﻿ What Is a Thing? 75 75

of a series. What we now take cognizance of is not created from any of' the things. We take what we ourselves somehow already have. What must be understood as mathematical is what we can learn in this way.

We take cognizance of all this and learn it without regard for the things. Numbers are the most familiar form of the mathematical because, in our usual dealing with things, when we calculate or count, numbers are the closest to that which we recognize in things without creating it from them. For this reason numbers are the most familiar form of the mathematical. In this way, this most familiar mathematical becomes mathematics. But the essence of the mathematical does not lie in number as purely delimiting the pure "how much," but vice versa. Because number has such a nature, therefore, it belongs to the learnable in the sense of μάθησις.

Our expression "the mathematical" always has two meanings. It means, first, what can be learned in the manner we have: indicated, and only in that way, and, second. the manner of learning and the process itself. The mathematical is that evident aspect of things within which we are always already moving and according to which we experience them as things at all, and as such things. The mathematical is this fundamental position we take toward things by which we take up things as already given to us, and as they should be given. Therefore, the mathematical is the fundamental presupposition of the knowledge of things.

Therefore, Plato put over the entrance to his Academy ) the words: Ἀγεωμέτρητος μηδεὶς εἰσίτω! "Let no one who has not grasped the mathematical enter here!"16 These words do not mean that one must be educated in only one subject—"geometry"—but that he must grasp that the fundamental condition for the proper possibility of knowing is

16 Elias Phlilosophus, sixth century A.D. Neoplatonist, in Aristotelis Categorias Commentaria (Commentaria in Aristotelem Graeca), A. Busse. ed. (Berlin, 1900), 118.18. Trans.