No. 52 (2017): Enero - junio
Articles

Aristotle ́s Philosophy of Mathematics

Miguel Martí Sánchez Universidad de Navarra

Bio

Published 2016-12-27

How to Cite

Sánchez, M. M. (2016). Aristotle ́s Philosophy of Mathematics. Tópicos, Revista De Filosofía, 52, 43-66. https://doi.org/10.21555/top.v0i52.784

Downloads

Download data is not yet available.

Abstract

Aristotle’s Philosophy of Mathematics can be defined as the research about three different issues: (1) what is the epistemological place of mathematics inside the realm of speculative sciences; (2) what is the method of mathematics, especially the method of geometry and arithmetic; and (3) what is the ontological status or kind of existence of mathematical entities. The primary aim of Aristotle is to build a bridge between mathematics, ontology and philosophy of nature, in order to make clear what is the object of each one.

Keywords

  • mathematics,
  • method,
  • subtraction,
  • ontology,
  • monad,
  • entity
  • ...More
    Less

References

  1. Annas, J. (1987). Die Gegenständen der Mathematik bei Aristoteles. En Mathematics and metaphysics in Aristotle = Mathematik und Metaphysik bei Aristoteles: Akten des X. Symposium Aristotelicum, Sigriswil, 6.- 12. September 1984 / Andreas Graeser (Ed./Hrsg.), 131-147.
  2. ____ (1976). Aristotle’s Metaphysics M-N. Oxford: Oxford Clarendon Press.
  3. Aristóteles (1996). Física. J. C. Calvo Martínez (trad.) Madrid: CSIC.
  4. ____ (1994). Metafísica. T. Calvo Martínez (trad.) Madrid: Gredos.
  5. Barnes, J. (1985). Aristotelian arithmetic. Revue de philosophie ancienne 3, 97-133.
  6. Boeri, Marcelo D. (2010). Acerca de los múltiples sentidos de prioridad. Buenos Aires: Colihue.
  7. Cencillo, L. (1958). Hyle. La materia en el Corpus Aristotelicum. Madrid: CSIC.
  8. Cleary, J. J. (1995). Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics. Leiden: Brill.
  9. ____ (1988). On the many senses of priority. Journal of the History of Philosophy. Carbondale: Southern Illinois University.
  10. ____ (1985). On the terminology of Abstraction in Aristotle. En Phronesis 30, 13-47.
  11. De Aquino, T. (1995). Commentary on Aristotle’s Metaphysics. Indiana: Dumb Ox Books.
  12. Egger, P. (1972). Über die Zahlen bei Aristoteles: Ihr Bau und Ihre Bedeutung. En Kant-Studien 63, 143-162.
  13. Einarson, B. (1936). On certain mathematical terms in Aristotle’s Logic.
  14. En American Journal of Philosophy 59, 33-54, 151-172.
  15. Gambra, J. M. (1996). El número en Aristóteles. En Thémata 17, 45-74.
  16. Happ, H. (1971). Hyle. Studien zum aristotelischen Materie-Begriff. Berlin- New York.
  17. Heath, T. (1949). Mathematics in Aristotle. Oxford: Oxford University Press.
  18. ____ (1921). A History of Greek Mathematics. (2 vol.) Nueva York: Dover.
  19. Jaeger, W. (2000). Aristóteles. Bases para la historia de su desarrollo intelectual. México: FCE.
  20. Joachim, H. H. (1922). On Coming-to-be and Passing-away. Oxford: Clarendon Press.
  21. Klein, J. (1968). Greek Mathematical Thought and the Origin of Algebra. Cambridge, Mass: MIT Press.
  22. Lear, J. (1982). Aristotle’s philosophy of Mathematics. En Philosophical review 91, 161-192.
  23. Mignucci, M. (1987). Aristotle’s Arithmetic. En Mathematics and metaphysics in Aristotle = Mathematik und Metaphysik bei Aristoteles: Akten des X. Symposium Aristotelicum, Sigriswil, 6.-12. September 1984 / Andreas Graeser (Ed./Hrsg.), 175-211.
  24. Mueller, I. (1970). Aristotle on Geometrical Objects. En Archiv für Gesichte der Philosophie 52, 156-171.
  25. Phillipe, M.-D. (1948). ’Αφαίρεσις, πρόσθεσις, χωρίζειν dans la philosophie d’Aristote. En Revue Thomiste 48, 461-479.
  26. Ross, W. D. (1936) Aristotle’s Physics. Oxford: Clarendon Press.
  27. ____ (1924). Aristotle’s Metaphysics. Oxford: Clarendon Press.
  28. Vigo, Alejandro G. (2011). Estudios aristotélicos. Pamplona: Eunsa.
  29. Wieland, W. (1962). Aristotelische Physik. Berlin: De Gruyter.
  30. ____ (1960/61) Das Problem der Prinzipienforschung und die aristotelische Physik. En Kant-Studien 52, 206-19.