ARISTOTLE ON CONTINUITY

CONTINUOUS CONNECTION IN PHYS. V 3 AND THE MATHEMATICAL ACCOUNT OF MOTION AND TIME IN PHYS. VI

Abstract

Wholes have parts, and wholes are prior to parts according to Aristotle. Aristotle’s accounts of continuity, in Phys. V 3 (plus sections in Metaph. Δ 6 and Ι 1) on the one hand and in Phys. VI on the other, are specified in terms of ways in which wholes are related to parts. The synthesis account in Phys. V 3 etc. applies primarily to bodies (in, e.g., anatomy). It indicates a variety of ways in which parts of a body are kept together by a common boundary and are thereby combined into a mostly inhomogeneous, functional whole. Only the analysis account in Phys. VI applies primarily to linear continua such as movements, paths of movements, and time. The structure it indicates is only superficially described as indefinite divisibility: what matters is the transfer of potential divisions from path to movement and time (and conversely) which, surprisingly, requires an equivalent to Dedekind’s continuity principle to be tacitly presupposed. – In the present paper, my agenda will focus on the exposition of the relevant theories offered by Aristotle in Phys. V 3 and Phys. VI 1-2, respectively, with a view to the applications envisaged by Aristotle and to the mathematics involved.