XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/22/2026 8:51 PM, Richard Damon wrote:   
   > On 1/22/26 7:33 PM, olcott wrote:   
   >> On 1/22/2026 6:17 PM, Richard Damon wrote:   
   >>> On 1/22/26 12:18 AM, olcott wrote:   
   >>>> On 1/21/2026 10:59 PM, Python wrote:   
   >>>>> Le 22/01/2026 à 04:54, olcott a écrit :   
   >>>>>> On 1/21/2026 9:37 PM, Richard Damon wrote:   
   >>>>>>> On 1/21/26 10:45 AM, olcott wrote:   
   >>>>>>>> On 1/21/2026 6:35 AM, Richard Damon wrote:   
   >>>>>>>>> On 1/20/26 11:54 PM, olcott wrote:   
   >>>>>>>>>> On 1/20/2026 10:04 PM, Richard Damon wrote:   
   >>>>>>>>>>> On 1/20/26 4:23 PM, olcott wrote:   
   >>>>>>>>>>>> On 1/19/2026 11:29 PM, Richard Damon wrote:   
   >>>>>>>>>>>>>> My system is not supposed to decide in advance whether   
   >>>>>>>>>>>>>> Goldbach is well‑founded. A formula becomes a truth‑bearer   
   >>>>>>>>>>>>>> only when PA can classify it in finitely many steps.   
   >>>>>>>>>>>>>> Goldbach may or may not be classifiable; that’s an open   
   >>>>>>>>>>>>>> computational fact, not a semantic requirement. This has   
   >>>>>>>>>>>>>> no effect on Gödel, because Gödel’s sentence is structurally   
   >>>>>>>>>>>>>> non‑truth‑bearing, not merely unclassified.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Which shows that you don't understand what logic systems are.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> The don't "Decide" on truths, they DETERMINE what is true.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Your problem is that either there is, or there isn't a   
   >>>>>>>>>>>>> finite length proof of the statement.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Semantics can't change in a formal system, or they aren't   
   >>>>>>>>>>>>> really semantics.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Your problem is you don't understand Godel statement, as it   
   >>>>>>>>>>>>> *IS* truth bearing as it is a simple statement with no   
   >>>>>>>>>>>>> middle ground, does a number exist that satisfies a given   
   >>>>>>>>>>>>> relationship. Either there is, or there isn't. No other   
   >>>>>>>>>>>>> possiblity.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> You confuse yourself by forgetting that words have actual   
   >>>>>>>>>>>>> meaning, and that meaning can depend on using the right   
   >>>>>>>>>>>>> context.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Godel's G is a statement in the system PA.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> It is a statement about the non-existance of a natural   
   >>>>>>>>>>>>> number that satisfies a particular computable realtionship.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> It is a statement defined purely by mathematics and thus   
   >>>>>>>>>>>>> doesn't "depend" on other meaning.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> It is a mathematical FACT, that for this relationship, no   
   >>>>>>>>>>>>> matter what natural number we test, none will satisfy it,   
   >>>>>>>>>>>>> so its assertation that no number satisfies it makes it true.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> PA augmented with its own True(PA,x) and False(PA,x)   
   >>>>>>>>>>>> is a decider for Domain of every expression grounded   
   >>>>>>>>>>>> in the axioms of PA.   
   >>>>>>>>>>>   
   >>>>>>>>>>> No, it becomes inconsistant.   
   >>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> A system at a higher level of inference than PA can   
   >>>>>>>>>>>> reject any expressions that define a cycle in the   
   >>>>>>>>>>>> directed graph of the evaluation sequence of PA   
   >>>>>>>>>>>> expressions. Then PA could test back chained inference   
   >>>>>>>>>>>> from expression x and ~x to the axioms of PA.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> But there is no "cycle" in the statement of G. It is PURELY a   
   >>>>>>>>>>> statement of the non-existance of a number that satisfies a   
   >>>>>>>>>>> purely mathematic relationship (which has no meaning by   
   >>>>>>>>>>> itself in PA).   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> Even the relationship cannot exist  PA.   
   >>>>>>>>>> Instead it is about PA in outside model theory   
   >>>>>>>>>   
   >>>>>>>>> No, it doesn't mention PA, it is about the numbers that are IN PA.   
   >>>>>>>>>   
   >>>>>>>>> Your problem is you forget to actually know what Godel's G is,   
   >>>>>>>>> a you only read the Reader's Digest version of the proof, as   
   >>>>>>>>> that is all you can understand.   
   >>>>>>>>>   
   >>>>>>>>> That, or you are saying that mathematics itself isn't in PA,   
   >>>>>>>>> and that you proof-theoretic stuff isn't in PA either,   
   >>>>>>>>>   
   >>>>>>>>> Sorry, you are just showing how ignorant you are.   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>> G_F ↔ ¬Prove_F(Gödel_Number(G_F)) contains a semantic   
   >>>>>>>> dependency loop, because evaluating G_F requires   
   >>>>>>>> evaluating Prove_F on the Gödel number of G_F, which   
   >>>>>>>> in turn requires evaluating G_F again;   
   >>>>>>>   
   >>>>>>> But that isn't G_F   
   >>>>>>>   
   >>>>>>> G_F is a statement that a particular relationship (lets call it   
   >>>>>>> R(x) ) will not be satisfied for any natural number x.   
   >>>>>>>   
   >>>>>>   
   >>>>>> That relationship has never existed inside actual   
   >>>>>> arithmetic   
   >>>>>   
   >>>>> It actually IS a relationship in the domain of PA. PUNTO.   
   >>>>>   
   >>>>> It is what it is. Denial is hopeless.   
   >>>>   
   >>>> When PA is actually given its own truth predicate   
   >>>> anchored only in its own axioms then for the first   
   >>>> time one see that meta-math truth in the standard   
   >>>> model of arithmetic never was actually true in PA   
   >>>> itself at all.   
   >>>>   
   >>>   
   >>> But PA can't be given such a truth predicate and reamin consistant.   
   >>>   
   >>   
   >> Unless the foundation model theory is replaced   
   >> with the foundation of proof theory and proof   
   >> theory itself is grounded in Haskell Curry's   
   >> notion of "true in the system".   
   >   
   > Try to show that working, and HAVE a truth predicate.   
   >   
   > Remember, a truth predicate is "True" if the input is a true expression,   
   > and "False" if the input is something else, being either a False   
   > statement, or a not-well-founded statement, or even just plain non-sense.   
   >   
      
   I have boiled that all down so it coherently all   
   holds together and proves itself completely true   
   entirely on the basis of the meaning of its words.   
   I can do this now in one half page of text.   
      
   I have worked on the feverishly most every waking   
   moment for weeks.   
      
   >>   
   >>> Your provblem is you are too stupid to understand the problem.   
   >>>   
   >>> I guess you claim is that if the meta arithmatic uses the fact that 2   
   >>> * 3 = 6, then maybe in the base arithmatic 2 * 3 might now be 8.   
   >>   
   >>   
   >   
      
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)