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Aristotelian Continua (2016)

Linnebo, O., Shapiro, S., Hellman, G.

Oxford University Press

In: Philosophia Mathematica

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Publication Date: 2016-06-21

Description: In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems (such as the existence of bisections) that have to be added as axioms. Building on some work by Linnebo, we then show how to take the ‘potential’ nature of the usual operations seriously, by using a modal language, and we show that the two approaches are equivalent.

Print ISSN: 0031-8019

Electronic ISSN: 1744-6406

Topics: Mathematics , Philosophy

Published by Oxford University Press

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