XPost: sci.math, comp.theory   
   From: news.x.richarddamon@xoxy.net   
      
   On 1/28/26 1:17 PM, olcott wrote:   
   > 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.   
      
   It is a KNOWLEDGE predicate, as you restrict its domain to only things   
   that are KNOWN, and exclude new deductions made from that knowledge.   
      
   Your just don't understand the purpose of logic.   
      
   >   
   >> 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.   
      
   But, syntactic system that create "infinite" domains can create   
   symantics, and in this case, can NOT have a "Truth Predicate" (as it is   
   properly defined) without becoming inconsistant.   
      
   Your problme is you think you can just define things how ever you want.   
   even if it makes your system inconsistant, which just shows you live in   
   a fantasy world where reality doesn't exist.   
      
   >   
   > Incompleteness only arose because what was true   
   > outside of PA could not be proved inside PA. This   
   > was a mere conflation error all along.   
   >   
      
   WRONG. The "truth" is in PA, as no such number actually exists.   
      
   All you are showing is youy don't understand what "Truth" actually is,   
   because you confuse it with "Knowledge", but without the independence   
   concept of "Truth", "Knowledge" becomes meaningless, as we can then   
   think we know things that are not actually true because we introduced   
   error or contradictions.   
      
   You are just showing your ignorance.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)