necessarily to all objects of human sensibility. To do this Kant
will have to show that the same functions of synthesis employed in
thinking about objects are also required to perceive objects in space
and time. He makes this point at the beginning of section 26:
Now the possibility of cognizing a priori through categories whatever objects
may come before our senses . . . is to be explained. For if the categories did not
serve in this way, it would not become clear why everything that may ever
come before our senses must stand under the laws that arise a priori from
the understanding alone. (B159“60)
Proving the necessity of the categories for cognition of objective states
of affairs in our space and time involves demonstrating their objective
reality.
Sections 22 and 23 merely reiterate these points, emphasizing the
role of intuition in distinguishing between a thought and a cognition
of an object. A concept to which no corresponding intuition could be
The Transcendental Deduction
128
given “would be a thought as far as its form is concerned,” but without
an object (Gegenstand), could not serve as a cognition (B146). Kant
repeats the point at B150“1 in section 24. Only when given reference to
intuition do the categories “acquire objective reality, i.e., application
to objects that can be given to us in intuition” (B150“1). The second
stage of the deduction, then, has to show that objects experienced in
space and time must be thought by means of the categories.

Section 24: the transcendental synthesis of imagination
This section contains the ¬rst part of the second stage; section 26
completes the proof. Here Kant argues that the categories are required
to represent one time in intuition, thus linking the categories to the
perception of time. (Although Kant does not emphasize it here, the
same process is required to represent one space.) The second step then
links the categories to empirical intuition. The argument in section 24
is hard to make out, however, because it is embedded in a discussion
of the “paradox” of self-representation, which is actually irrelevant to
the deduction. I shall discuss ¬rst the argument proper and then the
paradox as explained in sections 24 and 25.
The signi¬cance of time becomes clear if we see this stage as a
continuation of the ¬rst stage. There Kant argued that the categories
necessarily apply to objects of thought, which objects were in fact
one™s own representations. For humans, the form by which we intuit
our own representations in inner sense is time. From the Aesthetic
we know that there is only one time, and that all our representations
occupy determinate positions in this uni¬ed time. Thus Kant will
show in section 24 that the synthetic processes by which we locate
our representations in one time are governed by the categories.
Kant assigns the transcendental synthesis of the a priori spatiotemp-
oral manifold, called the ¬gurative synthesis, to the productive
imagination. At B151 he de¬nes the imagination as “the faculty for
representing an object even without its presence in intuition.” We
usually think of the imagination as the source of sensory images of
objects that are not present or are even nonexistent. Here, however,
Kant points out that the imagination plays a more basic role in expe-
rience, namely unifying the pure manifold into a representation of
one global time. This act is transcendental because it is a necessary
condition for representing anything as existing in time. Now although
The Transcendental Deduction 129
we do not perceive global time in its entirety, in perceiving determi-
nate times, we think of each duration as bounded by past and future
times, and thus as a ¬nite portion of in¬nite time. These past and
future times are of course not actually present in the perception; our
awareness of them is a construction of the imagination. Similarly,
our perceptions of ¬nite regions of space include the recognition that
these regions are embedded in an in¬nite space.
At B152 Kant attributes this ¬gurative synthesis to the productive
rather than to the reproductive imagination. Whereas the latter merely
“calls up” (and associates) previously apprehended representations,
the former produces a new representation. The ¬gurative synthesis
differs from the purely intellectual synthesis discussed in the ¬rst stage
because it issues in an intuition. Intuitions of determinate positions
and regions of one uni¬ed time require that the form of inner sense
be linked to the t.u.a. and the categories. So there must be a faculty
that mediates between the sensibility and the understanding. Now
Kant™s own descriptions of the imagination are fairly confusing. At
B151 he says the imagination belongs to sensibility; but at B152 and
B153 he says that its synthesis is an effect of the understanding on
sensibility. For several reasons it is most consistent with his theory
of faculties to treat the imagination as a separate power, mediating
between the understanding and the sensibility. At B154“5 Kant uses
examples of drawing ¬gures in space to illustrate the transcendental
synthesis of imagination. This is appropriate for two reasons: ¬rst, we
can produce an image of time only through spatial representation;
and second, the same imaginative processes are required to represent
determinate spatial regions.
In effect Kant uses the theory that time is the form of inner sense
to link the forms of intuition to the t.u.a. From the ¬rst stage of the
deduction we know that any manifold brought to the t.u.a. must con-
form to the categories. Section 24 establishes that the a priori manifold
given in inner sense is uni¬ed by the transcendental synthesis of the
imagination. Thus the imaginative synthesis of the temporal manifold
is also subject to the rules expressed in the categories. Alternatively,
from the standpoint of judgment, to recognize each ¬nite region of
time is to judge that it is part of the all-encompassing time. Thus the
temporal manifold must be thought by means of the categories. In
this way the pure manifold is “objecti¬ed,” or made a (formal) object
of thought.
The Transcendental Deduction
130
Section 26: link between categories and empirical intuition
In the ¬nal step, Kant needs to demonstrate the necessity of the
categories for “whatever objects may come before our senses, not
as far as the form of their intuition but rather as far as the laws
of their combination are concerned” (B159“60). In other words, he
must demonstrate that anything given through sensation “must stand
under the laws that arise a priori from the understanding alone”
(B160). His strategy is to link the categories to the synthetic processes
required to unify the empirical manifold, that is, the sensible qualities
constituting the matter of appearance. Kant calls this the synthesis
of apprehension, which results in “the composition of the manifold
in an empirical intuition, through which perception, i.e., empirical
consciousness of it (as appearance), becomes possible” (B160). In
Hume™s terms these are the processes by which one “bundles” sense
impressions. This was the primary focus of Kant™s analysis in the A
edition.
The key premise is that the synthetic operations performed on the
empirical manifold must conform to the operations unifying the a
priori manifold in the ¬gurative synthesis discussed in section 24.
There Kant argued that “space and time are represented a priori not
merely as forms of sensible intuition, but also as intuitions them-
selves (which contain a manifold), and thus with the determination
of the unity of this manifold in them” (B160“1). In a footnote he
distinguishes the form of intuition, the uncombined manifold given
a priori, from the formal intuition, the manifold uni¬ed by the tran-
scendental synthesis of imagination. The second half of this footnote
appears to contradict itself by attributing the unity of space and time
both to sensibility and to the understanding. Kant™s point, however, is
that the manifold as given in sensibility makes it possible to experience
one space and one time; synthesis by the understanding is required
to experience a uni¬ed space and time. Thus everything appearing in
intuition is subject to the synthetic functions that produce unity in
our experiences of space and time, namely the categories:

Consequently all synthesis, through which even perception itself becomes
possible, stands under the categories, and since experience is cognition
through connected perceptions, the categories are conditions of the possibil-
ity of experience, and are thus also valid a priori of all objects of experience.
(B161)
The Transcendental Deduction 131
In other words, the three types of synthesis Kant discusses in the Tran-
scendental Deduction are different aspects of the synthesis required
to perceive objects of spatiotemporal intuition. What Kant has shown
at each step is that only the categories can provide rules for unifying
representations brought to the t.u.a. His deduction proceeds from
the unity involved in the thought of an object (the intellectual syn-
thesis), to the unity experienced in the formal intuitions of space and
time (the ¬gurative synthesis), and ¬nally to the unity experienced in
objects perceived in space and time (the synthesis of apprehension).
It is important to recognize that these three syntheses are really three
aspects of one process that takes place in sense perception.
This is the point of Kant™s examples of perceiving a house and the
freezing of water at B162“3. When I perceive a house, my perception
of it as a determinate (measurable) object is constrained by the rules
governing the processes by which I “carve out” the region of space it
occupies. Similarly, my perception of the freezing of water as the ¬‚uid
state followed by the solid state must also conform to the rules by
which successive times are determined. Kant details these arguments
in the Axioms of Intuition and the Analogies of Experience, in justi-
fying the pure principles corresponding to the categories. These two
examples capture the two aspects of Kant™s conclusion, namely that
the categories provide rules for unifying the manifold into perceptions
of objects, as well as for connecting these perceptions in experience
of an objective order of events.

Sections 24“5: the paradox of self-knowledge
To complete this discussion, let us look at Kant™s view of self-
knowledge in sections 24 and 25. At B152“3 he describes the “para-
dox” of self-knowledge as following from the Aesthetic doctrine that
in inner sense we are presented to ourselves “only as we appear to
ourselves, not as we are in ourselves, since we intuit ourselves only as
we are internally affected, which seems to be contradictory, since we
would have to relate to ourselves passively.” The paradox follows from
transcendental idealism. Because space and time are merely subjec-
tive forms of sensibility, all objects intuited in space and time are only
appearances, and not things in themselves. This applies equally to
the empirical self, given in inner sense. Accordingly, we can no more
intuit the self in itself than we do physical objects in themselves. In
The Transcendental Deduction
132
the Analytic, however, Kant has shown that the “I” that thinks is
active and spontaneous. Judging is an activity consisting of synthetic
operations the “I” performs on the manifold given in intuition. So it
seems paradoxical to claim both that the “I” must be active and that
it can know itself only as it passively appears to itself.
Kant™s solution is to deny both that the “I think” is a cognition
of the self, and that we can cognize the thinking self. In transcen-
dental self-consciousness, Kant says, “I am conscious of myself not
as I appear to myself, nor as I am in myself, but only that I am. This
representation is a thinking, not an intuiting” (B157). Self-awareness in
the t.u.a. is not a cognition of the self as an object, but a merely formal
representation of one™s existence as thinking. (This is why Kant dis-
agrees with Descartes™s view that the “I” of the cogito must be a mental
substance.) This self-awareness is devoid of the intuition required to
distinguish oneself from other objects and thus to represent oneself
as a particular object. In his footnote at B157 Kant says, “The I think
expresses the act of determining my existence. The existence is thereby
already given, but the way in which I am to determine it, i.e., the
manifold that I am to posit in myself as belonging to it, is not yet
thereby given.” And at B158n he denies that we can intuit the activity
of thinking: “Now I do not have yet another self-intuition, which
would give the determining in me, of the spontaneity of which alone
I am conscious . . . thus I cannot determine my existence as that of
a self-active being, rather I merely represent the spontaneity of my
thought.” Thus Kant dispels the paradox by denying that the t.u.a.
is a cognition of the thinking self. It is only a formal awareness of the
activity of thinking, identical for all discursive intelligences. Since the
sensibility yields only appearances, we can know ourselves only as we
appear to ourselves, not as things in themselves. Although this too
seems paradoxical, the “I” of “I think” is neither an appearance nor a
thing in itself, but a condition of all thought.15

4. ka n t a nd inn ate i de a s: a new m odel
of t h e u nd e rs ta n di n g
When we compare Kant™s account of categories to previous theo-
ries, it is tempting to classify his view as a theory of innate ideas.
15 See chapter 12 of Allison, Kant™s Transcendental Idealism for a discussion of dif¬culties in the
notions of inner sense and apperception.
The Transcendental Deduction 133
After all, Kant agrees with the rationalists that the mind produces
representations whose content is not derived from sense experience.
Moreover, just as they believed that innate principles represented
necessary truths, Kant argues that the necessity of metaphysical and
mathematical knowledge can be traced to a priori concepts and intu-
itions. So readers are often surprised to ¬nd Kant explicitly rejecting
innate ideas in favor of a theory of “original acquisition” in his later
works. One famous passage occurs in the 1790 essay On a Discovery
whereby Any New Critique of Pure Reason Is To Be Made Super¬‚uous
by an Older One:
The Critique admits absolutely no implanted or innate representations. One
and all, whether they belong to intuition or to concepts of the understanding,
it considers them as acquired. But there is also an original acquisition . . .
According to the Critique, these are, in the ¬rst place, the form of things
in space and time, second, the synthetic unity of the manifold in concepts;
for neither of these does our cognitive faculty get from the objects as given
therein in-themselves, rather it brings them about, a priori, out of itself.
There must indeed be a ground for it in the subject, however, which makes
it possible that these representations can arise in this and no other manner,
and be related to objects which are not yet given, and this ground at least is
innate.16
To understand Kant™s position, we should begin with the claims char-
acteristic of innate or nativist theories of knowledge. As Falkenstein
points out, nativist theories deny one or both of two views main-
tained by empiricists: ¬rst, that all the original input to the mind is
derived from experience, and second, that the processes performed on
the original input result from past experience.17 Innate ideas philoso-
phers maintain that the mind contains original input and thus deny
the ¬rst view. Innate mechanisms philosophers claim that the mind
contains certain inborn processing mechanisms. The theory of innate
ideas typically includes these four claims:
1. The mind is the source of “innate” original input.
2. This original input can be recognized independently of sense expe-
rience.
3. The original input is the source of (innate) principles, which are
necessarily true.
4. These principles give us knowledge of things in themselves.
16 17
Theoretical Philosophy after 1781, 312. See Kant™s Intuitionism, 6“12, 91“6.
The Transcendental Deduction
134
Specifying these four theses allows us to contrast Kant™s theory with
the theory of innate ideas. Regarding both pure intuition and the
categories, Kant accepts 1 and 3, and rejects 2 and 4. As for 1, Kant
believes the mind “contains” innate input in the sense that the innate
capacities of sensing and thinking are the source of original represen-
tations. His view that no representations occur prior to experience,
however, commits him to rejecting 2. Kant also accepts 3, since one
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
experience to these principles. The understanding is the faculty of
concepts, and concepts are rules describing the nature of objects.
Even empirical laws of nature, although discovered a posteriori, express
necessary connections between features of objects. This necessity must
be grounded in principles governing the synthesis of all data given in
intuition. Thus pure principles are higher-order principles that govern
the application of speci¬c empirical concepts and laws to objects of
experience.
Following his distinction between mathematical and dynamical
categories in the Metaphysical Deduction, Kant distinguishes math-
ematical from dynamical principles. As we saw in chapter 4, at
B110 Kant labels the categories of quantity and quality mathematical
because they govern the operations that identify individual objects
and their properties in the data of intuition. The relational and modal
Schematism, Analytic of Principles I 145
categories are dynamical because they govern the relations of objects
to one another and to the subject. Kant now applies this distinction
to the principles. At A160/B199 he explains that mathematical princi-
ples pertain “merely to the intuition” of objects, whereas dynamical
principles pertain “to the existence of an appearance in general.” At
A178/B221 Kant also labels these constitutive vs. regulative principles.
In consequence, mathematical and dynamical principles differ in
their manner of evidence. The former are “unconditionally necessary”
and allow of intuitive certainty. By contrast, dynamical principles are
necessary “only under the condition of empirical thinking in an expe-
rience.” Therefore they lack “the immediate evidence that is character-
istic of the former” (A160/B199“200). As the Schematism points out,
the quantitative and qualitative features of objects governed by the
mathematical principles are exhibited in intuition. This is required
to intuit spatiotemporal objects at all. But the objective temporal
relations between states of affairs, and their relations to thinkers, are
merely thought. At A178“9/B221“2 Kant connects this point with the
fact that only the intuitions of objects, and not their existence, can be
constructed. That is, in intuition we are given a spatiotemporal array
to be discriminated into individual states of affairs, but we are not
given objective temporal positions and relations. Moreover, having
intuited an event, we can infer that it follows necessarily from some
prior state, but we cannot identify that state a priori. Now we turn
to the arguments for the mathematical principles in the Axioms of
Intuition and the Anticipations of Perception.

3 . th e a xioms of in tu i ti on
The synthetic a priori principles of quantity and quality govern the
mere intuition of objective states of affairs. The Axioms of Intu-
ition concern the synthesis of formal (spatiotemporal) properties;
they specify that to experience determinate objects, they must have
extensively measurable properties. The Anticipations of Perception
apply to the synthesis of the matter of intuition, the sensations corre-
lated with real properties of objects. They state that both sensations
and the properties corresponding to them must have some degree
of intensity. Although Kant refers to Axioms and Anticipations in
the plural, in fact there is only one principle for each heading. This
Schematism, Analytic of Principles I
146
is because the notions of extensive and intensive measurement each
incorporate all three categories under their respective headings.
Kant expresses the principle of the Axioms differently in the A
and B editions, but the point is the same.12 The A edition says, “All
appearances are, as regards their intuition, extensive magnitudes”
(A161). The B edition reads, “All intuitions are extensive magni-
tudes” (B201). Kant™s point is that appearances must have extensively
measurable spatiotemporal properties to be perceived as individual
objects or states of affairs. Thus the Axioms (and the Anticipations)
attempt to justify the application of pure mathematics to empiri-
cal objects. In the paragraph preceding the Axioms he explains that
these pure principles are not themselves mathematical principles, but
only principles “through which the former principles all acquire their
possibility” (A162/B202). This also explains the title “Axioms of Intu-
ition.” For although the Axioms are not themselves mathematical
axioms, they establish the validity of mathematical axioms for empir-
ical objects.13
The B edition contains a new argument in the ¬rst paragraph; the
A edition argument then follows in the second paragraph. Only the B
edition version refers to the schema of number, while the earlier ver-
sion focuses instead on the concept of extensive measurement. In both
cases, however, Kant argues that since the synthesis of space and time
underlies the synthesis of intuitions of objects in space and time, the
mathematical procedures governing the former must also apply to the
latter. The B edition argument explains that the synthetic processes
for representing determinate spaces and times require us to combine
the homogeneous spatiotemporal manifold into uni¬ed wholes. The
concepts governing this synthesis are the arithmetical concepts of
number. In other words, to perceive distinct empirical objects occu-
pying determinate spatiotemporal positions, the intuitions of these
objects must be extensively measurable. At B203 Kant concludes:
“appearances are all magnitudes, and indeed extensive magnitudes,
since as intuitions in space or time they must be represented through

12 I am indebted to Paton™s discussion, Kant™s Metaphysic of Experience, at 2:111“33.
13 Kant gives as axioms of geometry “space has only three dimensions” (B41), and “between
two points only one straight line is possible; two straight lines do not enclose a space, etc”
(A163/B204). For time: “It has only one dimension; different times are not simultaneous,
but successive” (B47).
Schematism, Analytic of Principles I 147
the same synthesis as that through which space and time in general are
determined.” As H. J. Paton points out, this implies that intuitions are
measurable as extensive quantities only insofar as they are intuitions
of objects. Dream objects and other “pseudo-objects of our imagi-
nation” cannot be measured since they do not occupy determinate
locations in objective space-time.14
The earlier version analyzes the notion of extensive measurement
and shows how it applies to space and time. Kant begins by de¬ning
an extensive magnitude as one in which the representation of the
parts precedes and makes possible the representation of the whole.
The key to the notion of extensive measurement is the successive addi-
tion of parts to generate a whole. When one draws a line, for example,
one begins at some point in space and then generates its parts suc-
cessively. Similarly, in thinking of determinate (measurable) times,
one thinks “the successive progress from one moment to another,”
whose addition produces a determinate duration (A163/B203). Exten-
sive magnitudes are those produced by combining or adding previ-
ously delineated parts. In a long footnote at B202, Kant labels a whole
of extensive parts an aggregate, and a whole of intensive parts a coali-
tion. The feature essential to extensive measurement is the addition
process; as we shall see below, degrees of intensity are not constructed
in the same way.
This helps clarify Kant™s conception of the connection between
the pure concepts of quantity and the schema of number. Recall from
chapter 4 that the quantitative logical concepts express the forms of
universal, particular, and singular judgments. The three categories
that result from schematizing these concepts are (respectively) unity,
plurality, and totality. When applied to objects, these categories make
it possible to measure spaces and times. For example, to measure the
length of an object or a time period, one must ¬rst select a unit of
measurement (e.g., a foot, a minute). Then one applies it repeatedly
as required to obtain the resulting magnitude, which is a totality
composed of a plurality of units. Extensive measurement consists in
adding the independently de¬ned units successively to arrive at the
resulting sum. This is the sense in which the representation of the parts
precedes the representation of the whole. Kant correlates the category

14 Paton, Kant™s Metaphysic of Experience, 2:120“1.
Schematism, Analytic of Principles I
148
of totality with the singular judgment (rather than the universal as one
might expect) because to discriminate or refer to individual objects
in space-time presupposes identifying de¬nite spatiotemporal regions
that are totalities measurable in terms of a plurality of units.15
The last two paragraphs of the section merely reiterate some views
of mathematics expressed earlier in the Introduction and the Aes-
thetic. Kant points out that arithmetic does not have general axioms
as such, but rather numerical formulae, which are singular judg-
ments although they are synthetic a priori. He also emphasizes the
main point of the argument, namely to demonstrate the objective
validity of procedures for measuring objects. If extensive measuring
processes did not apply to appearances, we could not determine their
spatiotemporal properties.
Many commentators criticize Kant for inconsistency, claiming that
the Axioms view that in measurement the parts precede the whole
contradicts his position in the Aesthetic, that space and time are given
as wholes that precede their parts.16 Following Paton, Melnick shows
that this charge is unfounded. In the Aesthetic, Kant is analyzing
the (pre-synthesized) data given in the pure forms of inner and outer
sense. As we saw in chapter 3, he holds that this indeterminate mani-
fold is given as a whole in which parts are discriminated by drawing
boundaries. By contrast, the argument in the Axioms addresses the
necessary conditions for constructing determinate regions out of this
pure manifold. As Melnick puts it, “The original representation of
space is required as a background for any construction in space and
thus cannot itself be constructed. Any spatial construction is in the
context of an original representation of unlimited space.” He points
out the role of the productive imagination in this process. What
grounds the application of geometry to spatial appearances is not
perception of shapes, but rules for constructing ¬gures: “Through
perception we become aware of how the shape of an object looks
(or feels), but not the rule of construction of the shape. This rule
(and what is necessarily bound up with this rule) is something that is

15 As Falkenstein points out, the natures of space and time constrain the construction of spatial
and temporal parts. The subject can choose the order of construction, but not the topology
or metric of space and time. See Kant™s Intuitionism, 244“7.
16 Three such commentators are Vaihinger, Kemp Smith, and Robert Wolff. See Melnick,
Kant™s Analogies of Experience, 18, for citations.
Schematism, Analytic of Principles I 149
brought to perception.”17 As Falkenstein says, the function of synthe-
sis is to turn a spatiotemporal array of representations (the data given
in intuition) into the representation of a spatiotemporal array.18 Far
from being incompatible, the doctrine of the Axioms completes the
analysis of spatial-temporal cognition begun in the Aesthetic.

4. th e a nticipations o f pe rce pt ion
This section is without doubt one of the most puzzling of the
Critique, for several reasons. First, Kant™s exposition does little to
explain the central notion of intensive magnitude. Second, the con-
clusion of the argument is not easy to identify, partly because of
changes in the two editions, and partly because of the terminology. In
particular, it is not clear whether the Anticipations principle concerns
sensations, or appearances, or both. Third, the arguments in both edi-
tions apparently depend on unjusti¬ed assumptions “ namely, that
sensations are caused by bodies outside us, and that physical interac-
tions between bodies are caused by intensive forces. In both cases the
argument would beg the question. And ¬nally, even if granted, these
assumptions are not suf¬ciently strong to demonstrate that either
sensations or properties of objects must be subject to a continuum
of degrees of intensity. No wonder most commentaries give the argu-
ment short shrift. Here I shall try to resolve some of these issues. As
we shall see, even by the most charitable reading, Kant cannot escape
some of these objections.19
One approach is to sketch the argument Kant ought to make at this
stage. Based on the Schematism and the Axioms, Kant needs to show
that only insofar as sensations are subject to procedures for measuring
intensive magnitudes can they be taken to give us information about
real properties of objects. Since the notion of an intensive magnitude
is the schema of the qualitative concepts, the argument will demon-
strate that these schematized concepts are necessary for “objectifying”
sensations. In short, the objectivity of the measuring procedure is
necessary to establish the objective reference of sensations. From this

17 See Melnick, Kant™s Analogies of Experience, 17“22.
18 Falkenstein, Kant™s Intuitionism, 249.
19 My interpretation has been greatly aided by discussions with Falkenstein.
Schematism, Analytic of Principles I
150
standpoint the argument parallels the Axioms argument, that the pro-
cedures of extensive measurement are necessary to confer objective
reference on the spatiotemporal features of appearances.
As with the Axioms, Kant revises the principle in the second edi-
tion, and adds a new proof at the beginning of the section. The A
edition principle states, “In all appearances the sensation, and the real,
which corresponds to it in the object (realitas phaenomenon), has an
intensive magnitude, i.e., a degree.” The B edition version reads:
“In all appearances the real, which is an object of the sensation,
has intensive magnitude, i.e., a degree” (A166/B207). Whereas the A
version claims that both sensations and real properties of objects must
have intensive magnitude, the B version appears to concern only the
objects of sensation. As suggested above, however, the point should
be that sensations must have a degree of intensity corresponding to an
intensive magnitude in the real properties of the object being sensed.
Thus the A edition version of the principle appears more precise.
Kant recognizes the paradox of an a priori principle “anticipating”
the nature of perception: “it seems strange to anticipate experience
precisely in what concerns its matter,” since this is given a posteriori
(A166“7). He does not directly answer the point until A175“6/B217“
18, where he distinguishes the quality of a sensation from its degree
of intensity. It is true that we cannot know a priori what qualities we
will sense; knowledge of sense qualities is contingent on the actual
experiences. What we can know a priori, however, is the “form” of
any sensation, namely that it must have a degree of intensity in order
to ¬ll space-time. As Paton puts it, the principle of the Anticipations
deals with the “form of the matter of appearance.”20
Before we examine the proofs we need to review some key terms,
previously discussed in chapter 3. Sensations are de¬ned in the Aes-
thetic as “the effect of an object on the capacity for representa-
tion, insofar as we are affected by it” (A19“20/B34). In chapter 3
we accepted Falkenstein™s view that sensations are modi¬cations of
the sense organs, and thus physical states. What Kant calls real of
sensation is the consciously represented sense quality, that which ¬lls
space and time. Color, sound, taste, odor, and warmth are examples of
sense qualities. Because qualities are the way we apprehend sensations,

20 See Kant™s Metaphysic of Experience, 2:134“5n5.
Schematism, Analytic of Principles I 151
there is a correspondence between the quality and the sensation. For
this reason Kant slides easily from talk about sensation to talk about
the quality of sensation, as at A175“6/B217“18.
Recall that appearance is the “undetermined object (Gegenstand)
of an empirical intuition” (A20/B34), where Gegenstand refers to an
existing thing. Thus appearances are whatever is given in intuition.
Now the term the real in appearance is ambiguous: it could refer
either to the represented quality or to the properties of objects. In the

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