Thus the criticisms which we have already passed upon Kant’s mode of formulating the distinction between formal and transcendental logic,[1104] are no less applicable to the sections now before us. The terminology which Kant is here employing is borrowed from the traditional logic, and is out of harmony with his Critical principles.
Kant’s description of the schema as a third thing, additional to category and intuition, and intermediate between them, is also a result of his misleading mode of formulating his problem. What Kant professes to do is to interpret the relation of the categories to the intuitional material as analogous to that holding between a class concept and the particulars which can be subsumed under it. This is implied in his use of the plate and circle illustration.[1105] But as the relation holding between categories and the material of sense is that of form and matter, structure and content, the analogy is thoroughly misleading. As all content, strictly so called, falls on the side of the intuitional material, there is no content, i.e. no quality or attribute, which is common to both. And thus it happens that the inappropriateness of the analogy which Kant is seeking to enforce is ultimately the sole ground which he is able to offer in support of his description of the schema as “a third thing.”
“Now it is clear [!] that there must be a third thing, which is homogeneous on the one hand with the category and on the other with the appearance, and which thus makes the application of the one to the other possible.”[1106]
On the contrary, the true Critical teaching is that category and intuition, that is to say, form and content, mutually condition one another, and that the so-called schema is simply a name for the latter as apprehended in terms of the former.
But there is a further complication. Kant, as we have already observed,[1107] defines judgment as being
“...the faculty of subsuming under rules, i.e. of distinguishing whether something does or does not stand under a given rule (casus datae legis).”
Now this view of judgment really connects with the syllogism, not with the proposition.[1108] As Kant states in his Logic, there are
“...three essential elements in all inference: (1) a universal rule which is entitled the major premiss; (2) the proposition which subsumes a cognition under the condition of the universal rule, and which is entitled the minor premiss; and lastly, (3) the conclusion, the proposition which asserts or denies of the subsumed cognition the predicate of the rule.”[1109]
Regarded in this way, as the application of a rule, subsumption is more broadly viewed and becomes a more appropriate analogy for the relation of category to content. And obviously it is this comparison that Kant has chiefly in mind in these introductory sections. For only when the subsumption is that of a particular instance under a universal rule, can the necessity of a mediating condition be allowed.
Such, then, are the straits to which Kant is reduced in the endeavour to hold loyally to his architectonic. He has to identify the two very different kinds of subsumption which find expression in the proposition and in the syllogism respectively; and when his analogy between logical subsumption, thus loosely interpreted, and synthetic interpretation, proves inapplicable, he uses the failure of the analogy as an argument to prove the necessity of “a third thing.” On his own Critical teaching, as elsewhere expounded, no such third thing need be postulated. Even the definitions which he proceeds to give of the various schemata do not really support this description of them.