
Re: Torkel Franzen argues
Posted:
May 8, 2013 11:44 PM


On 08/05/2013 8:11 AM, Nam Nguyen wrote: > 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.
For example, would you _accept_ the consistency of PA + ~cGC ("It is no big deal" you said)?
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

