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Logic, Epistemology, and the Unity of Science

Constructivity and Computability in Historical and Philosophical Perspective

Editors: Dubucs, Jacques, Bourdeau, Michel (Eds.)

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  • Offers an in depth look at the relationship between computability and constructivity
  • Follows the developments from Turing's ground-breaking linkage between computation and the machine and the final resolution between proof theoretical semantics and canonical proof feasibility
  • Examines how to bridge differences in the area rather than providing a comprehensive view over the work
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  • ISBN 978-94-017-9217-2
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Hardcover $119.99
price for USA in USD
Softcover $129.00
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  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: October 28, 2016
  • ISBN 978-94-024-0707-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering
About this book

Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day.

Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics.

This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic.

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Constructive Recursive Functions, Church’s Thesis, and Brouwer’s Theory of the Creating Subject: Afterthoughts on a Parisian Joint Session

    Pages 1-35

    Sundholm, Göran

  • The Developments of the Concept of Machine Computability from 1936 to the 1960s

    Pages 37-56

    Mosconi, Jean

  • Kolmogorov Complexity in Perspective Part I: Information Theory and Randomness

    Pages 57-94

    Ferbus-Zanda, Marie (et al.)

  • Kolmogorov Complexity in Perspective Part II: Classification, Information Processing and Duality

    Pages 95-134

    Ferbus-Zanda, Marie

  • Proof-Theoretic Semantics and Feasibility

    Pages 135-157

    Fichot, Jean

Buy this book

eBook $99.00
price for USA in USD
  • ISBN 978-94-017-9217-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
Softcover $129.00
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: October 28, 2016
  • ISBN 978-94-024-0707-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering
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Bibliographic Information

Bibliographic Information
Book Title
Constructivity and Computability in Historical and Philosophical Perspective
Editors
  • Jacques Dubucs
  • Michel Bourdeau
Series Title
Logic, Epistemology, and the Unity of Science
Series Volume
34
Copyright
2014
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-9217-2
DOI
10.1007/978-94-017-9217-2
Hardcover ISBN
978-94-017-9216-5
Softcover ISBN
978-94-024-0707-5
Series ISSN
2214-9775
Edition Number
1
Number of Pages
XI, 214
Number of Illustrations
1 b/w illustrations
Topics