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  1. Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge.Francisco Miguel Ortiz Delgado - 2023 - Tópicos: Revista de Filosofía 33 (66):41-65.
    This paper has two specific goals. The first is to demonstrate that the theorem in MetaphysicsΘ 9, 1051a24-27 is not equiva-lent 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 ar-gue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosoph-ical reason for the Aristotelian theorem being shorter than the Euclidean (...)
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  2. A Concepção Aristotélica de Demonstração Geométrica a partir dos Segundos Analíticos.Rafael Cavalcanti de Souza - 2022 - Dissertation, University of Campinas
    Nos Segundos Analíticos I. 14, 79a16-21 Aristóteles afirma que as demonstrações matemáticas são expressas em silogismos de primeira figura. Apresento uma leitura da teoria da demonstração científica exposta nos Segundos Analíticos I (com maior ênfase nos capítulo 2-6) que seja consistente com o texto aristotélico e explique exemplos de demonstrações geométricas presentes no Corpus. Em termos gerais, defendo que a demonstração aristotélica é um procedimento de análise que explica um dado explanandum por meio da conversão de uma proposição previamente estabelecida. (...)
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  3. Aristotle’s argument from universal mathematics against the existence of platonic forms.Pieter Sjoerd Hasper - 2019 - Manuscrito 42 (4):544-581.
    In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of which (...)
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  4. Aristotle and the Mathematical Tradition on diastēma and logos: an Analysis of Physics 3 3, 202a18-21.Monica Ugaglia - 2016 - Greek Roman and Byzantine Studies 56:49-67.
    ARISTOTLE'S PHYSICS 3.3 contains interesting evidence of an open debate in mathematics, concerning the interchangeability of the notions of diastēma and logos in the theory of harmonics. Because of the standard interpretation of the passage, however, this reference to harmonics has gone unnoticed: a slightly different understanding is proposed in this paper, which restores the relevance of the passage and its place in the contemporary debate.
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  5. Knowing by Doing: the Role of Geometrical Practice in Aristotle’s Theory of Knowledge.Monica Ugaglia - 2015 - Elenchos 36 (1):45-88.
    Aristotle’s way of conceiving the relationship between mathematics and other branches of scientific knowledge is completely different from the way a contemporary scientist conceives it. This is one of the causes of the fact that we look at the mathematical passage we find in Aristotle’s works with the wrong expectation. We expect to find more or less stringent proofs, while for the most part Aristotle employs mere analogies. Indeed, this is the primary function of mathematics when employed in a philosophical (...)
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  6. Aristotle on placing gnomons round.Monica Ugaglia & Fabio Acerbi - 2015 - Classical Quarterly 65 (2):587-608.
    The passage has been an object of scholarly debate: the lack of independent sources on the mathematical construction described by Aristotle, the terseness of the formulation and the resulting syntactical ambiguities make the exact interpretation of the text quite difficult, as already noted by Philoponus. What does it mean that the gnomons are ‘placed round the one and without’ (περὶ τὸ ἓν καὶ χωρίς)? And in what sense is this an indication of the even being ‘cut off, enclosed (ἐναπολαμβανόμενον), and (...)
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  7. Jacob Klein on the Dispute Between Plato and Aristotle Regarding Number.Edward C. Halper - 2011 - New Yearbook for Phenomenology and Phenomenological Philosophy 11:249-270.
    By examining Klein’s discussion of the difference between Plato and Aristotle regarding the ontology of number, this article aims to spells out the significanceof that debate both in itself and for the development of the later mathematical sciences. This is accomplished by explicating and expanding Klein’s account of the differences that exist in the understanding of number presented by these two thinkers. It is ultimately argued that Klein’s analysis can be used to show that the transition from the ancient to (...)
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  8. Jacob Klein on the Dispute Between Plato and Aristotle Regarding Number.Andrew Romiti - 2011 - New Yearbook for Phenomenology and Phenomenological Philosophy 11:249-270.
    By examining Klein’s discussion of the difference between Plato and Aristotle regarding the ontology of number, this article aims to spells out the significanceof that debate both in itself and for the development of the later mathematical sciences. This is accomplished by explicating and expanding Klein’s account of the differences that exist in the understanding of number presented by these two thinkers. It is ultimately argued that Klein’s analysis can be used to show that the transition from the ancient to (...)
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  9. Boundlessness and Iteration: Some Observations about the Meaning of άεί in Aristotle.Monica Ugaglia - 2009 - Rhizai. A Journal for Ancient Philosophy and Science (2):193-213.
    The aim of the paper is to show that the iterative (local and atemporal) meaning of the adverb ἀεί has a function of primary importance in Aristotle’s system, and that its use is strictly connected with the technical use of the same term in mathematics.
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  10. Aristotle and mathematics.Henry Mendell - 2008 - Stanford Encyclopedia of Philosophy.
  11. Aristóteles e o Uso da Matemática nas Ciências da Natureza.Lucas Angioni - 2003 - In M. Wrigley P. Smith (ed.), Coleção CLE (Universidade de Campinas, Brazil). CLE. pp. 207-237.
    I discuss the issue whether Aristotle's philosophy of science allows the use of mathematical premises or mathematical tools in general for explanaing phenomena in the natural sciences. I thereby discuss the concept of "metabasis eis allo genos" as it appears in Posterior Analytics I.7.
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  12. Aristotle and mathematics: aporetic method in cosmology and metaphysics.John J. Cleary - 1995 - New York: E.J. Brill.
    This book examines Aristotle's critical reaction to the mathematical cosmology of Plato's Academy, and traces the aporetic method by which he developed his own ...
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  13. Mathematics and Metaphysics in Aristotle. Proceedings of the 10th Symposium Aristotelicum, Sigriswil, 6–12 September 1984. [REVIEW]Werner Beierwaltes - 1991 - Philosophy and History 24 (1-2):15-17.
  14. Ontologie der ‘Mathematiks’ in der Metaphysik des Aristoteles. [REVIEW]John J. Cleary - 1990 - Ancient Philosophy 10 (2):310-312.
  15. Aristotle and Cantor: On the Mathematical Infinite.Joseph S. Catalano - 1969 - Modern Schoolman 46 (3):264-267.
  16. Aristotle's philosophy of mathematics.Hippocrates George Apostle - 1952 - [Chicago]: University of Chicago Press.