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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 mind, then, has a faculty of sensible receptivity (sensibility) through which it has the power to form pure intuitions. We have seen this power illustrated by the above thought-experiment; and Kant will later claim that it is crucially at work in the construction of geometrical figures and arithmetical products. He holds that the mind possesses two forms of sensible intuition: that by which extension and figure are represented is called ‘outer intuition’, and that by which succession and the simultaneous are represented is called ‘inner intuition’. It is because the mind possesses these two a priori forms of sensible intuition that it can also become conscious of appearances – that is, of empirical intuitions.When the object which exists independently of the mind (the thing in itself, or transcendental object) affects our sensibility, we become conscious of appearance(s) in outer or inner intuition: in other words, we have an outer or inner empirical intuition.