On Jan 21, 1:54 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).
Philosophy aside, have you ever known Friedman to actually formally prove anything of significance? I ask because my own experience interacting with him and reading his papers has shown him to be a total idiot.
When I wrote, ?Godel?s 1931 First Incompleteness Theorem is equivalent to the assertion that truth and provability do not coincide.? he interjected, ?This is incorrect. . . . There is a true sentence that is not provable. . . . There is a sentence that is neither provable nor refutable.? I didn?t respond to his comment because the proofs that his statements are implied by mine are trivial, and I was more interested in posting new ideas.
Another time Friedman tried to post a wff that expresses some unproven conjecture, but kept reposting because of mistakes. All the while he said he was making an important contribution to the problem by showing it can be expressed in logic. I pointed out that expressing unproven conjectures with logic is how texts often introduce the syntax and semantics of logic, and how it is so easy to express a variety of results.
> 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, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus