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results of Kant’s arguments can be summarized as follows. Time is the a priori form of our inner intuition (or inner sense). It is also the form of intuition in which every appearance without exception must be located, whether the appearance is additionally referred to outer sense (and so to space) or whether it is only located in inner sense (and so in time). Everything that appears to us is constituted of representations; and all representations are mental phenomena. But while some appearances are conceived merely as belonging to the subject’s own inner states, the form of which is time, others are also referred to outer sense, the form of which is space. Yet, since all appearances are in time, as the form in which the subject apprehends any manifold of representations as an appearance, it follows that all appearances, whether referred to outer sense or to inner sense (as a modification of the subject’s thoughts) must be in time:

      Time is the immediate condition of inner appearances (of our souls), and thereby the mediate condition of our outer appearances. Just as I can say a priori that all outer appearances are in space, and are determined a priori in conformity with the relations of space, I can also say from the principle of inner sense, that all appearances whatsoever, that is all objects of the senses, are in time, and necessarily stand in timerelations. (A 34/B 51)

      Two Problems about Kant’s Account of Space and Time

The first problem is this.Allowing that space and time are pure a priori intuitions, why should they not also attach, absolutely or relationally, to things in themselves? Admittedly, if they do, our mathematical judgments could not be known with a priori certainty to apply to them; but this is scarcely enough to show that a (possibly) differently structured absolute or relational space and time could not also exist. Yet Kant clearly holds that space and time belong only to the forms of intuition, and that they cannot be things in themselves or relations between things in themselves. (Indeed, if they were, this would have serious repercussions for his moral philosophy.) I believe that he would seek to justify his position along the following lines. Since it has been shown that space and time are pure intuitions, they are not the type of phenomena that can exist as things in themselves or as relations between such entities. A pure intuition is an intrinsic property or mode of the mind, and hence cannot exist in its own right (just as a pain cannot exist in its own right, but must exist as a mode of a substance). It makes no sense to suppose that what is an intrinsic property of the mind can exist on its own. A thing in itself, on the other hand, is essentially something that can exist in its own right. Equally, it makes no sense to hold that what is an intrinsic property of the mind can be a relation holding between things in themselves.

      The second problem concerns Kant’s claim that we can know with a priori certainty the structure of space and time (by means of mathematical demonstrations). Applying the point specifically to geometry, the objection is that even if we grant that geometrical demonstrations, presently carried out, can tell us now about how space must be structured, how do we know that these demonstrations will do so in the future? Perhaps the structure of space will change overnight, so that any knowledge that I now have about the structure of space will not be applicable to my experience tomorrow. His response to this does not emerge until the following chapter, the Transcendental Analytic, where the conditions necessary for the subject’s consciousness of its own existence through time are discussed. Kant will argue that a subject can have this consciousness of himself only provided that he can be conscious of all the outer objects of his senses existing in one space. However, if the rules governing the structure of space, and so spatial objects, are capable of changing between times, this would be impossible. It would, Kant argues, be impossible for the same I to be conscious of the unity of space. Accordingly, I (the same subject) cannot be conscious of a space which, at different times, is governed by differing sets of synthetic a priori rules. (A modified version of this reply can be employed against the objection that even if I do have a priori knowledge of the structure of this part of space, why might it not have happened that if I (the same subject) had now been conscious of another part of space, I should have discovered a different set of rules applying to that region of space.)

It is, incidentally, the requirement that without the recognition of one space, there could be no consciousness of oneself as the same subject through time, that explains, for Kant, why we each think of space as essentially one (as he held in Argument 3 of the Metaphysical Exposition of space).

What has the Transcendental Aesthetic achieved?

      Within the overall framework of the First Critique, the purpose of the Transcendental Aesthetic is to answer the question: How are synthetic a priori judgments possible in pure mathematics (where they are known to exist)? It has been answered by showing that space and time are not things in themselves or relations between things in themselves, but merely the forms of our sensibility.This answer equally shows that we cannot extend our mathematical knowledge to what exists outside our modes of intuition; in particular, it cannot be extended to things in themselves.While the synthetic a priori judgments of geometry and arithmetic are valid for space and time respectively – and thereby, as will be shown, for the empirical objects in space and time – they can have no validity beyond space and time (beyond, that is, outer and inner intuition) and the empirical objects that can exist in space and time (i.e. appearances). In short, their validity, as both synthetic and necessary, cannot be extended beyond the objects of our senses, beyond the objects of possible experience.

      These last points are well summed up in the final passage of the Transcendental Aesthetic, which was added for the second edition:

      Here, then, in pure a priori intuitions, space and time, we have one of the factors required for the solution of the general problem of transcendental philosophy: how are synthetic a priori judgments possible? When in a priori judgment we seek to go out beyond the given concept, we come in the a priori intuitions upon that which cannot be discovered in the concept but which is certainly found in the intuition corresponding to the concept, and can be connected with it synthetically. Such judgments, however, thus based on intuition, can never extend beyond objects of the senses; they are valid only for objects of possible experience. (B 73; italics original).

Of course, the Aesthetic will only really have achieved these results if Kant is correct in his derivation of the concepts of space and time. We have seen that the Transcendental Exposition of space (and similarly of time) depends on a view of geometry (and arithmetic) which is no longer generally accepted. It might be replied that if we were to reject his view of mathematics, this would merely mean that he is not called upon to explain how there can be synthetic a priori judgments in mathematics, since there is nothing to explain. This, it is alleged, simply lightens his burden – he now need only explain how there can be genuine synthetic a priori judgments in natural science.

      But that answer is unsatisfactory. The synthetic a priori nature of mathematics is required for what, as Kant himself acknowledges, are his strongest arguments for the ideality of space and time: namely, their Transcendental Expositions. His claim that space and time ‘belong to the subjective constitution of the mind’ plays a pivotal role in his defence of natural science against scepticism, and – at least as important to him – in his defence of freedom of the will. By his own lights, if the objects of our experience are things in themselves (which they will be if space and time are not ideal), there can be no possibility of proving the reality of either natural science or freedom of the will.

      The result is that, if the Transcendental Expositions of space and time are rejected, the whole burden of proof falls on the Metaphysical expositions, since these expositions also seek to establish that space and time are merely forms of our intuition. Alternatively, one might try to show that, at least with respect to natural science, the kernel of Kant’s arguments does go through even on a realist, rather than on an idealist, framework. Although a number of philosophers have made the attempt, I do not believe that this alternative strategy can be successful. When we consider Kant’s proofs for the three principles given in the Analogies section – and it is these principles which constitute the basis of natural science as he conceives it – we

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