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Topic: Torkel Franzen argues
Replies: 25   Last Post: May 17, 2013 3:52 PM

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Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: Torkel Franzen argues
Posted: May 8, 2013 9:28 AM
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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 2013-04-25, 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.

--
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



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