
Re: Torkel Franzen argues
Posted:
May 8, 2013 10:11 AM


On 08/05/2013 7:28 AM, Frederick Williams wrote: > Nam Nguyen wrote: >> >> On 05/05/2013 8:45 AM, Frederick Williams wrote: >>> Nam Nguyen wrote: >>>> >>>> On 04/05/2013 10:07 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? >>>> >>>> By claiming that the state of consistency of PA can be >>>> proved _IN_ a _different formal system_ . >>> >>> Your notion of infinite is very modest if does not go beyond two. >> >> That does _not_ mean there be only two, actually. >>> >>>>> >>>>>> 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. >>>> >>>> That's not a refute. Of course. >>>> >>>> (It's just an unsubstantiated claim). >>> >>> And yet an obviously true one. Suppose the question of the consistency >>> of PA is raised, a party to the discussion may say 'I accept that PA is >>> consistent and I feel no need to prove it.' No circle, no regression. >> >> The circularity rests with the argument on the _actual and objective_ >> state of consistency of PA, _not_ on the _wishful and subjective_ >> "acceptance" of anything. > > Mathematicians (like the rest of humanity) are forever accepting > things. It is no big deal. > Verification, proving, is a big deal.
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

