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tinguished between pure and applied geometry. The uninterpreted
formal system of pure geometry becomes applied when the non-
logical terms are interpreted in terms of points, lines, and spaces.
Based on this distinction, the logical positivists denied that either
geometry is synthetic a priori. Pure mathematics could not be syn-
thetic because its statements do not have truth values; applied geom-
etry could not be a priori because only experience could determine
which postulates were true of physical space. In fact, relativity theory
favors Riemannian geometry, since it predicts that in a gravitational
¬eld the angles of a triangle composed of light rays will be greater
than two right angles, and that between any two points light rays
can travel along more than one “straight” path. Kant has commonly
been charged with failing to distinguish pure from applied geometry.
But Brittan points out that although Kant lacks a notion of an unin-
terpreted formal system, at B15 he distinguishes pure from applied
mathematics, regarding the latter as empirical. Brittan defends Kant™s
view that pure geometry is synthetic given its “postulated” subject
matter: unless one takes the basic terms to refer to points, lines, and
planes, it is hard to see why a set-theoretical structure would count
as geometry.30

5. s um ma ry
The Transcendental Aesthetic presents Kant™s ¬rst arguments for
synthetic a priori judgments, those contained in mathematics and
mechanics. Kant traces this knowledge to the pure forms of intu-
ition, space and time. After distinguishing between the sensibility
and the understanding, he argues that our original representations
of space and time are given a priori in sensible intuition. The meta-
physical exposition contains two arguments that space and time are
known a priori, and two arguments that they originate in intuition
rather than the understanding. The transcendental exposition shows

30 Brittan, Kant™s Theory of Science, 81.
The Transcendental Aesthetic
72
that this analysis can account for synthetic a priori judgments in
mathematics and mechanics. These arguments show that space and
time are pure forms of sensible intuition. Because they are a pri-
ori they are contributed by the subject. It follows that they are only
forms under which objects appear to us, and not features of things
in themselves. Thus Kant concludes that space and time are both
transcendentally ideal and empirically real, since they are necessary
conditions of objects of experience. By locating space and time in the
subject, Kant can explain how it is possible to have knowledge that is
both synthetic and a priori, at the cost of denying that we can know
the nature of things in themselves.
c hap t e r 4

The Metaphysical Deduction: identifying
categories



Kant™s purpose in the Transcendental Analytic is to perform an
analysis of the understanding parallel to that of sensible intuition
in the Transcendental Aesthetic. There he showed that the sensibil-
ity contains pure forms, space and time, in which we receive the
empirical data of intuition. In the Analytic, Kant wants to prove that
the understanding similarly contributes pure concepts and princi-
ples to our knowledge of objects. Kant calls these pure concepts the
categories; the heart of the Analytic is the Transcendental Deduction
of the categories, where he justi¬es applying these concepts to objects
given in intuition. But Kant™s strategy is complex, and he carries it out
in four stages. First, before justifying the use of categories in experi-
ence, he must prove that the understanding does in fact produce pure
concepts. This is the task of the Metaphysical Deduction, where Kant
derives the categories from the logical forms of judgment. The Tran-
scendental Deduction of the categories then follows in chapter 2, in
both A edition and B edition versions. Stage three is carried out in the
Schematism, where Kant discusses the sensible conditions required
to apply pure concepts to objects of intuition. Finally Kant offers
detailed demonstrations of the pure principles of the understanding,
the synthetic a priori judgments based on the categories. These prin-
ciples constitute legitimate metaphysics. This chapter will focus on
Kant™s attempt to identify pure concepts of the understanding in the
Metaphysical Deduction; the following chapters will examine subse-
quent sections of the Analytic. Before we look at the text, however,
it will be helpful to discuss the philosophical issues connected with
Kant™s theory of categories.



73
The Metaphysical Deduction
74

1. t h e ph ilos oph i ca l b ac kg rou nd
Kant™s theory of pure concepts intersects with several questions con-
cerning the nature of knowledge. Here I shall focus on three issues
debated by Kant™s predecessors: the origin of ideas, the skeptical chal-
lenge to knowledge, and the notion of categorial concepts.

a. The origin of ideas
Since the ancient Greeks, philosophers disputed the origin of ideas.
Plato and Aristotle established the debates between rationalists and
empiricists. Plato believed that knowledge derives from innate ideas,
which he thought were present at birth, unconsciously, in the soul.
Reasoning consists in recollecting these ideas “ bringing them to
consciousness “ and yields necessary knowledge of eternal Forms.
Recollection could be aided by sense perception, although the con-
tent of innate knowledge is independent of sense experience. In the
modern period, the rationalists Descartes, Spinoza, and Leibniz held
versions of this theory.
Empiricists, following Aristotle, denied the existence of ideas not
derivable from sense experience. Locke, for example, devoted book I
of the Essay Concerning Human Understanding to refuting the theory
of innate ideas. Hume codi¬ed the empiricist theory of ideas in his
doctrine that all simple ideas are faint copies of simple impressions;
he argued that complex ideas not based immediately on impressions
were constructed from them by the imagination. Not only did empiri-
cists reject innate ideas, some even denied that there are general ideas.
Berkeley and Hume explicitly argued against ideas that are not partic-
ular sensible images. They admitted, however, that language contains
general terms such as “human” and “gold,” and they attempted to
show how such terms function in the absence of general ideas.
In one respect Kant™s categories resemble innate ideas, since their
content is not derived from sense impressions. But Kant denies that
the intellect has any ideas independent of its operations in expe-
rience.1 Kant believes neither rationalism nor empiricism provides
an adequate account of the relation between the intellect and the

1 See chapter 5, section 4 for a discussion of this point.
The Metaphysical Deduction 75
senses. The rationalists treated the understanding as a kind of mysti-
cal instantaneous intuition; furthermore, they could not account for
the application of innate ideas to the world without invoking divine
benevolence. The empiricists not only failed to recognize the differ-
ence between general concepts and sense impressions, they analyzed
thinking largely in terms of the associative functions of memory and
imagination. In sensualizing thought, they completely overlooked
the judgmental function of the intellect. Kant™s critical theory offers
a radically new analysis of the understanding, to remedy the defects
of both traditions.

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

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

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

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

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

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

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

4 Bernd D¨ r¬‚inger argues eloquently that Kant™s table of categories is based on a teleological
o
analysis, in “The Underlying Teleology of the First Critique.”
The Metaphysical Deduction 81
a capacity rather than a faculty.) By contrast, the understanding is
a spontaneous faculty that acts to perform a function. In describing
these acts as “discursive,” Kant recalls the Latin discursus, which means
“running through.” The understanding functions, he says, to unify
different representations by bringing them under a general represen-
tation, namely a concept. Thus it operates by “running through”
diverse representations and classifying them in terms of a concept.
Consider the unifying role of the concept ˜green.™ When one classi¬es
diverse objects (an apple, a leaf ) as green, one unites them into the
class of things falling under the concept. Now the German for “con-
cept” is Begriff, which comes from the verb begreifen, meaning “to
grasp.” A concept, then, represents the unity grasped at once in the
diverse things to which it applies. The function of concepts is to unify
diverse representations by representing a characteristic common to
them.
In the next step Kant identi¬es conceiving with judging: “Now
the understanding can make no other use of these concepts than that
of judging by means of them” (A68/B93). Here he departs from the
classical view that conceiving is logically prior to judging. His point
is that concepts have no use other than to think of something, an x,
as a thing of a certain kind F. But this act of conceiving an x as an F is
equivalent to thinking the proposition that x is F, which is an act of
judging. (We shall see below in the discussion of modality that not
all judgments make assertions; in a “problematic” judgment one may
only consider the proposition that x is F.) The key to deriving a list
of pure concepts, then, is the analysis of judgment.
Judgment, according to Kant, is “the mediate cognition of an
object, hence the representation of a representation of it” (A68/B93).
Considered most abstractly, a judgment is a way of representing an
object or objective state of affairs. It yields knowledge indirectly,
through its component concepts, which are also mediate represen-
tations of objects:
In every judgment there is a concept that holds of many, and that among
this many also comprehends a given representation, which is then related
immediately to the object. So in the judgment, e.g., “All bodies are divisi-
ble,” the concept of the divisible is related to various other concepts; among
these, however, it is here particularly related to the concept of body, and this
in turn is related to certain appearances that come before us. (A68“9/B93)
The Metaphysical Deduction
82
Here Kant points out that to predicate something of one or more
objects requires a predicate-concept, which is by its nature general,
and can apply to many things. But the objects of the predication
must themselves be picked out or represented by the subject-term. In
the sentence “All bodies are divisible,” the subject-term is “bodies”,
also a general representation. Concepts can be applied to existing
things only when connected to the data given in intuition. Thus
both the subject-concept ˜bodies™ and the predicate-concept ˜divisible™
represent objects indirectly, through sensible intuition. The entire
judgment, then, is a complex representation of objects by concepts.

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