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  1. added 2016-02-25
    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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  2. added 2016-02-25
    Knowing by Doing: The Role of Geometrical Practice in Aristotle’s Theory of Knowledge.Monica Ugaglia - 2015 - Elenchos 36:45-88.
    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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  3. added 2016-02-25
    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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  4. added 2016-02-25
    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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  5. added 2014-07-02
    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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  6. added 2014-04-02
    Klein on Aristotle on Number.Edward C. Halper - 2011 - New Yearbook for Phenomenology and Phenomenological Philosophy 11:271-281.
    Jacob Klein raises two important questions about Aristotle’s account of number: (1) How does the intellect come to grasp a sensible as an intelligible unit? (2) What makes a collection of these intelligible units into one number? His answer to both questions is “abstraction.” First, we abstract (or, better, disregard) a thing’s sensible characteristics to grasp it as a noetic unit. Second, after counting like things, we again disregard their other characteristics and grasp the group as a noetic entity composed (...)
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  7. added 2014-04-02
    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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  8. added 2014-04-02
    Aristotle and Cantor: On the Mathematical Infinite.Joseph S. Catalano - 1969 - Modern Schoolman 46 (3):264-267.
  9. added 2014-03-09
    Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics.John J. Cleary - 1995 - 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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  10. added 2014-03-07
    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.
  11. added 2013-04-14
    Aristotle's Philosophy of Mathematics.Hippocrates George Apostle - 1952 - University of Chicago Press.