Publication 2008 : An Edited Book
ONE HUNDRED YEARS OF INTUITIONISM (1907-2007)
Mark van ATTEN, Pascal BOLDINI, Michel BOURDEAU, Gerhard HEINZMANN (ed.)
With logicism and formalism, intuitionism is one of the main foundations for mathematics proposed in the twentieth century ; and since the seventies, notably its views on logic have become important also outside foundational studies, with the development of theoretical computer science.
The aim of the book is threefold : to review and complete the historical account of intuitionism ; to present recent philosophical work on intuitionism ; and to give examples of new technical advances and applications of intuitionism. This volume brings together 21 contributions by today's leading authors on these topics, and surveys the philosophical, logical and mathematical implications of the approach initiated in 1907 in L.E.J. Brouwer's dissertation.
Publication of Cerisy Symposiums (2007) [For more information]
Available from the CCIC [n°400]
Publisher : Birkhäuser Verlag AG
Collection : History of Mathematical Sciences
ISBN : 978-3-7643-8652-8
Length : 422 p.
Price : 124,79 €
Publication Date : 2008
Brouwer (Luitzen), Gödel (Kurt), Hilbert (David), Intuitionism, König (Julius), Martin-Löf (per), Mysticism, Poincaré (Henri), Wittgenstein (Ludwig)
Contributors
Preface
PART I. BROUWER AND BROUWERIAN INTUITIONISM
Another look at Brouwer's dissertation, by Dirk van DALEN
Brouwerian infinity, by Carl POSY
The new intuitionism, by Charles McCARTY
Truth and experience of truth, by Jacques DUBUCS
The proper explanation of intuitionistic logic : on Brouwer's demonstration of the Bar Theorem, by Göran SUNDHOLM & Mark van ATTEN
The intersection of intuitionism (Brouwer) and phenomenology (Husserl), by Richard TIESZEN
Brouwer on "hypotheses" and the middle Wittgenstein, by Mathieu MARION
Brouwer's notion of intuition and theory of knowledge by presence, by Mohammad ARDESHIR
Buddhist models of the mind and the common core thesis on mysticism, by Henk BARENDREGT
PART II. KINDRED SPIRITS
Remarks on the supposed French "semi-" or "pre-intuitionism", by Alain MICHEL
Poincarré : intuitionism, intuition, and convention, by Gerhard HEINZMANN & Philippe NABONNAND
Some of Julius König's mathematical dreams in his New Foudations of Logic, Arithmetic, and Set Theory, by Marcel GUILLAUME
Gödel, constructivity, impredicativity, and feasibility, by Jean FICHOT
Lorenzen's operative justification of intuitionistic logic, by Peter SCHROEDER-HEISTER
PART III. MATHEMATICAL PERSPECTIVES
The Hilbert-Brouwer controversy resolved ?, by Per MARTIN-LÖF
Proof theory and Martin-Löf Type Theory, by Anton SETZER
Some remarks on linear logic, by Mitsuhiro OKADA
Two applications of dynamic constructivism : Brouwer's continuity principle and choice sequences in formal topology, by Giovanni SAMBIN
A reverse look at Brouwer's Fan Theorem, by Douglas BRIDGES
Some applications of Brouwer's Thesis on Bars, by Wim VELDMAN
Concluding remarks at the Cerisy conference, by Michael DUMMETT
A bibliography of L.E.J. Brouwer, by Dirk van DALEN
References
Index of citations