David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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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
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Colin McLarty (2005). `Mathematical Platonism' Versus Gathering the Dead: What Socrates Teaches Glaucon. Philosophia Mathematica 13 (2):115-134.
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