Logicism, intuitionism, and formalism : what has become of them?
著者
書誌事項
Logicism, intuitionism, and formalism : what has become of them?
（Synthese library, v. 341）
Springer, c2009
- : hbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
The present anthology has its origin in two international conferences that were arranged at Uppsala University in August 2004: "Logicism, Intuitionism and F- malism: What has become of them?" followed by "Symposium on Constructive Mathematics". The rst conference concerned the three major programmes in the foundations of mathematics during the classical period from Frege's Begrif- schrift in 1879 to the publication of Godel' .. s two incompleteness theorems in 1931: The logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. The main purpose of the conf- ence was to assess the relevance of these foundational programmes to contemporary philosophy of mathematics. The second conference was announced as a satellite event to the rst, and was speci cally concerned with constructive mathematics-an activebranchofmathematicswheremathematicalstatements-existencestatements in particular-are interpreted in terms of what can be effectively constructed. C- structive mathematics may also be characterized as mathematics based on intuiti- isticlogicand,thus,beviewedasadirectdescendant ofBrouwer'sintuitionism.
The two conferences were successful in bringing together a number of internationally renowned mathematicians and philosophers around common concerns. Once again it was con rmed that philosophers and mathematicians can work together and that real progress in the philosophy and foundations of mathematics is possible only if they do. Most of the papers in this collection originate from the two conferences, but a few additional papers of relevance to the issues discussed at the Uppsala c- ferences have been solicited especially for this volume.
目次
- 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.
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