Mathematics

The way of doing physics typical of mathematical physics is contrasted with the way of doing physics theorised, and practised, by Aristotle, which is not extraneous to mathematics but deals with it in a completely different manner: not as a demonstrative tool but as a reservoir of analogies.

These two different uses are the tangible expression of two different underlying metaphysics of mathematics: two incommensurable metaphysics, which give rise to two incommensurable physics. I will illustrate this point by analyzing the paradigmatic case of Aristotle’s theory of motion and its relationship with hydrostatics (and with the theory of motion in a fluid). I will show that while Aristotle’s physics has been conceived in a fluid, it is impossible — and dangerous — to read it as the approximation of the Newtonian theory of motion in a fluid.