Inconsistent Continuous Functions

Abstract

The idea that motion or change is an inconsistent process has, as is well known, a long history. Recent nice work by Graham Priest [46] suggests that an inconsistent account of motion and change is at least possible. It is a further matter whether it is true; and despite Priest’s arguments, there does not seem to be a compelling reason for rejecting the existing consistent account from classical physics, which is mathematically both simple and elegant. Priest argues that the classical account has it that motion is being in different places at different times; whereas what he wants is an intrinsic account of motion according to which an instantaneous state ought to be unambiguously change or nonchange, independently of its (distance) relations to other states. Against this, one is inclined to argue that the relations are nonetheless present; that an account in which the relations alone carry the change is therefore inevitably simpler; and that being in different places at different times is surely necessary for motion, and more importantly (at least given a positive definite metric) sufficient as well.