XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 11/25/2025 6:18 PM, Python wrote:   
   > Le 26/11/2025 à 01:14, olcott a écrit :   
   >> On 11/25/2025 6:04 PM, Python wrote:   
   >>> Peter, every time someone points out that your system breaks Gödel by   
   >>> redefining truth as “things my system proves,” you reply that this is   
   >>> “a fundamentally different foundation,” as if giving a new name to   
   >>> the floor suddenly allowed you to float.   
   >>>   
   >>> Your new line — “Gödel incompleteness can only exist when syntax and   
   >>> semantics are divided” — is just the same move in a new hat. Gödel’s   
   >>> original 1931 proof is purely syntactic, requires zero model theory,   
   >>> and works even if you paint “SEMANTICS” on the side of the syntax   
   >>> with a big red brush. The diagonal argument doesn’t care about your   
   >>> ontology, your types, your Prolog unification, or how many decades   
   >>> you’ve stared at it.   
   >>>   
   >>> This is the whole problem: every time the theorem bites, you amputate   
   >>> the part of mathematics that hurts and say, “See, no wound!” You’ve   
   >>> solved incompleteness the same way a surgeon would solve mortality by   
   >>> outlawing death certificates.   
   >>>   
   >>> Your system makes True(x) computable exactly the way a shredder makes   
   >>> archival integrity computable: anything inconvenient simply becomes   
   >>> “not in the body of general knowledge expressible in language.” If   
   >>> Gödel sentences don’t fit, the bin is right there.   
   >>>   
   >>> That’s not “integrating semantics.”   
   >>> That’s declaring all troublesome meanings illegal.   
   >>>   
   >>   
   >> Perhaps you do not fully understand exactly what   
   >> semantic logical entailment is thus cannot directly   
   >> see how and why this totally eliminates undecidability   
   >> and undefinability. I have spent at least five full   
   >> time years on this one thing.   
   >>   
   >>> It’s a bold philosophical stance, sure.   
   >>> But it’s not mathematics.   
   >>   
   >> It is a brand new provably correct foundation   
   >> for correct reasoning that corrects all of the   
   >> shortcoming and incoherence of logic and math.   
   >   
   > Peter, every time you say “perhaps you do not fully understand semantic   
   > logical entailment,” it sounds like a man insisting that everyone else   
   > is holding the map upside down, while he proudly walks into the same   
   > lamp post for the fiftieth time.   
   >   
      
   Have you spent five full time years studying   
   the details of formalizing semantic logical   
   entailment directly in the formal system   
   with no need for a separate model theory?   
      
   > You keep repeating that five years of thinking have shown you how to   
   > “totally eliminate undecidability,” but undecidability is not a software   
   > bug you can delete with enough staring. It’s a mathematical theorem   
   > about computability. You cannot remove a proven limit by declaring, “My   
   > foundation does not believe in limits.”   
   >   
   > Your proposed cure — redefining truth as whatever your system can derive   
   > — is like solving the problem of unmeasurable sets by banning rulers.   
   > Yes, it “eliminates” the difficulty, but only in the same sense that   
   > closing your eyes eliminates the sun.   
   >   
   > Gödel’s syntactic diagonal argument does not care how many semantic   
   > stickers you glue on top. It applies to any consistent, effective,   
   > sufficiently expressive system.   
      
   It does not. It simply uses Gödel numbers in a system   
   woefully insufficiently expressive to say this tiny   
   little expression: G := (F ⊬ G)   
   meaning that G is defined as unprovable in F.   
      
   Gödel numbers merely hide the underlying unsound   
   inference.   
      
   Unless you can prove to me that you understand   
   what a directed graph of an evaluation sequence is   
   it will be assumed that you don't even have a   
   slight clue about this:   
      
   ?- G = not(provable(F, G)).   
   G = not(provable(F, G)).   
   ?- unify_with_occurs_check(G, not(provable(F, G))).   
   false.   
      
   That proves that this is semantically unsound:   
   G ↔ ¬Prov(⌜G⌝)   
      
   Failing to understand what I say counts as much less   
   than no rebuttal at all.   
      
   > If your system is effective and   
   > expressive, Gödel applies. If it’s not effective, you haven’t “solved   
   > undecidability”; you’ve stepped outside mathematics. If it’s not   
   > expressive enough to encode arithmetic, then it cannot be “the entire   
   > body of general knowledge.”   
   >   
   > Those are the only options.   
   >   
   > Claiming you’ve produced “a brand new provably correct foundation for   
   > correct reasoning” that fixes all shortcomings of logic and math is   
   > bold, certainly — but until you show a formal system rather than a   
   > proclamation, you are not correcting logic; you are advertising a logic-   
   > flavored product.   
   >   
   > Mathematics does not respond to ambition, only to proofs. So far, yours   
   > remain announcements.   
      
      
   --   
   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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