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From: herbzet on 3 Jul 2010 04:11


Nam Nguyen wrote:
> herbzet wrote:

> > The whole thing is nonsense, anyway. Clearly, PA
> > is consistent, or at least, its consistency is
> > at least as evident as the consistency of any
> > system which purports to prove it.
>
> Sometimes it's much ... much simpler and more logical, humble,
> humanistic to admit we don't know what we can't know, rather
> than pretending to possess some sort of an immortal knowledge.
>
> Suppose someone states "There are infinitely many universes
> and each has harbored a planet with intelligent life in its history."
>
> If there actually are infinitely many universes we can't know such
> fact. PA's consistency is like such a statement: if it's consistent,
> you can't never know that. Period.

I see a model for PA: the natural numbers. I conclude PA is consistent.

I would say I know this to a mathematical certainty.

--
hz
From: Marshall on 3 Jul 2010 11:03
On Jul 3, 1:11 am, herbzet <herb...(a)gmail.com> wrote:
> Nam Nguyen wrote:
>
> > Sometimes it's much ... much simpler and more logical, humble,
> > humanistic to admit we don't know what we can't know, rather
> > than pretending to possess some sort of an immortal knowledge.
> >
> > [...] PA's consistency is like such a statement: if it's consistent,
> > you can't never know that. Period.
>
> I see a model for PA: the natural numbers.  I conclude PA is consistent..
>
> I would say I know this to a mathematical certainty.

We've all said this to Nam a bazillion times. He's doesn't get it.


Marshall
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