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  1. 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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  2. Aristotle on Geometrical Potentialities.Naoya Iwata - 2021 - Journal of the History of Philosophy 59 (3):371-397.
    This paper examines Aristotle's discussion of the priority of actuality to potentiality in geometry at Metaphysics Θ9, 1051a21–33. Many scholars have assumed what I call the "geometrical construction" interpretation, according to which his point here concerns the relation between an inquirer's thinking and a geometrical figure. In contrast, I defend what I call the "geometrical analysis" interpretation, according to which it concerns the asymmetrical relation between geometrical propositions in which one is proved by means of the other. His argument as (...)
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  3. Die aristotelische Konzeption der Mathematik.Ulrich Felgner - 2020 - In Philosophie der Mathematik in der Antike und in der Neuzeit. Cham: Birkhäuser. pp. 27-43.
    Aristotelês (Ἀριστοτέλης) wurde 384 v.u.Z. in Stageira (im Grenzgebiet zwischen Thrakien und Makedonien) geboren. Er trat 367 in Platons „Akademie“ ein und blieb ihr Mitglied bis zu Platons Tod im Jahre 348/347. Im Jahre 343 wurde er am makedonischen Königshof Lehrer des damals 13-jährigen Alexander (später ;der Große‘ genannt). 336 kehrte er nach Athen zurück und wurde schon bald darauf Leiter des Lykeions. Zum Gebäude gehörte eine Wandelhalle (Peripatos, περίπατος). Die Mitglieder dieser Schule wurden daher „Peripatetiker“ genannt (περιπατέω = herumgehen).
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  4. The Platonist Absurd Accumulation of Geometrical Objects: Metaphysics Μ.2.José Edgar González-Varela - 2020 - Phronesis 65 (1):76-115.
    In the first argument of Metaphysics Μ.2 against the Platonist introduction of separate mathematical objects, Aristotle purports to show that positing separate geometrical objects to explain geometrical facts generates an ‘absurd accumulation’ of geometrical objects. Interpretations of the argument have varied widely. I distinguish between two types of interpretation, corrective and non-corrective interpretations. Here I defend a new, and more systematic, non-corrective interpretation that takes the argument as a serious and very interesting challenge to the Platonist.
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  5. Aristotle on the Purity of Forms in Metaphysics Z.10–11.Samuel Meister - 2020 - Ergo: An Open Access Journal of Philosophy 7:1-33.
    Aristotle analyses a large range of objects as composites of matter and form. But how exactly should we understand the relation between the matter and form of a composite? Some commentators have argued that forms themselves are somehow material, that is, forms are impure. Others have denied that claim and argued for the purity of forms. In this paper, I develop a new purist interpretation of Metaphysics Z.10-11, a text central to the debate, which I call 'hierarchical purism'. I argue (...)
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  6. 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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  7. Aristotle's Mathematicals in Metaphysics M.3 and N.6.Andrew Younan - 2019 - Journal of Speculative Philosophy 33 (4):644-663.
    Aristotle ends Metaphysics books M–N with an account of how one can get the impression that Platonic Form-numbers can be causes. Though these passages are all admittedly polemic against the Platonic understanding, there is an undercurrent wherein Aristotle seems to want to explain in his own terms the evidence the Platonist might perceive as supporting his view, and give any possible credit where credit is due. Indeed, underlying this explanation of how the Platonist may have formed his impression, we discover (...)
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  8. Mathematical Substances in Aristotle’s Metaphysics B.5: Aporia 12 Revisited.Emily Katz - 2018 - Archiv für Geschichte der Philosophie 100 (2):113-145.
    : Metaphysics B considers two sets of views that hypostatize mathematicals. Aristotle discusses the first in his B.2 treatment of aporia 5, and the second in his B.5 treatment of aporia 12. The former has attracted considerable attention; the latter has not. I show that aporia 12 is more significant than the literature suggests, and specifically that it is directly addressed in M.2 – an indication of its importance. There is an immediate problem: Aristotle spends most of M.2 refuting the (...)
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  9. The Now and the Relation between Motion and Time in Aristotle: A Systematic Reconstruction.Mark Sentesy - 2018 - Apeiron 51 (3):279-323.
    This paper reconstructs the relationship between the now, motion, and number in Aristotle to clarify the nature of the now, and, thereby, the relationship between motion and time. Although it is clear that for Aristotle motion, and, more generally, change, are prior to time, the nature of this priority is not clear. But if time is the number of motion, then the priority of motion can be grasped by examining his theory of number. This paper aims to show that, just (...)
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  10. Why Can't Geometers Cut Themselves on the Acutely Angled Objects of Their Proofs? Aristotle on Shape as an Impure Power.Brad Berman - 2017 - Méthexis 29 (1):89-106.
    For Aristotle, the shape of a physical body is perceptible per se (DA II.6, 418a8-9). As I read his position, shape is thus a causal power, as a physical body can affect our sense organs simply in virtue of possessing it. But this invites a challenge. If shape is an intrinsically powerful property, and indeed an intrinsically perceptible one, then why are the objects of geometrical reasoning, as such, inert and imperceptible? I here address Aristotle’s answer to that problem, focusing (...)
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  11. Abstraction and Diagrammatic Reasoning in Aristotle’s Philosophy of Geometry.Justin Humphreys - 2017 - Apeiron 50 (2):197-224.
    Aristotle’s philosophy of geometry is widely interpreted as a reaction against a Platonic realist conception of mathematics. Here I argue to the contrary that Aristotle is concerned primarily with the methodological question of how universal inferences are warranted by particular geometrical constructions. His answer hinges on the concept of abstraction, an operation of “taking away” certain features of material particulars that makes perspicuous universal relations among magnitudes. On my reading, abstraction is a diagrammatic procedure for Aristotle, and it is through (...)
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  12. Aristotelian Mechanistic Explanation.Monte Johnson - 2017 - In J. Rocca (ed.), Teleology in the Ancient World: philosophical and medical approaches. Cambridge: Cambridge University Press. pp. 125-150.
    In some influential histories of ancient philosophy, teleological explanation and mechanistic explanation are assumed to be directly opposed and mutually exclusive alternatives. I contend that this assumption is deeply flawed, and distorts our understanding both of teleological and mechanistic explanation, and of the history of mechanistic philosophy. To prove this point, I shall provide an overview of the first systematic treatise on mechanics, the short and neglected work Mechanical Problems, written either by Aristotle or by a very early member of (...)
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  13. Aristotle on mathematical objects.Janine Gühler - 2015 - Dissertation, University of St Andrews
    My thesis is an exposition and defence of Aristotle’s philosophy of mathematics. The first part of my thesis is an exposition of Aristotle’s cryptic and challenging view on mathematics and is based on remarks scattered all over the corpus aristotelicum. The thesis’ central focus is on Aristotle’s view on numbers rather than on geometrical figures. In particular, number is understood as a countable plurality and is always a number of something. I show that as a consequence the related concept of (...)
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  14. An Absurd Accumulation: Metaphysics M.2, 1076b11-36.Emily Katz - 2014 - Phronesis 59 (4):343-368.
    The opening argument in the Metaphysics M.2 series targeting separate mathematical objects has been dismissed as flawed and half-hearted. Yet it makes a strong case for a point that is central to Aristotle’s broader critique of Platonist views: if we posit distinct substances to explain the properties of sensible objects, we become committed to an embarrassingly prodigious ontology. There is also something to be learned from the argument about Aristotle’s own criteria for a theory of mathematical objects. I hope to (...)
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  15. Aristotle’s Critique of Platonist Mathematical Objects: Two Test Cases from Metaphysics M 2.Emily Katz - 2013 - Apeiron 46 (1):26-47.
    Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong (...)
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  16. Aristotle on Mathematical and Eidetic Number.Daniel P. Maher - 2011 - Hermathena 190:29-51.
    The article examines Greek philosopher Aristotle's understanding of mathematical numbers as pluralities of discreet units and the relations of unity and multiplicity. Topics discussed include Aristotle's view that a mathematical number has determinate properties, a contrast between Aristotle and French philosopher René Descartes in terms of their understanding of number and Aristotle's description of ways to understand eidetic numbers.
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  17. 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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  18. Aristotle and mathematics.Henry Mendell - 2008 - Stanford Encyclopedia of Philosophy.
  19. Aristotelian Infinity.John Bowin - 2007 - Oxford Studies in Ancient Philosophy 32:233-250.
    Bowin begins with an apparent paradox about Aristotelian infinity: Aristotle clearly says that infinity exists only potentially and not actually. However, Aristotle appears to say two different things about the nature of that potential existence. On the one hand, he seems to say that the potentiality is like that of a process that might occur but isn't right now. Aristotle uses the Olympics as an example: they might be occurring, but they aren't just now. On the other hand, Aristotle says (...)
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  20. Platonic number in the parmenides and metaphysics XIII.Dougal Blyth - 2000 - International Journal of Philosophical Studies 8 (1):23 – 45.
    I argue here that a properly Platonic theory of the nature of number is still viable today. By properly Platonic, I mean one consistent with Plato's own theory, with appropriate extensions to take into account subsequent developments in mathematics. At Parmenides 143a-4a the existence of numbers is proven from our capacity to count, whereby I establish as Plato's the theory that numbers are originally ordinal, a sequence of forms differentiated by position. I defend and interpret Aristotle's report of a Platonic (...)
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  21. Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics. Philosophia Antiqua, vol. 67. [REVIEW]Michael J. White - 1997 - Ancient Philosophy 17 (2):469-472.
  22. The Metaphysical Location of Aristotle's "Mathematika".Michael White - 1993 - Phronesis 38:166.
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  23. 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.
  24. Aristotle on Mathematical Objects.Edward Hussey - 1991 - Apeiron 24 (4):105 - 133.
  25. Ontologie der 'mathematiks' in der metaphysik Des aristoteles.John J. Cleary - 1990 - Ancient Philosophy 10 (2):310-312.
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  26. On the Terminology of 'Abstraction'in Aristotle.John J. Cleary - 1985 - Phronesis 30 (1):13 - 45.
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  27. Intelligible Matter and Geometry in Aristotle.Joe F. Jones Iii - 1983 - Apeiron 17 (2):94 - 102.
  28. Aristotle's Theory of Abstraction: A Problem About the Mode of Being of Mathematical Objects.John Joseph Cleary - 1982 - Dissertation, Boston University Graduate School
    This dissertation argues that Aristotle intended his so-called theory of abstraction to serve primarily as the resolution of a special problem in the philosophy of mathematics; i.e., the ontological status of mathematical objects. My general approach is dictated by the view that Aristotle's 'theories' must be understood in terms of the particular problems that he is trying to resolve. Thus, most of my dissertation is devoted to examining his treatment of the problem which I show to be relevant to the (...)
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  29. A ristotle on Perception and Ratios.Andrew Barker - 1981 - Phronesis 26 (3):248-266.
  30. A ristotle on Intelligible Matter.Stephen Gaukroger - 1980 - Phronesis 25 (1):187-197.
  31. "Aristotle's Metaphysics. Books M and N," translated with Introduction and Notes by Julia Annas.H. T. Walsh - 1978 - Modern Schoolman 55 (3):312-313.
  32. Aristotle’s Metaphysics. Books M and N. [REVIEW]O. J. - 1977 - Review of Metaphysics 31 (2):310-311.
    Miracles are not ordinarily looked for in the area of the Aristotelian Metaphysics. Least of all, perhaps, would one expect to be presented with a readable and lucid translation of Books M and N. Yet that is what has been given in the present scholarly volume. The difficult and often puzzling Greek text of the two books has been neatly rendered in attractive, idiomatic, precise, smooth flowing English.
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  33. Aristotle's "Metaphysics", Books [Gamma], [Delta], and [Epsilon]. Aristotle - 1971 - Oxford, Clarendon Press.
    Das historische Buch konnen zahlreiche Rechtschreibfehler, fehlende Texte, Bilder, oder einen Index. Kaufer konnen eine kostenlose gescannte Kopie des Originals durch den Verlag. 1907. Nicht dargestellt. Auszug:... I. TEIL DIE PROBLEME DER GRUNDWISSENSCHAFT ndem wir nunmehr an die von uns zu behandelnde Wissenschaft herantreten, gilt es zunachst uns klar zu werden uber die Fragen, uber die wir eine Entscheidung zu treffen haben. Es sind zum Teil solche, uber welche die Denker vor uns abweichende Ansichten geaussert haben; wir mussen aber auch (...)
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  34. Aristotle's Philosophy of Mathematics.Hippocrates George Apostle - 1952 - University of Chicago Press.