Kant's Transcendental Aesthetic
Introduction
In the Transcendental Aesthetic of his Critique of Pure
Reason, Kant argues that space and time are
subjective conditions of human sensibility. This he opposes
to the Newtonian, absolutist theory,
that space and time exist objectively and independently of
objects; and to the Leibnizian
relational theory, that space and
time are objective relations among objects. Kant also argues that
it is an error to apply the concepts of space and time to things in themselves. According to the Aesthetic, not only are
space and time subjective conditions of experience; they are
solely subjective conditions of experience, applicable only
to appearances and not at all to things in
themselves. Kant succeeds in demonstrating that, considered as
representations, space and time are necessary conditions of our
perception of outer and inner
objects. However, we will show that he fails in establishing that
space and time are actually prior to perception, and in showing that
space and time can exist only as representation. In
fact, we show that the Kant's arguments do not preclude the
possibility of an objectively relational space-time, à la Leibniz.
Structure of the argument
Kant's argument, at least in the B edition of the Critique, has a simple structure. The short
introduction (§1, B33--36) defines important terms
used in the Aesthetic (and elsewhere in the Critique). This is
followed by an discussion of space. This treatment is divided
into three parts. In the first, the ``Metaphysical exposition of [the] concept [of
space]'' (B37--40), Kant argues from first principles that
space must be a priori and must be an intuition. In the
Transcendental exposition of space (B40--42), he attempts to
demonstrate that the synthetic apriority of geometry depends on
space being an a priori intuition. Finally, the section of
conclusions (B42--45) demonstrates that, if space is indeed an a
priori intuition as has been (supposedly) proven, then it must be
the sensible form of outer experience; it can apply only to
appearances and not to things in themselves; and
it is empirically real but transcendentally ideal.
The treatment of time parallels that of space. Like the
exposition of space, there is a metaphysical exposition (B46--48), arguing from first
principles that time is an a priori intuition; and a
transcendental exposition
(B48--B49), which argues that time must be an a priori intuition in
order for us to make use of the synthetic a priori concept of
succession. There is also a section of conclusions (B49-53),
which demonstrates that, because time is an a priori intuition,
it is the sensible form of all inner
intuition and hence, mediately, the sensible form of all
experience.
Following the treatment of time are the Elucidation (B53--58) and
the ``General remarks on the transcendental aesthetic'' (B59--72).
These sections make claims not integral to the matter of space and
time as the forms of sensibility. We will thus
not treat those sections here.
Problems with the argument
We now consider the first two arguments in the metaphysical
exposition of space (B38--39). These arguments attempt to prove the
apriority of our representation of space. The first argument
claims that, in order for sensations to be related to things
outside us, those sensations must already have space as their
ground. That is, we could not conceive the existence of
objects other than ourselves without a prior representation of
space underlying them. Thus, claims Kant, space precedes
experience, making it a priori.
It is not entirely clear here why space necessarily precedes the
objects we place in it. In addition, Kant does not support his
claim that sensations must be represented in space before we
can distinguish ideas within ourselves from objects without.
Thus one alternative to the apriority of space is that we are
somehow able to, without a representation of space, differentiate
between objects which are within us and objects which are without
us. Then we place those external objects in an objective space
which is determined by objective relational properties of the
objects. Then, space as a representation would not be a
priori, but rather empirical in nature. This is, in fact, one
possible interpretation of the Leibnizian relationist position.
Kant offers other arguments against this possibility later on, but
we shall see that those arguments are not flawless themselves.
The second argument claims that, since we can represent space without
objects but not objects
without space, space is necessary to our representation of
objects, and thus a priori. Unfortunately, Kant does not define
``represent'' here. What does it mean to ``represent'' an object?
If it is taken to refer to conceptualisation, surely we can have a
concept of an object without placing the object in space: for
example, I can have a concept of God, but, since God is not an
appearance, I cannot place God
within space. Thus it is more likely that ``represent'' here means
``intuit''. That is, I cannot intuit or perceive an object
without putting it somewhere in space.
While it seems clear that we cannot sense, and hence cannot intuit,
external objects without space, it is not clear that we can
intuit space without objects. A relationist would argue that, since
space is nothing but relations among objects, it is meaningless without objects. Thus
space is not necessarily prior to objects, but may be intuited
simultaneously with them.
The third and fourth arguments in the metaphysical exposition of
space (B39--40) argue that space is an intuition. The first of
these arguments, number 3, proceeds from the singularity of space.
Since we perceive individual spaces as parts of the single
all-encompassing Space, spaces are defined by their
limitations within singular Space. Thus, claims Kant, an a
priori intuition grounds all concepts of space.
The argument here is not clear at all. Apparently, Kant wishes to
claim that, being singular, space must be an intuition (since
concepts are always general in nature). Since any concept of an
individual space must be contained within the intuition of
singular Space, that intuition must precede the concepts, and hence
be a priori. The argument against necessary apriority given above
holds here as well; we can imagine our representation of space being
simultaneous with our representation of the object; then, since
the concept of space is not a priori, there is no reason for the
intuition that precedes it to be so, either. Note that we are not
here arguing against our representation of space being an intuition:
however, if it is not a priori, we are not obliged to accept that no
real thing, neither concept nor intuition, can underlie this
representation.
The fourth argument begins with the statement that space is
represented as an infinite given
magnitude. Kant claims that, while concepts can contain infinite
numbers of representations under them (e.g., there are an
infinite number of possible intuitions corresponding to my
concept of ``dog''), concepts cannot contain such infinities
within themselves. Since an infinite number of spaces are
contained in Space, and thought through it, space
cannot be a concept, so it (being a representation) must be an
intuition.
This argument seems to be based on an unsupported assumption, namely
that concepts cannot be infinite. Kant makes no attempt to prove or
even support this claim in the Aesthetic. Neither is there an
explanation of why intuitions can be infinite. One objection
to Kant's argument is that, when we represent space, we do not
necessarily cognize the infinity of possible spaces contained
within. Kant is here unclear as to what it means for a
representation to ``contain an infinite set of representations
within itself'', so it is difficult to argue for or against Kant's
claim here. It may well be that Kant is equivocating
between ``within X'' as meaning ``thought immediately through X'' and as
meaning ``conceptually derivable from X''.
Transcendental exposition of space
In the transcendental exposition, Kant argues from the synthetic
apriority of geometry that space must be an a priori intuition.
In this case, it is not even necessary to consider the validity of
the argument: it is unsound. If geometry is considered as a pure, formal mathematics, its
proofs consist of logical deductions from given axioms and are
hence analytic. If it is considered as
a science of space, there is another problem. Modern physics,
especially general relativity, has satisfiably demonstrated that
spacetime is indeed non-Euclidean. Thus the ``common-sense''
and (Kant would say) a priori axioms of Euclidean geometry do
not apply to actual space on astronomical scales. Geometry as a
true and valid study of space, therefore, must have an
empirical basis if it is to be accurate, and is hence a
posteriori. Since in neither case is geometry synthetic a
priori, the entire argument of the transcendental exposition fails.
Conclusions on space
The first and second conclusions that Kant draws in this section (B42)
are that space does not represent a property of things in
themselves, and that it is not a relation among objects. This is
because space, being a priori, is intuited prior to the
intuition of the existence of the objects it comprehends or
that it relates. However, we have argued above that Kant does not
sufficiently demonstrate the apriority of space. In fact, we have
shown that the relationist position is indeed tenable despite
Kant's arguments to the contrary.
Kant's next conclusion (B42) is that space is ``the subjective
condition of sensibility, under which alone outer intuition is
possible for us''. This may well be the case for space qua
representation. Though Kant does not go so
far as to prove (rather than simply state) that, without space, we
can not distinguish the us from the not-us, it is the case that our
intuition of outer appearances is intimately bound to our
representation of space. However, if there is indeed a relation
of space outside of its rôle as representation (which we have
argued above to be a possibility), that relation is not merely a
subjective condition: it is an objective reality. Certainly, Kant
has not proved that space is ``nothing other than merely the
form of all appearances of outer sense'' (emphasis added).
Another conclusion made in this section (B43) is that space applies to
appearances only and not things in themselves. Space as
representation indeed applies only to appearances; a representation
cannot refer to a thing in itself. However,
space as an objective relation, if indeed it is, may well apply
to things in themselves. We could never prove this, since
metaphysics can meaningfully deal only with appearances, but
Kant has not proved that space cannot apply to things in themselves. Thus, while the empirical reality of
space is still most readily affirmed, the transcendental ideality
is only necessary if we consider space as a human representation.
In general, the most important conclusions on space depend on the
existence of space solely as a mental representation. Once we have
shown that an external, objective relation modelled by this
representation is possible, Kant's conclusions become much more
narrow. They then apply only to space as a representation---and
it is tautologous to state that a representation is transcendentally
ideal, or that is is subjective.
Transcendental arguments on time
Since the metaphysical arguments presented concerning time are
parallel to those concerning space, similar reasoning may be used
to show that Kant's reasoning is faulty. We thus consider Kant's
transcendental arguments on time. The first, curiously, appears
as the third argument in the metaphysical exposition; the
second is in the transcendental exposition.
The third argument of the metaphysical exposition (B47) is that we
know apodictically that different times are not simultaneous;
thus, the reasoning goes, non-simultaneity of time is an a priori
rule under which alone experience is possible. The problem here
is that Kant does not define ``simultaneous''. We must therefore
take the usual definition, which is ``occurring together in
time''. Then the statement that ``different times are not
simultaneous'' is mere tautology. The fact that this rule is a
priori is no surprise: the rule is analytic! Kant has thus proved
nothing about the apriority of time itself.
Even if we grant Kant the benefit of the doubt here, by taking a
different, unspecified, definition for ``simultaneous'', we
encounter another problem. That is, Einsteinian
special relativity has shown that ``simultaneity'' of two events
depends on the frame of reference from which the events are being
observed. Hence, we cannot really call time
``simultaneous'': events A and B can be simultaneous in frame X,
and B and C in frame Y, without A and C being simultaneous in either
frame of reference.
The other transcendental argument is presented in the
``Transcendental exposition of the concept of time'' (B48--49).
This argument demonstrates that time must be an a priori
intuition. No concept, it is claimed, could explain an object
having two contradictory predicates (one at time A, one at time
B); thus time qua representation must be an intuition. The
transcendental exposition also claims that, since the theory of
motion is synthetic a priori, the representation of time that
underlies it and allows for succession must be a priori. However,
Kant does not explain in the Aesthetic why, precisely, the
theory of motion should be a priori. We may make the same claims
here as we did for geometry: our common-sense ``a priori'' notions
of motion do not necessarily correspond to the full complexities of
reality, so the theory of motion is not necessarily a priori.
Thus, the representation of time may well be empirical in the same
was as space. Also, much as for space, it is only demonstrated here
that our representation of time is an intuition; if this
intuition is not a priori, then it could well be founded on some
external thing which is not an intuition.
Conclusions on time
The first conclusion Kant draws (B49) is that time cannot exist
independently, for then ``it would be actual without an actual
object''. This is, unfortunately, the whole of the argument. It
appears that here time is being treated as a representation (hence
it has an object); however, it is obvious that a representation
cannot exist alone. Kant fails to prove that an objective concept
of time (whether absolute or relational) is impossible; his
arguments fail for the same reasons as the arguments concerning
space. Likewise, Kant's claim that ``time cannot attach to
things as an objective determination'', because it must precede
the objects, depends on an apriority which Kant has not satisfactorily
proved.
Kant also labels time as an inner (rather than outer) intuition
(B49--50). This is apparently because time, not having shape or
position, cannot exist in space (hence ``outside''). Rather, we
give objects of outer intuition positions in time mediately,
through the (inner) representations we have of those outer
objects. Thus Kant places all appearance subjectively within
time. As mentioned above, he has not satisfactorily shown that time
does not exist independently of our intuition. Thus time is not
necessarily purely subjective; the argument against Kant here is
much the same as that for space.
Conclusion
Though we have attacked nearly every proposition made in the
expositions of space and time, much of Kant's philosophy
remains. Space and time are still, when considered as
representations, necessary for perception as we know it. However,
the representations of space and time are not necessarily
prior to representations of the objects they describe.
Finally, Kant is not at all successful in showing that
space and time are solely representations, and that they
do not apply to things in themselves. The most that
can be said is that our representations apply only to
appearances, and that a non-subjective relation of
spacetime might not apply to things in themselves.