David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 13 (2):115-134 (2005)
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 briefly to mathematical developments by Plato's associates Theaetetus and Eudoxus, and then to the past 200 years' developments in geometry
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
R. Urbaniak (2011). How Not To Use the Church-Turing Thesis Against Platonism. Philosophia Mathematica 19 (1):74-89.
E. Landry (2012). Recollection and the Mathematician's Method in Plato's Meno. Philosophia Mathematica 20 (2):143-169.
C. McLarty (2012). Introduction: Hypotheses and Progress. Philosophia Mathematica 20 (2):135-142.
Similar books and articles
Mark McEvoy (2012). Platonism and the 'Epistemic Role Puzzle'. Philosophia Mathematica 20 (3):289-304.
Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? International Studies in the Philosophy of Science 19 (1):65 – 84.
Øystein Linnebo (2008). The Nature of Mathematical Objects. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. 205--219.
Sandra Peterson (2011). Socrates and Philosophy in the Dialogues of Plato. Cambridge University Press.
Øystein Linnebo (2009). Platonism in the Philosophy of Mathematics. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
Colin Cheyne (1999). Problems with Profligate Platonism. Philosophia Mathematica 7 (2):164-177.
Mark Balaguer (1998). Platonism and Anti-Platonism in Mathematics. Oxford University Press.
Jonathan Fine (2011). Laughing to Learn: Irony in the Republic as Pedagogy. Polis 28 (2):235-49.
Added to index2010-08-17
Total downloads9 ( #173,263 of 1,413,322 )
Recent downloads (6 months)1 ( #154,079 of 1,413,322 )
How can I increase my downloads?