Kuhn, Lakatos, and the image of mathematics

Philosophia Mathematica 3 (3):225-247 (1995)
In this paper I explore possibilities of bringing post-positivist philosophies of empirical science to bear on the dynamics of mathematical development. This is done by way of a convergent accommodation of a mathematical version of Lakatos's methodology of research programmes, and a version of Kuhn's account of scientific change that is made applicable to mathematics by cleansing it of all references to the psychology of perception. The resulting view is argued in the light of two case histories of radical conceptual innovations
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DOI 10.1093/philmat/3.3.225
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E. Glas (1999). Thought-Experimentation and Mathematical Innovation. Studies in History and Philosophy of Science Part A 30 (1):1-19.
Jean-Pierre Marquis (1999). Mathematical Engineering and Mathematical Change. International Studies in the Philosophy of Science 13 (3):245 – 259.
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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