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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-
sentation, insofar as we are affected by it.” This means that a sensation
is a state caused in the perceiver by the presence of an object. Kant
adds the quali¬cation “insofar as we are affected by it” because he
will argue (as foreshadowed at B1) that experience also provides the
occasion for the subject to contribute a priori representations. This
de¬nition implies, then, that sensation supplies the a posteriori data of
sensibility. Later in the Critique (e.g., A28“9, B44“5) Kant emphasizes
that as effects on perceivers, sensations are inherently subjective, by
contrast with the representations of space and time. Kant next de¬nes

2 In the J¨ sche Logic, Kant de¬nes an intuition as a singular representation. See Lectures on Logic,
a
589. On this issue, see Hintikka, “On Kant™s Notion of Intuition,” Parsons, “Kant™s Philosophy
of Arithmetic,” and Thompson, “Singular Terms and Intuitions in Kant™s Epistemology.”
The Transcendental Aesthetic
40
an empirical intuition as “That intuition which is related to the object
through sensation.” In other words, an empirical intuition is an intu-
itive representation based on sensation. By contrast, pure intuition
is supplied a priori through the sensibility, and is not contingent on
the actual objects being sensed. Finally, Kant de¬nes an appearance
as “The undetermined object of an empirical intuition” (A20/B34).
Since “undetermined” means not conceptualized, this implies that an
appearance is constituted by the data given to the subject through
the sensibility. Unfortunately each of these de¬nitions raises more
questions than it answers.
Let us return to the term “intuition,” which has two related mean-
ings. Sometimes “intuition” means a conscious representation of a
particular object. At other times it means only the pre-conscious data
given through the sensibility. Now as we saw above, the blindness the-
sis (intuitions without concepts are blind) entails that all conscious
representations have both sensible and intellectual elements. In intro-
ducing this idea in the Analytic, Kant says, “Intuition and concepts
therefore constitute the elements of all our cognition, so that neither
concepts without intuition corresponding to them in some way nor
intuition without concepts can yield a cognition” (A50/B74). And in
the following paragraph he says, “Without sensibility no object would
be given to us, and without understanding none would be thought”
(A51/B75). Thus the suggestion in the Aesthetic that humans can
consciously represent objects by intuition alone is misleading. What
Kant should say is that the sensibility supplies the intuitive data for
representing objects, but that this data, prior to all intellectual pro-
cessing, is not yet a representation of which we are conscious. So here
is the ¬rst quali¬cation: throughout the Critique “intuition” some-
times refers to the pre-conscious data received through sensibility, and
sometimes to a conscious, intellectually processed perception. Cor-
respondingly, the term “empirical intuition” sometimes refers to the
raw empirical data, and sometimes to a conscious perception of an
empirical object. In the Aesthetic, Kant wants to identify just those
elements provided by the sensibility, and particularly those supplied a
priori, apart from all intellectual processes. Hence where appropriate
I replace his references to intuitions of objects by references to the
data given in intuition.
The Transcendental Aesthetic 41
The main question raised by the term “sensation” is whether it
refers to a mental state or a state of the perceiver™s body. There are
texts supporting both readings. In some passages Kant appears, like
Descartes, to take sensations as mental states representing qualities,
such as colors, sounds, and hot and cold. On the traditional causal
theory of perception, to which Kant evidently adheres, experiences
of these qualities are caused by contact between a physical object and
the perceiver™s physical sense organs. The physiological processes this
contact triggers in the nervous system result in a state of conscious-
ness of some sensible quality. The question is whether Kant thinks
of sensations as the physical changes in the perceiver™s body or as the
resulting mental states. At B44 he refers to “the sensations of colors,
sounds, and warmth, which, however, since they are merely sensa-
tions and not intuitions, do not in themselves allow any object to be
cognized.” Here he appears to use “sensation” for the conscious expe-
rience. Other references to sensation could also be taken in this way.
But there are strong reasons to think sensations are states of the body.
Falkenstein makes a persuasive case for this reading, pointing out
that Kant describes sensations as “ordered and placed” in space and
time (A20/B34).3 If sensations are ordered spatially, then they must
have spatial location and characteristics, so they must be physical
states. Since Kant holds that secondary qualities as we perceive them
are not real physical properties of bodies, this is a good reason to think
sensations are physical states of the perceiver rather than the qualities
we consciously experience.4 In any case, since the causal theory postu-
lates a correspondence between the physical state of the perceiver and
the experienced quality, our decision here will not affect our reading
of Kant™s arguments in the Aesthetic.
Finally we need to return to Kant™s de¬nition of “appearance” as
whatever is given in sensible intuition. This could apply to conscious
representation of the object, or to the intuited object itself. Kant uses
it both ways in the Critique. The main use of “appearance” is in

3 See Falkenstein, Kant™s Intuitionism, chapter 3, 103“34, for a detailed argument for this inter-
pretation.
4 At A172/B214 Kant says, “every sense must have a determinate degree of receptivity for the
sensations.” Moreover, at A21/B35 he describes impenetrability, hardness, and color as “that
which belongs to sensation” rather than sensations themselves.
The Transcendental Aesthetic
42
contrast to “thing in itself,” which clearly is an extra-mental thing.
Because the ultimate thrust of the critical philosophy is to argue
that knowledge is only of appearances and not things in themselves,
it seems clear that appearances are fundamentally mental. At the
same time, Kant will argue that appearances in general are not illu-
sions, that they have objective features. So generally “appearance”
means the empirical object we experience through the sensible data of
intuition.
The last two sets of terms are less problematic. Kant™s distinction
between the matter and form of intuition is functional: the matter
consists in the (intuited) elements, the form in the system for ordering
and relating them. In the Aesthetic, Kant argues that space and time
are merely the forms, systems of relations, lying “in the mind a priori”
(A20/B34), in which we receive sensations, the data given through our
contact with objects. In the Analytic, Kant will argue that humans also
possess certain a priori forms of thought or conceptual schemes for
ordering and relating the appearances given in sensibility. In general, a
form of experience, whether supplied by the sensibility or the intellect,
is a system for ordering and relating some content, which functions
as the matter relative to that form.
Finally Kant distinguishes between inner and outer sense. As
described at A22“3/B37, outer sense is our means of intuiting external
objects, and inner sense is our means of intuiting our own mental
states. Now in the de¬nition, the phrase “objects as outside us” is
ambiguous. It could mean either spatially external to or numeri-
cally distinct from the knowing subject. I take the latter meaning as
primary: since inner sense is our means of intuiting our own mental
states, outer sense must be our means of intuiting anything distinct
from our own mental states. Moreover, if “outer” meant spatially
external, then Kant™s conclusion that space is the form of outer sense
would be tautological. As for inner sense, Kant says by its means “the
mind intuits itself, or its inner state,” although it does not produce an
intuition “of the soul itself, as an object.” The function of inner sense
is to provide a direct awareness of our own mental states, which is all
we can intuit of the self as knowing subject. Inner sense is a kind of
re¬‚ective awareness. Kant™s theory that space is the form of outer sense
and time is the form of inner sense means ¬rst, that everything that
we intuit as distinct from our own mental states must be located in
The Transcendental Aesthetic 43
space; second, all mental states occur in time. Kant adds that “Time
can no more be intuited externally than space can be intuited as
something in us” (A23/B37). His point is that all representations are
inherently temporal. Similarly, space is not “in us” as a formal feature
of representing, as time is.
In this discussion Kant treats outer and inner sense as parallel and
independent modes of awareness. This is misleading, however, since
there are important differences between them. For one thing, Kant
views time as more universal than space, since time is a condition for
representing things outside the mind as well as our own mental states.
Space, by contrast, is only the form of outer intuition (A34/B50).
Another essential difference surfaces later in the section called the
Refutation of Idealism, added in the B edition. Here, at B274“9, Kant
argues that inner sense presupposes outer sense. Most commentators
agree that Kant should have treated space and time together because
of their interrelations. To understand the theory of the Aesthetic,
however, we can consider outer and inner sense as parallel.
Before examining the arguments, let us review the de¬nitions dis-
cussed so far:

An intuition is the kind of representation in which the knower
immediately apprehends a “given” or existing state of affairs.
More precisely, through intuition we are given a manifold (mul-
tiplicity) of sensible data for representing whatever exists.
Sensibility is our human capacity to intuit objects. Human sensi-
bility has two modes: an outer sense consisting of our physical
sense organs for intuiting things distinct from the mind, and a
re¬‚ective inner sense for intuiting our own mental states. In both
forms sensibility is passive or receptive rather than active.
The empirical data of intuition are originally given through sensa-
tions, which are modi¬cations of the sense organs. These physical
states result in representations of sensible qualities such as color,
taste, and hot and cold. Both the sensations and their corre-
sponding qualities are subjective effects in perceivers, since they
depend on the perceiver and the conditions of perception as well
as on objects. These empirical elements constitute the matter of
experience: sensations are the matter of intuition; consciously
represented qualities are the matter of appearance.
The Transcendental Aesthetic
44
Finally, all intuitive representations of which we are conscious are
appearances. The appearance is whatever is given to us through
sensibility. Sometimes by “appearance” Kant just means the con-
sciously represented intuitive data, both empirical and pure, and
sometimes he means the object so represented.

2. the pure forms of int ui t ion a n d synth eti c
a p r i o r i kn ow led g e
At A21/B35 Kant says transcendental aesthetic is “a science of all
principles of a priori sensibility.” In this section he will argue that
human sensibility contains two pure forms of intuition, space and
time, which are the basis of the synthetic a priori cognitions expressed
in mathematics and physics. Because these forms are contributed by
the subject, Kant will argue that they can account for the necessity
and universality characteristic of these sciences.
Before presenting his arguments, Kant sketches three possible the-
ories of space and time. He ¬rst says space and time could be “actual
entities.” This refers to the absolute theory of space and time as pro-
pounded by Isaac Newton and followers such as Samuel Clarke, who
defended it in the Leibniz“Clarke Correspondence.5 The absolutists
thought of space and time as real (although non-material) contain-
ers of all spatial and temporal objects. Because these “containers” are
necessary conditions of the existence of spatiotemporal objects, they
exist independently of the things occupying them. In this sense space
and time are both real and objective. Moreover, they are prior to the
objects they contain in two senses: ¬rst, objects must exist in space
and time, although space and time could exist without them (God
could have created empty space and time); and second, the spatial and
temporal relations among objects are derived from the spatiotempo-
ral positions these objects occupy. Absolute space and time are also
real as opposed to ideal, since their existence does not depend on the
experience of perceivers. Even if perceivers never existed, and even if
material objects never existed, absolute space and time could exist.

5 The classical texts are Newton™s Mathematical Principles of Natural Philosophy, 1:6“10; and
Leibniz, The Leibniz“Clarke Correspondence. I discuss these theories in Space and Incongruence,
chapters 2 and 3.
The Transcendental Aesthetic 45
As a second possibility, space and time could be “only determi-
nations or relations of things, yet ones that would pertain to them
even if they were not intuited.” This refers to the major competitor
to the absolute theory, the relational theory of space and time. It was
championed by both rationalists and empiricists, including Leibniz
and Berkeley.6 In general, relationists believe that space and time are
merely systems of relations whose existence depends on the prior exis-
tence of both perceivers and the objects or elements so related. Despite
their epistemological differences, Leibniz and Berkeley both criticize
the absolute theory as incoherent, since it entertains the existence of
real entities that are not themselves substances. For relationists, spa-
tial and temporal relations among things are constructed from the
(non-spatiotemporal) properties and relations of metaphysical sub-
stances. Although Leibniz™s monadic substances are not themselves
spatiotemporal, our experience of space and time corresponds to their
real properties. This is why Kant says relational space and time would
belong to things “even if they were not intuited.” The relationists
held space and time to be ideal and subjective, since they are “con-
structed” through mental processes involved in representing existing
things. Here the priority relations are reversed: empty space and time
could not exist, since where there are no substances there could be
no system of relations derived from them. And although spatiotem-
poral relations correspond to properties of monadic substances, their
peculiar spatial and temporal character depends on the perceptual
process.
The ¬nal possibility is Kant™s own theory, that space and time are
pure forms of human intuition. This theory denies both that they
are absolute or real as things in themselves, and that they are derived
from a prior experience of non-spatiotemporal things. Although Kant
rejects both the absolute and relational theories, his position incorpo-
rates some features of each. He will agree with the Newtonians that
space and time are logically independent of the objects they contain,
but he will deny that they are completely independent of human per-
ceivers. Kant will accept Leibniz™s view that things in themselves are
6 In addition to the Leibniz“Clarke Correspondence, Leibniz™s position is spelled out in “First
Truths,” and the letter to Bayle of 1702, both in Philosophical Papers and Letters, 268“71 and
583. Berkeley™s views appear in De Motu in The Works of George Berkeley Bishop of Cloyne,
4:1“52; and A Treatise Concerning the Principles of Human Knowledge, part I, articles 110“17.
The Transcendental Aesthetic
46
not spatiotemporal, but he will reject the idea that space and time are
constructed from relations or properties of experienced substances.
We shall see how he argues for these views in the metaphysical expo-
sition of space and time.
Kant™s strategy in the Aesthetic is complex but methodical. First
he divides the arguments or “expositions” into two kinds. The meta-
physical exposition exhibits the concept “as given a priori” (A23/B38).
Here Kant presents four arguments to establish that space and time
are a priori forms of sensible intuition, without presupposing that
we have synthetic a priori knowledge. The transcendental exposition,
which was separated out in the B edition, begins with the premise that
we have synthetic a priori knowledge, and argues that space and time
must be pure forms of intuition to account for that knowledge.7 On
this reading, the two expositions draw the same conclusion, but differ
in their starting points. The advantage of this strategy is to appeal to
readers whatever their position on synthetic a priori knowledge.
Following his treatment of outer and inner sense, Kant separates
the expositions of space and time. Although he intends the arguments
to be parallel, his presentation is sloppy and the arguments are not
properly arranged. First, whereas there are four arguments in the
metaphysical exposition for space, there are ¬ve for time. This is
because Kant mislocates the transcendental exposition in the third
paragraph of the metaphysical exposition. In addition, although Kant
is defending the same conclusions for space and time, we shall see
that the proofs occasionally differ. For the most part, however, the
thrust of the arguments is the same, so we shall generally treat them
together.
The ¬nal preliminary remark concerns the fact that Kant subtitles
these sections expositions of the concepts of space and time. Since he
is arguing that space and time are pure forms of intuition, and since
intuitions and concepts are distinct kinds of representations, this
heading is cause for confusion. The explanation, however, involves
Kant™s blindness thesis, according to which we are not conscious of
the intuitive data prior to any intellectual processing. Thus Kant

7 In “Kant™s ˜Argument from Geometry™,” Lisa Shabel argues, by contrast, that the transcen-
dental exposition assumes the conclusion of the metaphysical exposition, and then shows
how this analysis explains the synthetic a priori nature of geometry.
The Transcendental Aesthetic 47
cannot begin with premises describing this data. Instead, he must
analyze our conscious experiences of space and time, and then argue
that these experiences could have the features they do if and only if
space and time are forms of intuition. So the most straightforward
solution is to take the term “concept” here to refer to a representation
that has been intellectually processed, which includes perceptions
of spatiotemporal objects. In the expositions, as we shall see, Kant
returns to the standard use of “concept” for a general representation,
as opposed to an intuition.


A. The metaphysical exposition
The metaphysical exposition argues that our original representations
of space and time are a priori intuitions. The ¬rst two proofs conclude
that these representations are known a priori, supplying necessary
features of experience. The last two conclude that they originate in
intuition as part of the manifold given in sensibility. Putting these two
conclusions together yields the result that our original representations
of space and time are a priori or pure forms of sensible intuition.

1. The ¬rst exposition: space and time are logically independent
of the empirical data given in intuition
Here Kant argues that space and time are a priori in the weak sense
that they are not derived from the empirical data given in experi-
ence. The premises refer to this empirical data as sensations, and,
as we saw earlier, sensations are physical states of the perceiver. But
because the sensible qualities we consciously represent correspond to
these physical states, I shall refer to both sensations and sense qual-
ities as the empirical data given in intuition. The main point here
is that cognitions of space and time are not constructed from the
empirical data, and hence are not known a posteriori. As Falkenstein
explains, this argument is aimed against philosophers who held sensa-
tionist, constructivist theories of space and time cognition. This group
would include relationists such as Leibniz and Berkeley, as well as
Locke for his theory of time. Kant believes the empirical sensible
data are received in spatiotemporal arrays. Here is the argument for
space:
The Transcendental Aesthetic
48
For in order for certain sensations to be related to something outside me (i.e.,
to something in another place in space from that in which I ¬nd myself ),
thus in order for me to represent them as outside one another, thus not
merely as different but as in different places, the representation of space
must already be their ground. (A23/B38)

This is the argument for time:
For simultaneity or succession would not themselves come into perception
if the representation of time did not ground them a priori. Only under its
presupposition can one represent that several things exist at one and the
same time (simultaneously) or in different times (successively). (A30/B46)

The point is that any constructivist theory of space and time would
actually have to presuppose spatial and temporal systems of relations.
Now why does Kant think this?
One interpretation takes Kant™s premises to be based on
introspection: it just is apparent that the sensible data, whether pre-
conscious sensations or qualities experienced consciously, are given in
space and time. The color patches we see, for example, are spatially
extended and related to each other. Correspondingly, the physical sen-
sations causing these representations are located in our sense organs,
and are brought about by contact with objects located in space. The
same can be said for their temporal locations and relations. So it is
an obvious fact that the intuitive data are given in space and time.
While this version is plausible, it may not completely capture Kant™s
point. First, it does not explain why Kant thinks any constructivist
account must presuppose space and time. One might object that for
all we know, the pre-conscious data may not be ordered in space and
time. In this case the spatial and temporal frameworks we consciously
experience might arise through some constructive processes, as rela-
tionists maintain. To eliminate this possibility a stronger argument is
needed, that a constructivist account is not a possible account of our
experience.
Kant™s premises suggest such an argument, in effect a dilemma for
the constructivist, who thinks space and time are created from the
relations of the sensible data given empirically. Now either these rela-
tions are themselves spatiotemporal or they are not. If they are spatio-
temporal, then they presuppose the spatial-temporal frameworks
The Transcendental Aesthetic 49
encompassing such positions. So the constructivist cannot embrace
the ¬rst horn of the dilemma without begging the question. On the
other hand, if the relations among the sensible data are not spatial
and temporal, then the constructivist must explain how spatial and
temporal positions arise from these non-spatiotemporal features. This
horn of the dilemma has two aspects to it, one general and one spe-
ci¬c. The general problem is the one just stated, how one derives any
spatiotemporal features out of non-spatiotemporal features. The spe-
ci¬c problem is one Falkenstein calls the “localization” problem: if the
sensible elements are not given in spatial and temporal arrays, then
what could possibly determine the particular order or con¬gurations
in which they are experienced? Any answer to this question could
only be pure speculation. More important, it is hard to see how the
qualitative features of color patches could determine anything about
the order in which they are experienced. The spatiotemporal positions
and relations of the sensible data appear completely independent of
the content of that data.
The problem for the second horn relates to another point implicit
in the argument. Consider that for any theory that maintains that
global space and time are constructed from relations among sensible
elements, the elements must ¬rst be discriminated as numerically dis-
tinct. This requires identifying the individual relata independently of
their spatiotemporal positions. Now the exposition for space implies
that spatiotemporal position is both necessary and suf¬cient for dis-
criminating distinct sensible elements. Kant says we represent the
sensations “as outside and next to one another, thus not merely as dif-
ferent but as in different places” (A23/B39). Consider, for example,
how we identify two qualitatively identical color patches as numeri-
cally distinct. It can only be because of their different spatiotemporal
locations.
The ¬rst exposition argues that the original spatiotemporal mani-
folds are independent of the empirical data given in them, although
they are given with that data. In other words, the sensible manifold has
two aspects: the empirical data given a posteriori, and the spatiotem-
poral systems in which they are located. The logical independence of
these systems establishes their a priori status in the weak sense that
their content is not derived from the empirical data.
The Transcendental Aesthetic
50
2. The second exposition: space and time are necessary conditions
of experience
Here Kant argues that space and time are a priori in the strong sense
that they are necessary features of experience. His strategy is to show
that while it is possible for us to think of both space and time as
empty of objects, we cannot represent the absence of space and time
altogether. Here is the argument for space:
One can never represent that there is no space, though one can very well think
that there are no objects to be encountered in it. It is therefore to be regarded
as the condition of the possibility of appearances, not as a determination
dependent on them, and is an a priori representation that necessarily grounds
outer appearances. (A24/B38“9)
The argument for time is virtually identical:
In regard to appearances in general, one cannot remove time, though one
can very well take the appearances away from time. Time is therefore given
a priori. In it alone is all actuality of appearances possible. The latter could
all disappear, but time itself (as the universal condition of their possibility)
cannot be removed. (A31/B46)
The arguments differ only in the scope of their conclusions. Whereas
space is the condition of outer intuition and the possibility of appear-
ances, time is the condition of the actuality of all appearances. This
refers to the different domains of outer and inner sense: by outer
sense we represent things other than our representations; inner sense
applies to all representations. When Kant says time is a condition
of the “actuality” of appearance, he means that all appearances must
exist in time. Otherwise the point is the same: space and time are
both necessary features of appearances.
The problem here is how to interpret Kant™s premises. The argu-
ment maintains that although one can think space and time as empty,
one cannot represent the absence of space, or, as Kant says, “remove”
time. The ¬rst part is fairly clear, since “think” means conceive of
an empty space or time. As Falkenstein points out, this amounts to
the claim that it is possible to conceive that some experience might
be of a void space or time.8 The problem is the sense in which one

8 Kant does not believe, however, that any experience could prove that space and time are
empty (A172/B214). Falkenstein discusses Kant™s position on empty space and time in Kant™s
Intuitionism, 203“16.
The Transcendental Aesthetic 51
cannot represent the absence of space or time. The solution, I think,
depends on Kant™s intention to show that space and time are condi-
tions of appearances, and appearances are what is given in intuition.
His point is that we cannot conceive ourselves intuiting things that
are not located in space or time.
If this is correct, then the argument establishes that the original
representations of space and time are a priori in the strong sense that
they are necessary conditions of appearance. In other words, every-
thing given in intuition must be located in space and time. Although
Kant does not explain here what kind of necessity is involved, fol-
lowing the expositions he argues that space and time are necessary
as epistemic conditions or conditions of human experience. Kant is
not claiming that it is logically necessary that humans perceive things
spatiotemporally. Neither is he claiming that space and time have an
absolute metaphysical necessity. Rather, space and time are necessary
relative to human intuition. We shall return to this point below.
The conclusion of the ¬rst two metaphysical expositions, that space
and time are a priori representations, incorporates three theses:
1. The content of our spatial and temporal representations is logically
independent of (not derivable from) the empirical data given in
intuition (the ¬rst exposition);
2. Space and time are presupposed in the intuitions of objects (the
second exposition);
3. We can conceive of space and time as empty, but we cannot con-
ceive of anything appearing to us without space and time (the
second exposition).
These arguments establish the ¬rst half of Kant™s thesis “ that the
original representations of space and time are a priori. He next must
show that they originate in the intuitive data rather than in concepts
of the understanding.

3. The third exposition: space and time are intuitions because they
are particular representations
In this argument (the fourth for time), Kant wants to prove that space
and time are not discursive concepts of the understanding, but are
supplied in the intuitive data given in sensibility. Here he clearly uses
the term “concept” for a general representation of the understanding.
The Transcendental Aesthetic
52
Kant offers three reasons to conclude that space and time originate
in intuition. First, we can represent only one space/time; different
spaces/times are parts of one unique space/time. Second, in contrast
to the part“whole relation for concepts, the wholes of space/time are
prior to their parts; the parts arise only by drawing boundaries in
the whole. Finally, at A25/B39 and A32/B47, Kant mentions a point
that belongs in the transcendental exposition, namely that synthetic a
priori judgments concerning space and time are possible only if they
are intuitions. Here I shall discuss the ¬rst two arguments and reserve
the third for the discussion of the transcendental exposition.
(a) Space and time are unique particulars. Concerning space Kant
says: “For, ¬rst, one can only represent a single space, and if one
speaks of many spaces, one understands by that only parts of one
and the same unique space” (A25/B39). Similarly, he says of time:
“Different times are only parts of one and the same time. That repre-
sentation, however, which can only be given through a single object, is
an intuition” (A31“2/B47). The point is straightforward: global space
and time are themselves complete particulars (although not empirical
objects) rather than merely general or partial features of things. Their
particularity is shown by the fact that any ¬nite region is part of the
larger encompassing space or time. Put another way, any two distinct
spaces are themselves spatially related. Moreover, two qualitatively
indistinguishable regions of space are numerically distinct only by
virtue of being different regions of the same global space. The same is
true of time.9 Since concepts of the understanding are general rather
than particular, they could not be the source of our representations
of space and time.
(b) For space and time, the whole is prior to the parts, unlike the part“
whole relation for concepts. Kant™s second point reinforces the ¬rst by
contrasting the part“whole structures of space and time with that of
concepts. Of space he says:
these parts cannot as it were precede the single all-embracing space as its
components (from which its composition would be possible), but rather are
only thought in it. It is essentially single; the manifold in it, thus also the
general concept of spaces in general, rests merely on limitations. (A25/B39)

9 For this and the discussion that follows I am indebted to Melnick, Kant™s Analogies of Expe-
rience. See especially 7“30.
The Transcendental Aesthetic 53
The remark that follows, that “an a priori intuition (which is not
empirical) grounds all concepts of it,” is irrelevant to Kant™s point,
that the representation is intuitive rather than conceptual. It indicates,
however, that we do have general concepts of space and time, for
example, of spatial extensions and temporal durations. Nonetheless,
Kant is claiming that these general representations are derived from
our original intuitions of space and time as particulars.
The part“whole argument for time is, not surprisingly, mislocated
in the ¬fth paragraph, in the middle of the fourth exposition. The
portion relevant to the third exposition is this:
But where the parts themselves and every magnitude of an object can be
determinately represented only through limitation, there the entire repre-
sentation cannot be given through concepts, (for they contain only partial
representations), but immediate intuition must ground them. (A32/B48)
This argument makes an excursion into mereology, the science of
part“whole relations. Kant is contrasting the part“whole relation for
complex concepts with that for space and time. Recall that con-
cepts are general representations of features of individuals rather than
complete individuals. This is why Kant describes them as “partial
representations.” The generality of concepts entails that they can be
logically arranged in species“genus relationships. The concept ˜physi-
cal object,™ for example, has among its subordinate concepts ˜animal,™
which similarly has the concept ˜mammal™ subordinate to it. The ¬‚ip
side of the coin is that any complex concept contains as its compo-
nents other concepts. The concept ˜mammal™ contains (among others)
the more general concept ˜animal,™ which similarly contains the more
general concept ˜physical object,™ and so on. Now although the con-
cept ˜animal™ is a component of the concept ˜mammal,™ the former
concept can be apprehended independently of the latter. That is, we
can think of animality in general without thinking of mammals or
other types of animals. This is the sense in which the parts of com-
plex concepts are prior to or logically independent of the whole. The
content of any constituent concept is recognizable independently of
its inclusion in another concept. Later in the Critique Kant will char-
acterize wholes made up of independently existing parts as aggregates
or composites.10
10 See the Second Antinomy, A438/B466.
The Transcendental Aesthetic
54
Space and time, by contrast, are wholes that are logically prior
to their parts, which do not exist independently. For such wholes
the parts are created by drawing boundaries or introducing “limita-
tions” through the whole. Thus space and time are not composites
of independently existing spatial and temporal regions; instead, we
identify (¬nite) regions of space and time as we like, depending on
how we draw the boundaries. For Kant, a point in space or time is
not a part, but a limit whose “existence” depends on the previously
given whole. The upshot, then, is that our representations of space
and time are particulars, as shown by their part“whole structure, and
thus they must originate in intuition rather than concepts of the
understanding.

4. The fourth exposition: space and time are intuitions because they
are given as in¬nite in magnitude
The fourth exposition uses the fact that space and time are “given as
in¬nite” to prove that they originate in intuition. When Kant says
they are in¬nite, he means primarily that they are unbounded, but
he also believes they are in¬nitely divisible.11 His various statements
of the argument come at the point from several different angles. The
earliest version, in the A edition for space, claims that “A general
concept of space (which is common to a foot as well as an ell) can
determine nothing in respect to magnitude” (A25). That is, the general
concept of being extended spatially does not entail anything about
the divisibility or size of a space, and thus could not be the source of
our experience of space as in¬nitely divisible and unbounded.
In the B edition version for space, Kant emphasizes the difference
between the ways concepts and intuitions can “contain” an in¬nity
of representations:
Now one must, to be sure, think of every concept as a representation that
is contained in an in¬nite set of different possible representations (as their
common mark), which thus contains these under itself; but no concept,
as such, can be thought as if it contained an in¬nite set of representations
within itself. Nevertheless space is so thought (for all the parts of space,
even to in¬nity, are simultaneous). (B39“40)

11 For helpful discussions on the unbounded nature of space and time, see Falkenstein, Kant™s
Intuitionism, 232“2, and Parsons, “The Transcendental Aesthetic,” 71.
The Transcendental Aesthetic 55
As a general representation, a concept represents a characteristic that
has a potential in¬nity of instances. Those to which the concept actu-
ally applies are its extension, and are said to fall under the concept.
(The relation of a predicate to its extension is represented in set theory
as the relation of a set to its members.) But considered in terms of its
content or intension, no concept can be composed of an in¬nity of
concepts, for such a concept would be unthinkably complex. Thus
no concept could contain an in¬nity of parts within itself. Now as the
third exposition has shown, space and time each contain a (potential)
in¬nity of parts within the whole. In the ¬fth paragraph on time,
Kant says this: “The in¬nitude of time signi¬es nothing more than
that every determinate magnitude of time is only possible through
limitations of a single time grounding it. The original representation
time must therefore be given as unlimited” (A32/B47“8). Since spatial
and temporal parts do not exist independently, the process of carv-
ing out ¬nite spatiotemporal regions by drawing boundaries has no
limit in principle. (The ¬rst edition refers to “boundlessness in the
progression of intuition” at A25.)
Before going on to the transcendental exposition, it might be help-
ful to clarify Kant™s view of space-time cognition. According to Mel-
nick, when Kant says that space is given as an unlimited whole, he is
not making “the (absurd) claim that I can only empirically perceive
appearances occupying some part of space by perceiving the whole
of space.”12 Kant holds that we perceive only ¬nite spatiotemporal
regions. His statements about the whole of space and time make
claims about the form of every determinate representation in space
and time. Melnick thinks Kant should say that through our ¬nite per-
ceptions, we have a “pre-intuition” of each ¬nite region in space and
time as embedded in a continuous, in¬nitely divisible, unbounded
whole. On this theory, our intuitive capacities supply us, along with
the empirical data, a priori manifolds of spatial and temporal data. All
data given in intuition, both empirical and pure, are determinable but
indeterminate. That means that they are not received as discriminated
into determinate spatiotemporal regions. In the Transcendental Ana-
lytic, Kant will argue that such discrimination requires thinking the
manifold by pure concepts of the understanding.

12 Kant™s Analogies of Experience, 8.
The Transcendental Aesthetic
56

B. The transcendental exposition
Here Kant argues that space and time are pure intuitions based on
synthetic a priori cognitions. As explained at B40, the transcendental
exposition should show that the fact that space and time are pure
intuitions is both necessary and suf¬cient to account for synthetic
a priori judgments concerning space and time. These arguments are
fairly straightforward.
The argument for space depends on the fact that we have syn-
thetic a priori cognition of the nature of space, both directly and in
geometry. In the Introduction Kant claimed that the judgment that
a straight line is the shortest between two points is both synthetic
and known to be necessarily true (B16). Here he makes the same
point about our cognition of three-dimensional space. Recall that
synthetic a priori judgments are both informative and yet thought
with necessity. The transcendental exposition divides up these two
characteristics neatly, attributing the synthetic nature of geometry to
the intuitive character of space, and its a priori status to the a priori
status of the spatial manifold. First, the fact that knowledge of space
is synthetic shows that it cannot be originally derived from concepts
of the understanding, for only analytic judgments can be obtained
from concepts alone. But Kant believes there is no contradiction in
the idea that space could have had fewer or more dimensions. So spa-
tial cognition must be based in intuition. Furthermore, that intuition
cannot be empirical, for then we could not account for the necessity
and strict universality of geometry. By elimination, then, our original
representation of space must be pure intuition. If one accepts Kant™s
premise that we have synthetic a priori knowledge of space, as well
as his analysis of intuitions and concepts, this appears to be a sound
argument.
The argument for time does not, as one might expect, depend sim-
ilarly on the synthetic a priori status of arithmetic.13 Instead, Kant™s
examples of synthetic a priori judgments in the third metaphysical
exposition are, “It has only one dimension; different times are not
simultaneous, but successive” (A31/B47). In the of¬cial transcenden-
tal exposition he connects time with the possibility of experiencing
13 In the Prolegomena Kant does connect the pure intuition of time to arithmetic at section 10,
79.
The Transcendental Aesthetic 57
changing states of things through the perception of motion, and con-
sequently with the principles of mechanics. Only because time is an
a priori intuition, he says, can we comprehend
the possibility of an alteration, i.e., of a combination of contradictorily
opposed predicates (e.g., a thing™s being in a place and the not-being of
the very same thing in the same place) in one and the same object. Only
in time can both contradictorily opposed determinations in one thing be
encountered, namely, successively. (B48“9)
In other words, whereas the principle of non-contradiction rules out
the truth of a proposition and its negation, it is possible for an empir-
ical proposition and its negation to be true at different times. The
pure intuition of time, then, underlies “the general theory of motion,”
which includes synthetic a priori principles of mechanics. Kant does
not specify any such principles here, but in the Metaphysical Foun-
dations of Natural Science they include the laws that the quantity of
matter is conserved in all changes, that all changes in matter have
external causes, and that in all communication of motion, action and
reaction are always equal.14 Not until his discussion of mathemati-
cal construction in the Transcendental Dialectic does Kant explain
the difference between arithmetic and geometry. Although we will
examine those passages in more detail in chapter 11, for now let me
indicate Kant™s position brie¬‚y. The key idea is that arithmetic is
not the “science” of time because time does not provide a model
of pure arithmetic as space does of geometry. Although arithmetical
operations involve temporal processes, Kant does not assume that
the objects to which arithmetic and algebra apply must be temporal.
Thus for him the “science” of time is mechanics or the doctrine of
motion, that is, arithmetic as applied to spatial objects.

3 . spac e and time a s tra ns ce nd e nta lly i dea l
a nd empiric a lly re a l
In his concluding sections beginning at A26/B42 and A32/B39, Kant
argues for the transcendental ideality and empirical reality of space

14 MFNS, 541, 543, 544. The latter two are Kant™s versions of Newton™s ¬rst and third laws of
motion.
The Transcendental Aesthetic
58
and time. He actually foreshadows these conclusions in the transcen-
dental exposition of space. There he claims that the only way we
could have an outer intuition that precedes experience of objects and
is determined a priori is if “it has its seat merely in the subject, as its
formal constitution for being affected by objects and thereby acquir-
ing immediate representation, i.e., intuition, of them, thus only as
the form of outer sense in general” (B41). From the fact that space
and time are pure intuitions, Kant concludes that they are merely
forms of the subject™s intuition. This is the basis of the transcendental
ideality and empirical reality of space and time.
In the conclusions sections, Kant makes the essential argument in
two paragraphs labeled (a) and (b). Paragraph (a) claims that space
and time do not represent properties or relations of things in them-
selves, “For neither absolute nor relative determinations can be intu-
ited prior to the existence of the things to which they pertain, thus
be intuited a priori” (A26/B42). Clearly he agrees with Hume that,
were our intuitive capacities to give us information about things as
they exist independently of us, this knowledge could only be con-
tingent. So the ¬rst step rules out the possibility that space and
time provide information about properties or relations of things in
themselves.
In paragraph (b) Kant takes the next step, arguing that space and
time must therefore be subjective conditions of sensibility, or the
forms of outer and inner sense. This follows by elimination, since if
space and time are not “located” outside the subject, then the only
alternative is to attribute them to the subject™s cognitive capacities.
As Kant notes, this conclusion is indirectly supported by the fact
that it accounts for synthetic a priori spatial and temporal cognition,
because the forms in which we are affected by objects can be logically
independent of intuitions of the objects themselves.
In his conclusions on time, Kant adds a third paragraph labeled
(c) to emphasize that time has a broader scope than space, since
all appearances, both outer and inner, are subject to time. As the
form of inner sense, all our representing occurs in time; so repre-
sentations of outer or spatial things are also temporal. As Kant says
at A34/B50“1, time is “the immediate condition of the inner intu-
ition (of our souls), and thereby also the mediate condition of outer
appearances.”
The Transcendental Aesthetic 59
In Kant™s Transcendental Idealism, Henry Allison points out that
Kant™s notion of the form of intuition has several aspects to it.15 From
the subjective side, the forms of intuition are our particular modes
of intuiting. Kant believes it is a fact about our human capacity to
receive intuitive data that we intuit our mental states temporally, and
things other than our mental states spatially. But this has implications
for the objective side, since the forms of intuition are also forms of the
objects intuited. As we saw at A20/B34, the form is the system that
allows the matter (here the empirical data) to be organized and related.
As forms of the subject™s intuition, then, space and time provide the
structure of the items intuited empirically. The spatial and temporal
properties of appearances are due to their being given to perceivers
with spatiotemporal forms of intuition.
From his conclusions in paragraphs (a) and (b), Kant develops his
theory of the transcendental ideality and empirical reality of space and
time. The thesis that space and time are transcendentally ideal means
that they are nothing more than conditions of human sensibility. In
reference to space Kant states the point as follows:
We can accordingly speak of space, extended things, and so on, only from
the human standpoint. If we depart from the subjective condition under
which alone we can acquire outer intuition, namely that through which we
may be affected by objects, then the representation of space signi¬es nothing
at all. This predicate is attributed to things only insofar as they appear to us,
i.e., are objects of sensibility. (A26“7/B42“3)
He makes similar remarks about time at A34/B51. But if space and time
are only subjective representations, then all spatiotemporal appear-
ances are likewise subjective in the same sense. Kant spells out this
consequence in his General Observations:
We have therefore wanted to say that all our intuition is nothing but
the representation of appearance; that the things that we intuit are not in
themselves what we intuit them to be, nor are their relations so constituted
in themselves as they appear to us; and that if we remove our own subject
or even only the subjective constitution of the senses in general, then all
constitution, all relation of objects in space and time, indeed space and
time themselves would disappear, and as appearances they cannot exist in
themselves, but only in us. (A42/B59)

15 Allison, Kant™s Transcendental Idealism, 96“7.
The Transcendental Aesthetic
60
The transcendental ideality of space and time means that were there
no perceivers with these forms of intuition, space and time would
not exist; neither, consequently, would the spatiotemporal properties
of things. It follows that things in themselves, whatever they are,
are non-spatial and non-temporal. This is one of the controversial
implications of Kant™s analysis, which we shall discuss below. Here
Kant clearly rejects the theory of absolute space and time, according
to which (in Kant™s terms) space and time are transcendentally real,
since they exist independently of perceivers.
Despite their ideality, however, Kant also maintains that space and
time are empirically real. By this he means that they are not illusory,
that the objects that appear to us really are given in space and time.
Since, as Kant argued in the metaphysical exposition, space and time
are necessary features of appearances, it follows that all objects of intu-
ition are temporal, and all outer objects are spatial. Kant sometimes
describes space and time as objectively valid, as in his conclusions on
time: “Our assertions accordingly teach the empirical reality of time,
i.e., objective validity in regard to all objects that may ever be given
to our senses. And since our intuition is always sensible, no object
can ever be given to us in experience that would not belong under the
condition of time” (A35/B52). It is important to note the connection
between objective validity and truth values. That space and time are
objectively valid implies that we can make true or false judgments
about them as well as about spatiotemporal objects. In connecting
empirical reality with objective validity, Kant relativizes the notions
of an object and objective truth. Empirical realism entails that what
counts as an object for us, and therefore what counts as objective truth
for us, is relative to our cognitive capacities. The Aesthetic establishes
those conditions from the side of human sensibility. In the Transcen-
dental Analytic Kant examines the contribution of the understanding
to the objective conditions of cognition.
As a result of his “transcendental turn,” in the rest of the Critique
Kant generally uses the term “object” to refer to objects of knowledge
or appearances, and he typically reserves the term “thing” for things
in themselves. There are passages, of course, where Kant ignores this
distinction, such as at A30/B45, where he says that “objects in them-
selves are not known to us at all.” But generally he uses these terms
The Transcendental Aesthetic 61
in accordance with his conclusion that objects of experience are only
appearances.
We can now appreciate the peculiar sense in which space and time
are subjective, and the connection between transcendental subjectiv-
ity and the necessity of synthetic a priori judgments. At A28“9 and
A28/B44, Kant contrasts the subjectivity of space and time with the
subjectivity of secondary qualities, or experiences of color, sound, and
hot and cold:
Besides space, however, there is no other subjective representation related
to something external that could be called a priori objective. For one cannot
derive synthetic a priori propositions from any such representation, as one
can from intuition in space (§3). Strictly speaking, therefore, ideality does
not pertain to them, although they coincide with the representation of space
in belonging only to the subjective constitution of the kind of sense, e.g.,
of sight, hearing, and feeling, through the sensations of colors, sounds, and
warmth, which, however, since they are merely sensations and not intuitions,
do not in themselves allow any object to be cognized, least of all a priori.
(A28/B44; see also A28“9)
For scienti¬c realists like Descartes and Locke, secondary qualities
such as color, taste, heat, and so on are merely effects caused in per-
ceivers by contact with the primary qualities of physical objects. Sec-
ondary qualities are subjective in the sense that they can vary from
perceiver to perceiver, since they depend on the individual™s sense
organs as well as the conditions of perception. A color-blind person,
for example, will not see the full range of colors seen by someone
who is not color-blind. Now Kant assumes that all human perceivers
share the same forms of intuition. Thus the subjectivity of space
and time differs from the subjectivity of secondary qualities in two
ways. First, space and time are universally or species-subjective, since
they are forms of all human intuition. And this implies, second, that
space and time are necessary rather than contingent features of expe-
rience. By contrast, secondary qualities are not necessary features of
appearances, and so cannot provide a foundation for synthetic a priori
cognition. In addition, these qualities do not yield direct cognition
of objects, although scienti¬c realists assume there are correlations
between secondary qualities and the real properties causing the expe-
riences. That space and time are pure forms of intuition, however,
The Transcendental Aesthetic
62
can account for synthetic a priori knowledge of mathematics and
mechanics. The transcendental subjectivity of space and time means
that they are universal to humans and the ground of necessary fea-
tures of appearance. This is not to be confused with the empirical
subjectivity of contingent sensible qualities that vary from individual
to individual.
This contrast between transcendental and empirical subjectivity
is echoed in the distinction between transcendental and empirical
notions of appearance at A45/B62“3. As Allison explains, the oppo-
sition between the subjective or ideal and the objective or real marks
a division between what is in the mind and what is independent
of the mind.16 But this distinction can be drawn on both the tran-
scendental and empirical levels. Considered transcendentally, “the
mind” refers to all human subjects; empirically it designates only
individual subjects. Accordingly, there are both transcendental and
empirical versions of the distinction between appearances and things
in themselves:
We ordinarily distinguish quite well between that which is essentially
attached to the intuition of appearances, and is valid for every human sense
in general, and that which pertains to them only contingently because it is
not valid for the relation of sensibility in general but only for a particular
situation or organization of this or that sense. And thus one calls the ¬rst
cognition one that represents the object in itself, but the second one only its
appearance. This distinction, however, is only empirical. (A45/B62“3)
In other words, within experience we often call features such as colors
and tastes, which depend on the individual perceiver, mere appear-
ances. And we contrast those with the real physical properties of the
object, which we consider the thing in itself. Kant uses the example of
a rainbow: “we would certainly call a rainbow a mere appearance in a
sun-shower, but would call this rain the thing in itself, and this is cor-
rect, as long as we understand the latter concept in a merely physical
sense” (A45/B63). From the empirical standpoint, physical objects
are real, and the secondary qualities they appear to have are ideal
or mere appearances. At the empirical level the real or objective has
universal validity for all humans, is publicly available, and expresses
the relation between a perception and an object. The empirically
16 Kant™s Transcendental Idealism, 6“8.
The Transcendental Aesthetic 63
ideal or subjective varies among humans, represents a private experi-
ence, and thus expresses a relation merely between perceptions. From
the transcendental standpoint, however, empirically real objects are
themselves mere appearances. On this level the subjective or ideal
consists in necessary conditions of experience, which are valid for
all human subjects. The transcendentally real are things in them-
selves, which Kant believes we cannot know. Later, in the deduction
of the categories, Kant criticizes Hume for trying to account for tran-
scendentally ideal features of experience in terms of the empirically
ideal.
Kant™s notion of transcendental subjectivity is the key to the neces-
sity of synthetic a priori judgments. Earlier I called this an “epistemic”
necessity, since it is grounded in human cognitive capacities. Kant
reminds us repeatedly that it is logically possible for other subjects
to have other forms of intuition. It is just a brute fact about humans
that space and time are our forms of outer and inner sense. Although
we cannot explain this fact, it does explain why human experience
must have certain features. So space and time are necessary features
of objects of experience, although the fact that they are our forms of
intuition is not necessary. In the Transcendental Analytic Kant will
give a similar analysis of pure concepts of the understanding, deriving
their necessity from the logical forms by which humans judge. The
epistemic necessity of synthetic a priori judgments, then, is weaker
than either logical or absolute metaphysical necessity.
Before turning to some issues raised by the Aesthetic, we should
note Kant™s criticism of Leibniz™s analysis of the sensibility at A43“
4/B60“2. There Kant points out that Leibniz and his disciple Wolff
analyzed sensory representations as confused intellectual representa-
tions. But the metaphysical exposition shows that space and time,
and all the sensible data received in them, originate in the capacity
for intuition, which is distinct from the understanding. As Kant says,
The Leibnizian-Wolf¬an philosophy has therefore directed all investiga-
tions of the nature and origin of our cognitions to an entirely unjust point
of view in considering the difference between sensibility and the intellectual
as merely logical, since it is obviously transcendental, and does not concern
merely the form of distinctness or indistinctness, but its origin and content,
so that through sensibility we do not cognize the constitution of things in
themselves merely indistinctly, but rather not at all. (A44/B61“2)
The Transcendental Aesthetic
64
Here Kant classi¬es the difference between clear and confused repre-
sentation as “logical.” As he says later at B415n, “a representation is
clear if the consciousness in it is suf¬cient for a consciousness of the
difference between it and others.” Now degree of clarity is not what
distinguishes sensory from intellectual representations. Instead they
differ in kind “ both in their relation to the object and their content
as particular or general. In criticizing the Leibnizians, Kant carries
out one prong of his attack on reductionistic theories of ideas. In the
Transcendental Analytic, he will reject empiricism for an opposing
error, claiming that all ideas originate in sensory impressions.

4. cr it ic ism s of ka nt ™s t h e ory of s pace a nd tim e
The most common objections against the theory of the Aesthetic are
to the conclusions that things in themselves are non-spatial and non-
temporal (henceforth NST), and that geometry and arithmetic are
synthetic a priori. While this discussion will undoubtedly not settle
any of these issues, I hope to identify the signi¬cant issues presented
in the literature.

A. NST and the unknowability of things in themselves
From Kant™s time up to the present, critics have made two charges
against his conclusions on space and time. First, they have argued that
he does not adequately support NST. And second, they have pointed
out that both NST and the underlying presupposition that things in
themselves exist are apparently incompatible with the unknowability
thesis (UT). Here we will ¬rst examine whether NST is justi¬ed. In
my concluding remarks at the end of this book I return to UT and
the coherence of Kant™s idealism.
The criticism typically raised against NST is called the “neglected
alternative” view. This position was debated extensively by the
nineteenth-century German commentators Adolf Trendelenburg and
Kuno Fischer; the debates are discussed fully in Hans Vaihinger™s Com-
mentar zu Kants Kritik der reinen Vernunft.17 Trendelenburg pointed
out that even if one agrees that the space and time of our experience

17 Vaihinger, Commentar, 1:134“50.
The Transcendental Aesthetic 65
are subjective forms of intuition, it is still possible that things in
themselves are also spatiotemporal, although their space-time would
be numerically distinct from ours. Consequently, Kant™s arguments
do not preclude the possibility that appearances correspond to things
in themselves, even if we could never know the nature of the corre-
spondence.
In Kant™s Transcendental Idealism, Allison defends NST. His ¬rst
argument misses the mark, since it misconstrues the neglected alterna-
tive position, as maintaining that the numerically same spatiotempo-
ral frameworks are both subjective forms of intuition and also systems
relating things in themselves.18 He then considers the relevant thesis,
that there could be a correspondence between our forms of intuition
and spatiotemporal relations among things in themselves. He argues
that if this version avoids the charge of incoherence, “it does so only
by virtue of its utter vacuity” (320). While he may be right, it does not
explain why Kant thought he was justi¬ed in drawing the strong con-
clusion that things in themselves could not be spatiotemporal, rather
than taking an agnostic stand on the question. As Paton remarks, it
seems “we are entitled to say of things-in-themselves only that we do
not and cannot know them to be in space and time. Since we do not
know them at all, we cannot say what they are not.”19
In Space and Incongruence, I defend NST based on the incon-
gruent counterparts arguments, which Kant set out from 1768 up
through the critical period. Although Kant uses the arguments to
develop his distinction between the sensibility and the intellect, as
well as his theory that space and time are pure forms of intuition,
in his ¬nal versions in the Prolegomena of 1783 and the Metaphysical
Foundations of Natural Science of 1786, he claims the phenomenon
supports NST.20 Although the arguments are too complex to explain
here, by 1781 Kant took the existence of counterparts such as left and
right hands to demonstrate that the kinds of relations exhibited in
the space of our experience could not obtain among things in them-
selves. Although the argument itself does not appear in the Critique,
the theory of relations on which NST is based does. One part of the
18 See my Space and Incongruence, 93“9, for a discussion of Allison™s views.
19 Paton, Kant™s Metaphysics of Experience, 1:180.
20 See Space and Incongruence, chapters 3“5. A condensed version appears in Buroker, “The
Role of Incongruent Counterparts in Kant™s Transcendental Idealism.”
The Transcendental Aesthetic
66
theory is the metaphysical exposition views that space and time are
wholes which are prior to their parts, as well as independent of the
items located in them. The remainder occurs in the Transcenden-
tal Analytic section titled the Amphiboly of Concepts of Re¬‚ection.
Here Kant agrees with Leibniz that, as understood by reason, a sys-
tem of relations always presupposes independently existing relata.
Kant expresses this in terms of the distinction between the “inner”
or intrinsic determinations, and the “outer” or relational determina-
tions of existing things: “Through mere concepts, of course, I cannot
think of something external without anything inner, for the very rea-
son that relational concepts absolutely presuppose given things and
are not possible without these.” He goes on to remark that the space
of our intuition “consists of purely formal or also real relations,” with-
out presupposing something “absolutely inner” (A284/B340). When
Kant refers to what is thought through “mere concepts” he means the
logical conception of a relation. Here he agrees with Leibniz that rela-
tions among things in themselves logically presuppose independently
existing relata. But our intuition of space is of a system of relations that
is prior to and independent of the things occupying it. Accordingly,
in Space and Incongruence I argue that the existence of incongruent
counterparts convinced Kant that space and time are incompatible
with the kinds of relations that could obtain among things in them-
selves, as represented by mere thought. This incompatibility licenses
the strong conclusion that things in themselves could not be spatial
or temporal.
This interpretation stimulated considerable discussion in the lit-
erature.21 Recently Falkenstein has defended a “mitigated” version of
NST based primarily on the arguments of the Aesthetic. With respect
to the neglected alternative, his version maintains that if things in
themselves stood in spatiotemporal relations, those relations could not
correspond in any important way to our forms of intuition. Although
Falkenstein does not characterize his interpretation this way, it seems
to me an extension of my defense based on the theory of relations.
But he delves more deeply into Kant™s assumptions about orders and
relations, as well as the various versions of NST. For these reasons his

21 See Van Cleve and Frederick, eds., The Philosophy of Right and Left, for various viewpoints
and a detailed bibliography.
The Transcendental Aesthetic 67
account is the most thorough and charitable offered to date. Here I
shall sketch its outlines.22
In considering the neglected alternative, Falkenstein divides the rel-
evant possibilities into two: ¬rst, that space and time are themselves
substances; and second, the relationist view that they are constructed
from properties or relations of things in themselves. He ¬nds Kant™s
argument against the substantival view in the proof of the thesis of
the Second Antinomy, as the following reductio ad absurdum. If com-
posite self-subsisting things were not made up of simple parts, and
all composition were removed “in thought,” no composite or simple
part would remain. And therefore “no substance would be given.”
Thus self-substantial things must ultimately be composed of sim-
ple parts (A434/B462).23 Now space and time are not composed of
simple parts because they are in¬nitely divisible. Consequently they
could not correspond to any conceivable substantival things in them-
selves. This explains Kant™s remarks that were time self-subsistent, “it
would be something that was actual yet without an actual object”
(A32“3/B49), and that the absolute theorists have to admit “two eter-
nal and in¬nite self-subsisting non-entities (space and time), which
exist (yet without there being anything real)” (A39“40/B56). This dis-
poses of the substantival version of the claim that things in themselves
could be spatiotemporal.
Falkenstein thinks Kant™s strongest defense against the relational
version of the neglected alternative is based on an analysis of different
types of orders. Recall the ¬rst metaphysical exposition assumption
that the spatiotemporal positions of appearances are not determined
by the empirical contents. It follows that the spatiotemporal order
of appearances could not possibly be based on (intrinsic) proper-
ties of things in themselves. Falkenstein contrasts a “comparative
order” of things based on their intrinsic qualities, with the “presen-
tational” order of spatiotemporal locations: “In a comparative order,
the locations of the ordered elements are determined by some scalable
quality in the elements themselves. The order of colors in terms of
their brightness, saturation, and hue, or of sounds in terms of pitch
and volume is an example of a comparative order.”24 Thus we can
22 The arguments outlined here are contained in chapter 9 of Kant™s Intuitionism, 289“309.
23 I discuss this argument in chapter 9, section 2.
24 Falkenstein, Kant™s Intuitionism, 184. See 183“5 for this analysis.
The Transcendental Aesthetic
68
“locate” hues by their positions on a spectrum. But in this “color
space” the positions of the hues are ¬xed: green will always appear
between blue and yellow. The ¬rst metaphysical exposition shows,
however, that the spatiotemporal positions of appearances are com-
pletely independent of their intrinsic (scalar) qualities: the fact that a
color patch is green determines nothing about where or when it will
appear. This provides the desired support for NST, for “even if there
were a sense in which things in themselves might be in space or time,
it would have to be a very different sense from that in which, accord-
ing to the metaphysical expositions, the matters of appearance are
in space and time” (303). The incompatibility allowing Kant to rule
out a relationist alternative is that between the independent presen-
tational order of our spatiotemporal experience, and a comparative
order based on intrinsic features of things in themselves.

B. Is arithmetic analytic or synthetic?
Kant™s view that mathematics is synthetic a priori has also been much
debated by philosophers. The issues are complex, and are related
to three important developments since Kant™s time. These are, in
chronological order, the development of non-Euclidean geometries
in the nineteenth century, the failure of the Frege“Russell program
to reduce mathematics to logic in the early twentieth century, and
¬nally, the assumption in relativity theory that only empirical science
can determine whether space is Euclidean or non-Euclidean. The
¬rst development apparently supports the synthetic nature of geom-
etry, while the third poses a serious challenge to its a priori status.
The failure of the reduction program has the more startling result
of supporting Kant™s view that arithmetic is synthetic. This section
considers whether arithmetic propositions are synthetic, and the fol-
lowing section treats the synthetic a priori nature of geometry.
In claiming that arithmetic is synthetic a priori, Kant rejected Leib-
niz™s view that arithmetic propositions are founded on the principle
of contradiction. According to Leibniz, formulae such as “2 + 2 = 4”
could be demonstrated from de¬nitions of numbers and the analytic
axiom “If equals be substituted for equals, the equality remains.”25
25 Leibniz, second letter to Clarke, Leibniz“Clarke Correspondence, 5. Also the New Essays, book
IV, chapter 7, p. 413. My discussion here relies heavily on Brittan, Kant™s Theory of Science,
43“67.
The Transcendental Aesthetic 69
Leibniz thus held that mathematical truths could be reduced to logical
truths and de¬nitions. Early in the twentieth century both Gottlob
Frege and Bertrand Russell actually attempted the reduction. Frege
never doubted that geometry is synthetic, but he hoped to show
that arithmetic could be reduced to general logical laws and def-
initions.26 As Gordon Brittan explains in Kant™s Theory of Science,
the program would have two steps: the ¬rst would reduce differ-
ent branches of mathematics to arithmetic, and the second would
reduce arithmetic to logic. In their Principia Mathematica, Russell
and Whitehead attempted the second step by giving logical de¬ni-
tions of the arithmetical terms appearing in the ¬ve Peano axioms at
the basis of arithmetic, namely:
A.1: 0 is a number.
A.2: The successor of any number is a number.
A.3: No two numbers have the same successor.
A.4: 0 is not the successor of any number.
A.5: If P is a predicate true of 0, and whenever P is true of a number
n, it is also true of the successor of n, then P is true of every
number.27
The notions needing de¬ning are “0,” “is a number,” and “is the
successor of.” If this could be done successfully in set-theoretic terms,
then presumably all the properties of integers could be derived by
logical proof. Since Frege de¬ned analytic truths as those based on
general laws of logic and de¬nitions, a successful reduction would
show arithmetic to be analytic in his sense.
Now the reduction failed because of Russell™s famous discovery of
the paradox of set theory. As Russell showed, a contradiction arises
concerning the concept “is not a member of itself.” If we have the
class of all such things “ classes that are not members of themselves “
and we ask whether that class is or is not a member of itself, either
way a contradiction arises. If the class is a member of itself, then it
satis¬es the condition of members, so it is not a member of itself.
If it is not a member of itself, then it satis¬es the condition, so
it is a member of itself. Although Russell developed the theory of
types to avoid the paradox, it led Frege to give up his view that

26 See Frege, The Foundations of Arithmetic, 19“20.
27 See Brittan, Kant™s Theory of Science, 48.
The Transcendental Aesthetic
70
arithmetic is analytic. Ultimately he came to the conclusion that
the basis of all mathematics is geometry, which he believed to be
synthetic.28
Independently of the logical paradox, however, the attempt to
de¬ne arithmetical notions in set-theoretic terms would not have
convinced Kant that arithmetic is analytic. This is because, as Brit-
tan points out, the Zermelo“Fraenkel axiomatization of set theory
includes two existential assumptions: the axiom that there exists a
null set (null set axiom), and the axiom that there exists a set contain-
ing at least all natural numbers (axiom of in¬nity).29 Absent these
assumptions one cannot derive all of arithmetic. But for Kant all
existential judgments must be synthetic. In criticizing the ontological
argument he says, “in all fairness you must [concede], that every exis-
tential proposition is synthetic” (A598/B626). These considerations,
then, lend support to Kant™s view that arithmetic is synthetic in his
sense.

C. Is geometry synthetic a priori?
Kant™s view of geometry is less controversial than his view of arith-
metic. From Euclid up to the nineteenth century, philosophers gen-
erally regarded Euclid™s postulates as universally and necessarily true,
but not based on laws of formal logic. With the development of non-
Euclidean geometries in the nineteenth century by N. I. Lobachevsky
and G. F. B. Riemann, it became apparent that the ¬fth postulate of
Euclidean geometry is independent of the others, and thus can be
denied without contradiction. In Lobachevsky™s geometry, this entails
that through a point not on a given line, more than one line can be
drawn parallel to the given line, as well as that the sum of angles of
a triangle is always less than two right angles. Riemann™s geometry
denied both Euclid™s ¬fth postulate and the assumption that a straight
line can be extended to any length. In this geometry space is ¬nite;
through a point not on a given straight line, no straight line can be
drawn parallel to the given line, and the sum of angles of a triangle is
greater than two right angles. When later developments proved that

28 See Brittan, Kant™s Theory of Science, n. 40, 59, for the source.
29 Brittan, Kant™s Theory of Science, 58“9.
The Transcendental Aesthetic 71
both geometries are formally consistent, the question arose: which
geometry is true of our space?
Although the development of non-Euclidean geometries supports
the synthetic nature of geometry, following Hilbert, philosophers dis-
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

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