XPost: comp.theory, sci.math, sci.lang   
   XPost: comp.ai.philosophy   
   From: athel.cb@gmail.com   
      
   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).   
      
   --   
   athel   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)