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We can now consider Kant’s detailed arguments about space. He begins by saying that there are three possible views about space. The first view is the newtonian that they are existents of a substantial kind which could and would exist even if there were no things or events to occupy them and no persons to intuit them. The second view is the leibnizian that they are a system of actual and possible relations between actual and possible things of events, that these relations would hold whether the things and events were perceived or not. The third is Kant’s own view, which he here describes by saying that "they belong only to the form of intuition, and therefore to the subjective constitution of our minds, apart from which they could not be ascribed to anything whatever". Coming to detail we find that Kant tries to prove the following two things about space. (1) That our knowledge of space is in some sense a priori and not empirical. (2) That this knowledge is in some sense intuitive and not merely discursive. He has two arguments specially directed to prove the first point, and two specially directed to prove the second. In addition to these he has two other arguments, each of which is supposed to prove both points. The first is called the argument from incongruent counterparts, i.e. from the existence of such pairs of objects as left and right hands, objects and their mirror-images, etc. The second is from the nature of our knowledge of geometry. I shall now take these arguments in turn, and consider in each case what, if anything, the argument proves. What Kant proposed might, I think, be formulated as follows. He proposes to assign to each percipient his own absolute space, and to make it subjective and innate to each individual human mind. He thus gets rid of the metaphysical difficulties in Newton’s theory. But he is able to hold that each person’s innate absolute space is a kind of individual whole with which that person actually is or conceivably might be directly acquainted. This kind of acquaintance he calls pure or a priori intuition, in contrast to acquaintance with particular things in space, which involves sensation. When a person has a experience which we should describe as seeing an external object of a certain size and shape, localized at a certain place, what is happening is the following. (We are here confining our attention to the intuitive factors in the process, and ignoring the factors to belong to thought, which Kant regards as equally essential.) An independent foreign existent is producing an effect in the observer’s mind, which may be called a ’sense-impression’. This has a certain determinate sensible quality, e.g. a certain shade of red, but it has no spatial characteristics. Presumably, however, it has a certain determinate form of a certain determinable non-spatial characteristic which C. D. Broad has called the ’space-locating property’. The occurrence of such a sense-impression furnishes the occasion on which the observes’s mind automatically presents to itself a certain region of its innate intuited absolute space as pervaded by a certain sensible quality and thus marked out from the rest. That which determines the precise shape, size and location of the region thus marked out is the determinate form of the space-locating property possessed by the sense-impression. That which determines the sensible quality pervading that region is the sensible quality of the impression. Since each of us is directly acquainted, through pure intuition, with his own private absolute space, and since it is innate to and wholly dependent on his mind, Kant thinks that each of us can have genuine knowledge of its properties. This knowledge is our knowledge of pure geometry. Any extended external objects which a person could ever perceive would be simply a region of his own innate absolute space, which his mind presents to itself as marked out by certain sensible qualities on the occasion of having certain sensations. Therefore every proposition of pure geometry will certainly apply to every extended object that one could ever perceive. But there is no reason whatever to suppose that the independent foreign things, which produce the sensations on which our minds build up perceptions of extended localized, coloured objects, are themselves extended or localized, any more than there is to suppose that they are coloured. Suppose it were alleged that we derive our ideas of determinate shapes, sizes, and spatial relations by abstraction from perceived extended objects, and then proceed to generalise and amplify and idealise until we reach the refined concepts of pure geometry. Then I think that Kant would make two answers. (a) The empirical data would not lead to the concept of a single all-enbracing infinite and infinitely divisible three-dimensional space, unless the processes of abstracting and generalising and idealising were conducted in accordance with certain notions and principles which are innate in the mind. (b) In any case what you arrive at by all these processes is something which is logically prior to every particular extended localized perceptible object, viz. the innate absolute space in which any such object is simple a particular region marked out by certain sensible qualities. But this theory is open to several objections. First, Kant has not proved even that space is a priori. He has proved this about cause and substance, if we were to accept his arguments about the Transcendental Deduction of the Categories. But he never suggests that the form of spatial intuition might not change in course of time for the same person, or that it must be the same in its determinate details for everyone. Second, we can consider Kant’s distinction between pure and empirical intuition. Kant says that "the matter of all phenomena is given to us a posteriori only, its form must lie ready a priori in all sensation." But Kant offers no reason here for this assertion. Third, at the crucial stage in the second edition version of Transcendental Deduction, Kant provides the distinction between the form of intuition and the formal intuition. Kant says that time and space are each given twice - once as ’form of intuition’ and again as ’formal intuition’. A formal intuition is, in a sense, the representation of an ’object’. Since there should be a unity, a ’combination’(Zusammenfassung) or ’synthesis’ of a ’manifold’ is required. The results of this synthesis - time and space as ’objects’, i.e. unified ’formal intuitions’ - are said to be themselves ’given as intuitions’ whose unity ’precedes any concept’. But this synthesis is said tto be effected the understanding. Therefore, we can not provide the distinction between the synthesis of formal intuition and on of understanding. Fourth, Near the tail of the Critique, Kant makes the positive assertion that the notion of infinite space is, in his technical sense, an idea of reason. This would quite definitely make the notion conceptual, and would quite definitely rule out the possibility that any human being should be acquainted (even non-sensuously) with space as an individual whole.Finally, Kant evidently supposes that if space be a priori, in the sense of being a mind - dependent intuitum, my knowledge of its properties and therefore my knowledge of pure geometry must be a priori, in the sense of intuitively or demonstratively certain. But it is a pure hypothesis that the mere fact that something depends on our minds is a guarantee that we can have adequate and accurate knowledge of it. Even if space were mind-dependent, I should still have to learn about its properties by inspection. There would be no guarantee that its properties would be the same in all its parts, or the same on Tuesdays as on Fridays.
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