Intuitionistic Proof Versus Classical Truth The Role of Brouwer's Creative Subject in Intuitionistic Mathematics /

• Main Author: Martino, Enrico (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Logic, Epistemology, and the Unity of Science, 42
• Subjects: Mathematics-Philosophy.; Mathematical logic.; Philology.; Logic.; Philosophy of Mathematics.; Mathematical Logic and Foundations.; Mathematical Logic and Formal Languages.

This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers - both new and previously published - it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author expl...

Table of Contents:

• Brouwer, Dummett and the bar theorem
• Creative subject and bar theorem
• Natural intuitionistic semantics and generalized Beth semantics
• Connection between the principle of inductive evidence and the bar theorem
• On the Brouwerian concept of negative continuity
• Classical and intuitionistic semantical groundedness
• Brouwer's equivalence between virtual and inextensible order
• An intuitionistic notion of hypothetical truth for which strong completeness intuitionistically holds
• Propositions and judgements in Martin-Löf
• Negationless Intuitionism
• Temporal and atemporal truth in intuitionistic mathematics
• Arbitrary reference in mathematical reasoning
• The priority of arithmetical truth over arithmetical provability
• The impredicativity of the intuitionistic meaning of logical constants
• The intuitionistic meaning of logical constants and fallible models.