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:
>
> >He also implied that the traditional set theory community is on the
> >wrong track. I certainly applaud Harvey's program, but I assume that
> >since Harvey is devoting himself to this program, he believes that
> >the results he gets are TRUE. What I don't understand is what he'll
> >tell mathematicians who want to know why they should believe this.
>
>Yes, of course I believe that the results that I get are TRUE, but what
>results? The results that it is necessary and sufficient to use large
>cardinals to get such and such, or such and such can only be done with
>large cardinals, or such and such is outright equivalent to the
>1-consistency or consistency of large cardinals, etcetera.
>
>That is where my role as f.o.m. expert ends, and where, if I wish to
>continue, my role as ph.o.m. begins.
>
>Namely, my f.o.m. expert role is to show that basic natural elementary
>universally accessible concrete mathematics - part of the unremoveable
>furniture of mathematics as we know it - is inexorably tied up with large
>cardinals, through their 1-consistency or consistency.

It is precisely when foundational issues come to the fore that 
philosophical questions become inescapable. Harvey has written on "The 
Necessary Use of  Large Cardinals" not on "Equivalences with 1-Consistency 
of Large Cardinals" presumably because he really believes (though he's 
reluctant to admit it) that the combinatorial consequences he drew were 
TRUE. Otherwise, why bother?

Martin



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