Aristotle on the metaphysical status of mathematical entities
type: CreativeWork
description: The purpose of this dissertation is to provide an account of the metaphysical status of mathematical entities in Aristotle. Aristotle endorses a form of realism about mathematical entities: for him as well as for Platonists, anti–realism, the view that mathematical objects do not exist, is not a viable option. The thesis consists of two main parts: a part dedicated to the objects of geometry, and a part dedicated to numbers. Furthermore, I have included an introductory chapter about a passage in the second chapter of Book B of the Physics (193b31- 194a7) where Aristotle endorses a form of naïve realism with regard to mathematical entities. Many of the passages that give us an insight into Aristotle’s philosophy of mathematics are to be found in the third chapter of Book M of the Metaphysics. Aristotle’s primary concern there, however, is not so much to present his own positive account as to provide answers to a series of (not so obvious) Platonic arguments. In the second chapter of my thesis, I discuss some of those arguments and highlight their role in Aristotle’s own position about the metaphysical status of geometrical entities. In a passage that is of crucial importance to understand Aristotle’s views regarding the mode of existence of the objects of mathematics (Meta. M.3, 1078a25-31), Aristotle allows for the potential existence of them. I argue that Aristotle’s sketchy remarks in Meta. M.3 point towards a geometry based on the commonsensical notion of the solid. This account can be further developed if we take into consideration the purpose of the preceding chapter M.2: to refute Platonic arguments that attribute greater metaphysical status to ‘limit entities’ (entities bounding and within a physical body), that is, to points, lines, and surfaces. According to Aristotle, such ‘limit entities’ have only a potential existence–what does this claim amount to? To answer this question, I will explore a more traditional reading of this claim and I will also put forw…
abstract: The purpose of this dissertation is to provide an account of the metaphysical status of mathematical entities in Aristotle. Aristotle endorses a form of realism about mathematical entities: for him as well as for Platonists, anti–realism, the view that mathematical objects do not exist, is not a viable option. The thesis consists of two main parts: a part dedicated to the objects of geometry, and a part dedicated to numbers. Furthermore, I have included an introductory chapter about a passage in the second chapter of Book B of the Physics (193b31- 194a7) where Aristotle endorses a form of naïve realism with regard to mathematical entities. Many of the passages that give us an insight into Aristotle’s philosophy of mathematics are to be found in the third chapter of Book M of the Metaphysics. Aristotle’s primary concern there, however, is not so much to present his own positive account as to provide answers to a series of (not so obvious) Platonic arguments. In the second chapter of my thesis, I discuss some of those arguments and highlight their role in Aristotle’s own position about the metaphysical status of geometrical entities. In a passage that is of crucial importance to understand Aristotle’s views regarding the mode of existence of the objects of mathematics (Meta. M.3, 1078a25-31), Aristotle allows for the potential existence of them. I argue that Aristotle’s sketchy remarks in Meta. M.3 point towards a geometry based on the commonsensical notion of the solid. This account can be further developed if we take into consideration the purpose of the preceding chapter M.2: to refute Platonic arguments that attribute greater metaphysical status to ‘limit entities’ (entities bounding and within a physical body), that is, to points, lines, and surfaces. According to Aristotle, such ‘limit entities’ have only a potential existence–what does this claim amount to? To answer this question, I will explore a more traditional reading of this claim and I will also put forw…
author: Pappas, Vangelis
language: en
keywords: Aristotle, philosophy of mathematics, realism
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/8bd6363f-5e7c-4041-87c8-2ccaef3acffe/download
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2019-07-19
date modified: 2026-07-22T22:24:24Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.37304