@article{Shatalov_2020, title={Continuity and Mathematical Ontology in Aristotle}, volume={14}, url={https://www.revistas.usp.br/filosofiaantiga/article/view/169952}, DOI={10.11606/issn.1981-9471.v14i1p30-61}, abstractNote={<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>}, number={1}, journal={Journal of Ancient Philosophy}, author={Shatalov, Keren Wilson}, year={2020}, month={May}, pages={30-61} }