Intuitionistic Proof Versus Classical Truth
The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics
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Beschreibung
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 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.
Offers a new analysis of the role of Brouwer’s creative subject
Details realistic aspects in the idealization of the creative subject
Examines the hidden role of acts of choice even in classical logic and mathematics
Offers a new analysis of the role of Brouwer’s creative subject Details realistic aspects of the idealization of the creative subject Examines the hidden role of acts of choice even in classical logic and mathematics
Autor*in
Enrico Martino
Themen in »Intuitionistic Proof Versus Classical Truth«
Informal Intuitionistic Proof Creative Subject Bar Theorem Type Theory Constructivism Inductive Evidence Semantical Groundedness Impredicativity Intuitionistic Choice Sequences Beth-Models Fallible Models Brouwer realistic truth Brouwer classical truth Brouwer intuitionistic truth Brouwer creative subject
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“Anyone with an interest in the murkier aspects of intuitionism will find this book well worth reading.” (Peter Fletcher, Studia Logica, Vol. 107, 2019)
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