On the Notion of Truth in Mathematical Intuitionism Cover Image

O pojęciu prawdy w intuicjonizmie matematycznym
On the Notion of Truth in Mathematical Intuitionism

Author(s): Zbigniew Tworak
Subject(s): Philosophy
Published by: Uniwersytet Warszawski - Wydział Filozofii i Socjologii, Instytut Filozofii
Keywords: intuitionism; truth; knowledge; verification; existence of a proof; law of excluded middle; Brouwer; Heyting; Dummett; Prawitz

Summary/Abstract: The basic philosophical idea of intuitionism is that mathematical entities exist only as mental constructions and that the notion of truth of a proposition should be equated with its verification or the existence of proof. However different intuitionists explained the existence of a proof in fundamentally different ways. There seem to be two main alternatives: the actual and potential existence of a proof. The second proposal is also understood in two alternative ways: as knowledge of a method of construction of a proof or as knowledge-independent and tenseless existence of a proof. This paper is a presentation and analysis of these alternatives.

  • Issue Year: 18/2010
  • Issue No: 4 (72)
  • Page Range: 49-76
  • Page Count: 28
  • Language: Polish