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The Prefaces and the Introduction 29
representations such as concepts. In fact he will argue that synthetic
a priori judgments rest on a priori intuitions and on a priori con-
cepts. Although many philosophers reject Kant™s view that there are
a priori intuitions and concepts, the distinction between necessary
and contingent judgments is generally accepted. Which judgments
are necessary, and whether there are synthetic a priori judgments are,
however, controversial issues.
Kant™s second major distinction is between analytic and synthetic
judgments. Unlike the distinction between a priori and a posteriori
representations, which concerns the origin of cognition, this distinc-
tion is logical and concerns the content of judgment. It does, how-
ever, have epistemological consequences. Kant™s ¬rst characterization
is based on the idea of conceptual containment. Regarding af¬rmative
subject-predicate judgments, Kant says those in which the predicate
is (covertly) contained in the subject are analytic; those in which the
predicate is not contained in the subject are synthetic. His exam-
ples are “All bodies are extended” and “All bodies are heavy.” Kant
thinks the concept “body” includes the concept “extended” but not
the concept “weight.” Analytic judgments are merely clarifying since,
if one already understands the concepts, the judgment adds no new
knowledge. Synthetic judgments, however, are ampliative, since the
predicate concept adds something that is not part of its content to
the subject concept.
From the notion of concept containment, Kant moves to the more
general idea that analytic judgments are those whose truth value can
be determined by means of the law of non-contradiction, the logical
principle that a judgment P and its negation not-P cannot both be
true simultaneously. At A7/B10, he points out that if the predicate is
contained in the subject, then the predicate would be identical with
at least part of the subject. And in these cases, one already has in
the subject all the information one needs to make the judgment “in
accordance with the principle of contradiction” (B12). In synthetic
judgments, there is no identity between the subject and predicate, and
so the principle of non-contradiction is not suf¬cient for determining
their truth values.
Now there are several remarks to make here. First, although Kant™s
intentions are clear, his account is not general enough. (This is in
fact a problem in Hume™s discussion as well.) First, Kant makes the
The Prefaces and the Introduction
30
original distinction in terms of subject-predicate judgments. But he
also recognizes more complex forms of judgments such as conditionals
(“If . . . then . . .”) and disjunctions (“Either . . . or . . .”). And it is
not clear how “concept containment” would work for these complex
forms. Second, Kant admits that he is only considering af¬rmative
subject-predicate judgments, although he claims it is easy to apply his
distinction to negative judgments. In other words, it seems we would
want to label the judgment “No bachelor is married” analytic rather
than synthetic, although the concept of being married is clearly not
contained in the concept of bachelor. A third problem concerns the
relation between analyticity and truth. Again, it looks as if the concept
containment criterion works only for analytically true (af¬rmative)
judgments in which the predicate is in fact contained in the subject.
But the analytic-synthetic distinction should apply to both true and
false judgments. Since the logical character of the judgment is at stake
here, we should consider judgments in pairs, so that any judgment
P and its negation not-P would fall under the same classi¬cation.
That is, because the truth of “All bachelors are unmarried” entails
the falsity of “Some bachelor is married,” we should recognize both
analytic truths and analytic falsehoods. In both cases the truth value
of the judgment can be determined by the principles of logic and the
meanings of the terms alone. Fortunately, there is a way to generalize
Kant™s distinction to incorporate all judgments, simple and complex,
af¬rmative and negative, true and false.
Following Kant™s reference to the principle of non-contradiction,
we can reformulate the distinction this way: a judgment and its nega-
tion are both analytic if and only if one of the pair is self-contradictory,
or false by virtue of the de¬nitions of words or its logical form. (This
is actually close to one of Hume™s criteria for relations of ideas.) Thus
the judgments “All bachelors are unmarried” and “Some bachelor is
married” would be analytic: the ¬rst is true and the second is false
(actually self-contradictory) by the de¬nition of “bachelor.” By con-
trast, Hume™s famous examples “The sun will rise tomorrow” and
“The sun will not rise tomorrow” are synthetic, since neither judg-
ment is self-contradictory. Mere de¬nitions of terms or logical form
are not suf¬cient to determine the truth values of synthetic judg-
ments. In this particular case, actual experience is required to know
which of the pair will be true.
The Prefaces and the Introduction 31
This reformulated criterion can also be applied to complex judg-
ments. In some cases complex judgments will be analytic by virtue
of their logical form, or the meanings of logical operators, regard-
less of the content of their constituent judgments. For example, the
judgment “Either the sun will rise tomorrow or the sun will not
rise tomorrow” will be a true analytic judgment since it has the form
“Either P or not-P” which is logically true in classical systems of logic.
And by the same token the conjunction “The sun will rise tomorrow
and the sun will not rise tomorrow” will be a false analytic judgment
because judgments of the form “P and not-P” are self-contradictory
or logically false. In other cases, complex judgments would be ana-
lytic by virtue of the meanings of non-logical terms: “If something
is red, then it is colored” would be a true analytic judgment, and “If
something is round all over, then it is square all over” would be a false
analytic judgment. Finally, this way of making the distinction would
make all existence claims about logically possible objects synthetic,
which is in fact Kant™s view. This characterization, then, ¬ts consis-
tently with both his examples and his arguments for synthetic a priori
judgments. Based on textual grounds as well as the principle of char-
ity, we shall treat the analytic-synthetic distinction as reformulated
here.
In principle, with two sets of distinctions, it looks as if there could
be four kinds of judgments: analytic a priori, analytic a posteriori,
synthetic a priori, and synthetic a posteriori. In fact, however, only
three kinds of judgments are possible. At A7/B11“12 Kant discusses
the possible combinations and explains the problematic character of
synthetic a priori judgments. First he notes that there are no analytic
a posteriori judgments. All judgments of experience or a posteriori
judgments are synthetic, “For it would be absurd to ground an analytic
judgment on experience” since determining their truth value requires
appealing only to logical form or meanings of terms. Just as it is
obvious how we come by analytic a priori judgments, it is obvious
that synthetic a posteriori judgments such as “Some swans are white”
are based on experience, both for their content and their truth value.
The problematic case is synthetic a priori judgments, since neither
meanings of terms nor experience can account for their features.
Because they are synthetic, their truth value cannot be based logically
on their content; nor can it be derived from experience, since they are
The Prefaces and the Introduction
32
a priori and hence thought with necessity. In the judgment “Every
event has a cause,” there is no logical connection between the concepts
of an event in time and being caused: an uncaused event is conceivable.
But experience cannot ground this judgment either, since it cannot
confer necessity and universality on the principle. As Kant poses
the problem at A9/B13, “What is the unknown = X here on which the
understanding depends when it believes itself to discover beyond the
concept of A a predicate that is foreign to it yet which it nevertheless
believes to be connected with it?” In short, how can there be ampliative
or informative judgments that are nevertheless necessarily true? This
is the technical problem driving the critical philosophy.
Another approach to the problem of synthetic a priori judgments
concerns their necessity. This point is important because it is the sub-
ject of some misunderstanding among commentators. Recall that for
Kant all a priori judgments are necessary. Now this is easily under-
stood with analytic judgments, since their necessity is clearly logical
or conceptual. But the necessity characteristic of synthetic a priori
judgments cannot be logical necessity. Kant admits that an uncaused
event is logically possible, and yet we think it necessary that every
event has a cause. So an alternative description of Kant™s project is to
account for this peculiar kind of non-logical necessity. As we examine
his arguments we will begin to appreciate what kind of necessity this
is. For now let us call it an “epistemic” necessity.
In section V Kant takes a preliminary stab at convincing the reader
that mathematics, natural science, and metaphysics in fact contain
synthetic a priori judgments. Although mathematical inferences may
rely on logical principles, the fundamental propositions of arithmetic
and geometry are synthetic a priori. First he claims that arithmetic
formulae such as “7 + 5 = 12” are not analytic, despite their necessity,
because the mere concept of 7 + 5 does not determine the distinct
individual that results from the act of addition: “no matter how long I
analyze my concept of such a possible sum I will still not ¬nd twelve in
it” (B15). Similarly, he argues that postulates of geometry are synthetic:
“That the straight line between two points is the shortest is a syn-
thetic proposition. For my concept of the straight contains nothing
of quantity, but only a quality” (B16). Kant thinks the arithmetical
sum and the geometrical lines both have to be constructed with the
aid of sensible intuition, which adds a non-conceptual content to our
The Prefaces and the Introduction 33
cognition. Now these controversial claims are based on Kant™s com-
plex theory of mathematics, which he details only in the Discipline
of Pure Reason in the Doctrine of Method. In both the Aesthetic
and the Analytic, he sketches the process of construction required for
mathematical knowledge. In general, the informative character of all
synthetic judgments depends on the role of intuition.
Kant also claims from B17“18 that physics and metaphysics con-
tain synthetic a priori judgments. The examples from physics are
conservation principles: in all physical interactions the quantity of
matter remains constant, and action and reaction are always equal in
communication of motion among particles. Kant believes these prin-
ciples are actually physical versions of the metaphysical principles “In
all change of appearances substance persists, and its quantum is nei-
ther increased nor diminished in nature” and “All alterations occur in
accordance with the law of the connection of cause and effect.” Kant
argues for these latter principles in the section titled the Analogies of
Experience, in the Transcendental Analytic.
In the closing sections VI and VII Kant returns to Hume, whose
arguments he obviously takes seriously. He notes here, as elsewhere,
that Hume saw the problem of how we could make informative
judgments that we believed to be necessarily true, but did not arrive
at the correct solution to the problem. Hume concluded that our
belief in necessary connections of existing things arises from a psy-
chological association based on repeated experiences. For Kant, this
is tantamount to explaining an objective necessity in terms of a psy-
chologically subjective necessity. Thus Hume regarded metaphysical
knowledge as a “mere delusion” (B20). In fact, in the last paragraph
of the Enquiry Concerning Human Understanding, Hume writes:
If we take in our hand any volume; of divinity or school metaphysics, for
instance; let us ask, Does it contain any abstract reasoning concerning quan-
tity or number? No. Does it contain any experimental reasoning concerning
matter of fact and existence? No. Commit it then to the ¬‚ames: For it can
contain nothing but sophistry and illusion.

Kant remarks in his preface to the Prolegomena of 1783, that Hume
“threw no light on this kind of knowledge; but he certainly struck a
spark from which light might have been obtained, had it caught some
in¬‚ammable substance and had its smouldering ¬re been carefully
The Prefaces and the Introduction
34
nursed and developed.” So although Hume showed that metaphysical
knowledge could not be justi¬ed by rational insight into the nature
of things, his account of metaphysical beliefs went seriously astray.
Finally, in section VII, Kant describes the critical theory as “tran-
scendental” philosophy. The term “transcendental” is a key term,
which has several uses depending on the context. Here Kant says, “I
call all cognition transcendental that is occupied not so much with
objects but rather with our mode of cognition of objects in so far as
this is to be possible a priori” (A11/B25). He means that the Critique
contains a theory about the necessary conditions for knowing objects
rather than adding to our knowledge of them. If knowledge of objects
is empirical (or ¬rst-order) knowledge, then the critical philosophy
is a (second-order) theory about such knowledge. In general Kant
uses the term “transcendental” to characterize the necessary condi-
tions of cognition. It is important not to confuse this with the term
“transcendent,” which usually means going beyond experience. For
theoretical reason, the idea of God is a transcendent idea.

4. th e a na ly t ic-s ynt h e ti c con t rovers y
Kant™s views about synthetic a priori knowledge raise questions that
are still debated by philosophers. Two contested aspects of his theory
concern the analytic-synthetic distinction and his theory of mathe-
matics. Here I shall brie¬‚y discuss the ¬rst issue, treating the second
question in chapter 3. Following Kant, the analytic-synthetic distinc-
tion became a staple of contemporary philosophy, largely accepted
(with some rede¬nition) by Frege and the logical positivists. But in
1950 Morton G. White published “The Analytic and the Synthetic:
An Untenable Dualism,” which rejected the notion of analytic state-
ments. Two years later Willard Van Orman Quine took up the attack
in his classic paper, “Two Dogmas of Empiricism.” After arguing that
the de¬ning process cannot give us an account of analyticity, Quine
rejects the view that one can separate linguistic from factual compo-
nents of the meaning of a statement. Because knowledge is a “web
of belief,” underdetermined by experience, there are no statements
immune to revision in the future, including the laws of logic. Not all
philosophers were persuaded by these attacks. In 1956 H. P. Grice and
P. F. Strawson published “In Defense of a Dogma,” in which they offer
The Prefaces and the Introduction 35
an alternative de¬nition of synonymy to save the analytic-synthetic
distinction. Similarly, in “The Signi¬cance of Quine™s Indeterminacy
Thesis,” Michael Dummett points out that in “Two Dogmas,” Quine
himself de¬nes an analytic statement as one such that no recalcitrant
experience would lead us to regard it as not true. Moreover, in his later
work Word and Object, Quine explicitly allows for stimulus-analytic
sentences. Thus there are good reasons to reject Quine™s argument in
“Two Dogmas.”

5. su mma ry
In the Prefaces and the Introduction Kant lays the foundation for his
critical theory. The Prefaces introduce the problem of metaphysics
through the idea that reason naturally poses questions about reality
that are not easily answered. Since ancient Greece, philosophers have
debated whether a priori knowledge is possible, as well as what it
consists in. The second edition Preface explains the problem in terms
of the Copernican revolution: a priori knowledge is possible only if
the subject contributes features to experience, so that what appears
depends on the subject™s cognitive capacities. This requires giving
up the traditional assumption that knowledge conforms to things
as they exist independent of the subject. And this, in turn, leads to
Kant™s transcendental idealism, the view that knowledge is only of
appearances, and that things in themselves cannot be known. The
Introduction presents the technical analysis at the basis of the criti-
cal philosophy. This requires two fundamental distinctions, between
a priori and a posteriori representations, and between analytic and
synthetic judgments. Of the three possible types of judgment, the
problematic case is synthetic a priori judgments, since they are both
informative and necessary. Kant argues that this is the proper classi-
¬cation of metaphysics and mathematics. The task for the Critique
is to show that there is such knowledge, and to justify its application
to experience.
c h a pt er 3

The Transcendental Aesthetic




Kant will argue in the Transcendental Aesthetic that human sub-
jects have two pure forms of intuition, space and time, which are the
source of synthetic a priori knowledge of mathematics and mechanics.
Because these forms are part of the subject™s sensibility, he will further
conclude that space and time are transcendentally ideal, although
they are also empirically real. Thus in the Transcendental Aesthetic
Kant takes an important step in establishing the unknowability of
things in themselves. These conclusions are based on profound argu-
ments concerning the nature of space and time cognition. Although
Kant does not identify his targets, thinkers such as Descartes, Locke,
Berkeley, Newton, and Leibniz held opposing theories of both the
ontological status of space and time, and our knowledge of them.

1 . t he sens ibilit y a n d th e i nt el l ect
Kant says at A22/B36 that the Transcendental Aesthetic will examine
the sensibility, to determine whether it contributes a priori knowledge
to experience. To accomplish this task, he must isolate the sensibility
from the intellect, and then, within sensibility, separate a posteriori
from a priori elements. Unfortunately this leaves the impression that
Kant™s arguments are based on premises concerning the a priori data of
sensibility. But his theory of judgment prevents him from proceeding
in this manner. In the Transcendental Analytic Kant will argue that
all conscious representations, including sense perceptions, must have
both sensible and intellectual aspects. (He obscures this point in the
Aesthetic by speaking as though the sensibility alone could produce
intuitions of objects.) But if all conscious representations incorpo-
rate concepts, humans cannot have access to the raw data received
36
The Transcendental Aesthetic 37
by the senses. Kant says this later in a famous passage at A51/B75:
“Thoughts without content are empty, intuitions without concepts
are blind.” Following Lorne Falkenstein, I shall call this the “blindness
thesis.”1 Thus Kant cannot begin with the isolated a priori elements
of sensibility. Instead he must argue that, based on perceptions of
spatial-temporal objects, our representations of space and time orig-
inate in a priori or pure forms of sensibility. It is Kant™s conclusions
rather than his premises that isolate the pure forms of intuition from
other aspects of knowledge. Because all perceptions have intellectual
as well as a posteriori and a priori elements, pure forms of intuition
can be distinguished only by an act of abstraction.
Before making this argument, Kant de¬nes the key technical terms:
intuition (Anschauung), sensibility (Sinnlichkeit), sensation (Emp¬nd-
ung), appearance (Erscheinung), and the distinctions between matter
(Materie) and form (Form) of intuition, and between inner sense
(innere Sinn) and outer sense (¨ ussere Sinn). As earlier mentioned,
a
the meanings of these terms vary with the context of the discussion.
Although most of these terms have problematic aspects, we shall settle
on de¬nitions that are consistent with the arguments in the Aesthetic.
The critical theory begins with a fundamental distinction between
a lower-order capacity to receive impressions through the senses, and
higher-order capacities of the intellect and imagination to process this
data. Broadly, this is the distinction between the sensibility and the
intellect. The sensibility is a passive receptivity rather than an active
faculty; through the senses we are given data or affected by objects
(A19/B33). By contrast, intellectual activities are spontaneous.
Kant actually begins with the term “intuition,” which designates
both a kind of representation and the process by which subjects
acquire them. As a representation, an intuition is a cognition through
which the subject is immediately related to an object (A19/B33). Since
“immediate” means direct, this de¬nes an intuition as a represen-
tation in which an existing state of affairs is given to the subject.
As a cognitive process, intuition takes place insofar as the subject
senses objects present to it. Although it is a brute fact that human
intuition is sensible, the relation between intuition and sensibility is

1 Falkenstein, Kant™s Intuitionism, especially 54“9, and 72“4. I am greatly indebted to Falken-
stein™s interpretation.
The Transcendental Aesthetic
38
contingent. Later Kant will claim that it is logically possible for there
to be subjects who intuit existing things by other means, including
the intellect. (In fact, this is a traditional view of God™s knowledge.)
For humans, however, intuition is possible only through the senses.
This is apparent through introspection.
Now humans can also represent objects that are not given. In
this case the subject is mediately or indirectly related to the object.
Obviously we can think about things that are not present to us, and,
in fact, that may not even exist. If I think about the Eiffel Tower
when not perceiving it, or a nonexistent object such as a unicorn, I
am representing something, although the object is not given through
the representation. Whereas an intuition yields information about
some existing state of affairs, a mere thought does not. The basic
representation required for thinking is a concept (Begriff ), which,
as Kant tells us, is produced by the understanding (A19/B33). So to
think about an object, I must conceive it in some way. Kant gives his
detailed analysis of concepts in the Transcendental Analytic. For now
he simply introduces the notion to contrast it with an intuition. He
remarks at the end of the ¬rst paragraph of the Aesthetic, however, that
for a concept to function as a cognition of an object, it must ultimately
relate to sensible intuitions. This is another way of putting his point
from the Analytic, that thoughts without content are meaningless. As
we shall see, sensible intuition ultimately supplies the original content
of all cognitive thought.
At the last sentence in the ¬rst paragraph, Kant says that thought
relates to intuition by certain marks (Merkmale). In addition to differ-
ing as immediate versus mediate representations of objects, intuitions
differ from concepts as representations of particulars, or singular rep-
resentations, differ from general representations. For example, the
fourth argument on time at A32/B47“8 includes this premise: “That
representation, however, which can only be given through a single
object, is an intuition.” For example, a perception of a cat is a singu-
lar representation, whereas the concept of a cat is composed of general
features common to cats (say, having four legs and a tail). General
representations are partial in the sense that they do not represent
complete individuals, but only their properties. Now it also seems
obvious by re¬‚ection that the objects we know through the senses are
particulars: what we experience as existing are individual cats rather
The Transcendental Aesthetic 39
than catness in general. Of course the particular cats we experience
must have general feline features, but these are features of those par-
ticular cats. To put the point another way, the sensibility provides data
about particulars; through concepts of the understanding we think
their general features, by marks contained in the complex concept.
One question raised in the literature is which criterion of intuition “
immediacy or singularity “ is more basic. For several reasons, I take
immediacy as essential and singularity as contingent in the Cri-
tique.2 First, where Kant™s primary concern is epistemology, he uses
the immediacy criterion in his of¬cial de¬nition of the term. More-
over, as I pointed out above, it is just a fact about human experience
that the existing things we directly experience are particulars and
not universals. Now there is no logical impossibility in the idea that
a subject might intuit the existence of universals. Plato, for exam-
ple, thought that the soul directly apprehends the Forms, universals
such as justice, beauty, and triangularity. Descartes and Leibniz held
variants of the view that humans are capable of intellectual intu-
ition. But Kant denies that humans have intellectual intuition on
factual, not logical grounds. For these reasons, I take immediacy to
be essential to intuition, and singularity, despite its importance, to be
contingent.
At A19“20/B34, Kant introduces three closely related terms: “sen-
sation,” “empirical intuition,” and “appearance.” Let us ¬rst examine
his de¬nitions, and then consider some questions about them. Kant
de¬nes a sensation as “The effect of an object on the capacity for repre-

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