Logic, Epistemology, and the Unity of Science

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.)

  • 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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eBook $159.00
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Hardcover $209.00
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Softcover $209.00
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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?

Table of contents (17 chapters)

  • Kant and Real Numbers

    Atten, Mark

    Pages 3-23

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

    Floyd, Juliet

    Pages 25-44

  • Truth and Proof in Intuitionism

    Prawitz, Dag

    Pages 45-67

  • Real and Ideal in Constructive Mathematics

    Sambin, Giovanni

    Pages 69-85

  • In the Shadow of Incompleteness: Hilbert and Gentzen

    Sieg, Wilfried

    Pages 87-127

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-94-007-4435-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-94-007-4434-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
price for USA
  • ISBN 978-94-017-8238-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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
  • 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