Points, Units and Numbers: Metaphysics M.2 (1076b36-39)

https://doi.org/10.25100/pfilosofica.v0i50.8701

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Published: Jan 15, 2020
Issue: No. 50 (2020): Núm. 50 (2020): Praxis Filosófica No. 50
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Authors

  José Edgar González-Varela Institute of Philosophical Research, Universidad Nacional Autónoma de México, Mexico City, Mexico.
Abstract

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
Author Biography

José Edgar González-Varela, Institute of Philosophical Research, Universidad Nacional Autónoma de México, Mexico City, Mexico.

Full researcher at the Institute of Philosophical Research of the Universidad Nacional Autónoma de México. Doctor of Philosophy from the University of Sheffield, United Kingdom. His areas of specialization are the history of ancient philosophy, particularly the metaphysics of Plato and Aristotle, and contemporary metaphysics. He has published articles on these topics in specialized journals such as Philosophy and Phenomenological Research, Phronesis, Apeiron, Revista Latinoamericana de Filosofía, Diánoia and Ideas y Valores.

How to Cite
González-Varela, J. E. (2020). Points, Units and Numbers: Metaphysics M.2 (1076b36-39). Praxis Filosófica, (50), 21–40. https://doi.org/10.25100/pfilosofica.v0i50.8701
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