Epistemology versus Ontology
Essays on the Philosophy and Foundations of Mathematics in Honour of Per MartinLöf
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 MartinLöf
 Contains contributions from mathematicians and philosophers
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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 MartinLöf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and MartinLöf. What is the relation between prooftheoretical semantics in the tradition of Gentzen, Prawitz, and MartinLöf and Wittgensteinian or other accounts of meaningasuse? What can prooftheoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
 Table of contents (17 chapters)


Kant and Real Numbers
Pages 323

Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing
Pages 2544

Truth and Proof in Intuitionism
Pages 4567

Real and Ideal in Constructive Mathematics
Pages 6985

In the Shadow of Incompleteness: Hilbert and Gentzen
Pages 87127

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 MartinLöf
 Editors

 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
 9789400744356
 DOI
 10.1007/9789400744356
 Hardcover ISBN
 9789400744349
 Softcover ISBN
 9789401782388
 Series ISSN
 22149775
 Edition Number
 1
 Number of Pages
 XXVIII, 388
 Topics