Phronesis 65 (1):76-115 (2020)

Authors
Edgar González-Varela
National Autonomous University of Mexico
Abstract
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.
Keywords Aristotle  composition  geometry  grounding  mathematical objects  priority  regress argument  separation
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DOI 10.1163/15685284-12342074
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References found in this work BETA

On What Grounds What.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
The Question of Realism.Kit Fine - 2001 - Philosophers' Imprint 1:1-30.
On the Plurality of Grounds.Shamik Dasgupta - 2014 - Philosophers' Imprint 14.

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