Overview
- 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
Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 42)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Keywords
- 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
- Brouwer Michael Dummett
- Brouwer Saul Kripke
- Brouwer Per Martin-Löf
- Brouwer Arend Heyting
About this book
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.
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Bibliographic Information
Book Title: Intuitionistic Proof Versus Classical Truth
Book Subtitle: The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics
Authors: Enrico Martino
Series Title: Logic, Epistemology, and the Unity of Science
DOI: https://doi.org/10.1007/978-3-319-74357-8
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: Springer International Publishing AG 2018
Hardcover ISBN: 978-3-319-74356-1Published: 05 March 2018
Softcover ISBN: 978-3-030-08971-9Published: 22 December 2018
eBook ISBN: 978-3-319-74357-8Published: 23 February 2018
Series ISSN: 2214-9775
Series E-ISSN: 2214-9783
Edition Number: 1
Number of Pages: XIII, 170
Number of Illustrations: 1 b/w illustrations
Topics: Philosophy of Mathematics, Mathematical Logic and Foundations, Philology, Mathematical Logic and Formal Languages, Logic