Constructivity and Computability in Historical and Philosophical Perspective

Nonfiction, Religion & Spirituality, Philosophy, Logic, Computers, Advanced Computing, Computer Science
Cover of the book Constructivity and Computability in Historical and Philosophical Perspective by , Springer Netherlands
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9789401792172
Publisher: Springer Netherlands Publication: August 27, 2014
Imprint: Springer Language: English
Author:
ISBN: 9789401792172
Publisher: Springer Netherlands
Publication: August 27, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Netherlands

Cover of the book Individual Orientation in Education by
Cover of the book From Phenomenology to Thought, Errancy, and Desire by
Cover of the book The Trinity by
Cover of the book Political Equilibrium: A Delicate Balance by
Cover of the book Gender and Equestrian Sport by
Cover of the book Cardiac Rate and Rhythm by
Cover of the book Ethical Values in International Decision-Making by
Cover of the book A History of Diabetes in Pregnancy by
Cover of the book New Frontiers in Bryology by
Cover of the book Choctaw Verb Agreement and Universal Grammar by
Cover of the book Nano Devices and Circuit Techniques for Low-Energy Applications and Energy Harvesting by
Cover of the book Defending Hypatia by
Cover of the book Catalysis by Unique Metal Ion Structures in Solid Matrices by
Cover of the book Perspectives on the Teaching of Geometry for the 21st Century by
Cover of the book Japanese and Western Phenomenology by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy