Logicism, Intuitionism, and Formalism What Has Become of Them [Hardcover]

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.

Preface.- Notes on the Contributors.- Introduction; Sten Lindstr?m, Erik Palmgren.- I. LOGICISM AND NEO-LOGICISM.-Protocol Sentences for Lite Logicism; John Burgess.- Frege's Context Principle and Reference to Natural Numbers; ?ystein 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-L?f.- 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.-'G?del'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-L?f 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; S?ren Stenlund.- Index.

Sten Lindstr?m is Professor of Philosophy at Ume? University and has been a Research Fellow at the Swedish Collegium for Advancedl#t