XPost: comp.theory, sci.math
From: polcott333@gmail.com
On 11/29/2025 10:22 PM, dart200 wrote:
> On 11/29/25 5:50 PM, olcott wrote:
>> On 11/29/2025 7:37 PM, dart200 wrote:
>>> On 11/29/25 4:38 PM, Richard Damon wrote:
>>>> On 11/29/25 5:12 PM, dart200 wrote:
>>>>> On 11/29/25 1:15 PM, Richard Damon wrote:
>>>>>> On 11/29/25 3:48 PM, dart200 wrote:
>>>>>>> On 11/29/25 12:24 PM, Richard Damon wrote:
>>>>>>>> On 11/29/25 1:57 PM, dart200 wrote:
>>>>>>>>> On 11/29/25 6:26 AM, olcott wrote:
>>>>>>>>>> On 11/29/2025 2:33 AM, dart200 wrote:
>>>>>>>>>>> On 11/29/25 12:00 AM, wij wrote:
>>>>>>>>>>>> I just found that Goldbach conjecture may be a (A)NP problem
>>>>>>>>>>>> if stated:
>>>>>>>>>>>>
>>>>>>>>>>>> Q: Given an even integer n, n>2. Is n the sum of two prime
>>>>>>>>>>>> numbers?
>>>>>>>>>>>>
>>>>>>>>>>>> Proof Q∈ANP:
>>>>>>>>>>>> v= AKS Primality Test // Ptime algorithm
>>>>>>>>>>>> C= {| n=a+b } // card(C)∈ O(|Q|)
>>>>>>>>>>>>
>>>>>>>>>>>> bool gbf(int n) { // n is an even number
>>>>>>>>>>>> int a,b;
>>>>>>>>>>>> for(a=3; a>>>>>>>>>>> b=n-a;
>>>>>>>>>>>> if(v(a)&&v(b)) return true;
>>>>>>>>>>>> }
>>>>>>>>>>>> return false;
>>>>>>>>>>>> }
>>>>>>>>>>>> Thus, Q∈ANP (ANP=NP).
>>>>>>>>>>>>
>>>>>>>>>>>> Goldbach conjecture is likely a NPC problem.
>>>>>>>>>>>> If so, from the ℙ≠ℕℙ result of
>>>>>>>>>>>> https://sourceforge.net/projects/cscall/files/MisFiles/PNP-
>>>>>>>>>>>> proof- en.txt/download
>>>>>>>>>>>>
>>>>>>>>>>>> We can conclude that no formal proof can solve Goldbach
>>>>>>>>>>>> conjecture, if formal
>>>>>>>>>>>> proof is a Ptime algorithm.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> boring semantic paradox variant
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>>>>>> I have always assessed that the Goldbach conjecture
>>>>>>>>>> to be proven true requires an infinite proof. It seems
>>>>>>>>>> best dismissed as insignificant.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> i fully believe the goldbach conjecture is a premise about
>>>>>>>>> natural numbers that can be proven at some point one way or
>>>>>>>>> another,
>>>>>>>>>
>>>>>>>>> i believe the same is true about the collatz conjecture,
>>>>>>>>>
>>>>>>>>> and rienmann hypothesis.
>>>>>>>>>
>>>>>>>>> when we do prove them, it will increase the totality of
>>>>>>>>> machines we can compute halting in regards to
>>>>>>>>>
>>>>>>>>
>>>>>>>> Fine thing to beleive, but we do know that there do exists true
>>>>>>>> propositions that can not be proven.
>>>>>>>
>>>>>>> unless you can prove something undecidable, then it cannot just
>>>>>>> be supposed to be so
>>>>>>>
>>>>>>
>>>>>> Which Godel did.
>>>>>>
>>>>>> It may be a highly artificial statement, but he showed that it
>>>>>> existed.
>>>>>
>>>>> it is an incredibly artificial ...
>>>>>
>>>>> "a truth that exists as true without proof" is mind numbingly
>>>>> artificial construct that in fact has a proof, just not in a formal
>>>>> system ...
>>>>
>>>> It is without proof IN THAT SYSTEM.
>>>>
>>>> It IS proven in a system with extra knowledge, knowledge that was
>>>> used to build thee particular form of the relationship that we use
>>>> to test the number.
>>>>
>>>> The key point is that relationship uses only operations in the base
>>>> system
>>>>
>>>>>
>>>>> like maybe we just didn't find the formal system robust enough to
>>>>> describe what we're doing in godel's proof
>>>>
>>>> His system is totally formal.
>>>>
>>>> The point is that the interprestation can't be made in the base
>>>> system the statement is expressed in, only a meta-system derived by
>>>> adding choices to that original system.
>>>>
>>>> The point that is made is that in ANY sufficiently expressive
>>>> system, there are statements which are true in it that can't be proven.
>>>>
>>>> Adding certain axioms/knowledge to that system to make it "higher
>>>> order" can allow some to be proven and resolved.
>>>>
>>>> No matter how finitely high you go with this, you will ALWAYS end up
>>>> with some statements that can't be proven.
>>>>
>>>> Only by adding an infinite number of these axioms/knowledge might it
>>>> be possible to prove every statement, but then the system doesn't
>>>> meet the initial requirements of a Formal Logic system of having a
>>>> finite number of axioms.
>>>
>>> or we just haven't found a robust enough set of axioms to deal with it
>>>
>>
>> The axioms are simply the currently existing
>> finite set of basic facts of general knowledge
>> of the actual world.
>
> well sure axioms are just the set of premises we accept because of what
> we can do with them
>
Yet when we do have the complete finite set
of basic facts of the world and we only allow
semantic logical entailment from these facts
then Gödel incompleteness within this formal
system cannot possibly occur. It can still
occur in teeny tiny toy systems like PA.
I have given this about 20,000 hours of thought
over 20 years. You can still find my work in
sci.logic going back to 2004.
>>
>> It took me 28 years to this come up this idea
>> it shouldn't take 28 more years for another
>> human to understand it.
>>
>
> it is kinda crazy how people assert incompleteness is certainly innate
> vs an indication we haven't found all necessary axioms yet
>
> idk where the certainty comes from
>
Hubris and ego.
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning" computable.
This required establishing a new foundation
for correct reasoning.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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