On Jan 21, 9:54 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > Zuhair <zaljo...@gmail.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). Presumably because his research into these matters is (partly?) > funded by the Templeton Foundation, he's chosen to illustrate this point > -- made previously in terms of "concept calculus" etc. -- by means of > vaguely theological bandying about of somewhat arbitrary formalism. > > -- > Aatu Koskensilta (aatu.koskensi...@uta.fi) > > "Wovon man nicht sprechen kann, dar ber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
As far as what he displayed I don't see anything "natural", I see the "supernatural" that is been formalized. If ZFC according to what he is saying is provable to be consistent in some system that is "mutually interpretable" with supernaturally based system, then this does imparts unnaturalness of ZFC. It would be interesting to see a "natural" principle based theory that is mutually interpretable with ZFC itself, since that would be 'really' interesting. Measuring fantasies is not really that rewarding at all.