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From: herbzet on 3 Jul 2010 15:12


Nam Nguyen wrote:
> herbzet wrote:
> > Nam Nguyen wrote:
> >> Nam Nguyen wrote:
> >>> herbzet wrote:
> >>>> Marshall wrote:
> >>>>> herbzet wrote:
> >>>>>> What is PA + (1)?
> >>>>> The successor to PA.
> >>>> The more I look at this, the funnier it gets.
> >>> Same here.
> >>>
> >>>> Make it stop!
> >>> Right. _Stop_ believing you "know" _exactly_ what the natural numbers be!
> >> Seriously, relativity in sciences (including mathematics) isn't an
> >> one-man conviction in "sci.logic", "sci.math". The mere mentioning
> >> of the 5th postulate, Hilbert-era's truth-equals-provability, SR,
> >> QM, should be a reminder that belief of any absoluteness in sciences
> >> is an ancient belief, which is no longer adequate for describing physical
> >> reality, or abstraction.
> >>
> >> If we scorn or laugh at the relativity of the standardness of a purported
> >> "model" of L(PA), a.k.a collectively as "the natural numbers", then we're
> >> no better that those who laughed at Riemann's ideas, at SR, at QM's uncertainty.
> >> At least those people had a valid excuse: they were in a different time in
> >> the past. We don't have such excuse!
> >>
> >> Seriously, all the nasty bickering aside, think about the whole thing logically.
> >> Think about the 4 reasoning Principles:
> >>
> >> - Principle of Consistency.
> >> - Principle of Compatibility.
> >> - Principle of Symmetry.
> >> - Principle of Humility.
> >>
> >> Would you think these are nonsensical principles honestly speaking?
> >
> > Probably.
> >
> > Who said anything about "absolute knowledge"? I think you're
> > tilting at a windmill.
>
> Oh, but by FOL definition of a formal system consistency, it must be
> either absolutely true or absolutely false that PA is consistent!
> (Ditto for inconsistency).

True -- it is a theorem of FOL that phi xor ~phi for any FOL
formula phi.

> Of course nobody should prevent you from saying:
>
> "I don't know"!

Sometimes I do know.

> See how easy when we're truthful to ourself!

Well, I try as best I can.

--
hz
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