Overview
- 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
Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 27)
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About this book
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?
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Keywords
Table of contents (17 chapters)
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Front Matter
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Philosophy of Logic and Mathematics
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Front Matter
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PHILOSOPHY OF LOGIC AND MATHEMATICS
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Foundations
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Front Matter
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FOUNDATIONS
Editors and Affiliations
Bibliographic Information
Book Title: Epistemology versus Ontology
Book Subtitle: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf
Editors: P. Dybjer, Sten Lindström, Erik Palmgren, G. Sundholm
Series Title: Logic, Epistemology, and the Unity of Science
DOI: https://doi.org/10.1007/978-94-007-4435-6
Publisher: Springer Dordrecht
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer Science+Business Media Dordrecht. 2012
Hardcover ISBN: 978-94-007-4434-9Published: 11 July 2012
Softcover ISBN: 978-94-017-8238-8Published: 09 August 2014
eBook ISBN: 978-94-007-4435-6Published: 10 July 2012
Series ISSN: 2214-9775
Series E-ISSN: 2214-9783
Edition Number: 1
Number of Pages: XXVIII, 388
Topics: Logic, Mathematical Logic and Foundations, Epistemology, Ontology, History of Mathematical Sciences