On Monday, January 21, 2013 10:54:45 AM UTC-8, Aatu Koskensilta wrote: > Zuhair <email@example.com> writes:
> > Harvey Friedman had presented several formulations of theories using > > some concepts in theology relative to which ZFC is provable to be > > consistent! So some kind of mentioning of the supernatural (or what is > > mutually interpretable with it!) is needed to prove ZFC's > > consistency. > > > See: http://www.cs.nyu.edu/pipermail/fom/2013-January/016881.html > > > Doesn't that say that mathematics following ZFC is only grounded in > > Mythology driven principles!
> No. Friedman has explicitly stated he basically thinks whenever we > look into any field of human thought we will find basic, fundamental, > and natural principles which, when formalized, have the consistency > strength of set theory (possibly extended with some large cardinal > axioms).
FWIW, those "fundamental and natural principles" would have to include falsifiability, and set theory, like much of theology, is not consistent with falsifiability. Also, the notion of "consistency strength" is probably not one of those "fundamental and natural principles".