XPost: sci.logic, sci.logic   
   From: polcott333@gmail.com   
      
   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.   
      
   https://claude.ai/share/45d3ca9c-fa9a-4a02-9e22-c6acd0057275   
      
   > Tarski shows that if there is there is a formula that is true if its   
   > argument encodes a true sentence and false if its argument encodes a false   
   > statements (its value does not matter if the argument does not encode   
   > a sentence) then it is possible to encode a sentence that says "the truth   
   > formula returns false if given my encoding" and give it to the truth   
   > formula, which would then return the negation of the value it returns.   
   > As that would be a contradiction there cannot be a truth formula and   
   > therefore no definition truth.   
   >   
   > At least for some systems it is possible to have a truth predicate in   
   > a metatheory even if not in the system itself.   
   >   
      
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
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