fom wrote: > > On 5/4/2013 11:07 AM, Frederick Williams wrote: > > Nam Nguyen wrote: > >> > >> On 26/04/2013 11:09 AM, Nam Nguyen wrote: > > > >>> On 2013-04-25, FredJeffries <email@example.com> wrote: > >>>> > >>>> Now PA has been proved consistent in ZF or NBG, but then that > >>>> brings the consistency of axioms for set theory. > >> > >> Exactly right. And exactly my point. > >> > >> Somewhere, somehow, a circularity or an infinite regression > >> of _mathematical knowledge_ will be reached, > > > > How does one reach an infinite regression? > > > >> and at that point > >> we still have to confront with the issue of mathematical relativity. > > > > It is not the case that either we go round in a circle or we regress > > forever. > > Out of curiosity, how do you come to that conclusion?
I was thinking of the question of PA's consistency. If someone just accepts it, then he neither goes in a circle nor does he regress forever.
> I have > come to the exact opposite conclusion. The only sense I can > make of foundations is that it is more like a jigsaw puzzle > that must address circularity and regress directly and with > the objective of making it harmless.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting