Date: Apr 5, 2013 11:30 PM Author: namducnguyen Subject: Re: Matheology § 224 On 05/04/2013 8:51 PM, Virgil wrote:

> In article <nlL7t.371032$O02.109836@newsfe18.iad>,

> Nam Nguyen <namducnguyen@shaw.ca> wrote:

>

>> On 05/04/2013 6:11 PM, Virgil wrote:

>>> In article <_pJ7t.186674$rk7.149719@newsfe05.iad>,

>>> Nam Nguyen <namducnguyen@shaw.ca> wrote:

>>>

>>>> In so far as a _perceived_ language structure would enable

>>>> us to interpret the concept of the natural numbers, such

>>>> a perception is a theology; in it, there are 2 offshoot

>>>> theologies which we'll _forever_ (i.e. even in principle of

>>>> logic) struggle to choose for acceptance:

>>>>

>>>> - cGC being true

>>>> - ~cGC being true.

>>>

>>> According to Wikipedia

>>> CGC can be an abbreviation for:

>>> ¤ Chen Guangcheng a civil rights activist in the People's Republic

>>> of China who drew international attention to human rights issues in

>>> rural areas

>>> ¤ Canadian Grenadier Guards

>>> ¤ Cambridge Gliding Centre

>>> ¤ Canada Games Company

>>> ¤ The Capital Group Companies, an investment management organization

>>> ¤ the Canine Good Citizen certification

>>> ¤ Cerebellar granule cell

>>> ¤ Certified general contractor, a type of unlimited contractor in

>>> Florida, USA as opposed to registered (limited)

>>> ¤ Board-Certified Genetic Counselor

>>> ¤ United States Coast Guard Cutter

>>> ¤ Color Glass Condensate

>>> ¤ Comics Guaranty LLC, a grading service for the comic book

>>> collecting industry

>>> ¤ Conspicuous Gallantry Cross

>>> ¤ Constrained geometry complex

>>> ¤ Career Guidance Council, is a not-to-profit organization

>>> ¤ Consumer generated content, also known as Consumer generated media

>>> ¤ Co-operative Grocer Chain Japan, known as CGC Japan

>>

>>

>> Sure. Here cGc means the FOL formula written in L(PA) that would stand

>> as:

>>

>> cGC <-> "There are infinitely many counter examples of the Goldbach

>> Conjecture".

>

> Then you presume that the Goldbach conjecture will never be settled?

> It has not been around as long as the FLT, which finally was settled in

> the affirmative.

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:

Case 1 - ~GC is true: we found _one specific even natural_ > 4 that

isn't a sum of two primes.

But that of course has no bearing on either cGC or ~cGC!

So you can't setttle cGC or ~cGC on the account that ~GC

is true. And ~GC can still be settled as true!

Case 2: GC is true in the naturals as the standard structure for L(PA),

and it's said NEG(PA |- GC) and NEG(PA |- ~GC).

But if GC is undecidable in PA, there's no proof left in FOL but

_structure theoretically verifying_ the truth value of GC in

this structure.

But how would you _verify_ GC be true in this structure?

So, what you have left is just a _pure unverified intuition_

which is nothing more or less than a mathematical (theology-

like) _belief_ : _no structure theoretical proof_ !

In summary, only in Case 1 could you settle GC, but _in both cases_

you still can _never_ settle cGC and ~cGC.

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

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