Logica Universalis

, Volume 8, Issue 2, pp 193–214 | Cite as

Toward a Clarity of the Extreme Value Theorem

  • Karin U. Katz
  • Mikhail G. KatzEmail author
  • Taras Kudryk


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.

Mathematics Subject Classification (2010)

Primary 26E35 Secondary 00A30 01A85 03F55 


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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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Karin U. Katz
    • 1
  • Mikhail G. Katz
    • 1
    Email author
  • Taras Kudryk
    • 2
  1. 1.Department of MathematicsBar Ilan UniversityRamat GanIsrael
  2. 2.Department of MathematicsLviv National UniversityLvivUkraine

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