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

• Κύριος συγγραφέας: Martino, Enrico (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Logic, Epistemology, and the Unity of Science, 42
• Θέματα: 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 explores Brouwer's idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer's work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics. 

 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.