49 found
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  1. Philosophy of mathematics and deductive structure in Euclid's Elements.Ian Mueller - 1981 - Mineola, N.Y.: Dover Publications.
    A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions — rather than strictly historical and mathematical issues — and features several helpful appendixes.
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  2. Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Ian Mueller - 1983 - British Journal for the Philosophy of Science 34 (1):57-70.
     
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  3. Aristotle on Geometrical Objects.Ian Mueller - 1970 - Archiv für Geschichte der Philosophie 52 (2):156-171.
  4.  30
    Aristotle and Logical Theory.Ian Mueller & Jonathan Lear - 1982 - Philosophical Review 91 (4):625.
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  5.  53
    Greek mathematics and Greek logic.Ian Mueller - 1974 - In John Corcoran (ed.), Ancient Logic and its Modern Interpretations. Boston: Reidel. pp. 35--70.
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  6. Euclid's elements and the axiomatic method.Ian Mueller - 1969 - British Journal for the Philosophy of Science 20 (4):289-309.
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  7. Mathematical method and philosophical truth.Ian Mueller - 2000 - Filozofski Vestnik 21 (1):131-155.
     
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  8.  49
    The completeness of Stoic propositional logic.Ian Mueller - 1979 - Notre Dame Journal of Formal Logic 20 (1):201-215.
  9. Platonism and the study of Nature.Ian Mueller - 1997 - In Jyl Gentzler (ed.), Method in ancient philosophy. Oxford University Press UK. pp. 67--90.
     
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  10.  52
    Stoic and Peidpatetic Logic.Ian Mueller - 1969 - Archiv für Geschichte der Philosophie 51 (2):173-187.
  11.  68
    Mathematics and Education: Some Notes on the Platonic Program.Ian Mueller - 1991 - Apeiron 24 (4):85 - 104.
  12. Greek Mathematics (Arithmetic, Geometry, Proportion Theory) to the Time of Euclid.Ian Mueller - forthcoming - A Companion to Ancient Philosophy.
  13.  4
    Greek Mathematics to the Time of Euclid.Ian Mueller - 2018 - In Sean D. Kirkland & Eric Sanday (eds.), A Companion to Ancient Philosophy. Evanston, Illinois: Northwestern University Press. pp. 686–718.
    This chapter contains sections titled: Euclid's Elements First Principles Aspects of Euclid's Plane Geometry Proportionality Greek Arithmetic and its History On the History of Greek Geometry Conclusion Bibliography.
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  14.  18
    The Anatomy of Neoplatonism.Ian Mueller - 1991 - Philosophical Quarterly 41 (165):510-512.
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  15.  51
    On some academic theories of mathematical objects.Ian Mueller - 1986 - Journal of Hellenic Studies 106:111-120.
    In his critical study of Speusippus Leonardo Tarán (T.) expounds an interpretation of a considerable part of the controversial books M and N of Aristotle's Metaphysics. In this essay I want to consider three aspects of the interpretation, the account of Plato's ‘ideal numbers’ (section I), the account of Speusippus’ mathematical ontology (section II), and the account of the principles of that ontology (section III). T. builds his interpretation squarely on the work of Harold Cherniss (C.), to whom I will (...)
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  16.  55
    Parmenides133a-134e: Some Suggestion.Ian Mueller - 1983 - Ancient Philosophy 3 (1):3-7.
  17.  29
    Remarks on Euclid’s Elements I,32 and the Parallel Postulate.Ian Mueller - 2003 - Science in Context 16 (3).
  18.  20
    Remarks on Physics and Mathematical Astronomy and Optics in Epicurus, Sextus Empiricus, and Some Stoics.Ian Mueller - 2004 - Apeiron 37 (4):57 - 87.
  19.  28
    Studies in Plato's Two-Level Model (review).Ian Mueller - 2000 - Journal of the History of Philosophy 38 (2):272-273.
    In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Studies in Plato's Two-Level ModelIan MuellerHolger Thesleff. Studies in Plato's Two-Level Model. Helsinki: Societas Scientarum Fennica, 1999. Pp. vi + 143. N. P.After some 30 years of incisive intervention in Platonic scholarship, Holger Thesleff here offers us "an attempt to elaborate and ground more firmly some basic theses which I have propounded in various contexts before," (1) a rather modest description of what he also describes as an (...)
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  20. Aporia 12.Ian Mueller - 2009 - In Michel Crubellier & André Laks (eds.), Aristotle's Metaphysics Beta Symposium Aristotelicum. Oxford University Press.
  21.  22
    Euclide d’Alexandrie. Les Éléments: Vol. II. Livres V-VI.Ian Mueller - 1996 - Ancient Philosophy 16 (1):266-270.
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  22.  14
    Euclide D’Alexandrie. Les Éléments.Ian Mueller - 2000 - Ancient Philosophy 20 (1):243-247.
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  23.  8
    Grundprobleme der Geschichte der antiken WissenschaftKurt von Fritz.Ian Mueller - 1974 - Isis 65 (1):112-114.
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  24.  25
    Greek Mathematical Philosophy.Ian Mueller, Edward A. Maziarz & Thomas Greenwood - 1970 - Philosophical Review 79 (3):427.
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  25.  11
    Heterodoxy and Doxography in Hippolytus’ ‘Refutation of All Heresies’.Ian Mueller - 1987 - In Wolfgang Haase (ed.), Philosophie, Wissenschaften, Technik. Philosophie. De Gruyter. pp. 4309-4374.
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  26.  18
    lamblichus and Proclus' Euclid Commentary.Ian Mueller - 1987 - Hermes 115 (3):334-348.
  27.  43
    Joan Kung's Reading of Plato's "Timaeus".Ian Mueller - 1989 - Apeiron 22 (4):1 - 27.
  28.  13
    Joan Kung's Reading of Plato's Timaeus.Ian Mueller - 1989 - Apeiron 22 (4):1-28.
  29.  25
    Proclus: Neo-Platonic Philosophy and Science.Ian Mueller & Lucas Siorvanes - 1998 - Philosophical Review 107 (4):600.
    Proclus Platonic Academy) is undoubtedly one of the most influential figures in the history of western philosophy; his writings did more to shape pre-twentieth-century understandings of Plato than any other person. But today few students of ancient philosophy would cite Proclus as an authority on Plato, and only a few scholars and certain people whom many would identify as enthusiasts or mystics are likely to have read a whole work of Proclus, even in translation. And although there are some passages (...)
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  30.  4
    Parmenides133a-134e: Some Suggestion.Ian Mueller - 1983 - Ancient Philosophy 3 (1):3-7.
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  31. Sur les principes des mathématiques chez Aristote et Euclide.Ian Mueller - 1991 - In Jules Vuillemin & Rushdī Rāshid (eds.), Mathématiques et philosophie de l'antiquité à l'age classique: hommage à Jules Vuillemin. Paris: Diffusion, Presses du CNRS.
  32.  5
    Space-filling pyramids from Aristotle to Jan Brozek.Ian Mueller - 2018 - Revue Philosophique de la France Et de l'Etranger 2:159-180.
  33.  14
    Working with Trivial Authors.Ian Mueller - 2000 - Apeiron 33 (3):247 - 258.
  34.  62
    Zeno's paradoxes and continuity.Ian Mueller - 1969 - Mind 78 (309):129-131.
    In this note i argue against harold n. lee's assertion ("mind," october, 1965) that resolution of zeno's paradoxes is closely connected with the modern mathematical distinction between density and continuity. zeno's paradoxes would arise as much if space or time is dense as they do if it is continuous. in fact the paradoxes only arise if one combines a mathematical analysis of space and time with a non-mathematical conception of motion.
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  35.  65
    The Method of Analysis: Its Geometrical Origin and Its General Significance. [REVIEW]Ian Mueller - 1976 - Journal of Philosophy 73 (6):158-162.
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  36.  44
    Die Stoische Logik. [REVIEW]Ian Mueller - 1977 - Philosophical Review 86 (2):226-229.
  37. Physics and astronomy: Aristotle's physics II.2.193b22–194a12this paper was prepared as the basis of a presentation at a conference entitled “writing and rewriting the history of science, 1900–2000,” Les treilLes, France, september, 2003, organized by Karine Chemla and Roshdi Rashed. I have compared Aristotle's and ptolemy's views of the relationship between astronomy and physics in a paper called “astrologogeômetria and astrophysikê in Aristotle and ptolemy,” presented at a conference entitled “physics and mathematics in antiquity,” leiden, the netherlands, June, 2004, organized by Keimpe Algra and Frans de Haas. For a discussion of hellenistic views of this relationship see Ian Mueller, “remarks on physics and mathematical astronomy and optics in epicurus, sextus empiricus, and some stoics,” in Philippa Lang , re-inventions: Essays on hellenistic and early Roman science, apeiron 37, 4 : 57–87. I would like to thank two Anonymous readers of this essay for meticulous corrections and th. [REVIEW]Ian Mueller - 2006 - Arabic Sciences and Philosophy 16 (2):175-206.
    In the first part of chapter 2 of book II of the Physics Aristotle addresses the issue of the difference between mathematics and physics. In the course of his discussion he says some things about astronomy and the ‘ ‘ more physical branches of mathematics”. In this paper I discuss historical issues concerning the text, translation, and interpretation of the passage, focusing on two cruxes, the first reference to astronomy at 193b25–26 and the reference to the more physical branches at 194a7–8. In (...)
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  38.  83
    Plato’s Philosophy of Mathematics. [REVIEW]Ian Mueller - 1997 - Ancient Philosophy 17 (2):458-461.
  39.  8
    Aristotle's Metaphysics: Books M and N. [REVIEW]Ian Mueller - 1978 - Philosophical Review 87 (3):479-485.
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  40.  9
    Euclide d’Alexandrie. Les Éléments. [REVIEW]Ian Mueller - 1996 - Ancient Philosophy 16 (1):266-270.
  41.  51
    Galen. [REVIEW]Ian Mueller - 2000 - Ancient Philosophy 20 (1):247-250.
  42.  10
    Grundprobleme der Geschichte der antiken Wissenschaft by Kurt von Fritz. [REVIEW]Ian Mueller - 1974 - Isis 65:112-114.
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  43.  1
    Galen. [REVIEW]Ian Mueller - 2000 - Ancient Philosophy 20 (1):247-250.
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  44. Hippolytus "Retractatus": A Discussion of Catherine Osborne, "Rethinking Early Greek Philosophy". [REVIEW]Ian Mueller - 1989 - Oxford Studies in Ancient Philosophy 7:233.
  45.  21
    L'architecture Du Divin: Mathematique Et Philosophie Chez Plotin Et Proclus By Annick Charles-saget. [REVIEW]Ian Mueller - 1984 - Isis 75:415-415.
  46. On the Movement and Progression of Animals by Aristotle; Michael of Ephesus; Anthony Preus. [REVIEW]Ian Mueller - 1982 - Isis 73:591-592.
  47.  34
    Proclus. [REVIEW]Ian Mueller - 1998 - Philosophical Review 107 (4):600-603.
  48.  18
    Review of Frans de Haas (ed.), Jaap Mansfeld (ed.), Aristotle: On Generation and Corruption, Book I, Symposium Aristotelicum[REVIEW]Ian Mueller - 2005 - Notre Dame Philosophical Reviews 2005 (6).
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  49.  45
    Thrasyllan Platonism. [REVIEW]Ian Mueller - 1996 - Ancient Philosophy 16 (1):246-255.