TY - JOUR
AU - Shatalov, Keren Wilson
PY - 2020/05/22
Y2 - 2023/12/01
TI - Continuity and Mathematical Ontology in Aristotle
JF - Journal of Ancient Philosophy
JA - J. anc. philos. (Engl. ed.)
VL - 14
IS - 1
SE -
DO - 10.11606/issn.1981-9471.v14i1p30-61
UR - https://www.revistas.usp.br/filosofiaantiga/article/view/169952
SP - 30-61
AB - <p>In this paper I argue that Aristotle's understanding of mathematical continuity constrains the mathematical ontology he can consistently hold. On my reading, Aristotle can only be a mathematical abstractionist of a certain sort. To show this, I first present an analysis of Aristotle's notion of continuity by bringing together texts from his Metaphysica and Physica, to show that continuity is, for Aristotle, a certain kind of per se unity, and that upon this rests his distinction between continuity and contiguity. Next I argue briefly that Aristotle intends for his discussion of continuity to apply to pure mathematical objects such as lines and figures, as well as to extended bodies. I show that this leads him to a difficulty, for it does not at first appear that the distinction between continuity and contiguity can be preserved for abstract mathematicals. Finally, I present a solution according to which Aristotle's understanding of continuity can only be saved if he holds a certain kind of mathematical ontology.</p>
ER -