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Logicism, Intuitionism, and Formalism: What Has Become of Them? (Synthese
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Logicism, Intuitionism, and Formalism: What Has Become of Them? (Synthese Library) Hardcover - 2009 - 1st Edition

by Sten Lindström,Erik Palmgren,Krister Segerberg, Viggo Stoltenberg-Hansen,

From the publisher

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.

From the rear cover

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in the famous Hilbert-Brouwer controversy in the 1920s.

The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics.

The volume will be of interest primarily to researchers and graduate students of philosophy, logic, mathematics and theoretical computer science. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.

Details

  • Title Logicism, Intuitionism, and Formalism: What Has Become of Them? (Synthese Library)
  • Author Sten Lindström,Erik Palmgren,Krister Segerberg, Viggo Stoltenberg-Hansen,
  • Binding Hardcover
  • Edition number 1st
  • Edition 1
  • Pages 512
  • Publisher Springer, New York, New York
  • Date 2009
  • ISBN 9781402089251
  • Themes
    • Aspects (Academic): Philosophical

About the author

Sten Lindstrm is Professor of Philosophy at Ume University and has been a Research Fellow at the Swedish Collegium for Advanced Study (SCAS). He has published papers on intensional logic, belief revision and philosophy of language, and co-edited the books Logic, Action and Cognition: Essays in Philosophical Logic (Kluwer, 1997) and Collected Papers of Stig Kanger with Essays on his Life and Work, I-II (Kluwer, 2001).

Erik Palmgren is Professor of Mathematics at Uppsala University. His research interests are mainly mathematical logic and the foundations of mathematics. He is presently working on the foundational programme of replacing impredicative constructions by inductive constructions in mathematics, with special emphasis on point-free topology and topos theory.

Krister Segerberg is Emeritus Professor of Philosophy at Uppsala University and the University of Auckland. He is the author of papers in modal logic, the logic of action, belief revision and deontic logic, as well as the books An Essay in Classical Modal Logic (1971) and Classical Propositional Operators: An Exercise in the Foundations of Logic (1982).

Viggo Stoltenberg-Hansen is professor of Mathematical Logic at Uppsala University. His main interests include computability and constructivity in mathematics.

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Logicism, Intuitionism, and Formalism : What Has Become of Them?

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