The Foundations of Intuitionistic Mathematics PDF Download

Author: Stephen Cole Kleene
Publisher:
ISBN:
Category : Intuitionistic mathematics
Languages : en
Pages : 222

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Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080957595
Category : Mathematics
Languages : en
Pages : 215

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The Foundations of Intuitionistic Mathematics

Author: Stephen Cole Kleene
Publisher:
ISBN:
Category : Intuitionistic mathematics
Languages : en
Pages : 228

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Author: Arend Heyting
Publisher:
ISBN:
Category :
Languages : en
Pages : 145

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Author: Enrico Martino
Publisher: Springer
ISBN: 3319743570
Category : Mathematics
Languages : en
Pages : 173

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Book Description
This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.

Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255

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Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Author: A. Heyting
Publisher: Elsevier
ISBN: 1483278158
Category : Mathematics
Languages : de
Pages : 645

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Book Description
L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

Author: L.A. Harrington
Publisher: Elsevier
ISBN: 9780080960401
Category : Mathematics
Languages : en
Pages : 407

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Book Description
This volume discusses various aspects of Harvey Friedman's research in the foundations of mathematics over the past fifteen years. It should appeal to a wide audience of mathematicians, computer scientists, and mathematically oriented philosophers.

Author: Sten Lindström
Publisher: Springer Science & Business Media
ISBN: 1402089260
Category : Mathematics
Languages : en
Pages : 509

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Book Description
This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Author: Abraham Adolf Fraenkel
Publisher:
ISBN:
Category :
Languages : en
Pages : 297

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Book Description