Chiara Martini

Epicurus’ original version of atomism takes atoms to be physically indivisible but not completely unanalysable: each atom contains a finite number of minima. This paper explores the nature of the minima by focusing on a specific question: in which sense are the minima minimal? I do so by investigating the notions of parthood and divisibility into parts that are at play in paragraphs 56–59 of the Letter to Herodotus, where the theory of minima is introduced. By focusing on the analogy (noticed by Francesco Verde) between Epicurean minima and Aristotelian limits, I argue that the minima should be understood as the minimal realiser of the atom’s physical functions. This allows me to keep together two very plausible but apparently incompatible claims: (i) the minima are supposed to block the paradoxes of theoretical divisibility, but (ii) their existence and their indivisibility can only be justified in physical (rather than geometrical) terms

Graduate Papers from the 2022 Joint Session. 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.