[FOM] Quotation of Brouwer on Cantor

Torkel Franzen torkel at sm.luth.se
Thu Sep 8 15:25:55 EDT 2005

 A.R.D.Mathias says:

>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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