"The first part of the Critique, the ‘Transcendental Aesthetic’, has two objectives: to show that we have synthetic a priori knowledge of the spatial and temporal forms of outer and inner experience, grounded in our own pure intuitions of space and time; and to argue that transcendental idealism, the theory that spatiality and temporality are only forms in which objects appear to us and not properties of objects as they are in themselves, is the necessary condition for this a priori knowledge of space and time (see Space; Time).

Much of the section refines arguments from the inaugural dissertation of 1770. First, in what the second edition labels the ‘Metaphysical Exposition’, Kant argues that space and time are both pure forms of intuition and pure intuitions. They are pure forms of intuition because they must precede and structure all experience of individual outer objects and inner states; Kant tries to prove this by arguing that our conceptions of space and time cannot be derived from experience of objects, because any such experience presupposes the individuation of objects in space and/or time, and that although we can represent space or time as devoid of objects, we cannot represent any objects without representing space and/or time (A 23–4/B 38–9; A 30–1/B 46). They are pure intuitions because they represent single individuals rather than classes of things; Kant tries to prove this by arguing that particular spaces and times are always represented by introducing boundaries into a single, unlimited space or time, rather than the latter being composed out of the former as parts, and that space and time do not have an indefinite number of instances, like general concepts, but an infinite number of parts (A 24/B 39–40; A 31–2/B 47–8).

Next, in the ‘Transcendental Exposition’, Kant argues that we must have an a priori intuition of space because ‘geometry is a science which determines the properties of space synthetically and yet a priori’ (B 40). That is, the propositions of geometry describe objects in space, go beyond the mere concepts of any of the objects involved – thus geometric theorems cannot be proved without actually constructing the figures – and yet are known a priori. (Kant offers an analogous but less plausible argument about time, where the propositions he adduces seem analytic (B 48).) Both our a priori knowledge about space and time in general and our synthetic a priori knowledge of geometrical propositions in particular can be explained only by supposing that space and time are of subjective origin, and thus knowable independently of the experience of particular objects.

Finally, Kant holds that these results prove transcendental idealism, or that space and time represent properties of things as they appear to us but not properties or relations of things as they are in themselves, let alone real entities like Newtonian absolute space; thus his position of 1768 is now revised to mean that space is epistemologically but not ontologically absolute (A 26/B 42; A 32–3/B 49–50; A 39–40/B 56–7). Kant’s argument is that ‘determinations’ which belong to things independently of us ‘cannot be intuited prior to the things to which they belong’, and so could not be intuited a priori, while space and time and their properties are intuited a priori. Since they therefore cannot be properties of things in themselves, there is no alternative but that space and time are merely the forms in which objects appear to us.

Much in Kant’s theory has been questioned by later philosophy of mathematics. Kant’s claim that geometrical theorems are synthetic because they can only be proven by construction has been rendered doubtful by more complete axiomatizations of mathematics than Kant knew, and his claim that such propositions describe objects in physical space yet are known a priori has been questioned on the basis of the distinction between purely formal systems and their physical realization.

Philosophical debate, however, has centred on Kant’s inference of transcendental idealism from his philosophy of mathematics. One issue is the very meaning of Kant’s distinction between appearances and things in themselves. Gerold Prauss and Henry Allison have ascribed to Kant a distinction between two kinds of concepts of objects, one including reference to the necessary conditions for the perception of those objects and the other merely leaving them out, with no ontological consequences. Another view holds that Kant denies that things in themselves, and not merely their concepts, are spatial and temporal, and that spatial and temporal properties are, literally, properties only of our own representations of things. Kant makes statements that can support each of these interpretations; but proponents of the second view, including the present author, have argued that it is entailed by both Kant’s argument for and his use of his distinction, the latter especially in his theory of free will (see §8).

The debate about Kant’s argument for transcendental idealism, already begun in the nineteenth century, concerns whether Kant has omitted a ‘neglected alternative’ in assuming that space and time must be either properties of things as they are in themselves or of representations, but not both, namely that we might have a priori knowledge of space and time because we have an a priori subjective representation of them while they are also objective properties of things. Some argue that there is no neglected alternative, because although the concepts of appearances and things in themselves are necessarily different, Kant postulates only one set of objects. This author has argued that the ‘neglected alternative’ is a genuine possibility that Kant intends to exclude by arguing from his premise that propositions about space and time are necessarily true: if those propositions were true both of our own representations and of their ontologically distinct objects, they might be necessarily true of the former but only contingently true of the latter, and thus not necessarily true throughout their domain (A 47–8/B 65–6). In this case, however, Kant’s transcendental idealism depends upon a dubious claim about necessary truth.'

Guyer, Paul