Date: Apr 6, 2013 3:59 AM
Author: namducnguyen
Subject: Re: Matheology § 224

On 06/04/2013 1:33 AM, Virgil wrote:
> 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.


I'm not talking about "prohibition"; I'm talking about the lack of
logically inferring one from the other, in general.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------