regard to mathematics. For he makes it clear that what should above all convince his readers of the correctness of his views of space and time is that these views alone can explain our possession of the synthetic a priori judgments of mathematics (see A 46–9/B 63–6).
Of course, the regressive method does not exclude the use of a direct manner of proof, either of space and time or of the pure concepts of the understanding. And to the extent that the direct method is employed in the first edition, it is still to be found in the second. However, given Kant’s own preference for the regressive method of proof for space and time even in the first edition, it would, I submit, be a mistake to deny its importance to his overall strategy. It is true that his famous transcendental deduction of the pure concepts of the understanding does not require the prior acceptance of the first principles of pure natural science: their certainty is employed only as a means of rejecting an empiricist derivation of the ‘pure’ concepts (B 128). But the transcendental deduction does require the prior acceptance of his views on space and time; and these views are, by Kant’s own admission, made ‘completely convincing’ because they alone can explain the synthetic a priori nature of mathematics (A 46/B 63).
But how can the regressive method be of primary importance to Kant when, in the later Critique of Practical Reason, he claims that the First Critique has been able to ‘overthrow’ scepticism with regard to natural science and mathematics (CPractR, 5:53)? There is, in reality, no inconsistency between this claim and the primacy of the regressive method. His point in the Critique of Practical Reason is that once it is recognized that the objects of the senses are mind-dependent (appearances), and not things in themselves, we can explain why scepticism concerning the objective validity of both natural science and mathematics can have no force.The sceptic alleges that no reply to his doubts can be offered; and he would be right, Kant agrees, if the objects of the senses were things in themselves. But, given that these objects are mind-dependent (appearances), we are enabled to overthrow scepticism by showing that both natural science and mathematics must apply to spatio-temporal objects. This attack on scepticism does not contradict Kant’s employment of the regressive method in the First Critique.Far from it: the attack relies on our first accepting the existence of mathematics, as a body of synthetic a priori judgments holding for the structure of space and time, in order to render completely certain the mind-dependence (the ideality) of space and time. Once this has been achieved, Kant is in a position to explain (in the Principles of Pure Understanding) why pure mathematics and natural science must apply to the objects in space and time. It is the explanation of these two disciplines’ objective validity – why they must apply to spatio-temporal objects – that Kant regards as overthrowing scepticism. The regressive method plays a vital initial role in this explanation because, as he sees it, that method can alone render fully convincing the ideal status of space and time.
3 The Transcendental Aesthetic: The Nature of Space and Time
In the Transcendental Aesthetic, Kant considers the relationship between space and time, on the one hand, and the modes or forms by which our senses are affected, on the other. These modes or forms he calls ‘the forms of our sensible intuition’. He will argue that space and time must be identified with the forms of our sensible intuition. It is this identification that will enable an explanation to be given of how pure mathematics can be a body of synthetic a priori judgments. Remember that, for Kant, it is certain that pure mathematics is a genuine body of such judgments: the question at issue is to account for their certainty.
All very well, you may say, but what are the forms of our sensible intuition? In common with most philosophers of the seventeenth and eighteenth centuries (as well as many before and since), Kant takes it that our senses can only give us any awareness of an object that exists outside the mind by means of sensations that it causes – or otherwise occasions – within the mind. Our capacity to apprehend sensations, occasioned by this mind-independent object, he calls ‘sensibility’ or ‘the faculty of representation’. The idea is that when this mind-independent object – to which he gives various names, including ‘the transcendental object’ and ‘the thing in itself’ – acts upon the mind’s faculty of representation, or sensibility, it produces an empirical intuition. An empirical intuition is a sense field containing a manifold of sensations (or representations). This manifold is collectively termed ‘an appearance’.An appearance always has two kinds of feature. First, there is the matter of the appearance: this corresponds to the content of the various sensations. In the case of an outer appearance – Kant’s own example is the representation of a body – its matter corresponds to the appearance’s particular colour, texture, hardness or softness, and so on (in other words, its secondary qualities). Second, there is the form of the appearance: in the case of an outer appearance, this corresponds to its particular extension and figure.
His claim is that although the matter of an appearance depends upon the way in which our faculty of representation happens to be affected by the transcendental object, the form or forms in which any possible appearance is located – the ways in which the sensations’ contents can appear individually and be disposed collectively – must already exist in the mind. ‘That in which alone the sensations can be posited and ordered in a certain form, cannot itself be sensation; and therefore, while the matter of all appearance is given to us a posteriori only, its form must lie a priori in the mind, and so must allow of being considered apart from all sensation’ (A 20/B 34).
When it is said that the form of any appearance must already exist in the mind, Kant does not of course mean that the particular extension or shape of any actual outer appearance already exists in the mind. Its particular shape and extension will depend upon how, in a given case, the sensations are disposed. This, in turn, will depend upon the way in which we are affected by the transcendental object. But the possibility of our having sensations, and of our apprehending their contents in particular relationships, does require the mind to possess its own mode or modes of sensible receptivity. Without such a mode or modes of receptivity already existing in the mind, it would be impossible to be conscious of an appearance. For an appearance is constituted by an array of sensations, sensed in a particular relationship. In short, Kant’s point is that if the mind did not possess a faculty for apprehending sensations and for sensing the relationships between them, there could be no consciousness of an appearance. Unless there exists in the mind a mode or modes of receptivity by which it can become conscious of sensations and their relationships, no consciousness of an appearance would be possible. So, while the matter of an appearance depends on the ways in which our mind happens to be affected by the transcendental object – and hence the specific contents of sensations can be determined only empirically or a posteriori – there must exist in the mind, independently of any action of the transcendental object upon it (and hence a priori), a mode or modes of sensible receptivity by which it is able to apprehend sensations, both singly and collectively. Such a mode of receptivity Kant calls an a priori or pure form of sensible intuition.
The point is illustrated, and further developed, by means of a thought-experiment with an outer appearance. If we subtract from the empirical intuition of a body the contribution made by sensations, viz. the body’s colour, texture, etc.; and if we also subtract anything that the understanding may contribute, viz. features like force and permanence; we still possess the capacity to draw the shape or outline of that appearance – or indeed of any possible outer appearance – even though no actual appearance is now being apprehended. Our capacity to draw the form – the extension and shape – of any possible outer appearance, even when no appearance is actually present to the senses, shows that there must exist in the mind the capacity to form pure intuitions. This further supports Kant’s claim that our sensibility must itself possess the form or forms necessary for apprehending and relating together the matter of any appearance. With respect to the form of an outer appearance, he says that ‘extension and figure . . . belong to pure intuition, which even without any actual object of the senses or sensation, exists in the mind a priori as a mere form of sensibility’ (A 21/B 35).
The
