XPost: comp.theory, sci.math, sci.lang   
   XPost: comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/16/2026 12:12 PM, athel.cb@gmail.com wrote:   
   >   
   > Richard Damon  posted:   
   >   
   >> On 1/15/26 11:20 PM, olcott wrote:   
   >>> 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.   
   >>   
   >> Right, which just doesn't work in the system.   
   >>   
   >>>   
   >>> *That exactly maps to this*   
   >>>   
   >>> All deciders essentially: Transform finite string   
   >>> inputs by finite string transformation rules into   
   >>> {Accept, Reject} values.   
   >>   
   >> Nope. The problem is you don't understand what a "Finite String   
   >> Transformation rule" is.   
   >>   
   >>>   
   >>> Proof‑theoretic semantics didn't exist when Gödel   
   >>> wrote his paper.   
   >>   
   >> So, that means they don't apply to the basic system.   
   >>   
   >> Remember, the context of the system, which includes its "semantics" are   
   >> DEFINED by the system. IT COULDN'T have meant something that wasn't   
   >> defined yet.   
   >>   
   >>>   
   >>>> 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.   
   >>>   
   >>   
   >> But we don't know actual "facts" about the real world, just have a set   
   >> of observations and most likely explanations.   
   >>   
   >> In other words, your system is based on the ASSUMPTION that we are 100%   
   >> correct in our imperical deductions.   
   >>   
   >> I could ask, WHICH set of "facts" are you going to take?   
   >>   
   >> The ones that show the earth is the center of the universe? Those WERE   
   >> the best conclusions at one point.   
   >>   
   >> All you are doing is showing you fundamentally don't understand what   
   >> "truth" is.   
   >>   
   >> Or what "Formal Logic" is.   
   >   
   > The problem I have wih Pete Olcott's posts over the past 20 years at least is   
   > that he doesn't have a clue what a human language is.   
   >   
   > I don't mind if he wants to bore readers of comp.theory, sci.logic, sci.math,   
   > and comp.ai.philosophy with his stuff (though others may), but can he not   
   drop   
   > sci.lang from the list?   
   >   
   > In any case it's rarely acceptable to send the sama message to more than   
   three   
   > groups (even as many as that).   
   >   
      
   The actual problem on this aspect is that most   
   everyone in the world rejects even the idea of   
   Montague Semantics before having any idea what it is.   
      
   --   
   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)