[10] It may be objected that, from Kant's point of view, the thought of a rule of construction, and the thought of the principle of the whole to be constructed, are the same thing from different points of view. But if this be insisted on, the schema and its corresponding conception become the same thing regarded from different points of view; consequently the schema will not be a more concrete conception of an object than the corresponding conception, but it will be the conception itself.
If, therefore, Kant succeeds in finding schemata of the categories in detail in the sense in which they are required for the solution of his problem, i. e. in the sense of more concrete conceptions involving the thought of time and relating to objects, we should expect either that he ignores his general account of a schema, or that if he appeals to it, the appeal is irrelevant. This we find to be the case. His account of the first two transcendental schemata makes a wholly irrelevant appeal to the temporal process of synthesis on our part, while his account of the remaining schemata makes no attempt to appeal to it at all.
"The pure _schema_ of _quantity_, as a conception of the understanding, is _number_, a representation which comprises the successive addition of one to one (homogeneous elements). Accordingly, number is nothing else than the unity of the synthesis of the manifold of a homogeneous perception in general, in that I generate time itself in the apprehension of the perception."[11]
It is clear that this passage, whatever its precise interpretation may be,[12] involves a confusion between the thought of counting and that of number. The thought of number relates to objects of apprehension and does not involve the thought of time. The thought of counting, which presupposes the thought of number, relates to our apprehension of objects and involves the thought of time; it is the thought of a successive process on our part by which we count the number of units contained in what we already know to consist of units.[13] Now we must assume that the schema of quantity is really what Kant says it is, viz. number, or to express it more accurately, the thought of number, and not the thought of counting, with which he wrongly identifies it. For his main problem is to find conceptions which at once are more concrete than the categories and, at the same time, like the categories, relate to objects, and the thought of counting, though more concrete than that of number, does not relate to objects. Three consequences follow. In the first place, although the schema of quantity, i. e. the thought of number, is more concrete than the thought of quantity,[14] it is not, as it should be, more concrete in respect of time; for the thought of number does not include the thought of time. Secondly, the thought of time is only introduced into the schema of quantity irrelevantly by reference to the temporal process of _counting_, by which we come to apprehend the number of a given group of units. Thirdly, the schema of quantity is only in appearance connected with the nature of a schema in general, as Kant describes it, by a false identification of the thought of number with the thought of the process on our part by which we count groups of units, i. e. numbers.