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 M. 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… Expand
32 Citations

Figures from this paper

Controversies in the Foundations of Analysis: Comments on Schubring’s Conflicts
  • 10
  • PDF
Ten Misconceptions from the History of Analysis and Their Debunking
  • 42
  • PDF
A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos
  • 10
  • PDF
Meaning in Classical Mathematics: Is it at Odds with Intuitionism?
  • 29
  • PDF
Leibniz's laws of continuity and homogeneity
  • 37
  • PDF
THE TENSION BETWEEN INTUITIVE INFINITESIMALS AND FORMAL MATHEMATICAL ANALYSIS
  • 10
  • PDF
...
1
2
3
4
...

References

SHOWING 1-10 OF 178 REFERENCES
Idealization in Cassirer's Philosophy of Mathematics†
  • 19
Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy
  • 15
Yearning for the Impossible: The Surprising Truths of Mathematics
  • 16
  • PDF
The mysteries of adaequare: A vindication of fermat
  • 14
  • Highly Influential
  • PDF
...
1
2
3
4
5
...