Date: Apr 5, 2013 11:38 PM
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.email@example.com>,
>> Nam Nguyen <firstname.lastname@example.org> wrote:
>>> On 05/04/2013 6:11 PM, Virgil wrote:
>>>> In article <_pJ7t.email@example.com>,
>>>> Nam Nguyen <firstname.lastname@example.org> 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
>>>> 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
>>>> ¤ 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
>>>> ¤ Co-operative Grocer Chain Japan, known as CGC Japan
>>> Sure. Here cGc means the FOL formula written in L(PA) that would stand
>>> cGC <-> "There are infinitely many counter examples of the Goldbach
>> 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
The problem is that you, we, have been so "trained" on IP (Induction
Principle) that we _don't even suspect_ IP has some loopholes.
There is no remainder in the mathematics of infinity.