Date: Apr 6, 2013 3:33 AM
Author: Virgil
Subject: Re: Matheology � 224

In article <19P7t.14441$yV1.11862@newsfe29.iad>,
Nam Nguyen <namducnguyen@shaw.ca> wrote:

> On 06/04/2013 12:13 AM, Nam Nguyen wrote:
> > On 06/04/2013 12:08 AM, Virgil wrote:
> >> In article <bWN7t.281592$O52.191417@newsfe10.iad>,
> >> Nam Nguyen <namducnguyen@shaw.ca> wrote:
> >>

> >>> On 05/04/2013 10:31 PM, Virgil wrote:
> >>>> In article <VFM7t.356449$PC7.98356@newsfe03.iad>,
> >>>> Nam Nguyen <namducnguyen@shaw.ca> wrote:
> >>>>

> >>>>> Then you don't seem to understand the nature of cGC, depending on the
> >>>>> formulation of the Conjecture but being a _different_ formula.
> >>>>>
> >>>>> For GC (the Goldbach conjecture), there naturally are 2 cases:

> >>>>
> >>>> What if the GC is eventually proved true in all systems?

> >>>
> >>> What do you mean by "all" systems?

> >>
> >> At least all systems in which a set of positive naturals with the usual
> >> forms of addition and multiplication are possible.

> >
> > What do you mean by "positive naturals", "usual forms", "possible"?
> > That's way too "intuitive" to conclude anything definitely, right?

>
> In any rate, "proved true in all [formal] systems" is a mixed-up
> of technical terminologies: formal systems prove syntactical theorems,
> truths are verified in language structures. The two paradigms are
> different and _independent_ : proving in one doesn't logical equate
> to the other.


But being able to prove something in one system does not, as far as I
know, prohibit being able to prove it other systems.
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