Cargando…

Constructivity and computability in historical and philosophical perspective

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 large...

Descripción completa

Detalles Bibliográficos
Autores principales: Dubucs, Jacques, Bourdeau, Michel
Lenguaje:eng
Publicado: Springer 2014
Materias:
Acceso en línea:http://cds.cern.ch/record/2622776
_version_ 1780958612201406464
author Dubucs, Jacques
Bourdeau, Michel
author_facet Dubucs, Jacques
Bourdeau, Michel
author_sort Dubucs, Jacques
collection CERN
description 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 log.
id cern-2622776
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2014
publisher Springer
record_format invenio
spelling cern-26227762021-04-21T18:48:24Zhttp://cds.cern.ch/record/2622776engDubucs, JacquesBourdeau, MichelConstructivity and computability in historical and philosophical perspectiveMathematical Physics and MathematicsRanging 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 log.Springeroai:cds.cern.ch:26227762014
spellingShingle Mathematical Physics and Mathematics
Dubucs, Jacques
Bourdeau, Michel
Constructivity and computability in historical and philosophical perspective
title Constructivity and computability in historical and philosophical perspective
title_full Constructivity and computability in historical and philosophical perspective
title_fullStr Constructivity and computability in historical and philosophical perspective
title_full_unstemmed Constructivity and computability in historical and philosophical perspective
title_short Constructivity and computability in historical and philosophical perspective
title_sort constructivity and computability in historical and philosophical perspective
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2622776
work_keys_str_mv AT dubucsjacques constructivityandcomputabilityinhistoricalandphilosophicalperspective
AT bourdeaumichel constructivityandcomputabilityinhistoricalandphilosophicalperspective