David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 20 (2):135-142 (2012)
The unifying theme of this issue is Plato’s dialectical view of mathematical progress and hypotheses. Besides provisional propositions, he calls concepts and goals also hypotheses. He knew mathematicians create new concepts and goals as well as theorems, and abandon many along the way, and erase the creative process from their proofs. So the hypotheses of mathematics necessarily change through use — unless Benson is correct that Plato believed mathematics could reach the unhypothetical goals of dialectic. Landry discusses Plato on mathematical and philosophical problem solving. Arsen and White relate Plato’s philosophy to mathematics in his time, and to Aristotle
|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
Colin McLarty (2005). `Mathematical Platonism' Versus Gathering the Dead: What Socrates Teaches Glaucon. Philosophia Mathematica 13 (2):115-134.
Citations of this work BETA
No citations found.
Similar books and articles
Mark McEvoy (2013). Experimental Mathematics, Computers and the a Priori. Synthese 190 (3):397-412.
Moon-Heum Yang (2005). The Relationship Between Hypotheses and Images in the Mathematical Subsection of the Divided Line of Plato's Republic. Dialogue 44 (2):285-312.
H. H. Benson (2012). The Problem is Not Mathematics, but Mathematicians: Plato and the Mathematicians Again. Philosophia Mathematica 20 (2):170-199.
Imre Lakatos (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
Massimo Pigliucci (2009). Hypotheses? Forget About It! Philosophy Now (Jul/Aug):47.
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4):351-360.
Daniel G. Campos (2007). Peirce on the Role of Poietic Creation in Mathematical Reasoning. Transactions of the Charles S. Peirce Society 43 (3):470 - 489.
Lawrence Resnick (1959). Confirmation and Hypothesis. Philosophy of Science 26 (1):25-30.
Joke Meheus (2005). Empirical Progress and Ampliative Adaptive Logics. Poznan Studies in the Philosophy of the Sciences and the Humanities 83 (1):193-217.
H. S. Arsen (2012). A Case For The Utility Of The Mathematical Intermediates. Philosophia Mathematica 20 (2):200-223.
David Atkinson, Jeanne Peijnenburg & Theo Kuipers (2009). How to Confirm the Conjunction of Disconfirmed Hypotheses. Philosophy of Science 76 (1):1-21.
Andrew Arana (2007). Review of D. Corfield's Toward A Philosophy Of Real Mathematics. [REVIEW] Mathematical Intelligencer 29 (2).
Added to index2012-03-30
Total downloads12 ( #137,761 of 1,140,113 )
Recent downloads (6 months)1 ( #147,976 of 1,140,113 )
How can I increase my downloads?