The Perfection of Bodies: Aristotle's De Caelo I.1

In this paper we give a detailed reconstruction of the first chapter of De Caelo I.1. Aristotle attempts to prove there that bodies are complete and perfect in virtue of being extended in three dimensions. We offer an analysis of this argument and argue that it gives important insight into the role the notion of body plays in physical science. Contrary to other interpretations, we argue that it is an argument about physical, as opposed to mathematical, bodies and that the perfection and completeness of bodies is due to their nature. Moreover, Aristotle heavily relies in his proof on the premise that the number three implies perfection, a view he ascribes to the Pythagoreans. We review the possible sources of this view, as well as its role in Aristotle's argumentative strategy.