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GIANLUIGI OLIVERI, Criticism and Growth of Mathematical Knowledge, Philosophia Mathematica, Volume 5, Issue 3, October 1997, Pages 228–249, https://doi.org/10.1093/philmat/5.3.228
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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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