Mathematics and Physics

Abstract

In the last chapter the subject of our investigations is mathematics and its role as an auxiliary discipline for physics. It is undenied, I presume, that mathematics as a pure construction of the human mind has foundations of its own independent of physics and indeed of any other discipline. Many would, however, say that the reverse does not hold — that the physics of our day cannot exist without mathematics applied to and indeed, as it were, embodied in it. But even this has been denied: there are attempts at an elimination of mathematics from physics to a certain extent. 1 The other extreme was Kant’s position. For Kant mathematics and physics are at least partially identical, at any rate in geometry. Elimination of geometry from physics would then be impossible without destroying the latter. In the papers of the present chapter it is assumed without discussion that for the formulation of physical theories the use of mathematics is at least very expedient if not indispensable. There is then, of course, the question of which status one allows mathematics to have by itself and how it occurs as such when applied to physical science.