[FOM] Arnon-Friedman-Weaver discussion
martin@eipye.com
martin at eipye.com
Mon Feb 27 16:32:14 EST 2006
A subscriber writes:
>This has gotten tedious enough that I suggest you impose >a cooling-off period -- no discussions of predicativity >for the next 2 weeks or something like that.
Certainly by now everyone who has been following the
discussion knows that Arnon and Weaver believe that
predicativity is distinquished among possible foundations
by having a clear philosophical basis. Arnon believes that
predicativity in proofs guarantees "certainty". Weaver
(whose predicativity may go beyong Arnon's) believes that
predicativity provides a "a stunninglyexact fit" for
almost all that mathematicians do. Friedman refuses to
grant predicativity a special role, arguing that it is one
of a hierarchy of foundational "places to stop" and that
we are too ignorant to make any definitive choice, and
also that such impredicative methods as are formalized in
ZFC are both freely used and widely accepted. Neither side
will convince th other. So do let's call it quits, at
least for a while.
Martin
More information about the FOM
mailing list