Note 67 — Introductory material

Helmholtz's criterion of apriority is difficult to discover, as he never, to my knowledge, gives a precise statement of it. From his discussion of physical and transcendental Geometry[84], however, it would appear that he regards as empirical whatever applies to empirical matter. For he there maintains, that even if space were an à priori form, yet any Geometry, which aimed at an application to Physics, would, since the actual places of bodies are not known à priori, be necessarily empirical[85]. It seems the more probable that he regards this as a possible criterion, as it is adopted, in several passages, by his disciple Erdmann[86], and so strange a test could hardly be accepted by a philosopher, unless he had found it in his master. I have called this a strange test, because it seems to me completely to ignore the work of the Critical Philosophy. For if there is one thing which, one might have hoped, had been made sufficiently clear by Kant's Critique, it is this, that knowledge which is à priori, being itself the condition of possible experience, applies—and in Kant's view, applies only—to empirical matter. Helmholtz and Erdmann, therefore, in setting up this test without discussion, simply ignore the existence of Kant and the possibility of a transcendental argument. Helmholtz assumes always that empirical knowledge must be wholly empirical, that there can be no à priori conditions of the experience in question, that experience will always be possible, and may give any kind of result. Thus in discussing "physical" Geometry, he assumes that the possibility of empirical measurement involves no à priori axioms, and that no à priori element can be contained in the process. This assumption, as we shall see in Chapter III., is quite unwarrantable: certain properties of space, in fact, are involved in the possibility of measuring matter. In spite of the fact, therefore, that we apply measurement to empirical matter, and that our results are therefore empirical, there may well be an à priori element in measurement, which is presupposed in its possibility. Such a criterion, therefore, must pronounce everything empirical, but must itself be pronounced worthless.