Date: Apr 5, 2013 11:38 PM Author: namducnguyen Subject: Re: Matheology § 224 On 05/04/2013 9:30 PM, Nam Nguyen wrote:

> 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.

Of course this is just a summary, a bird eye view.

You can prove that it's impossible to structure theoretically

verify the truth value of either cGC or ~cGC, using some logic

anti-induction principles.

The problem is that you, we, have been so "trained" on IP (Induction

Principle) that we _don't even suspect_ IP has some loopholes.

It does!

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

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