Continuity and Mathematical Ontology in Aristotle

Authors

  • Keren Wilson Shatalov Illinois Institute of Technology

DOI:

https://doi.org/10.11606/issn.1981-9471.v14i1p30-61

Keywords:

ontology, mathematics, Aristotle

Abstract

In this paper I argue that Aristotle's understanding of mathematical continuity constrains the mathematical ontology he can consistently hold. On my reading, Aristotle can only be a mathematical abstractionist of a certain sort. To show this, I first present an analysis of Aristotle's notion of continuity by bringing together texts from his Metaphysica and Physica, to show that continuity is, for Aristotle, a certain kind of per se unity, and that upon this rests his distinction between continuity and contiguity. Next I argue briefly that Aristotle intends for his discussion of continuity to apply to pure mathematical objects such as lines and figures, as well as to extended bodies. I show that this leads him to a difficulty, for it does not at first appear that the distinction between continuity and contiguity can be preserved for abstract mathematicals. Finally, I present a solution according to which Aristotle's understanding of continuity can only be saved if he holds a certain kind of mathematical ontology.

Downloads

Download data is not yet available.

References

Annas, Julia. "Aristotle, Number, and Time." The Philosophical Quarterly, Vol. 25, No. 99 (Apr., 1975): 97-113

Annas, Julia. Aristotle's Metaphysica Book M and N. Oxford, Clarendon Press (1976)

Berryman, Sylvia. "Continuity and Coherence in Early Peripatetic Texts," in Eudemus of Rhodes, ed. István Bodnár, William W. Fortenbaugh. Rutgers University Studies in Classical Humanities, XI. New Brunswick, Transaction Publishers (2002): 157-169

Bostock, David (1991) 'Aristotle on Continuity in Physica VI', in L. Judson, ed., Aristotle's Physica: A Collection of Essays, (Oxford: Clarendon Press), 179-212

Corkum, Phil. "Aristotle on Mathematical Truth." British Journal for the History of Philosophy, Vol. 20, No. 6 (Oct. 2012): pp. 1057-1076

Corkum, Phil. "Aristotle on Ontological Dependence". Phronesis, Vol. 53, No. 1 (2008), pp. 65-92

Dedekind, Richard. "Continuity and Irrational Numbers," in Essays on the Theory of Numbers, trans. Wooster Woodruff Beman. New York, Dover Publications, Inc. (1963)

Euclid. Elements, trans. Sir Thomas L. Heath, in Great Books, Vol. 11, ed. Robert Maynard Hutchins. Chicago, Encyclopaedia Britannica, Inc. (1952)

Furley, David. "The Greek Commentators' Treatment of Aristotle's Theory of the Continuous," in Infinity and Continuity in Ancient and Medieval Thought, ed. Norman Kretzmann. Ithaca, Cornell University Press (1982): 17-36

Kretzmann, Norman, Ed. Appendix A, in Infinity and Continuity in Antiquity and the Middle Ages, Cornell UP (1982): pp. 309-321

Lear, Jonathan. "Aristotelian Infinity." Proceedings of the Aristotelian Society, New Series, Vol. 80 (1979 - 1980): 187-210

Lear, Jonathan. "Aristotle's Philosophy of Mathematics." The Philosophical Review, Vol. 91, No. 2 (Apr., 1982): 161-192

Mendell, Henry, "Aristotle and Mathematics", The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.), URL <http://plato.stanford.edu/archives/win2008/entries/aristotle-mathematics/>.

Mueller, Ian. "Aristotle on Geometry." Archiv für Geschichte der Philosophie, vol. 52 (1970): 156171

Miller, Fred. "Aristotle against the Atomists", in Norman Kretzmann ed., Infinity and Continuity in Antiquity and the Middle Ages, Cornell UP (1982): 87-111

Panza, Marco. 'Aristotle's Continuity.' Unpublished. Nov. 2011. Used with permission from the author.

Ross, David. Aristotle's Physica. Oxford, Clarendon Press (1936)

Studtmann, Paul. "Aristotle's Category of Quantity: A Unified Interpretation." Apeiron: A Journal for Ancient Philosophy and Science, Vol. 37, No. 1 (March 2004): 69-91

Wedin, Michael. Aristotle's Theory of Substance: The Categoriae and Metaphysica Zeta. Oxford, Oxford University Press (2000)

White, Michael J. The Continuous and The Discrete. Oxford, Clarendon Press: 1992.

Downloads

Published

2020-05-22

Issue

Section

Articles

How to Cite

Continuity and Mathematical Ontology in Aristotle. (2020). Journal of Ancient Philosophy, 14(1), 30-61. https://doi.org/10.11606/issn.1981-9471.v14i1p30-61