Sensitive mathematical objects and intelligible mathematical objects

  • Víctor Hugo Chica Pérez Universidad de Antioquia
  • Luis F. Echeverri Universidad de Antioquia
  • Edwin Zarrazola Universidad de Antioquia
Keywords: Mathematical objects, Greek antiquity, arithmetic, logistics

Abstract

In this paper we study the concept of mathematical object as it was understood by ancient mathematical thought, particularly by Plato and Aristotle. We are going to prove that it is not right to interpret the duality of this concept in Plato’s works as consequence of an ontological division between two kinds of mathematical objects, i.e. the sensitive and the intelligible ones. We want to prove that such a division is not a real one because, as a matter of fact, Plato is proposing a differentiation between two possible ways to be related with mathematical objects: the way of the philosophers and the way of the non–philosophers. Moreover, we show that our interpretation is able to clarify the ambiguity around the concept of μоνάς and therefore eliminate the false distinction between the two subject matters devoted to the study of discrete mathematical objects: the λоγιστική and the ἀριθμητική.

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Author Biographies

Víctor Hugo Chica Pérez, Universidad de Antioquia

Instituto de Filosofía
Universidad de Antioquia
Medellín Colombia
E–mail: vchica1@gmail.com

Luis F. Echeverri, Universidad de Antioquia

Instituto de Matemáticas
Universidad de Antioquia
Medellín, Colombia
E–mail: lfecheve@mat.ucm.es

Edwin Zarrazola, Universidad de Antioquia

Instituto de Matemáticas
Universidad de Antioquia
Medellín, Colombia
E–mail: edwin.zarrazola@udea.edu.co

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Published
2017-07-30
How to Cite
Chica Pérez, V. H., Echeverri, L. F., & Zarrazola, E. (2017). Sensitive mathematical objects and intelligible mathematical objects. Estudios De Filosofía, (55), 187-205. https://doi.org/10.17533/udea.ef.n55a11
Section
Original or Research articles