On Jan 21, 1:07 pm, Zuhair <zaljo...@gmail.com> wrote: > Harvey Friedman had presented several formulations of theories using > some concepts in theology relative to which ZFC is provable to be > consistent!
To prove something consistent, you have to define what it means for it to be consistent. To prove a system of formal wffs consistent, we have a (recursive) function f over wffs that maps a wff into its negation, and it is not consistent iff there is a w such that w and f(w) are provable. But how does this apply to ZFC? ZFC is a collection of statements that are best expressed in English - attempts to formalize them create debate as to what a particular expression means. In other words, where is the formal syntax that precisely specifies the axioms and rules of ZFC? There are none - it is not that formal.
> 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! > > Doesn't that mean that ZFC based mathematics is too imaginary that > even if consistent still it is based and rooted in fantasy that cannot > really meet reality! > > Why should one follow such a system so grounded? > > With the scientific triumph it looks that mathematics is ought to be > revolutionized to parallel science instead of absolutist tendencies of > the old era of Religion and mythology as it seems to be currently > rooted in?! > > Zuhair