XPost: comp.theory, comp.ai.philosophy, sci.math   
   From: 643-408-1753@kylheku.com   
      
   ["Followup-To:" header set to comp.theory.]   
   On 2025-11-22, olcott  wrote:   
   > On 11/22/2025 10:45 AM, Kaz Kylheku wrote:   
   >> On 2025-11-22, olcott  wrote:   
   >>> On 11/22/2025 12:08 AM, Kaz Kylheku wrote:   
   >>>> On 2025-11-22, olcott  wrote:   
   >>>>> With the halting problem counter example input   
   >>>>> where input D does the opposite of whatever   
   >>>>> decider H reports this specific H/D is exactly   
   >>>>> isomorphic to the Liar Paradox.   
   >>>>   
   >>>> No it isn't. The Liar Paradox has an indeterminate   
   >>>> truth value; the H/D pair does not contain any   
   >>>> proposition with an indeterminate truth value.   
   >>>>   
   >>>   
   >>> With the halting problem counter example input   
   >>> where input D does the opposite of whatever decider   
   >>> H reports this specific H/D pair is exactly   
   >>> isomorphic to the Liar Paradox.   
   >>>   
   >>> When the behavior of D depends on the return   
   >>> value of H and D does the opposite of whatever   
   >>> H returns the H/D pair itself is a yes/no question   
   >>> that lacks a correct yes/no answer.   
   >>   
   >> Umm, no; there has to be a self-negation in order to have a Liar   
   >> Paradox. For instance "This sentence has four words" contains a   
   >> contradiction: the sentence's "behavior" of having a word count of five   
   >> contradicts an assertion that is found in the same sentence. Yet there   
   >> is no paradox: the sentence readily identifies as having a false value.   
   >>   
   >>> Every yes/no question that lacks a correct yes/no answer   
   >>> is isomorphic to this question:   
   >>   
   >> The correct answer is 1 in the H/D pair in which H returns 0.   
   >> It is not lacking. Just like the correct answer is "five words"   
   >> in "This sentence has four words".   
   >   
   > Neither return value is correct because D does   
      
   No, since 0 is incorrect, 1 is correct.   
   D() terminates.   
      
   > the opposite of whatever value is returned just   
   > like "This sentence is not true" is true if it   
      
   No, it is a bit like 'This sentence has four words".   
   The claim made by the sentence is incorrect;   
   the correct claim is five.   
      
   > is not true and not true if it is true, thus   
   > it is neither true nor false therefore not a   
   > proposition.   
      
   No such thng is going on in the H(D) case.  H(D) returns false. D() then   
   terminates.   
      
   It is we, the outside observer, who remark that H(D)'s return value   
   doesn't match the D behavior.   
      
   But we are not part of the test case.   
      
   >>> Is this sentence true or false: "This sentence is not true" ?   
   >>> What correct Boolean value should H return to D?   
   >>   
   >> The correct value is 1.   
   >>   
   >   
   > int D()   
   > {   
   >    int Halt_Status = H(D);   
      
   Here we can replace H(D) by 0 without changing D because   
   we know that term has that value. This is a valid mathematical   
   substitution.   
      
   >    if (Halt_Status)   
   >      HERE: goto HERE;   
   >    return Halt_Status;   
   > }   
   >   
   > You know that you are lying about this. Does that   
   > give you a cheap thrill?   
      
   You yourself know that D() returns at that UTM(D) returns 1.   
      
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