FOM: Re: 11:F.O.M. & Math Logic
Harvey Friedman
friedman at math.ohio-state.edu
Sun Dec 14 08:50:23 EST 1997
Barwise quotes from me (5:47AM 12/14/97):
>>3. More bluntly - mathematics, including mathematical logic, operates on a
>>kind of code of silence. One simply doesn't want to talk openly about
>>significance; particularly about other ways of looking at things that may
>>assume greater significance, and involve a change in research perspective.
>>One lapses into: well, if its hard, complicated, and intricate, and made
>>some sense some time, then it is OK; and it is OK to judge everybody's work
>>in these terms - i.e., is it hard, complicated, and intricate? How hard,
>>complicated, and intricate?
>>
>>4. But whereas 3 is a time honored way that most fields of mathematics
>>operate, I don't think that it can really work for the mathematical logic
>>that is disconnected from applications and from FOM. It is in danger of
>>being marginalized.
And then writes:
>We agree for once!
Well, our disagreements included
a) the status of nonstandard analysis and infinitesimals;
b) the status of first order predicate calculus and the usual set theoretic
foundations of mathematics.
I think that if we had the energy to continue the debate systematically,
getting down to the least common denominator of disagreement - which may be
more fundamental than it appears on the surface - we could also come to an
appropriate agreement. This would certainly be better than the pervasive
code of silence that so many of our colleagues adhere to. Even our little
bit of arguing is already better than the code of silence!
Incidentally, there is a bad typo in 11:F.O.M. & Math Logic. In the
pragraph beginning with "Thus the distinction..." replace "the latter" with
"the former."
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