[FOM] Quotation of Brouwer on Cantor
torkel at sm.luth.se
Thu Sep 8 15:25:55 EDT 2005
>I have a note in my files that Poincaré, in an address at the 1908 Rome
>Congress, said something to the effect that Cantorian set theory was a
>grave mathematical malady from which mankind would in time awake.
>But I have no copy of Poincaré's address here to check.
Just in case Michael Detlefsen isn't reading the list at the moment:
As noted by Martin Davis, this is another one of those extremely
dubious sayings. There was a recent discussion of Poincare's supposed
comment in sci.math recently. I quote from a message by
Keith Ramsay in that group:
On 7 Sept. 1998 Michael Detlefsen commented that the original
of the remark appears in Poincare's 1908 essay, "The Future
of Mathematics" (appearing as chapter 2 of _Science and
Method_). Here's how he quotes it (I word-wrapped it):
#"... 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."
Thus the sense of the passage seems to be that it is set theory that
needs to be cured of a disease (the paradoxes).
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