XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   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.   
      
   --   
   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   
    * Origin: you cannot sedate... all the things you hate (1:229/2)