A Case For The Utility Of The Mathematical Intermediates

Philosophia Mathematica 20 (2):200-223 (2012)
Abstract
Many have argued against the claim that Plato posited the mathematical objects that are the subjects of Metaphysics M and N. This paper shifts the burden of proof onto these objectors to show that Plato did not posit these entities. It does so by making two claims: first, that Plato should posit the mathematical Intermediates because Forms and physical objects are ill suited in comparison to Intermediates to serve as the objects of mathematics; second, that their utility, combined with Aristotle’s commentary on Plato’s posit of Intermediates, provides good reason to conclude that Plato did posit them
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