XPost: sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 10/6/2025 7:36 AM, Mikko wrote:   
   > On 2025-10-05 14:09:37 +0000, olcott said:   
   >   
   >> On 10/5/2025 5:26 AM, Mikko wrote:   
   >>> On 2025-10-04 13:30:22 +0000, olcott said:   
   >>>   
   >>>> On 10/4/2025 5:11 AM, Mikko wrote:   
   >>>>> On 2025-10-02 10:15:13 +0000, olcott said:   
   >>>>>   
   >>>>>> On 10/2/2025 5:03 AM, Mikko wrote:   
   >>>>>>> On 2025-10-01 16:33:46 +0000, olcott said:   
   >>>>>>>   
   >>>>>>>> On 10/1/2025 5:13 AM, Mikko wrote:   
   >>>>>>>>> On 2025-10-01 01:48:56 +0000, olcott said:   
   >>>>>>>>>> On 9/30/2025 7:54 AM, Mikko wrote:   
   >>>>>>>>>>> On 2025-09-29 12:24:30 +0000, olcott said:   
   >>>>>>>>>>>   
   >>>>>>>>>>>> On 9/27/2025 5:07 AM, Mikko wrote:   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Any sentence that is neither true nor false   
   >>>>>>>>>>>> must be rejected from any system of logic.   
   >>>>>>>>>>>> Non-truth bearers in logic systems are like   
   >>>>>>>>>>>> turds in birthday cakes.   
   >>>>>>>>>>>   
   >>>>>>>>>>> Every sentence of logic that is not tautology or   
   >>>>>>>>>>> dontradiction is   
   >>>>>>>>>>> true in some contexts and false in others.   
   >>>>>>>>>>   
   >>>>>>>>>> A mere false assumption   
   >>>>>>>>>   
   >>>>>>>>> No, it is true on the basis of the meanings of the words.   
   >>>>>>>>   
   >>>>>>>> The syntax of formal logical languages allows   
   >>>>>>>> some expressions to be created having pathological   
   >>>>>>>> self-reference(Olcott 2004).   
   >>>>>>>   
   >>>>>>> No syntax is enough for self-reference.   
   >>>>>>   
   >>>>>> Syntax is enough for self-reference.   
   >>>>>   
   >>>>> No, self-reference is a semantic feature. A string without meaning   
   >>>>> does not refer.   
   >>>>>   
   >>>>   
   >>>> Self-reference can be detected in a string with a name.   
   >>>>>> Tarski's Liar Paradox from page 248   
   >>>>>>     It would then be possible to reconstruct the antinomy of the liar   
   >>>>>>     in the metalanguage, by forming in the language itself a sentence   
   >>>>>>     x such that the sentence of the metalanguage which is correlated   
   >>>>>>     with x asserts that x is not a true sentence.   
   >>>>>>     https://liarparadox.org/Tarski_247_248.pdf   
   >>>>>>   
   >>>>>> Formalized as:   
   >>>>>> x ∉ True if and only if p   
   >>>>>> where the symbol 'p' represents the whole sentence x   
   >>>>>> https://liarparadox.org/Tarski_275_276.pdf   
   >>>>>>   
   >>>>>>> The semantics determines whether   
   >>>>>>> any syntactic construct is a self-reference. For example. the   
   >>>>>>> arithmetic   
   >>>>>>> semantics of a formal language of arithmetics do not permit a self-   
   >>>>>>> reference.   
   >>>>>>   
   >>>>>> Gödel uses tricks for that.   
   >>>>>   
   >>>>> Tarski used the same tricks.   
   >>>>   
   >>>> Yet they only actually boil down to   
   >>>> Incomplete(F) ↔ ∃G ((F ⊬ G) ∧ (F ⊬ ¬G)).   
   >>>> and this   
   >>>> LP := ~True(LP)   
   >>>   
   >>> The system they considered has no symbol for :=. Instead, they construct   
   >>> something like LP <-> ~True(LP). Gödel then shows that that the   
   >>> expression   
   >>> that asserts its own unprovability is is not provable and therefore   
   >>> true.   
   >>   
   >> Claude AI eventually agreed that both Gödel's 1931   
   >> Incompleteness theorem and the Tarski Undefinability   
   >> theorem are anchored in liar paradox like expression   
   >> that should have been rejected as not a truth bearer.   
   >   
   > Gödel proved that every sentence of a first order theory that is not   
   > the negation of any sentnece of that theory is true in some model of   
   > that theory. Therefore every sentence of every first order theory is   
   > a truth-bearer.   
   >   
   > As long as you don't understand that "The liar's paradox is not true"   
   > is true and therefore a valid basis for a proof you cannot say anything   
   > about Tarski's proof but are stuck to straw men.   
   >   
      
   *The Liar Paradox is rejected*   
   (thus unavailable for subsequent analysis)   
   True(English, "This sentence is not true")==INCORRECT   
      
   *I explained this in complete detail to Claude AI*   
   https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275   
      
   The most important aspect of Gödel's 1931 Incompleteness theorem   
   are these plain English direct quotes of Gödel from his paper:   
   ...there is also a close relationship with the “liar” antinomy,14 ...   
   ...14 Every epistemological antinomy can likewise be used for a similar   
   undecidability proof...   
   ...We are therefore confronted with a proposition which asserts its own   
   unprovability. 15 ...   
   (Gödel 1931:40-41)   
      
   Gödel, Kurt 1931.   
   On Formally Undecidable Propositions of Principia Mathematica And   
   Related Systems   
      
   https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Und   
   cidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf   
      
      
   Basically Claude AI completely validated all of my work   
   on Tarski Undefinability and Gödel 1931 Incompleteness.   
   https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275   
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)