A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography

@article{Katz2012ABC,
  title={A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography},
  author={Karin U. Katz and Mikhail G. Katz},
  journal={Foundations of Science},
  year={2012},
  volume={17},
  pages={51-89}
}
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… 

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