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E-grāmata: Intuitionistic Proof Versus Classical Truth: The Role of Brouwer's Creative Subject in Intuitionistic Mathematics

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Intuitionistic Proof Versus Classical Truth: The Role of Brouwer's Creative Subject in Intuitionistic MathematicsPalielināt
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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 Brouwers 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 Brouwers work. These figures includeMichael 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.

Recenzijas

Anyone with an interest in the murkier aspects of intuitionism will find this book well worth reading. (Peter Fletcher, Studia Logica, Vol. 107, 2019)

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.- Brouwers 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.
Enrico Martino was associated professor (now retired) of Logic and Philosophy of Mathematics in the department of Mathematics and, subsequently of FISPPA of the University of Padua. His main interests are Philosophy of Logic and Mathematics.  
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