Intuitionistic Proof Versus Classical Truth
The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics
Authors: Martino, Enrico
Free Preview- 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
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- About this book
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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 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.
- About the authors
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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.
- Reviews
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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)
- Table of contents (15 chapters)
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Brouwer, Dummett and the Bar Theorem
Pages 1-14
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Creative Subject and Bar Theorem
Pages 15-22
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Natural Intuitionistic Semantics and Generalized Beth Semantics
Pages 23-26
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Connection Between the Principle of Inductive Evidence and the Bar Theorem
Pages 27-30
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On the Brouwerian Concept of Negative Continuity
Pages 31-45
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Table of contents (15 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Intuitionistic Proof Versus Classical Truth
- Book Subtitle
- The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics
- Authors
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- Enrico Martino
- Series Title
- Logic, Epistemology, and the Unity of Science
- Series Volume
- 42
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-74357-8
- DOI
- 10.1007/978-3-319-74357-8
- Hardcover ISBN
- 978-3-319-74356-1
- Softcover ISBN
- 978-3-030-08971-9
- Series ISSN
- 2214-9775
- Edition Number
- 1
- Number of Pages
- XIII, 170
- Number of Illustrations
- 1 b/w illustrations
- Topics
