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 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
Related categories

91 found
1 — 50 / 91
  1. 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 (...)
  2. added 2018-04-15
    VIastos on Elenchus and Mathematics.Kenneth Seeskin - 1993 - Ancient Philosophy 13 (1):37-53.
  3. 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.
  4. added 2017-12-15
    Matter and Infinity in the Presocratic Schools and Plato (Review). [REVIEW]Samuel Scolnicov - 1970 - Journal of the History of Philosophy 8 (1):92-95.
  5. 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 (...)
  6. added 2017-10-01
    Philosophy and Mathematics in the Teaching of Plato: the Development of Idea and Modernity.N. V. Mikhailova - 2014 - Liberal Arts in Russia 3 (6):468-479.
    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 (...)
  7. added 2017-09-25
    Codici Nel Pentateuco E Matematica Egizio-Platonica.Gian Carlo Duranti - 1994 - Arcipelago.
  8. added 2017-09-22
    Philosophy and Mathematics, From Plato to the Present.Robert J. Baum - 1973 - San Francisco, Freeman, Cooper.
  9. added 2017-09-22
    Platons Verhältnis Zur Mathematik.Seth Demel - 1931 - Philosophical Review 40 (3):306-306.
  10. added 2017-06-29
    The Generation of Numbers in Plato's Parmenides.R. E. Allen - 1970 - Classical Philology 65 (1).
  11. added 2017-06-29
    Greek Mathematical Philosophy.Edward A. Maziarz - 1968 - New York: Ungar.
  12. added 2017-06-29
    Forms and Numbers: A Study in Platonic Metaphysics (II).A. E. Taylor - 1927 - Mind 36 (141):12-33.
  13. added 2017-06-29
    Forms and Numbers: A Study in Platonic Metaphysics (I.).A. E. Taylor - 1926 - Mind 35 (140):419-440.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. added 2017-03-23
    The Evolution of the Euclidean Elements.Wilbur Richard Knorr - 1975 - Dordrecht, Holland: D. Reidel Publishing Company.
  19. 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 (...)
  20. added 2017-02-16
    Plato's Mathematical Imagination. The Mathematical Passages in the Dialogues and Their Interpretation.Robert S. Brumbaugh - 1954 - Journal of Philosophy 53 (13):415-418.
  21. 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.
  22. added 2017-01-28
    The Significance of the Mathematical Element in the Philosophy of Plato.Irving Elgar Miller - 1904 - University of Chicago Press.
  23. added 2017-01-28
    The Nuptial Number of Plato its Solution and Significance.James Adam - 1891 - C. J. Clay and Sons.
  24. 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.
  25. added 2017-01-23
    Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - Palgrave-Macmillan.
  26. 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.
  27. 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.
  28. added 2016-12-08
    Plato and the Irrationals — Part 2.Joseph A. Novak - 1983 - Apeiron 17 (1):14 - 27.
  29. added 2016-12-08
    Plato and the Irrationals.Joseph A. Novak - 1982 - Apeiron 16 (2):71 - 85.
  30. added 2016-12-08
    Pappus, Plato and the Harmonic Mean.Malcolm Brown - 1975 - Phronesis 20 (2):173-184.
  31. added 2016-12-08
    Plato's Form of Equal.R. S. Bluck - 1959 - Phronesis 4 (1):5-11.
  32. added 2016-12-08
    Plato's Philosophy of Mathematics. [REVIEW]C. C. V. - 1956 - Review of Metaphysics 9 (4):712-712.
  33. 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.
  34. 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 (...)
  35. 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 (...)
  36. added 2016-08-05
    Greek Mathematical Thought and the Origin of Algebra.Jacob Klein - 1968 - M. I. T. Press.
  37. added 2016-08-05
    Plato's Philosophy of Mathematics.Anders Wedberg - 1955 - Greenwood Press.
  38. 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.
  39. 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 (...)
  40. added 2015-08-28
    Early Education in Plato's Republic.Michelle Jenkins - 2015 - British Journal for the History of Philosophy 23 (5):843-863.
    In this paper, I reconsider the commonly held position that the early moral education of the Republic is arational since the youths of the Kallipolis do not yet have the capacity for reason. I argue that, because they receive an extensive mathematical education alongside their moral education, the youths not only have a capacity for reason but that capacity is being developed in their early education. If this is so, though, then we must rethink why the early moral education is (...)
  41. added 2015-04-29
    Plato's Philosophy of Mathematics.Paul Pritchard - 1995 - Academia Verlag.
    Available from UMI in association with The British Library. ;Plato's philosophy of mathematics must be a philosophy of 4th century B.C. Greek mathematics, and cannot be understood if one is not aware that the notions involved in this mathematics differ radically from our own notions; particularly, the notion of arithmos is quite different from our notion of number. The development of the post-Renaissance notion of number brought with it a different conception of what mathematics is, and we must be able (...)
  42. added 2015-04-24
    Annotations to the Speech of the Muses (Plato Republic 546b-C).Michael Jacovides & Kathleen McNamee - 2003 - Zeitschrift für Papyrologie und Epigraphik 144:31-50.
  43. added 2015-04-19
    Kallikles i geometria. Przyczynek do Platońskiej koncepcji sprawiedliwości [Callicles and Geometry: On Plato’s Conception of Justice].Marek Piechowiak - 2013 - In Zbigniew Władek (ed.), Księga życia i twórczości. Księga pamiątkowa dedykowana Profesorowi Romanowi A. Tokarczykowi. Wydawnictwo Polihymnia. pp. vol. 5, 281-291.
  44. added 2015-04-19
    Plato's Ideal Numbers.R. Petrie - 1911 - Mind 20 (78):252-255.
  45. added 2015-04-18
    Mathematical Entities in the Divided Line.M. J. Cresswell - 2012 - Review of Metaphysics 66 (1):89-104.
    The second highest level of the divided line in Plato’s Republic appears to be about the entities of mathematics—entities such as particular triangles. It differs from the highest level in two respects. It involves reasoning from hypotheses, and it uses visible images. This article defends the traditional view that the passage is indeed about these mathematical ‘intermediates’; and tries to show how the apparently different features of the second level are related, by focussing on Plato’s need to give an account (...)
  46. added 2015-04-17
    Is Plato a Coherentist? The Theory of Knowledge in Republic V–VII.Edith Gwendolyn Nally - 2015 - Apeiron 48 (2):149-175.
  47. added 2015-04-17
    Diagrams, Dialectic, and Mathematical Foundations in Plato.Richard Patterson - 2007 - Apeiron 40 (1):1 - 33.
  48. added 2015-04-16
    La Geometria Dell'anima: Riflessioni Su Matematica Ed Etica in Platone.Paolo Pagani - 2012 - Orthotes.
    Questo testo nasce da alcune indagini sul nesso tra matematica e filosofia in ambiente “accademico”. È interessante notare che l'esplorazione di tale nesso costituisce un felice tratto di continuità tra gli studi più classici e ...
  49. added 2015-04-15
    Plato on Commensurability and Desire.Martha C. Nussbaum & Rosalind Hursthouse - 1984 - Aristotelian Society Supplementary Volume 58 (1):55 - 96.
  50. added 2015-04-14
    Plato's Mathematical Construction.R. Netz - 2003 - Classical Quarterly 53 (2):500-509.
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