Aristotle on Mathematical Truth

Corkum, Phil

doi:10.1080/09608788.2012.731230

Cited by 19 publications

(7 citation statements)

References 20 publications

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“…I will argue that the mathematical ontologies ascribed to Aristotle by Mueller (1970) and Annas (1976) cannot solve the problem. On the other hand, I argue that Corkum (2012) and Lear (1982) offer readings of Aristotle's understanding of mathematical abstraction which, while differing from each other in certain significant respects, are both consistent with my reading of Aristotle on continuity and contiguity. §1 Two kinds of continuity: [relational] and [nonrelational]continuity For Aristotle, as for anyone, contiguity is a relation.…”

Section: Continuity and Mathematical Ontology In Aristotle Keren Wilsmentioning

confidence: 68%

Continuity and Mathematical Ontology in Aristotle

Shatalov

2020

J. anc. philos. (Engl. ed.)

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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.

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Section: Continuity and Mathematical Ontology In Aristotle Keren Wilsmentioning

confidence: 68%

Continuity and Mathematical Ontology in Aristotle

Shatalov

2020

J. anc. philos. (Engl. ed.)

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“…In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are excellent discussion about the nature of mathematical objects, see Corkum (2012), who convincingly-for me-concludes that mathematicals are fictions "with an ontological status." equal to two right angles.…”

Section: The Theoremsmentioning

confidence: 99%

Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge

Delgado¹

2023

Tópicos (México)

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This paper has two specific goals. The first is to demonstrate that the theorem in Metaphysics Θ 9, 1051a24-27 is not equivalent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I argue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosophical reason for the Aristotelian theorem being shorter than the Euclidean one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theorems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amendments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge.

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“…Hussey (1991) defends a fictionalist interpretation of Aristotle. The strengths and weaknesses of these interpretations have been discussed by Corkum (2012). White (1993) discusses a spectrum of miscellaneous interpretations of the nature and location of mathematical objects in the framework of Aristotle’s philosophy.…”

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confidence: 99%