Date: Apr 6, 2013 2:20 AM
Author: namducnguyen
Subject: Re: Matheology § 224

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 <> wrote:

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

There is no remainder in the mathematics of infinity.