In view of the derivation of the forms of thought from the forms of judgment Kant does not stop to give a detailed proof that the categories are concepts, and that they are pure.  Their discursive (not intuitive) character is evident from the fact that their reference to the object is mediate only (and not, as in the case of intuition, immediate), and their a priori origin, from the necessity which they carry with them, and which would be impossible if their origin were empirical.  Here Kant starts from Hume’s criticism of the idea of cause.  The Scottish skeptic had said that the necessary bond between cause and effect can neither be perceived nor logically demonstrated; that, therefore, the relation of causality is an idea which we—­with what right?—­add to perceived succession in time.  This doubt (without the hasty conclusions), says Kant, must be generalized, must be extended to the category of substance (which had been already done by Hume, pp. 226-7, though the author of the Critique of Reason was not aware of the fact), and to all other pure concepts of the understanding.  Then we may hope to kindle a torch at the spark which Hume struck out.  The problem “It is impossible to see why, because something exists, something else must necessarily exist,” is the starting point alike of Hume’s skepticism and Kant’s criticism.  The former recognized that the principle of causality is neither empirical nor analytic, and therefore concluded that it is an invention of reason, which confuses subjective with objective necessity.  The latter shows that in spite of its subjective origin it has an objective value; that it is a truth which is independent of all experience, and yet valid for all who have experience, and for all that can be experienced.

Of the two questions, “How can the concepts which spring from our understanding possess objective validity?” and, “How (through what means or media) does their application to objects of experience take place?” the first is answered in the Deduction of the Pure Concepts of the Understanding, and the second in the chapter on their Schematism.

The Deduction, the most difficult portion of the Critique, shows that the objective validity of the categories, as concepts of objects in general, depends on the fact that through them alone experience as far as regards the form of thought is possible, i.e._, it is only through them that any object whatever can be thought.  All knowledge consists in judgments; all judgments contain a connection of representations; all connection—­whether it be conscious or not, whether it relates to concepts or to pure or empirical intuitions—­is an act of the understanding; it cannot be given by objects, but only spontaneously performed by the subject itself.  We cannot represent anything as connected in the object unless we have ourselves first connected it.  The connection includes three conceptions:  that of the manifold to be connected