XPost: comp.theory, sci.logic, sci.math   
   XPost: sci.lang   
   From: polcott333@gmail.com   
      
   On 1/15/2026 9:28 PM, Richard Damon wrote:   
   > On 1/15/26 6:43 PM, olcott wrote:   
   >> On 1/15/2026 5:50 AM, Richard Damon wrote:   
   >>> On 1/15/26 12:27 AM, olcott wrote:   
   >>>> On 1/14/2026 9:44 PM, Richard Damon wrote:   
   >>>>> On 1/14/26 5:11 PM, olcott wrote:   
   >>>>>> On 1/14/2026 3:36 PM, olcott wrote:   
   >>>>>>> Interpreting incompleteness as a gap between mathematical truth   
   >>>>>>> and proof depends on truth-conditional semantics; once this is   
   >>>>>>> replaced by proof-theoretic semantics a framework not yet   
   >>>>>>> sufficiently developed at the time of Gödel’s proof the notion of   
   >>>>>>> such a gap becomes unfounded.   
   >>>>>>>   
   >>>>>>   
   >>>>>> Gödel and Turing incompleteness results expose the limits of   
   >>>>>> denotational and truth-conditional semantics, not limits of proof   
   >>>>>> or computation per se. When meaning is grounded operationally or   
   >>>>>> proof- theoretically, the problematic self-referential   
   >>>>>> constructions are rejected as semantically unfounded rather than   
   >>>>>> treated as determinate but unknowable facts.   
   >>>>>>   
   >>>>>   
   >>>>> The problem is that "Computation" relys on truth-conditional   
   >>>>> semantics, as the behavior of a program *IS* what it actually does,   
   >>>>> not what you can generically prove about it.   
   >>>>>   
   >>>>   
   >>>> Proof in terms of the behavior of DD simulated by HHH.   
   >>>   
   >>> Since your HHH doesn't correctly simulate DD,   
   >> Proof-theoretic semantics proves that I have been   
   >> correct all along.   
   >>   
   >   
   > Nope, only in a system that USES proof-theoretic semantics, which don't   
   > meet the requirements for the systems that Godel uses.   
   >   
      
   It is the same ∀x ∈ T ((True(T, x) ≡ (T ⊢ x))   
   that I have been talking about for years except that   
   it is now grounded in well-founded proof‑theoretic   
   semantics.   
      
   *That exactly maps to this*   
      
   All deciders essentially: Transform finite string   
   inputs by finite string transformation rules into   
   {Accept, Reject} values.   
      
   Proof‑theoretic semantics didn't exist when Gödel   
   wrote his paper.   
      
   > They don't even meet the requirements for your goal, as such systems can   
   > not encode human knowledge, as everything we know about the real world   
   > just violates the requrements of needing to be derived from the axioms   
   > of the system, as real-world knowledge isn't based on an axiomatic system.   
      
   everything we know about the real world   
   is encoded as a finite set of atomic facts   
   that ARE the Haskell Curry Axioms:   
      
      Thus, given {T}, an elementary theorem   
      is an elementary statement which is true.   
      
   --   
   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)