Overview
- 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
Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 34)
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Table of contents (7 chapters)
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Front Matter
Keywords
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.
Editors and Affiliations
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
DOI: https://doi.org/10.1007/978-94-017-9217-2
Publisher: Springer Dordrecht
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer Science+Business Media Dordrecht 2014
Hardcover ISBN: 978-94-017-9216-5Published: 09 September 2014
Softcover ISBN: 978-94-024-0707-5Published: 10 September 2016
eBook ISBN: 978-94-017-9217-2Published: 27 August 2014
Series ISSN: 2214-9775
Series E-ISSN: 2214-9783
Edition Number: 1
Number of Pages: XI, 214
Number of Illustrations: 1 b/w illustrations
Topics: Logic, Theory of Computation, Mathematical Logic and Foundations