On Jan 22, 11:02 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > Zuhair <zaljo...@gmail.com> writes: > > On Jan 21, 9:54 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > > >> 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. > > > As far as what he displayed I don't see anything "natural", I see the > > "supernatural" that is been formalized. > > There can be natural principles regarding supernatural things, in the > sense that these principles are naturally suggested (to many people) by > the concepts involved. As implied above, I would argue that Friedman's > ("supernatural" and "divine") systems aren't really very natural from a > theological point of view, but this is probably for someone more expert > in theological matters to comment on. > > > 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. > > Why? > > -- If one tells me that he managed to prove consistency of ZFC in some 'supernaturally' based system then this would initially cast some kind of unnaturalness on ZFC itself, however this would be confirmed if it is shown that ZFC can ONLY be so proved consistent. On the other hand all this would abolish in my own opinion if one presents a proof of consistency of ZFC in some 'naturally' based formalization. Of course I can paraphrase what Harvey is saying by saying that some concepts involving the supernatural are so strong that they are stronger than ZFC, of course the focus would be about that system and ZFC would not be the main concern here, since in many ways speech about the supernatural is already expected to be stronger than about the natural!