A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography |
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Authors: | Karin Usadi Katz Mikhail G Katz |
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Institution: | (1) Bar Ilan University, Ramat Gan, Israel;; |
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Abstract: | We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions.
We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind,
and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to
Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography,
teaching, and research. |
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Keywords: | |
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