The Platonist Absurd Accumulation of Geometrical Objects: Metaphysics Μ.2

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  • 1 Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, Circuito Mario de la Cueva s/n, 04510, Ciudad de México, Mexico

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In the first argument of Metaphysics Μ.2 against the Platonist introduction of separate mathematical objects, Aristotle purports to show that positing separate geometrical objects to explain geometrical facts generates an ‘absurd accumulation’ of geometrical objects. Interpretations of the argument have varied widely. I distinguish between two types of interpretation, corrective and non-corrective interpretations. Here I defend a new, and more systematic, non-corrective interpretation that takes the argument as a serious and very interesting challenge to the Platonist.

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