Constructivity and Computability in Historical and Philosophical Perspective
Language: English
Published by Springer, 2014
Series: Book 23 of 41 - Logic, Epistemology, and the Unity of Science
- Hardcover
- New
Seller: Books Puddle, New York, NY, U.S.A.Books Puddle
AbeBooks seller since November 22, 2018
Condition: New
£ 67.02
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pp. 228.
Seller Inventory # 26359356901
- Title
- Constructivity and Computability in Historical and Philosophical Perspective
- Publisher
- Springer
- Publication year
- 2014
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 940179216X
- ISBN 13
- 9789401792165
- Series
- Book 23 of 41: Logic, Epistemology, and the Unity of Science
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.
"Synopsis" may belong to another edition of this title.
From the Back Cover
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.
"About the title" may belong to another edition of this title.
Books Puddle
New York, NY, U.S.A.
AbeBooks seller since November 22, 2018
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