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.
Original language | English |
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Pages (from-to) | 51-89 |
Number of pages | 39 |
Journal | Foundations of Science |
Volume | 17 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2012 |
Bibliographical note
Funding Information:Mikhail G. Katz: Supported by the Israel Science Foundation grant 1294/06.
Funding
Mikhail G. Katz: Supported by the Israel Science Foundation grant 1294/06.
Funders | Funder number |
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Israel Science Foundation | 1294/06 |
Keywords
- Abraham Robinson
- Adequality
- Archimedean continuum
- Bernoullian continuum
- Burgess
- Cantor
- Cauchy
- Completeness
- Constructivism
- Continuity
- Dedekind
- Du Bois-Reymond
- Epsilontics
- Errett Bishop
- Felix Klein
- Fermat-Robinson standard part
- Infinitesimal
- Law of excluded middle
- Leibniz-Łoś transfer principle
- Nominalism
- Nominalistic reconstruction
- Non-Archimedean
- Rigor
- Simon Stevin
- Weierstrass