About this topic
Summary (Under construction.) This category will index four overlapping topics: 1) Plato's philosophy of mathematics, in the sense of his remarks on mathematical reality and mathematical knowledge, 2) the presence and philosophical function of mathematics in the dialogues, 3) the role of mathematics and mathematicals in dialectic and the "theory of forms", and 4) the mathematical elements of Plato's late ontology, including the so-called "unwritten doctrines". For so-called "mathematical Platonism," see the category by that name (link below).
Key works (Under construction) Taylor 1926, Klein 1968 (of which Hopkins 2011 includes a detailed commentary),  Knorr 1975, Sayre 1983
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92 found
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  1. added 2019-10-17
    Mathematics and the Conversion of the Mind: Republic Vii 522c1-531e3.lan Robins - 1995 - Ancient Philosophy 15 (2):359-391.
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  2. added 2019-09-09
    Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line.Miriam Byrd - 2018 - International Journal of the Platonic Tradition 12 (2):111-131.
    This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the (...)
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  3. added 2019-06-06
    Measuring Humans Against Gods: On the Digression of Plato’s Theaetetus.Jens Kristian Larsen - 2019 - Archiv für Geschichte der Philosophie 101 (1):1-29.
  4. added 2019-06-06
    Philosophy and Mathematics in the Teaching of Plato: The Development of Idea and Modernity.N. V. Mikhailova - 2014 - Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 3 (6):468.
    It is well known that the largest philosophers differently explain the origin of mathematics. This question was investigated in antiquity, a substantial and decisive role in this respect was played by the Platonic doctrine. Therefore, discussing this issue the problem of interaction of philosophy and mathematics in the teachings of Plato should be taken into consideration. Many mathematicians believe that abstract mathematical objects belong in a certain sense to the world of ideas and that consistency of objects and theories really (...)
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  5. added 2019-06-06
    ‘Mathematical Platonism’ Versus Gathering the Dead: What Socrates Teaches Glaucon &Dagger.Colin McLarty - 2005 - Philosophia Mathematica 13 (2):115-134.
    Glaucon in Plato's _Republic_ fails to grasp intermediates. He confuses pursuing a goal with achieving it, and so he adopts ‘mathematical platonism’. He says mathematical objects are eternal. Socrates urges a seriously debatable, and seriously defensible, alternative centered on the destruction of hypotheses. He offers his version of geometry and astronomy as refuting the charge that he impiously ‘ponders things up in the sky and investigates things under the earth and makes the weaker argument the stronger’. We relate his account (...)
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  6. added 2019-06-06
    Plato’s Mathematical Construction.Reviel Netz - 2003 - Classical Quarterly 53 (2):500-509.
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  7. added 2019-06-06
    Plato’s Philosophy of Mathematics. [REVIEW]Ian Mueller - 1997 - Ancient Philosophy 17 (2):458-461.
  8. added 2019-06-06
    La génesis de las dimensiones en Platón.Juao de Dios Bares - 1992 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 7 (1-3):451-471.
    This paper deals with the ontological genesis of the series point-line-plane-solid in Plato’s philosophy. The texts of the Dialogues concerning this subject are presented, and passages of the Unwritten Doctrines that we know from Aristotle and other sources are specially considered. Certain problems within this context, such as the postulation of indivisible Iines, or the relation between each of the dimensions and the figures that can be placed in them, are considered in detail.
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  9. added 2019-06-06
    Platonism and Mathematics. [REVIEW]H. J. Blumenthal - 1991 - The Classical Review 41 (1):101-103.
  10. added 2019-06-06
    Plato’s Arithmological Ordering of Being: A Review of Plato’s Trilogy. [REVIEW]David Lawrence Levine - 1980 - Southwestern Journal of Philosophy 11 (2):109-128.
  11. added 2019-06-06
    Theo Gerard Sinnige, "Matter and Infinity in the Presocratic Schools and Plato". [REVIEW]Samuel Scolnicov - 1970 - Journal of the History of Philosophy 8 (1):92.
  12. added 2019-06-06
    Mathematics in Plato and Aristotle. [REVIEW]D. J. Allan - 1950 - The Classical Review 64 (3-4):112-114.
  13. added 2019-06-06
    Plato's Geometrical Number and the Comment of Proclus. [REVIEW]R. G. Bury - 1919 - The Classical Review 33 (1-2):45-46.
  14. added 2019-06-06
    Plato' Nuptial Number. [REVIEW]C. H. W. Johns - 1907 - The Classical Review 21 (8):246-247.
  15. added 2019-01-28
    A Likely Account of Necessity: Plato's Receptacle as a Physical and Metaphysical Foundation for Space.Barbara Sattler - 2012 - Journal of the History of Philosophy 50 (2):159-195.
    This paper aims to show that—and how—Plato’s notion of the receptacle in the Timaeus provides the conditions for developing a mathematical as well as a physical space without itself being space. In response to the debate whether Plato’s receptacle is a conception of space or of matter, I suggest employing criteria from topology and the theory of metric spaces as the most basic ones available. I show that the receptacle fulfils its main task–allowing the elements qua images of the Forms (...)
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  16. added 2018-04-15
    VIastos on Elenchus and Mathematics.Kenneth Seeskin - 1993 - Ancient Philosophy 13 (1):37-53.
  17. added 2018-04-15
    Elenchus and Mathematics: A Turning-Point in Plato's Philosophical Development.Gregory Vlastos - 1988 - American Journal of Philology 109 (3):362-396.
  18. added 2017-10-06
    Mathematics and the Conversion of the Mind: Republic VII 522c1-531e.lan Robins - 1995 - Ancient Philosophy 15 (2):359-391.
    An account of how the mathematical sciences turn the mind away from becoming and towards being. There are four main conclusions. 1. The study of numbers, when treated independently of the other sciences, uses a particular conception of the nature of numbers to detach the mind from the influence of perceptible objects. 2. The study of ratios and proportions, explicitly the core of Plato's harmonics, is fundamental also to plane and solid geometry and astronomy. 3. Ratios and proportion form the (...)
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  19. added 2017-09-25
    Codici Nel Pentateuco E Matematica Egizio-Platonica.Gian Carlo Duranti - 1994 - Arcipelago.
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  20. added 2017-09-22
    Philosophy and Mathematics, From Plato to the Present.Robert J. Baum - 1973 - San Francisco, Freeman, Cooper.
  21. added 2017-09-22
    Platons Verhältnis Zur Mathematik.Glenn R. Morrow - 1931 - Philosophical Review 40 (3):306-306.
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  22. added 2017-06-29
    The Generation of Numbers in Plato's Parmenides.R. E. Allen - 1970 - Classical Philology 65 (1).
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  23. added 2017-06-29
    Greek Mathematical Philosophy.Edward A. Maziarz - 1968 - New York: Ungar.
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  24. added 2017-06-29
    Forms and Numbers: A Study in Platonic Metaphysics (II).A. E. Taylor - 1927 - Mind 36 (141):12-33.
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  25. added 2017-06-29
    Forms and Numbers: A Study in Platonic Metaphysics (I.).A. E. Taylor - 1926 - Mind 35 (140):419-440.
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  26. added 2017-03-23
    Kenneth M. Sayre, Plato's Late Ontology: A Riddle Resolved Reviewed By.Richard D. McKirahan Jr - 1986 - Philosophy in Review 6 (4):177-179.
  27. added 2017-03-23
    Kenneth M. Sayre, "Plato's Late Ontology. A Riddle Resolved". [REVIEW]Daniel H. Frank - 1985 - Journal of the History of Philosophy 23 (4):579.
  28. added 2017-03-23
    Plato's Late Ontology: A Riddle Resolved: With a New Introduction and the Essay, "Excess and Deficiency at Statesman 283c-285c".Kenneth M. Sayre - 1983 - Parmenides.
  29. added 2017-03-23
    The Evolution of the Euclidean Elements.Wilbur Richard Knorr - 1975 - Dordrecht, Holland: D. Reidel Publishing Company.
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  30. added 2017-03-05
    Univocity, Duality, and Ideal Genesis: Deleuze and Plato.John Bova & Paul M. Livingston - 2017 - In Contemporary Encounters with Ancient Metaphysics. Edinburgh University Press.
    In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and (...)
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  31. added 2017-02-16
    Plato's Mathematical Imagination. The Mathematical Passages in the Dialogues and Their Interpretation.H. G. Apostle - 1956 - Journal of Philosophy 53 (13):415-418.
  32. added 2017-01-28
    On the Babylonian Origin of Plato's Nuptial Number.George A. Barton - 1908 - Journal of the American Oriental Society 29:210-219.
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  33. added 2017-01-28
    The Significance of the Mathematical Element in the Philosophy of Plato.Irving Elgar Miller - 1904 - University of Chicago Press.
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  34. added 2017-01-28
    The Nuptial Number of Plato its Solution and Significance.James Adam - 1891 - C. J. Clay and Sons.
  35. added 2017-01-26
    Plato's Mathematics P. Pritchard: Plato's Philosophy of Mathematics. Pp. Vii + 191. Sankt Augustin: Academia Verlag, 1995. DM 58. ISBN: 3-88345-637-3. [REVIEW]Malcolm Schofield - 1998 - The Classical Review 48 (1):84-85.
  36. added 2017-01-23
    Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - Palgrave-Macmillan.
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  37. added 2017-01-23
    Inventing Intermediates: Mathematical Discourse and Its Objects in Republic VII.Lee Franklin - 2012 - Journal of the History of Philosophy 50 (4):483-506.
  38. added 2017-01-21
    Plato's Mathematics - Pritchard P.: Plato's Philosophy of Mathematics. (International Plato Studies, 5.) Pp. Vii + 191. Sankt Augustin: Academia Verlag, 1995. DM 58. ISBN: 3-88345-637-3. [REVIEW]Malcolm Schofield - 1998 - The Classical Review 48 (01):84-85.
  39. added 2016-12-08
    Plato and the Irrationals — Part 2.Joseph A. Novak - 1983 - Apeiron 17 (1):14 - 27.
  40. added 2016-12-08
    Plato and the Irrationals.Joseph A. Novak - 1982 - Apeiron 16 (2):71 - 85.
  41. added 2016-12-08
    Pappus, Plato and the Harmonic Mean.Malcolm Brown - 1975 - Phronesis 20 (2):173-184.
  42. added 2016-12-08
    Plato's Form of Equal.R. S. Bluck - 1959 - Phronesis 4 (1):5-11.
  43. added 2016-12-08
    Plato's Philosophy of Mathematics. [REVIEW]C. C. V. - 1956 - Review of Metaphysics 9 (4):712-712.
    A straightforward presentation of Plato's views on the nature of mathematics, with special attention to the status of mathematical objects and to the method of mathematical thinking. Mr. Wedberg has summarized his interpretations of Platonic doctrines in a clear and well-organized fashion, devoting one chapter to Plato's views on geometry, one to his views on arithmetic; he then supports these interpretations by a close examination of the relevant passages, not only in Plato's Dialogues, but in Aristotle as well. A comprehensive (...)
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  44. added 2016-08-31
    Figure, Ratio, Form: Plato's Five Mathematical Studies.Mitchell Miller - 1999 - Apeiron 32 (4):73-88.
    A close reading of the five mathematical studies Socrates proposes for the philosopher-to-be in Republic VII, arguing that (1) each study proposes an object the thought of which turns the soul towards pure intelligibility and that (2) the sequence of studies involves both a departure from the sensible and a return to it in its intelligible structure.
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  45. added 2016-08-30
    Beginning the 'Longer Way'.Mitchell Miller - 2007 - In G. R. F. Ferrari (ed.), The Cambridge Companion to Plato's Republic. Cambridge University Press. pp. 310--344.
    At 435c-d and 504b ff., Socrates indicates that there is a "longer and fuller way" that one must take in order to get "the best possible view" of the soul and its virtues. But Plato does not have him take this "longer way." Instead Socrates restricts himself to an indirect indication of its goals by his images of sun, line, and cave and to a programmatic outline of its first phase, the five mathematical studies. Doesn't this pointed restraint function as (...)
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  46. added 2016-08-05
    The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein.Burt C. Hopkins - 2011 - Indiana University Press.
    Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their (...)
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  47. added 2016-08-05
    Greek Mathematical Thought and the Origin of Algebra.Jacob Klein - 1968 - M. I. T. Press.
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  48. added 2016-08-05
    Plato's Philosophy of Mathematics.ANDERS WEDBERG - 1955 - Greenwood Press.
  49. added 2016-04-07
    Plato on Why Mathematics is Good for the Soul.Myles Burnyeat - 2000 - In T. Smiley (ed.), Mathematics and Necessity: Essays in the History of Philosophy. pp. 1-81.
  50. added 2016-01-19
    One, Two, Three… A Discussion on the Generation of Numbers in Plato’s Parmenides.Florin George Calian - 2015 - New Europe College:49-78.
    One of the questions regarding the Parmenides is whether Plato was committed to any of the arguments developed in the second part of the dialogue. This paper argues for considering at least one of the arguments from the second part of the Parmenides, namely the argument of the generation of numbers, as being platonically genuine. I argue that the argument at 142b-144b, which discusses the generation of numbers, is not deployed for the sake of dialectical argumentation alone, but it rather (...)
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