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Constructivity and Computability in Historical and Philosophical Perspective (eBook)

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2014 | 2014
XI, 214 Seiten
Springer Netherland (Verlag)
978-94-017-9217-2 (ISBN)

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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.


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.

Preface; Jacques Dubucs and Michel Bourdeau.- Chapter 1. Constructive Recursive Functions, Church’s Thesis, and Brouwer’s Theory of the Creating Subject: Afterthoughts on a Parisian Joint Session; Göran Sundholm.- Chapter 2. The developments of the concept of machine computability from 1936 to the 1960s; Jean Mosconi.- Chapter 3. Kolmogorov Complexity in perspective, Part I: Information Theory and Randomness; Marie Ferbus-Zanda and Serge Grigorieff.- Chapter 4. Kolmogorov Complexity in perspective, Part II: Classification, Information Processing and Duality; Marie Ferbus-Zanda.- Chapter 5. Proof-theoretic semantics and feasibility; Jean Fichot.- Chapter 6. Recursive functions and constructive mathematics; Thierry Coquand.- Chapter 7. Gödel and intuitionism; Mark van Atten.

Erscheint lt. Verlag 27.8.2014
Reihe/Serie Logic, Epistemology, and the Unity of Science
Logic, Epistemology, and the Unity of Science
Zusatzinfo XI, 214 p. 1 illus.
Verlagsort Dordrecht
Sprache englisch
Themenwelt Geisteswissenschaften Philosophie Allgemeines / Lexika
Geisteswissenschaften Philosophie Logik
Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Allgemeines / Lexika
Technik
Schlagworte BHK interpretation • Canonical Proof • classification theory • Computing machines • Contructive mathematics • Effective procedures • Kolmogorov complexity • Proof-theoretical Semantics • recursion theory • Turing Machine
ISBN-10 94-017-9217-8 / 9401792178
ISBN-13 978-94-017-9217-2 / 9789401792172
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