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
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
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DOI 10.1007/s11787-014-0102-8
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What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Foundations of Constructive Analysis.John Myhill - 1972 - Journal of Symbolic Logic 37 (4):744-747.
A Primer of Infinitesimal Analysis.John L. Bell - 1998 - Cambridge University Press.

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