[FOM] philosophical literature on intuitionism

Prof. Dirk van Dalen dirk.vandalen at phil.uu.nl
Fri Oct 17 17:41:05 EDT 2008

The FOM message of Dr Forster can hardly be 
anything  but a, admittedly amusing, practical 
joke. The first sentence "I'm curious to know 
what the people who dreamt this stuff up actually 
thought they were doing." is one of the cutest 
characterizations of philosophical research.

On the whole it is surprising that a scientist 
should have difficulty in finding reading 
material on intuitionism, especially in our day 
of the internet and google. In the case of 
Brouwer there is no reason to despair; one could 
for example read Brouwer's own  texts. They are 
generally available, and not excessively 
complicated. There are even collected works with 
translations of Dutch texts.  It is, in fact, 
unthinkable that a Cambridge man like Dr. Forster 
has not read the classics of the philosophy of 
mathematics, including Brouwer - preferably in German, or maybe even Dutch.
There is a faint suggestion in the message that 
seems to question whether one should want to read 
Brouwer at all. This is of course one way of 
looking at historical figures and writings.
Anyway, the reactions show that many readers have 
taken the message seriously, so let me provide 
some pointers towards the 'elusive' reading material:

Brouwer 1908A, 1913C, 1919D, 1924N, 1927B, 1928A, 
1929A, 1930A, 1949C, 1952B,  1975, 1981A, 1992.
The full bibliographic information is to be found in preprint 175 in

Some major Brouwer publications:
-Cambridge Lectures on Intuitionism, (Ed. D. van 
Dalen). Cambridge University Press. Cambridge, 1981A
-Intuitionismus, (Ed. D. van Dalen) 
Bibliographisches Institut, Wissenschaftsverlag. 
Mannheim. [Berlin 1927 lectures and parts of an 
unpublished book on real functions]
-Mathematik, Wissenschaft und Sprache. 
Monatshefte für Mathematik und Physik, 36,  1929A.
-Die Struktur des Kontinuums, Wien 1930A.
-Consciousness, Philosophy and Mathematics. 
Proceedings of the 10th   International
Congress of Philosophy, Amsterdam, 1949C.
-Über die Bedeutung des Satzes vom 
ausgeschlossenen Dritten in der 
Mathematik  insbesondere in der 
Funktionentheorie. Journ. r. u. angew. Mat. 154, 1924N

A choice from the secondary literature:
Becker, O, Mathematische Existenz, Jahrbuch f. 
Phenomenologie und phaenomenologischer Forschung 8, 1927.

Weyl, H,  Über die neue Grundlagenkrise der 
Mathematik, Math. Zeitschrift, 10,1921,39-79
   ~~          The open world. Three lectures on 
the Metaphysical Implications  of Science, Yale University Press, 1932.
   ~~          Philosophy of Mathematics, Princeton University Press, 1949.

Atten, M. van, On Brouwer, Wadsworth, (London), 2003,
  ~~                  Brouwer meets 
Husserl,  Springer, Synthese Library, Dordrecht, 2007.

Heyting, A,  Mathematische Grundlagenforschung. 
Intuitionismus, Beweistheorie, Springer Verlag, Berlin, 1934.
  ~~              Intuitionism, an Introduction, 
North-Holland, Amsterdam, 1956.

Stigt, W.P.van, Brouwer's Intuitionism, North Holland, Amsterdam, 1990.

Mancosu, P., From Brouwer to Hilbert. The Debate on the Foundations
of Mathematics in the 1920s, Oxford University Press, Oxford, 1998.

A.S. Troelstra & D. van Dalen, Constructivism in 
Mathematics. Volume 1,2, North-Holland, Amsterdam, 1988

Mark van Atten, Pascal Boldini, Michel Bourdeau, 
and Gerhard Heinzmann (eds.), 1907--2007: One 
Hundred Years of Intuitionism, Birkhäuser, Basel, 
2008 [contains the Brouwer bibliography]

Largeault, Intuitionisme et théorie de la demonstration. Vrin. Paris, 1992

J. van Heijenoort, From Frege to Gödel, Harvard University Press.
Cambridge, MA. 1967

Special issue Perspectives on Intuitionism (ed. 
R. Tieszen). Philosophia Mathematica, 1998.

-Bibliography of Mathematical Logic, vol. VI. 
Proof theory and Constructive Matematics. Springer, Berlin, 1987

There are a number of useful papers in

Finally there happens to be a biography that 
contains apart from the personal and historical 
information elaborations of Brouwer's foundational ideas.

D. van Dalen.  Mystic, Geometer and Intuitionist: 
The Life of L.E.J. Brouwer. Vol 1. The Dawning 
Revolution Oxford University Press. 1999
    ~~                 Mystic, Geometer and 
Intuitionist: The Life of L.E.J. Brouwer. Volume 
2: Hope and Disillusion Oxford University Press. 2005


Prof . Dr. D. van Dalen
Department of Philosophy
Utrecht University
P.O. Box  80.126
3508 TC  Utrecht     The Netherlands
tel. 030-2531834, fax 030-2532816

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