XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 11/25/2025 8:36 PM, Python wrote:   
   > Le 26/11/2025 à 03:34, olcott a écrit :   
   >> On 11/25/2025 8:09 PM, Python wrote:   
   >>> Le 26/11/2025 à 03:03, olcott a écrit :   
   >>>> On 11/25/2025 7:45 PM, Python wrote:   
   >>>>> Le 26/11/2025 à 02:43, olcott a écrit :   
   >>>>>>   
   >>>>>> Montague Grammar is the syntax of English semantics   
   >>>>>> that is why he called it Montague Grammar. This is   
   >>>>>> all anchored in Rudolf Carnap meaning postulates   
   >>>>>   
   >>>>> Peter, Montague Grammar does not make truth = provability.   
   >>>>> It maps English into logic — it does not turn logic into a magic   
   >>>>> incompleteness-proof shredder.   
   >>>>>   
   >>>>   
   >>>> The predicate Bachelor(x) is stipulated to mean ~Married(x)   
   >>>> where the predicate Married(x) is defined in terms of billions   
   >>>> of other things such as all of the details of Human(x).   
   >>>>   
   >>>> Two Dogmas of Empiricism by Willard Van Orman had no idea   
   >>>> how we know that Bachelors are unmarried. Basically we   
   >>>> just look it up in the type hierarchy, that is the simple   
   >>>> proof of its truth.   
   >>>>   
   >>>>> If your claim were right, every linguist using Montague’s system   
   >>>>> would have accidentally solved Godel’s theorem in the 1970s.   
   >>>>> They didn’t.   
   >>>>   
   >>>> I spoke with many people very interested in linguistics   
   >>>> on sci.lang for many years. Even ordinary semantics   
   >>>> freaks them out.   
   >>>>   
   >>>> None of them ever had the slightest clue about Montague   
   >>>> Grammar. Except for one they all had very severe math   
   >>>> phobia. Formal semantics got them very aggravated.   
   >>>>   
   >>>>> Because encoding semantics as syntax does not erase diagonalization   
   >>>>> — it just gives it nicer types.   
   >>>>>   
   >>>>   
   >>>> G ↔ ¬Prov(⌜G⌝)   
   >>>> Directed Graph of evaluation sequence   
   >>>> 00 ↔               01 02   
   >>>> 01 G   
   >>>> 02 ¬               03   
   >>>> 03 Prov            04   
   >>>> 04 Gödel_Number_of 01  // cycle   
   >>>>   
   >>>> Proves that the evaluation of the above G is stuck   
   >>>> in an infinite loop whether you understand this or not.   
   >>>>   
   >>>>> Montague built a translation function.   
   >>>>> You’re treating it like a trapdoor that makes unprovable truths   
   >>>>> disappear.   
   >>>>> It doesn’t.   
   >>>>> Only your theory does that.   
   >>>>   
   >>>> When True(L,x) is exactly one and the same thing as   
   >>>> Provable(L,x) then if you are honest you will admit   
   >>>> that they cannot possibly diverge thus within this   
   >>>> system Gödel incompleteness cannot possibly exist.   
   >>>>   
   >>>> Seeing how this makes perfect sense and is absolutely   
   >>>> not any sort of ruse may take much more dialogue.   
   >>>   
   >>> Réponse proposée (courte, mordante, ASCII-safe)   
   >>>   
   >>> Peter, you keep repeating the same pattern:   
   >>>   
   >>   
   >> Because you utterly refuse to pay enough attention.   
   >>   
   >>> Take a normal semantic fact (like bachelor = unmarried).   
   >>>   
   >>> Declare that because some meanings can be defined, all meaning   
   >>> reduces to proof.   
   >>>   
   >>   
   >> All *objects of thought* can be defined in terms of other   
   >> *objects of thought*   
   >>   
   >> Kurt Gödel in his 1944 Russell's mathematical logic gave the following   
   >> definition of the "theory of simple types" in a footnote:   
   >>   
   >> By the theory of simple types I mean the doctrine which says that the   
   >> objects of thought (or, in another interpretation, the symbolic   
   >> expressions) are divided into types, namely: individuals, properties   
   >> of individuals, relations between individuals, properties of such   
   >> relations, etc.   
   >>   
   >>> Then insist that since in your system True = Provable by definition,   
   >>> Godel “cannot possibly exist.”   
   >>>   
   >>> But that is not a refutation — that is simply renaming the problem   
   >>> out of existence.   
   >>>   
   >>> Your “directed graph infinite loop” does not show an error in Godel;   
   >>> it shows that Prolog refuses cyclic terms.   
   >>> Mathematics does not.   
   >>>   
   >>   
   >> That you fail to understand that it conclusively   
   >> proves that the expression is semantically   
   >> unsound is your ignorance on not my mistake.   
   >   
   > Peter, your entire argument now rests on one mistake:   
   >   
   > You think that a self-referential fixed point is “semantically unsound”   
   > because Prolog refuses to unify a cyclic term.   
   >   
   > But Prolog’s occurs-check does not detect “semantic unsoundness.”   
   > It detects infinite data structures in Prolog.   
   >   
   > Mathematics is not Prolog.   
   >   
   > Lambda calculus allows fixed points.   
   > Type theory allows fixed points.   
   > Arithmetic allows fixed points.   
   > Diagonalization is a fixed point.   
   >   
   > G <-> not Prov(F,G)   
   > cycle -> therefore invalid   
   >   
   > My calculator overflows on 10^100   
   > therefore big integers are semantically unsound.   
   >   
   > My calculator overflows on 10^100   
   > therefore big integers are semantically unsound.   
   >   
   > No, Peter.   
   > It is your implementation that cannot handle the structure, not the   
   > mathematics.   
   >   
   > As for “objects of thought are typed,” yes — and typed systems also   
   have   
   > Godel-style incompleteness theorems.   
   > HOL, type theory, Montague-style semantics, all of them.   
   >   
   > Typing does not prevent diagonalization.   
   > It just prevents nonsense terms like phi(phi).   
   > Godel’s construction never uses those.   
   >   
   > You are not proving G is “semantically unsound.”   
   > You are proving that your framework cannot express diagonalization.   
   > But any framework that cannot express diagonalization also cannot   
   > express arithmetic — and therefore cannot be “the entire body of objects   
   > of thought.”   
   >   
   > In short:   
   >   
   > You didn’t refute Godel.   
   > You refuted your own system’s ability to model arithmetic.   
   >   
      
   You have proven that you have some technical competence   
   by even knowing those words.   
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
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