FOM: Foundationalism JoeShipman at
Sun Sep 13 19:51:38 EDT 1998

In a message dated 9/13/98 12:46:06 PM Eastern Daylight Time,
rhersh at writes:

<< I disagree with your conditional condemnation of the Fields Prize C
 ommittee.  Better you should acknowledge that the mathematical
 community has standards of evaluation which are broader and I
 think deeper than your own. >>

Reuben -- 

No, I wasn't condemning them!  I said
   IF the Fields medalists and the committees that selected them knew that the
*important* results of the medalists had incomplete proofs
  THEN either
1) You are correct about the dispensability of foundations
2) The committees are to be condemned.

I don't believe that the premise of this syllogism is satisfied because my
understanding is that Thom, Thurston, and Witten (well, Thom and Thurston
anyway) HAD provided complete proofs of SOME of their most important claims.

If I am wrong about this, I am willing to provisionally admit that item 1) of
the disjunction in the conclusion holds unless I can establish that item 2)
holds (of course the benefit of the doubt should go to the committees, one
should presume they are acting in good faith until contrary evidence appears).
This would mean that my view of the professional importance of foundations
needs to be modified to better accomodate your views.

Other people on this list may feel more justified than I in asserting that in
fact item 2) holds, but really I'd like to have the premise established first
before scrutinizing the motives of such eminent mathematicians.

I'll answer your other reply tomorrow. 

-- Joe

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