Synthese

, Volume 192, Issue 8, pp 2345–2360 | Cite as

Aristotelian finitism

S.I. : Infinity

Abstract

It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of some of the arguments considered by Aristotle both in favour of and against the existence of actual infinities. I argue that Aristotle has good reason to resist the traditional arguments offered in favour of the existence of the infinite and that, while there is a lacuna in his own ‘logical’ arguments against actual infinities, his arguments against the existence of infinite magnitude and number are valid and more well grounded than commonly supposed.

Keywords

Aristotle Aristotelian commentators Infinity Mathematics Metaphysics 

References

  1. Barnes, J. (Ed.). (1984). The complete works of Aristotle: The revised oxford translation. Princeton: Princeton University Press.Google Scholar
  2. Bostock, D. (1972). Aristotle Zeno, and the potential infinite. Proceedings of the Aristotelian Society, 73, 37–51.Google Scholar
  3. Burnyeat, M. (1987). Platonism and mathematics: A prelude to discussion. In A. Graeser (Ed.), Mathematics and Metaphysics in Aristotle, 213–40. Haupt: Bern. P.Google Scholar
  4. Charlton, W. (1991). Aristotle’s potential infinites. In L. Judson (Ed.), Aristotle’s Physics A collection of essays (pp. 129–149). Oxford: Clarendon Press.Google Scholar
  5. Coope, U. (2012). Aristotle on the infinite. In C. Shields (Ed.), The Oxford handbook of Aristotle (pp. 267–286). Oxford: Oxford University Press.Google Scholar
  6. Edwards, M. J. (1994). Philoponus: On Aristotle Physics 3. London: Duckworth.Google Scholar
  7. Heath, T. L. (1926). The thirteen books of Euclid’s Elements (Vol. 3). Cambridge: Cambridge University Press.Google Scholar
  8. Hintikka, J. (1966). Aristotelian infinity. The Philosophical Review, 75, 197–218.Google Scholar
  9. Hussey, E. (1983). Aristotle, Physics: Books III and IV. Oxford: Clarendon Press.Google Scholar
  10. Lear, J. (1979). Aristotelian infinity. Proceedings of the Aristotelian Society, 80, 187–210.Google Scholar
  11. Mayberry, J. P. (2000). The foundations of mathematics in the theory of sets. Cambridge: Cambridge University Press.Google Scholar
  12. McGinnis, J. (2010). Avicennan infinity: A select history of the infinite through Avicenna. Documenti e Studi sulla Tradizione Filosofica Medievale, 21, 199–222.Google Scholar
  13. Pritchard, P. (1995). Plato’s philosophy of mathematics. Sankt Augustin: Academia Verlag.Google Scholar
  14. Rescher, N., & Khatchadourian, H. (1965). Al-Kindī’s epistle on the finitude of the universe. Isis, 56, 426–433.Google Scholar
  15. Ross, D. (1936). Aristotle’s Physics: A revised text with introduction and commentary. Oxford: Clarendon Press.Google Scholar
  16. Trifogli, C. (2000). Oxford physics in the thirteenth century (ca. 1250–1270): Motion, infinity, place & time. Leiden: Brill.Google Scholar
  17. Urmson, J. O. (2002). Simplicius: On Aristotle Physics 3. London: Duckworth.Google Scholar
  18. Waterlow, S. (1984). Aristotle’s now. The Philosophical Quarterly, 34, 104–128.Google Scholar
  19. White, M. (1992). The continuous and the discrete: Ancient physical theories from a contemporary perspective. Oxford: Clarendon Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of OxfordOxfordUK

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