Toward a Clarity of the Extreme Value Theorem

Karin U. Katz, Mikhail G. Katz, Taras Kudryk

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)193-214
Number of pages22
JournalLogica Universalis
Issue number2
StatePublished - May 2014


  • Benacerraf
  • Bishop
  • Cauchy
  • Kaestner
  • Kronecker
  • Peirce
  • constructive analysis
  • continuity
  • extreme value theorem
  • grades of clarity
  • hyperreal
  • infinitesimal
  • law of excluded middle
  • ontology
  • principle of unique choice
  • procedure
  • trichotomy
  • uniqueness paradigm


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