The legacy of Lakatos: Reconceptualising the philosophy of mathematics

Philosophia Mathematica 5 (2):116-134 (1997)
Abstract
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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DOI 10.1093/philmat/5.2.116
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Mathematics as a Quasi-Empirical Science.Gianluigi Oliveri - 2004 - Foundations of Science 11 (1-2):41-79.
Objects and Processes in Mathematical Practice.Uwe Riss - 2011 - Foundations of Science 16 (4):337-351.
The 'Popperian Programme' and Mathematics.Eduard Glas - 2001 - Studies in History and Philosophy of Science Part A 32 (1):119-137.

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