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RESEARCH ARTICLE
Ontology of Mathematical Entities: Substantialisation
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1 Afyon Kocatepe Üniversitesi, Fen-Edebiyat Fakültesi, Felsefe Bölümü 03200, Afyon,
Türkiye
Received: 19 December 2023 | Published online: 23 March 2024
© 2024 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Mathematics embodies a complex universe of abstract concepts in human thought. However, the ontology of mathematical objects requires a deep analysis in order to understand not only the physical world, but also beyond the abstract world. This paper considers the fundamental qualities of mathematical objects and how we can use Aristotle's theory of substance to understand these entities. Aristotle's account of mathematical objects may be incomplete, but by using his understanding of substance, I aim to present my own assessment in the most favourable light to Aristotle. Rather than being a direct assessment of Aristotle, this paper aims to explain my view as the most favourable possible.
Keywords
Aristotle
philosophy of mathematics
substance
substantiation.
References
- Aristoteles. (1831). Aristotelis Opera. In I. Bekker (Ed.), edidit Academia Regia Borussica. apud G. Reimerum.
- Bäck, A. T. (2000). Aristotle’s Theory of Predication. Brill.
- Barnes, J. (1993). Aristotle’s Philosophy of the Sciences. Oxford Studies in Ancient Philosophy, 11, 225–241.
- Bronstein, D. (2016). Aristotle on Knowledge and Learning: The Posterior Analytics. Oxford University Press UK.
- Ebert, T. (1998). Aristotelian Accidents. Oxford Studies in Ancient Philosophy, 16, 133–159.
- Hamlyn, D. W. (1961). Aristotle on Predication. Phronesis, 6(2), 110–126.
- Katz, E. (2018). Mathematical Substances in Aristotle’s Metaphysics B.5: Aporia 12 Revisited. 100(2), 113–145.
- Le Goff, J. (2010). Les Intellectuels au Moyen Age. Points.
- Lear, J. (1982). Aristotle’s Philosophy of Mathematics. The Philosophical Review, 91(2), 161–192.
- Philoponi, I. (1898). in Aistotelis Categorias Commentarium. Berolini.
- Studtmann Paul. (2002). The Body Problem in Aristotle. 35(3), 211–234.