"... it has come to pass that we have encountered certain paradoxes,
certain apparent contradictions that would have delighted Zeno the Eleatic
and the school of Megara. And then each must seek the remedy. For my part,
I think, and I am not the only one, that the important thing is never to
introduce entities not completely definable in a finite number of words.
Whatever be the cure adopted, we may promise ourselves the joy of the
doctor called in to follow a beautiful pathologic case."
This is not unqualified praise of turn of the century set theory. At the
same time, however, it is not sheer insult ... surely nothing like calling
set theory a 'disease' that is to be cured. To fill out one's understanding
of Poincare's views of set theory, one should also read the later essays
"The logic of infinity" and "Mathematics and logic". Both appear in the
LAST ESSAYS ... collection. The former is a fairly careful development of
P's diagnosis and prescribed cure for the paradoxes (viz. the one mentioned
in the above quote). The latter is a curious but interesting attempt to set
out something like the 'philosophical psychology' that Poincare takes to
underlie the paradoxes. Of particular concern are the divergences between
realists and idealists.
Greetings from South Bend (doesn't have quite the same ring to it as
'Greetings from Montevideo' or even 'Greetings from Berkeley' does it?),
Mic Detlefsen
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Michael Detlefsen
Department of Philosophy
University of Notre Dame
Notre Dame, Indiana 46556
U.S.A.
e-mail: Detlefsen.1@nd.edu
FAX: 219-631-8609
Office phone: 219-631-7534
Home phone: 219-232-7273
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