One Hundred Years Of Intuitionism 1907-2007

by Van Atten, Mark; Boldini, Pascal; Bourdeau, Michel; Heinzmann, Gerhard

• ISBN13: 9783764386528
• ISBN10: 3764386525
• Format: Hardcover
• Copyright: 2008-09-22
• Publisher: Birkhauser

Summary

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.

Table of Contents

Contributors	p. X
Preface	p. XII
Brouwer and Brouwerian intuitionism
Another look at Brouwer's dissertation	p. 3
Brouwerian infinity	p. 21
The new intuitionism	p. 37
Truth and experience of truth	p. 50
The proper explanation of intuitionistic logic: on Brouwer's demonstration of the Bar Theorem	p. 60
The intersection of intuitionism (Brouwer) and phenomenology (Husserl)	p. 78
Brouwer on 'hypotheses' and the middle Wittgenstein	p. 96
Brouwer's notion of intuition and theory of knowledge by presence	p. 115
Buddhist models of the mind and the common core thesis on mysticism	p. 131
Kindred spirits
Remarks on the supposed French 'semi-' or 'pre-intuitionism'	p. 149
Poincare: intuitionism, intuition, and convention	p. 163
Some of Julius Konig's mathematical dreams in his New Foundations of Logic, Arithmetic, and Set Theory	p. 178
Godel, constructivity, impredicativity, and feasibility	p. 198
Lorenzen's operative justification of intuitionistic logic	p. 214
Mathematical perspectives
The Hilbert-Brouwer controversy resolved?	p. 243
Proof theory and Martin-Lof Type Theory	p. 257
Some remarks on linear logic	p. 280
Two applications of dynamic constructivism: Brouwer's continuity principle and choice sequences in formal topology	p. 301
A reverse look at Brouwer's Fan Theorem	p. 316
Some applications of Brouwer's Thesis on Bars	p. 326
Concluding remarks at the Cerisy conference	p. 341
A bibliography of L.E.J. Brouwer	p. 343
References	p. 391
Index of citations	p. 417
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