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
http://www.phil.uu.nl/preprints/lgps/list.html
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unpublished book on real functions]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
www.phil.uu.nl/~dvdalen/papers.htm
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
030-6663857(home)