David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 5 (2):116-134 (1997)
Kitcher and Aspray distinguish a mainstream tradition in the philosophy of mathematics concerned with foundationalist epistemology, and a ‘maverick’ or naturalistic tradition, originating with Lakatos. My claim is that if the consequences of Lakatos's contribution are fully worked out, no less than a radical reconceptualization of the philosophy of mathematics is necessitated, including history, methodology and a fallibilist epistemology as central to the field. In the paper an interpretation of Lakatos's philosophy of mathematics is offered, followed by some critical discussion, and an extension to a social constructivist position (which might well have been unacceptable to Lakatos).
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Alison Pease, Alan Smaill, Simon Colton & John Lee (2009). Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics. Foundations of Science 14 (1-2):111-135.
Uwe Riss (2011). Objects and Processes in Mathematical Practice. Foundations of Science 16 (4):337-351.
Eduard Glas (2001). The 'Popperian Programme' and Mathematics. Studies in History and Philosophy of Science Part A 32 (1):119-137.
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