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.

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

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