XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/28/2026 10:34 AM, Tristan Wibberley wrote:   
   > On 20/01/2026 21:39, olcott wrote:   
   >   
   >> a meta‑level system is required to stand above PA and   
   >> filter expressions before PA ever evaluates them. The   
   >> meta‑system performs the structural work PA cannot do:   
   >> it detects cycles, blocks diagonalization, rejects   
   >> non‑truth‑bearers, and prevents PA from entering   
   >> infinite loops.   
   >   
   >   
   > Then the truth predicate is a restricted truth predicate.   
   >   
      
   It is only restricted to its domain of knowledge   
   expressed in language. This excludes semantic nonsense   
   like pathological self-reference, type mismatch errors   
   and unknowns such as the truth value of the Goldbach   
   conjecture.   
      
   > I think Tarski's findings don't directly apply to what Olcott is doing   
   > as they are stated for systems with negation (of statements) carrying   
   > the semantics of contradiction. PA doesn't seem to have that in its   
   > axioms; then there's the matter of universal generality: is that a   
   > predicate, connective, or an operation? Some of those take the truth   
   > "predicate" away from Elementary Theorems, some of them don't but   
   > negation must lose its naivety as it becomes an operation.   
   >   
   > How does one characterise PA among:   
   >   
   > - syntactical system   
   > - schematic system   
   > - abstract formal system   
   > - concrete formal system   
   > etc...   
   >   
   > understanding that there is some overlap.   
   >   
      
   What I am proposing is that PA is entirely syntactic   
   and when we add a truth predicate anchored entirely   
   in the axioms of PA that this predicate itself is   
   at a meta-level. When we explicitly add this predicate   
   then we can really see what is actually true in PA   
   itself and this has always been provable in PA.   
      
   Incompleteness only arose because what was true   
   outside of PA could not be proved inside PA. This   
   was a mere conflation error all along.   
      
   --   
   Copyright 2026 Olcott

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

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