Abstract

GONZALEZ-VARELA, José Edgar. Points, Units and Numbers: Metaphysics M.2 (1076b36-39). Prax. filos. [online]. 2020, n.50, pp.21-40. ISSN 0120-4688.  https://doi.org/10.25100/pfilosofica.v0i50.8701.

In Metaphysics M.2 Aristotle develops several objections against the Platonist introduction of mathematical objects as non-sensible substances, separate from sensibles. His first objection has a two-fold nature. Firstly, Aristotle argues that positing separate geometrical objects produces an absurd accumulation. Secondly, he suggests that this geometrical argument can be extended to the case of units and numbers. In this paper I explain this arithmetical extension. Scholars have interpreted this extension in, what I call, a ‘maximalist’ way. Here I defend a different, ‘minimalist’, interpretation.

Keywords : Priority; Geometric Objects; Mathematical Numbers; Platonism; Separation.

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