[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.


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