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

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Constructivity and Computability in Historical and Philosophical Perspective

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2214-9775 ded 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’s978-94-024-0707-5978-94-017-9217-2Series ISSN 2214-9775 Series E-ISSN 2214-9783

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Kolmogorov Complexity in Perspective Part II: Classification, Information Processing and Duality,ompression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two du

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Book 2014between 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

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,Gödel and Intuitionism,pretation as being based on a new intuitionistic insight obtained by applying phenomenology, and also notes that relate the new notion of reductive proof to phenomenology. In an appendix, attention is drawn to notes from the archive according to which Gödel anticipated autonomous transfinite progressions when writing his incompleteness paper.

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Kolmogorov Complexity in Perspective Part I: Information Theory and Randomness,ry and the mathematical formalization of randomness based on Kolmogorov complexity. This last application goes back to the 1960s and 1970s with the work of Martin-Löf, Schnorr, Chaitin, Levin, and has gained new impetus in the last years.

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Book 2014 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