XPost: comp.theory, sci.logic, sci.math   
   XPost: comp.lang.prolog, comp.software-eng   
   From: polcott333@gmail.com   
      
   On 2/11/2026 6:56 AM, Richard Damon wrote:   
   > On 2/10/26 11:59 PM, olcott wrote:   
   >> We completely replace the foundation of truth conditional   
   >> semantics with proof theoretic semantics. Then expressions   
   >> are "true on the basis of meaning expressed in language"   
   >> only to the extent that all their meaning comes from   
   >> inferential relations to other expressions of that language.   
   >> This is a purely linguistic PTS notion of truth with no   
   >> connections outside the inferential system.   
   >>   
   >> Well-founded proof-theoretic semantics reject expressions   
   >> lacking a "well-founded justification tree" as meaningless.   
   >> ∀x (~Provable(T, x) ⇔ Meaningless(T, x))   
   >>   
   >   
   > The problem is that you new system can't handle mathematics.   
   >   
   > The problem, as has been pointed out, is that mathematics, by the axiom   
   > of induction, accepts as true statements that can be established by an   
   > infinite number of steps as true, and shows a method to solve SOME of them.   
   >   
   > Also, "Halting" is a well-founded property of ALL machines, as they MUST   
   > either Halt or not, and HALTING is always provable, so those machines   
   > that do not halt, must be non-halting.   
   >   
   > Your "logic" essentially denies the property of the excluded middle for   
   > systems that have infinite members, but some statements are inherently   
   > of the class of the excluded middle.   
   >   
   > As I have said, TRY to show how your PTS can establish the mathematics   
   > of the Natural Numbers.   
   >   
   > Try to even fully define ADDITION without the need for allowing   
   > unbounded steps.   
   >   
      
   ∀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)))   
      
      "What is the appropriate notion of truth for sentences whose   
      meanings are understood in epistemic terms such as proof or   
      ground for an assertion? It seems that the truth of such   
      sentences has to be identified with the existence of proofs or   
      grounds..." https://doi.org/10.1007/s11245-011-9107-6   
      
   Spend 20 hours carefully studying this and get back to me.   
   https://plato.stanford.edu/entries/proof-theoretic-semantics/   
      
   It makes "true on the basis of meaning expressed in language"   
   reliably computable for the entire body of knowledge.   
      
   --   
   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)