Aristotle’s Philosophy of Geometry

Abstract

AbstractA principal interpretative difficulty for Aristotle’s philosophy of geometry is that he seems to maintain both that sensible things are not the objects of geometry and that geometrical objects are in the sensible world. In this paper I offer a philosophical defence of what I take to be Aristotle’s position. Briefly, geometrical objects are certain sensibles (e.g. skilfully produced construction drawings) just insofar as they are quantitative and continuous. A geometrical object, then, is what some scholars call a ‘kooky object’: a sensible object just insofar as it has a certain property or set of properties. I call this the ‘kooky objects interpretation’; it is a refinement of the ‘properties interpretation’ (a view I give elsewhere). I develop the view and argue that it is superior to an alternative reading—the ‘parts interpretation’. I show that the kooky objects interpretation addresses the difficulties motivating the parts interpretation while steering clear of its problems.