The intermediate character of mathematics and the ontological structure of its elements by Plato and Aristotle

Authors

  • Gilfranco Lucena dos Santos Universidade Federal da Paraíba

DOI:

https://doi.org/10.14195/1984-249X_19_5

Keywords:

Plato, Aristotle, Mathematics

Abstract

This article examines the ontological structure of mathematical “objects”, focusing on the opposing views of books VI-VII of Plato’s Republic and books XIII-XIV of Aristotle’s Metaphysics. Plato understands Mathematics as a means or a path (method) of obtaining a philosophical education, and considers the “subject” of Mathematics as á½‘ποθέσει, rather than Î¿á½ÏƒÎ¯Î±Î¹ (separate entities). In agreement with Plato, Aristotle seeks to describe the ontological structure of mathematical “objects” not as Î¿á½ÏƒÎ¯Î±Î¹, but as quantity, quality or relation; which is to say, as the separable elemental properties (στοιχηῖαι) of entities. I will argue that while neither Plato nor Aristotle understood the objects of Mathematics as separated entities, Aristotle’s description is more effective by virtue of its consideration of an “object’s” separable elemental properties as the “subject” of mathematics.

Author Biography

  • Gilfranco Lucena dos Santos, Universidade Federal da Paraíba

    Mestre em Filosofia pela Universidade Federal de Pernambuco. Doutor em Filosofia pelo Programa de Doutorado Integrado UFPE-UFPB-UFRN. Professor Adjunto do Curso de Filosofia da Universidade Federal da Paraíba.

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Published

2016-12-29

Issue

No. 19 (2017): Revista Archai nº19 (Janeiro, 2017)

Section

Articles

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How to Cite

The intermediate character of mathematics and the ontological structure of its elements by Plato and Aristotle. (2016). Revista Archai, 19, 129. https://doi.org/10.14195/1984-249X_19_5