XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 11/21/2025 3:25 AM, Mikko wrote:   
   > On 2025-11-20 14:52:19 +0000, Tristan Wibberley said:   
   >   
   >> On 20/11/2025 08:46, Mikko wrote:   
   >>> Regardless of what anybody accepts or rejects, Liar's Paradox is not   
   >>> a truth bearer and therefore not a part of any valid inference.   
   >>   
   >> Eh?! How did you infer that it's not part of any valid inference then?   
   >   
   > I made a mistake. Of course, if there is a way to express it, it can   
   > be used in an inference, at least as a hypothesis.   
   >   
   >> Nice demonstration of the liar paradox in one of its many forms though   
   >> and that G is not defined as Olcott says it is.   
   >   
   > A related paradox is that Olcott rejects the Liar paradox but   
   > uses it in an attempt to refute Gödel's and Tarksi's proofs.   
   >   
   >>> In   
   >>> particular, it is not a part of any vaild inference that connects   
   >>> the halting problem to the statement that "true on the basis of   
   >>> meaing is broken". Nobdy here has even shown an invalid inference   
   >>> that concludes "true on the basis of meaning is broken" form Liar's   
   >>> Paradox or anything else.   
   >>   
   >> You don't even know what it means for that to be broken.   
   >   
   > That knowledge is not necessary in order to see that no connection   
   > between the halting problem and that or any related claim is shown.   
   >   
   >> I'm not even sure, since "true on the basis of meaning" isn't quoted   
   >> to form:   
   >>   
   >>   "true on the basis of meaning" is broken.   
   >   
   > If Olcott would try to justify his claim that might what his intended   
   > meaning is. But as he doesn't it does not matter.   
   >   
      
   When an input D to a decider H is encoded to do the   
   opposite of whatever H returns this H/D pair is   
   isomorphic to the Liar Paradox.   
      
   ?- LP = not(true(LP)).   
   LP = not(true(LP)).   
   ?- unify_with_occurs_check(LP, not(true(LP))).   
   false.   
      
   The above definitively proves that the Liar   
   Paradox is semantically unsound because its   
   resolution has an infinite resolution loop.   
      
   Because the halting problem is isomorphic to   
   the Liar Paradox the Halting Problem is refuted   
   by proxy.   
      
   So more than a mere paradox both the Halting   
   Problem and the Liar Paradox are rejected as   
   errors of reasoning.   
      
   When we start with a complete set of atomic   
   facts of the world expressed in language and   
   the only inference step allowed is semantic   
   logical entailment then no paradox can be   
   derived and True(Language L, Expression E)   
   can always be computed.   
      
   The language to encode all of this is an   
   extended form of Montague Grammar uniting   
   syntax and semantics as one. This discards   
   the whole notice of model theory.   
      
   It makes a syntactic proof the same thing as   
   semantic logical entailment. The Atomic facts   
   of the world are stored in a knowledge ontology   
   inheritance hierarchy.   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)