fom
Posts:
1,968
Registered:
12/4/12


Re: Torkel Franzen argues
Posted:
May 5, 2013 11:03 AM


On 5/5/2013 9:47 AM, Frederick Williams wrote: > 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 20130425, FredJeffries <fredjeffries@gmail.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. >
That is probably "standard mathematics". In a thread discussing belief and proof I pointed out that there can be secondorder consequences that cannot be proven in a sound deductive system. That may be an analog to the notion of true justified belief since it is related to consequence but cannot be adequately proven.
I suppose I can place your statement into that kind of context unproblematically.
What I would like to think is that there is an implicit circularity if one takes belief out of the picture.
Thanks.

