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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

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