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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 5, 2013 10:45 AM
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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.

> >
> >> 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.

--
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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