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Logicism, intuitionism and formalism : what has become of them?

Publisher: [Dordrecht] ; [London] : Springer, cop. 2009.
Series: Synthese Library (Dordrecht), 341.
Edition/Format:   Print book : Conference publication : English
Summary:

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  Read more...

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Genre/Form: History
Material Type: Conference publication
Document Type: Book
ISBN: 9781402089251 1402089252
OCLC Number: 690338907
Notes: Issu de deux conférences tenues à "Uppsala university", Suède, en août 2004.
Description: 1 vol. (XII-512 p.) ; 25 cm.
Contents: Preface.- Notes on the Contributors.- Introduction; Sten Lindstroem, Erik Palmgren.- I. LOGICISM AND NEO-LOGICISM.- Protocol Sentences for Lite Logicism; John Burgess.- Frege's Context Principle and Reference to Natural Numbers; Oystein Linnebo.- The Measure of Scottish Neo-Logicism; Stewart Shapiro.- Natural Logicism via the Logic of Orderly Pairing; Neil Tennant.- II. INTUITIONISM AND CONSTRUCTIVE MATHEMATICS.- A Constructive Version of the Lusin Separation Theorem; Peter Aczel.- Dini's Theorem in the Light of Reverse Mathematics; Josef Berger, Peter Schuster.- Journey in Apartness Space; Douglas Bridges, Luminita Vita.- Relativisation of Real Numbers to a Universe; Hajime Ishihara.- 100 years of Zermelo's Axiom of Choice: What Was the Problem With It?; Per Martin-Loef.- Intuitionism and the Anti-Justification of Bivalence; Peter Pagin.- From Intuitionistic to Point-Free Topology; Erik Palmgren.- Program Extraction in Constructive Mathematics; Helmut Schwichtenberg.- Brouwer's Approximate Fixed-Point Theorem is Equivalent to Brouwer's Fan Theorem; Wim Veldman.- III. FORMALISM.- 'Goedel's Modernism: On Set-Theoretic Incompleteness,' Revisited; Mark van Atten, Juliette Kennedy.- Tarski's Practice and Philosophy: Between Formalism and Pragmatism; Hourya Benis Sinaceur.- The Constructive Hilbert-Program and the Limits of Martin-Loef Type Theory; Michael Rathjen.- Categories, Structures, and the Frege-Hilbert Controversy: the Status of Meta-Mathematics; Stewart Shapiro.- Beyond Hilbert's Reach?; Wilfried Sieg.- Hilbert and the Problem of Clarifying the Infinite; Soeren Stenlund.- Index.
Series Title: Synthese Library (Dordrecht), 341.
Responsibility: edited by Sten Lindstrom ... Erik Palmgren ... Krister Segerberg ... [et al.].
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