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Titlebook: Constructivity and Computability in Historical and Philosophical Perspective; Jacques Dubucs,Michel Bourdeau Book 2014 Springer Science+Bu

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书目名称Constructivity and Computability in Historical and Philosophical Perspective
编辑Jacques Dubucs,Michel Bourdeau
视频videohttp://file.papertrans.cn/237/236142/236142.mp4
概述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 re
丛书名称Logic, Epistemology, and the Unity of Science
图书封面Titlebook: Constructivity and Computability in Historical and Philosophical Perspective;  Jacques Dubucs,Michel Bourdeau Book 2014 Springer Science+Bu
描述.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
出版日期Book 2014
关键词BHK interpretation; Canonical Proof; Classification theory; Computing machines; Contructive mathematics;
版次1
doihttps://doi.org/10.1007/978-94-017-9217-2
isbn_softcover978-94-024-0707-5
isbn_ebook978-94-017-9217-2Series ISSN 2214-9775 Series E-ISSN 2214-9783
issn_series 2214-9775
copyrightSpringer Science+Business Media Dordrecht 2014
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https://doi.org/10.1007/978-3-642-56569-4lability was developed more and more as a theory of computation by an idealized machine, or in the form of a general theory of algorithms. I will only deal here with the former aspect, a development that stems from the concepts introduced in 1936 by Turing. I will try to show how Turing’s ideas were
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https://doi.org/10.1007/978-3-642-56569-4omplexity are presented: randomness and classification. The survey is divided in two parts in the same volume..Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov compl
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https://doi.org/10.1007/978-3-642-56569-4sts on a realist conception of the realm of mathematical objects. It must be recalled that the latter is not completely immune to such a reproach inasmuch as some vestige of realism is still present in its foundations (1). This realism takes the form of two different idealisations of human abilities
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https://doi.org/10.1007/978-94-017-9217-2BHK interpretation; Canonical Proof; Classification theory; Computing machines; Contructive mathematics;
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978-94-024-0707-5Springer Science+Business Media Dordrecht 2014
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