伯吉斯对当代数学及其史学中唯名论倾向的批判
A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography
摘要：
我们分析的发展，在数学严谨的观点，伯吉斯批判唯名论重建。我们应用这样的批评重建无穷小分析完成的努力，康托，戴德金，维尔斯特拉斯;重建柯西的基础工作与工作的博耶和格拉比纳;和主教的建构主义重建经典分析。我们研究了历史编纂，教学和研究的唯名论处置的影响。
英文摘要：
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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