XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 11/29/2025 4:12 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 ...   
   >   
   > like maybe we just didn't find the formal system robust enough to   
   > describe what we're doing in godel's proof   
   >   
      
   I spent years creating just that system for   
   just that purpose: G := (F ⊬ G)   
      
   G says of itself that it cannot be proven in F.   
   Its called Olcott's Minimal Type Theory   
      
   >>   
   >>> and even if u prove something undecidable,   
   >>>   
   >>> that does not prove that a more robust system cannot defeat the cause   
   >>> of it being undecidable   
   >>   
   >> Sure he did, as he showed that *ANY* system that met the basic   
   >> requirements of being able to have the properties of the Natural   
   >> Numbers can support his proof of a statement that can not be proven in   
   >> the system.   
   >   
   > no, ur dealing with unknown unknowns. u can't use a proof by   
   > contradiction to rule out progress on unknown unknowns   
   >   
   > i can't really demonstrate the implications of this except with my   
   > reflective computing proposal, which as it stands takes incompleteness   
   > and isolates to a demonstrably insignificant subset of computing,   
   >   
   > and who knows if it can be taken farther and ruled out completely by   
   > some manner i just haven't thot of yet...   
   >   
   >>   
   >>>   
   >>>>   
   >>>> Yes, proving them might expand our knowledge about the number system   
   >>>> is some interesting way.   
   >>>>   
   >>>> The Goldbach conjecture, if false, will have a simple proof of that,   
   >>>> just show the even number and that no pair of primes smaller than it   
   >>>> add to it.   
   >>>>   
   >>>> Collatz is trickier, as you will need to actually prove that the   
   >>>> 3x+1 / /2 sequence NEVER gets to 1, even after an infinite number of   
   >>>> steps. Unless we find a higher cycle (which would be a direct proof)   
   >>>> we would need to show that the pattern keeps growing without bound.   
   >>>   
   >>>   
   >>   
   >   
   >   
      
      
   --   
   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   
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