Geometrical Changes: Change and Motion in Aristotle’s Philosophy of Geometry

Abstract

Abstract It is often said that Aristotle takes geometrical objects to be absolutely unmovable and unchangeable. However, Greek geometrical practice does appeal to motion and change, and geometers seem to consider their objects apt to be manipulated. In this paper, I examine if and how Aristotle’s philosophy of geometry can account for the geometers’ practices and way of talking. First, I illustrate three different ways in which Greek geometry appeals to change. Second, I examine Aristotle’s ontology of geometrical objects and argue that although the truth-makers of geometrical statements are in fact unmovable because they are properties of sensible objects, geometers ‘separate them in thought’ and treat them as substances apt to be modified. Finally, I examine whether allowing for the possibility of manipulating these semi-fictional geometrical individuals creates problems for the applicability of geometry. I find that it does not, insofar as one accepts that geometry is not meant to track physical change but merely to study the instantaneous geometrical configuration of sensible bodies, and is thus only applicable at the instant.