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Topic: The Invalidity of Godel's Incompleteness Work.
Replies: 87   Last Post: Oct 25, 2013 2:44 PM

 Messages: [ Previous | Next ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: The Invalidity of Godel's Incompleteness Work.
Posted: Oct 20, 2013 1:22 PM

On 20/10/2013 7:59 AM, fom wrote:
> On 10/20/2013 1:55 AM, Nam Nguyen wrote:
>> On 04/10/2013 9:47 PM, Nam Nguyen wrote:
>>> Two major theorems Godel's Incompleteness are:
>>>
>>> - Incompleteness: Any formal system T that is consistent _and_ adequate
>>> enough to describe the concept of the natural numbers, would have
>>> G(T)
>>> as a statement that is true but not provable in T.
>>>
>>> - Completeness: Any consistent formal system has to have a model.
>>>
>>> On the Incompleteness, since the requirement that T be _informally_
>>> adequate enough to describe the concept of the natural numbers is _not_
>>> a syntactical notion [as that of a T's consistency], it's logically
>>> invalid to assume that T always be syntactically consistent, simply
>>> because we _informally assume_ T adequately describe the concept of
>>> the natural numbers. QED.

>>
>> More to the point, on Incompleteness, the 2 assumptions
>>
>> C1 = T is consistent.
>> C2 = T is adequate enough to describe the concept of the natural
>> numbers.
>>
>> are distinct as well as necessary. But since it's impossible to
>> logically guarantee that if T satisfies the _informal_ notion of C2,
>> T would also satisfy the _formal_ notion of C1, Incompleteness is an
>> invalid theorem.
>>
>> Note: by "formal" notion here, we'd mean a notion where the concept
>> of rules of inference is required, but also where the concept of the
>> natural numbers (or related notions such as recursion, induction,
>> language structure, etc...) is _NOT_ required.
>>

>
> Well, one interpretation of the problem is
> that anything based upon "what is prior" and
> "what is posterior" with a first step is
> interpretable relative to the ordinal sequence
> of natural numbers.

Kindly let me and the fora know what your _FORMAL definition_
of the "natural numbers". I don't know what your definition
is so I don't see any relevance between your paragraph above and my
thesis here. (For the record, my definition of the concept of natural
numbers is such that it could be only of _informal knowledge_ ).

>
> Rules of inference are stepwise syntactic transformations.
>
> How do you formulate a deductive theory which
> is not interpretable in relation to the ordinal
> sequence of natural numbers from which you
> wish to assert independence?
>
> Aristotle has a discussion concerning four forms
> of priority (which, unaccountably, turns into
> five forms by the end of the passage). Deductions
> and ordinal sequences are bound in this way and
> cannot be undone.
>
> which is indemonstrable and inconceivable.
>
> Incompleteness merely reflects that numbers and
> deductions cannot be placed into the relation of
> priority with respect to one another.

Kindly let me and the fora know what your summarized but
concise meta disproof of my thesis here concerning, say,
GIT.

If it's not a disproof (or an acknowledgement I've been correct)
kindly accept my apology that I'm not interested in anything else,
due to my time availability.

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

NYOGEN SENZAKI

Date Subject Author
10/4/13 namducnguyen
10/5/13 Peter Percival
10/6/13 LudovicoVan
10/6/13 LudovicoVan
10/9/13 fom
10/18/13 Peter Percival
10/18/13 namducnguyen
10/19/13 Peter Percival
10/19/13 fom
10/19/13 Peter Percival
10/19/13 fom
10/19/13 namducnguyen
10/19/13 fom
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 fom
10/19/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/19/13 namducnguyen
10/19/13 fom
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 fom
10/19/13 fom
10/19/13 namducnguyen
10/19/13 fom
10/19/13 fom
10/19/13 Peter Percival
10/19/13 namducnguyen
10/19/13 Peter Percival
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/20/13 namducnguyen
10/20/13 fom
10/24/13 namducnguyen
10/24/13 fom
10/24/13 namducnguyen
10/24/13 Peter Percival
10/24/13 namducnguyen
10/24/13 Peter Percival
10/24/13 fom
10/24/13 fom
10/20/13 fom
10/25/13 Rock Brentwood