Suppose, however, we waive the difficulty involved in the plurality of the categories. There remains the equally fundamental difficulty that any single principle of synthesis contains in itself no ground for the different ways of its application.[2] Suppose it to be conceded that in the apprehension of definite shapes we combine the manifold in accordance with the conception of figure, and, for the purpose of the argument, that the conception of figure can be treated as equivalent to the category of quantity. It is plain that we apprehend different shapes, e. g. lines[3] and triangles[4], of which, if we take into account differences of relative length of sides, there is an infinite variety, and houses,[5] which may also have an infinite variety of shape. But there is nothing in the mind's capacity of relating the manifold by way of figure to determine it to combine a given manifold into a figure of one kind rather than into a figure of any other kind; for to combine the manifold into a particular shape, there is needed not merely the thought of a figure in general, but the thought of a definite figure. No 'cue' can be furnished by the manifold itself, for any such cue would involve the conception of a particular figure, and would therefore imply that the particular synthesis was implicit in the manifold itself, in which case it would not be true that all synthesis comes from the mind.
This difficulty takes a somewhat different form in the case of the categories of relation. To take the case of cause and effect, the conception of which, according to Kant, is involved in our apprehension of a succession, Kant's view seems to be that we become aware of two elements of the manifold A B as a succession of events in the world of nature by combining them as necessarily successive in a causal order, in which the state of affairs which precedes B and which contains A contains something upon which B must follow (i. e. a cause of B), which therefore makes it necessary that B must follow A.[6] But if we are to do this, we must in some way succeed in selecting or picking out from among the elements of the manifold that element A which is to be thus combined with B. We therefore need something more than the category. It is not enough that we should think that B has a cause; we must think of something in particular as the cause of B, and we must think of it either as coexistent with, or as identical with, A.