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 <firstname.lastname@example.org> 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 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.