Criticism and growth of mathematical knowledge

Philosophia Mathematica 5 (3):228-249 (1997)
Abstract
This paper attempts to show that mathematical knowledge does not grow by a simple process of accumulation and that it is possible to provide a quasi-empirical (in Lakatos's sense) account of mathematical theories. Arguments supporting the first thesis are based on the study of the changes occurred within Eudidean geometry from the time of Euclid to that of Hilbert; whereas those in favour of the second arise from reflections on the criteria for refutation of mathematical theories.
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DOI 10.1093/philmat/5.3.228
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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.

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