Measure and Continuity in Aristotle’s Physics V,3 (and Neighbourhoods)

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"As surprising as it might appear prima facie, it is not so much after a little reflexion. Whatever role measure could have played in Aristotle’s time in physics and mathematics, was depending on the content of the available mathematical theories, which is something Aristotle had less to say on, or even about which he never tried to say something. His attitude toward mathematics was always unequivocal: he certainly tried (without much success, by the way, as shown by the quite ambiguous claims of Metaphysics M 1-3) to understand its epistemic nature by so continuing, in a quite different direction, a reflexion already initiated by Plato, but he always took it as a datum, as an established portion of knowledge that is not to be contradicted. He never tried to improve or clarify it. What he says about measure seems to confirm this attitude. To clarify this point, a short survey of the mathematical conceptions of measure at his time, and of the way they differ from our present ones, is in order."


This is a pre-copy-editing, author-produced PDF of a chapter accepted for publication in Giovanna Giardina (Ed.), To Metron. Sur la notion de mesure dans la philosophie d'Aristote. This version may not exactly replicate the final published version.