Kant - Andrew Ward

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therefore, but that we are actually in possession of such judgments in natural science. What is needed is an explanation of how we can possess them.

      The role of mathematics and natural science in Kant’s overall strategy

      Whatever reservations there may be concerning Kant’s claims about the status of the fundamental judgments of mathematics and natural science, it is a central part of his strategy that these judgments – most importantly, those in mathematics – are acknowledged, at the beginning of his critical enquiries, as having genuine synthetic a priori validity. By the time he wrote the second edition of the First Critique,he had self-consciously adopted what he calls ‘the regressive method’ of substantiating his position. That is, he begins with what he regards as two sets of incontestably genuine synthetic a priori judgments – the judgments of pure mathematics and pure natural science – and proceeds to argue back from them to their necessary presuppositions. He had, in fact, given a key place to this regressive procedure, in the first edition, with 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).

      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.

      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.

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