Kant. Andrew Ward

and that these judgments hold for the structure of space. The point now is to explain how this can be. Since the judgments are synthetic, it cannot be that they are proved merely from analysis of the concepts involved. Such a procedure could only produce analytic a priori judgments. But neither can the judgments proceed by consulting experience. At best, this could only give us synthetic a posteriori truths about how the differing singular figures, presented in empirical intuition, have each, in fact, been discovered to be structured. Rather, the proofs will need to proceed on the basis of our own a priori construction of figures in intuition. That is, we shall need ourselves to produce the specific sense fields (by means of the construction of geometrical figures in accordance with our own a priori concepts), and to base the proofs on these constructions. Not only will this explain how we can be in possession of synthetic a priori judgments holding for the structure of outer intuition; it should also make it possible to understand how the necessity of these judgments applies equally to the structural relationships among the appearances presented in outer intuition.

      By way of analogy, compare the case of a mathematician constructing geometrical figures on a television screen, and thereby (with a knowledge of the curvature of the screen) producing demonstrations – at least as Kant would have it – which hold for these figures. In theory, prior to any transmitted images appearing on the screen, the mathematician could determine the rules governing the possible structural relations of these images.The geometry of the screen would lay down, in advance of the appearance of any transmitted images, the rules concerning how they could be internally structured and related to one another. Of course, the images on the screen will be physical images; and as such, they will be taken, at the common-sense level, to exist whether or not we are, or could be, aware of them. Equally, at the common-sense level, the screen exists independently of our possible awareness of it. Such independence does not apply to what Kant understands by appearances and by a priori intuition. In particular, we do not first apprehend a unified intuition and then construct a geometrical figure upon it: rather, it is the construction of the figure, in accordance with our a priori geometrical concepts, that brings into existence a unified intuition. None the less, the analogy does bring out a crucial point in the transcendental exposition: namely, that it is because we possess the capacity to construct figures a priori in outer intuition, and thereby to demonstrate synthetic a priori judgments about these geometrical figures, that even prior to any experience, we can be in possession of synthetic, yet necessary, rules governing the structure of the appearances in outer intuition.

Still, it may be objected, all that the argument explains so far is how geometry, as a body of synthetic a priori judgments, can describe the structure of outer intuition (and thereby how we can grasp its application to what is given in outer intuition, viz. appearances). It has not explained how geometry is able to describe the structure of space (and the possible structural forms of objects in space). That, of course, is so if space is not identified with the form of our outer sense, i.e. with pure outer intuition. But unless we do identify the two, there can be no explanation of how geometry is a body of synthetic a priori truths holding for the structure of space. For if space referred not to our form of outer sense, but to what exists in itself (absolutely or relationally), then, since the mathematician produces his geometrical demonstrations by recourse to outer intuition, there can be no guarantee that what necessarily holds for any construction in intuition must hold for space (and, a fortiori, for empirical objects in space). In other words, if space is not a property of the mind but exists independently of it, any demonstration that rests on what is a property of the mind (outer intuition) cannot be acknowledged to hold with certainty for what exists independently of the mind. Since, however, geometrical demonstrations are acknowledged to hold with certainty for the structure of space, then space and the form of our outer sense, pure outer intuition, must be one and the same. Such an identification can alone account for the status of geometry.

      There is a good summary of the upshot of the Transcendental Exposition at A 48–9/B 66:

      If, therefore, space (and the same is true for time) were not merely a form of your intuition, containing conditions a priori, under which alone things can be outer objects to you, and without which subjective condition outer objects are in themselves nothing, you could not in regard to outer objects determine anything whatsoever in an a priori and synthetic manner. It is, therefore, not merely possible or probable, but indubitably certain, that space and time, as the necessary conditions of all outer and inner experience, are merely subjective conditions of all our intuition, and that in relation to these conditions all objects are therefore mere appearances, and not given to us as things in themselves which exist in this manner.

      Time is a pure (or a priori) intuition

      As Kant’s arguments for the nature of time run parallel to those for space, I shall not discuss them in detail, but merely summarize them. The importance of time to his Copernican revolution will emerge properly only later, when we examine the proofs for the fundamental laws of pure natural science and the conditions of our own continued self-consciousness.

In the Metaphysical Exposition of time, it is first argued that time is a priori, in that it is not dependent upon our experiences but is, rather, a precondition of our having any experience at all. Time contains only relations, three of them: ‘succession, coexistence, and that which is coexistent with succession, the enduring’ (B 67). What this comes to is that everything that appears to us, whether in space or as a mere modification of the subject’s own thoughts, must do so under the aspect of time, and in accordance with one or more of these three time relations. For instance, when we experience spatial objects, and their states, we must always perceive them as coexisting or in succession (with their substance remaining – enduring – throughout any change). But our empirical consciousness of any instance of these relations itself presupposes our recognition of a single temporal continuum within which the apprehended sensations can be related. We cannot, therefore, derive our concept of time empirically, i.e. from the experience of coexistence or succession; rather, the experience of these relations always presupposes our recognition of time. Moreover, while we cannot be conscious of an appearance except under the aspect of time, we can think of time as empty of appearances – as in the imaginative construction of an arithmetical proof. Hence, time cannot be derived from our empirical intuitions, but must underlie them as an a priori condition.

      It is argued, second, that time is an a priori intuition and not a general concept. For different times are necessarily all parts of one and the same temporal continuum, and time is also thought of as boundless or unlimited in extent. These are characteristics which, as Kant had maintained in his analogous discussion of space, can be given only through a priori intuition, and not by means of a general concept.

In the Transcendental Exposition of time, he again concludes, independently of the above considerations, that time must be an a priori intuition. For if, and only if, it is, can we explain our possession of certain synthetic a priori judgments which refer to temporal relations. Time makes possible the synthetic a priori body of propositions that is arithmetic: ‘arithmetic creates its concept of number by successive addition of its units in time [i.e. one after the other]’ (Prol, Sect. 10; 4:283). It also makes possible that a priori body of propositions dealing with pure mechanics, viz. by making possible the concept of motion: ‘Only in time can two contradictory opposed predicates (being in two different places) meet in one and the same object, namely one after the other.Thus our concept of time explains that body of a priori synthetic knowledge which is exhibited in the doctrine of motion’ (B 49; italics original).The point that Kant is making in these passages is this. If time were attached to things in themselves, absolutely or relationally, then the synthetic a priori judgments in arithmetic and mechanics could not be known to hold for relations in time (but only for relations in our inner intuition). For we prove them by recourse to the form of our inner intuition, as in the construction of an arithmetical sum. Whereas, if time is equated with the form of our inner intuition, we have no difficulty in understanding how such synthetic a priori judgments are possible. Now since it is certain that we are in possession of these judgments, and that they do hold for relations in time, it follows that time must be equated with the a priori form of our