We may now consider Kant's conclusion in abstraction from the arguments by which he reaches it. It raises three main difficulties.

In the first place, it is not the conclusion to be expected from Kant's own standpoint. The phenomenal character of space is inferred, not from the fact that we make judgements at all, but from the fact that we make judgements of a particular kind, viz. a priori judgements. From this point of view empirical judgements present no difficulty. It should, therefore, be expected that the qualities which we attribute to things in empirical judgements are not phenomenal, but belong to things as they are. Kant himself implies this in drawing his conclusion concerning the nature of space. "Space does not represent any quality of things in themselves or things in relation to one another; that is, it does not represent any determination of things which would attach to the objects themselves and would remain, even though we abstracted from all subjective conditions of perception. For neither absolute nor relative[56] determinations of objects can be perceived prior to the existence of the things to which they belong, and therefore not a priori."[57] It is, of course, implied that in experience, where we do not discover determinations of objects prior to the existence of the objects, we do apprehend determinations of things as they are in themselves, and not as they are in relation to us. Thus we should expect the conclusion to be, not that all that we know is phenomenal—which is Kant's real position—but that spatial (and temporal) relations alone are phenomenal, i. e. that they alone are the result of a transmutation due to the nature of our perceiving faculties.[58] This conclusion would, of course, be absurd, for what Kant considers to be the empirically known qualities of objects disappear, if the spatial character of objects is removed. Moreover, Kant is prevented by his theory of perception from seeing that this is the real solution of his problem, absurd though it may be. Since perception is held to arise through the origination of sensations by things in themselves, empirical knowledge is naturally thought of as knowledge about sensations, and since sensations are palpably within the mind, and are held to be due to things in themselves, knowledge about sensations can be regarded as phenomenal.

On the other hand, if we consider Kant's conclusion from the point of view, not of the problem which originates it, but of the distinction in terms of which he states it, viz. that between things as they are in themselves and things as perceived by us, we are led to expect the contrary result. Since perception is the being affected by things, and since the nature of the affection depends upon the nature of our capacity of being affected, in all perception the object will become distorted or transformed, as it were, by our capacity of being affected. The conclusion, therefore, should be that in all judgements, empirical as well as a priori, we apprehend things only as perceived. The reason why Kant does not draw this conclusion is probably that given above, viz. that by the time Kant reaches the solution of his problem empirical knowledge has come to relate to sensation only; consequently, it has ceased to occur to him that empirical judgements could possibly give us knowledge of things as they are. Nevertheless, Kant should not have retained in his formulation of the problem a distinction irreconcilable with his solution of it; and if he had realized that he was doing so he might have been compelled to modify his whole view.

The second difficulty is more serious. If the truth of geometrical judgements presupposes that space is only a property of objects as perceived by us, it is a paradox that geometricians should be convinced, as they are, of the truth of their judgements. They undoubtedly think that their judgements apply to things as they are in themselves, and not merely as they appear to us. They certainly do not think that the relations which they discover apply to objects only as perceived. Not only, therefore, do they not think that bodies in space are phenomena, but they do not even leave it an open question whether bodies are phenomena or not. Hence, if Kant be right, they are really in a state of illusion, for on his view the true geometrical judgement should include in itself the phenomenal character of spatial relations; it should be illustrated by expressing Euclid I. 5 in the form that the equality of the angles at the base of an isosceles triangle belongs to objects as perceived. Kant himself lays this down. "The proposition 'all objects are beside one another in space' is valid under[59] the limitation that these things are taken as objects of our sensuous perception. If I join the condition to the perception, and say 'all things, as external phenomena, are beside one another in space', the rule is valid universally, and without limitation."[60] Kant, then, is in effect allowing that it is possible for geometricians to make judgements, of the necessity of which they are convinced, and yet to be wrong; and that, therefore, the apprehension of the necessity of a judgement is no ground of its truth. It follows that the truth of geometrical judgements can no longer be accepted as a starting-point of discussion, and, therefore, as a ground for inferring the phenomenal character of space.

There seems, indeed, one way of avoiding this consequence, viz. to suppose that for Kant it was an absolute starting-point, which nothing would have caused him to abandon, that only those judgements of which we apprehend the necessity are true. It would, of course, follow that geometricians would be unable to apprehend the necessity of geometrical judgements, and therefore to make such judgements, until they had discovered that things as spatial were only phenomena. It would not be enough that they should think that the phenomenal or non-phenomenal character of things as spatial must be left an open question for the theory of knowledge to decide. In this way the necessity of admitting the illusory character of geometry would be avoided. The remedy, however, is at least as bad as the disease. For it would imply that geometry must be preceded by a theory of knowledge, which is palpably contrary to fact. Nor could Kant accept it; for he avowedly bases his theory of knowledge, i. e. his view that objects as spatial are phenomena, upon the truth of geometry; this procedure would be circular if the making of true geometrical judgements was allowed to require the prior adoption of his theory of knowledge.

The third difficulty is the most fundamental. Kant's conclusion (and also, of course, his argument) presupposes the validity of the distinction between phenomena and things in themselves. If, then, this distinction should prove untenable in principle, Kant's conclusion with regard to space must fail on general grounds, and it will even have been unnecessary to consider his arguments for it. The importance of the issue, however, requires that it should be considered in a separate chapter.

Note to page 47.

The argument is not affected by the contention that, while the totality of spaces is infinite, the totality of colours or, at any rate, the totality of instances of some other characteristic of objects is finite; for this difference will involve no difference in respect of perception and conception. In both cases the apprehension that there is a totality will be reached in the same way, i. e. through the conception of the characteristic in general, and the apprehension in the one case that the totality is infinite and in the other that it is finite will depend on the apprehension of the special nature of the characteristic in question.

FOOTNOTES

[1] B. 58, M. 35.