Logica Universalis 8 (2):193-214 (2014)
Abstract |
We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches to the extreme value theorem. We argue that a given pre-mathematical phenomenon may have several aspects that are not necessarily captured by a single formalisation, pointing to a complementarity rather than a rivalry of the approaches
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Keywords | Benacerraf Bishop Cauchy constructive analysis continuity extreme value theorem grades of clarity hyperreal infinitesimal Kaestner Kronecker law of excluded middle ontology Peirce principle of unique choice procedure trichotomy uniqueness paradigm |
Categories | (categorize this paper) |
DOI | 10.1007/s11787-014-0102-8 |
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Internality, Transfer, and Infinitesimal Modeling of Infinite Processes†.Emanuele Bottazzi & Mikhail G. Katz - forthcoming - Philosophia Mathematica.
Proofs and Retributions, Or: Why Sarah Can’T Take Limits.Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz & Mary Schaps - 2015 - Foundations of Science 20 (1):1-25.
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