FOM: the Urbana meeting

[Martin Davis]

At 04:33 AM 6/27/00 -0400, Harvey Friedman wrote:
>Reply to Martin Davis 6/20/00 1:35PM:
>
> > Some time ago in a telephone conversation, Harvey told
> >me that I am an "extreme Platonist". Being a great fan of Harvey's
> >work on the necessary use of large cardinals, I took his comment
> >quite seriously and began to wonder. Is that really me?
>
>Yes, because I under the impression that you think that any
>intelligible set theoretic question, quantifying even over all sets -
>regardless of where they lie in the cumulative hierarchy - is a well
>defined mathematical problem in the same sense as, say, the Riemann
>hypothesis or the twin prime conjecture.

I do believe that every sentence in the language of set theory has a 
definite truth value (whether human beings will ever be able to determine 
it or not). If this makes me an "extreme platonist" - so be it. My own 
understanding is that the term usually is taken to involve ontological 
commitments that I'm not prepared to make. I'm certainly aware of the 
difference in kind between such problems as RH and twin primes on the one 
hand and CH or the existence of inaccessibles on the other. I don't know 
how Harvey intends "in the same sense as" to be taken.

>That there is an absolute
>right and an absolute wrong answer. And that it is part of normal
>mathematical activity to work on such questions just as it is
>to work on RH or TP, at least in the sense that there is no
>special difference in kind between the two activities that justifies
>calling one "normal mathematical activity" and the other "not normal
>mathematical activity."

Here is Harvey's tendency to turn all such questions into questions of 
mathematical sociology as mathematics is practiced today. But - if we must, 
of course there is such a difference today (though I would not choose a 
pejorative like "not normal" which only obscures the real issues). The 
paradox is that it is Harvey's own work which is doing so much to erase 
this distinction!

Martin





                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
                          (Add 1 and get 0)
                        http://www.eipye.com