XPost: comp.theory, sci.math, sci.lang.semantics   
   XPost: comp.ai.nat-lang   
   From: news.x.richarddamon@xoxy.net   
      
   On 1/20/26 11:49 PM, olcott wrote:   
   > On 1/20/2026 10:00 PM, Richard Damon wrote:   
   >> On 1/20/26 1:13 PM, olcott wrote:   
   >>> On 1/19/2026 11:29 PM, Richard Damon wrote:   
   >>>> On 1/19/26 12:56 PM, olcott wrote:   
   >>>>> Back in 2020 I proved that Wittgenstein was correct   
   >>>>> all along. His key essence of grounding truth in   
   >>>>> well-founded proof theoretic semantics did not exist   
   >>>>> at the time that he made these remarks. Because of   
   >>>>> this his remarks were misunderstood to be based   
   >>>>> on ignorance instead of the profound insight that   
   >>>>> they really were.   
   >>>>>   
   >>>>   
   >>>> Nope.   
   >>>>   
   >>>>> According to Wittgenstein:   
   >>>>> 'True in Russell's system' means, as was said: proved   
   >>>>> in Russell's system; and 'false in Russell's system'   
   >>>>> means: the opposite has been proved in Russell's system.   
   >>>>> (Wittgenstein 1983,118-119)   
   >>>>   
   >>>> Which is only ONE interpretation, (and not a correct one).   
   >>>>   
   >>>   
   >>> All we need to do to make PA complete   
   >>> is replace model theoretic semantics   
   >>> with wellfounded proof theoretic sematics   
   >>> and ground true in OA the way Haskell   
   >>> Curry defines it entirely on the basis   
   >>> of the axioms of PA,   
   >>   
   >> Nope, doesn't work.   
   >>   
   >> THe system breaks as it can't consistantly determine the truth value   
   >> of some statements.   
   >   
   > Just to make it simpler for you to understand think   
   > of it as a truth and falsity recognizer that gets   
   > stuck in an infinite loop on anything else.   
   > So PA is complete for its domain.   
      
   Nope, as your idea to make it complete breaks everything.   
      
   >   
   >>   
   >>>   
   >>> ∀x ∈ PA ((True(PA, x)  ≡ (PA ⊢ x))   
   >>> ∀x ∈ PA ((False(PA, x) ≡ (PA ⊢ ~x))   
   >>> ∀x ∈ PA (~WellFounded(PA, x) ≡ (~True(PA, x) ∧ (~False(PA, x))   
   >>> Then PA becomes complete.   
   >>   
   >> And, in proof-theoretic semantics, this is just not-well-founded as   
   >> there are statements that you can not determine if any of these are   
   >> applicable or not.   
   >>>   
   >>> This is very similar to my work 8 years ago   
   >>> where the axioms are construed as BaseFacts.   
   >>> It was pure proof theoretic even way back then.   
   >>>   
   >>> The ultimate foundation of [a priori] Truth   
   >>> Olcott Feb 17, 2018, 12:42:55 AM   
   >>> https://groups.google.com/g/sci.logic/c/dbk5vsDzZbQ/m/4ajW9R08CQAJ   
   >>   
   >> At least that accepted that there were statement that it couldn't   
   >> handle as they were neiteher true or false.   
   >>   
   >> With your addition, we get that there are statements that can be none   
   >> of True, False, or ~WellFounded.   
   >>   
   >   
   > This was the earliest documented work that   
   > can be classified as well-founded proof theoretic semantics.   
   > My actual work is documented to go back to 1998.   
      
   But it isn't well-founded, as it isn't actualy based on proof.   
      
   >   
   >>>   
   >>>>>   
   >>>>> Formalized by Olcott as:   
   >>>>>   
   >>>>> ∀F ∈ Formal_Systems ∀𝒞 ∈ WFF(F) (((F⊢𝒞)) ↔ True(F,   
   𝒞))   
   >>>>> ∀F ∈ Formal_Systems ∀𝒞 ∈ WFF(F) (((F⊬𝒞)) ↔ ¬True(F,   
   𝒞))   
   >>>>> ∀F ∈ Formal_Systems ∀𝒞 ∈ WFF(F) (((F⊢¬𝒞)) ↔ False(F,   
   𝒞))   
   >>>>   
   >>>> Which can be not-well-founded, as determining *IF* a statement is   
   >>>> proveable or not provable might not be provable, or even knowable.   
   >>>>   
   >>>> So, therefore you can't actually evaluate your statement.   
   >>>>   
   >>>   
   >>> All meta-math is defined to be outside the scope of PA.   
   >>   
   >> But we don't need "meta-math" to establish the answer.   
   >>   
   >> It is a FACT that no number will satisfy the Relationship,   
   >   
   > That relationship does not even exist outside of meta-math   
   >   
   >   
      
   So, numbers don't exsist?   
   OR is it the "for all" part that doesn't exist, and thus your   
   proof-theoretic logic can't exist either?   
      
   Sorry, you are just stuck trying to outlaw that which you need.   
      
   --- SoupGate-Win32 v1.05   
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