Epistemology versus Ontology
Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf
Editors: Dybjer, P., Lindström, S., Palmgren, E., Sundholm, B.G. (Eds.)
Free Preview- Comprehensive overview of the philosophical problems of the foundational framework in current mathematics
- Demonstrates the impact of the work of the eminent academic: Per Martin-Löf
- Contains contributions from mathematicians and philosophers
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- About this book
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This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
- Table of contents (17 chapters)
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Kant and Real Numbers
Pages 3-23
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Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing
Pages 25-44
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Truth and Proof in Intuitionism
Pages 45-67
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Real and Ideal in Constructive Mathematics
Pages 69-85
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In the Shadow of Incompleteness: Hilbert and Gentzen
Pages 87-127
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Table of contents (17 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Epistemology versus Ontology
- Book Subtitle
- Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf
- Editors
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- P. Dybjer
- Sten Lindström
- Erik Palmgren
- B.G. Sundholm
- Series Title
- Logic, Epistemology, and the Unity of Science
- Series Volume
- 27
- Copyright
- 2012
- Publisher
- Springer Netherlands
- Copyright Holder
- Springer Science+Business Media Dordrecht.
- eBook ISBN
- 978-94-007-4435-6
- DOI
- 10.1007/978-94-007-4435-6
- Hardcover ISBN
- 978-94-007-4434-9
- Softcover ISBN
- 978-94-017-8238-8
- Series ISSN
- 2214-9775
- Edition Number
- 1
- Number of Pages
- XXVIII, 388
- Topics
