XPost: comp.theory, sci.math   
   From: 046-301-5902@kylheku.com   
      
   On 2025-11-29, olcott  wrote:   
   > On 11/29/2025 2:39 PM, Kaz Kylheku wrote:   
   >> On 2025-11-29, olcott  wrote:   
   >>> On 11/28/2025 11:52 PM, Kaz Kylheku wrote:   
   >>>>> I have shown that the original assumptions are   
   >>>>> incoherent just like   
   >>>>   
   >>>> You have not. Only that your understanding is incoherent.   
   >>>>   
   >>>   
   >>> The halting problem instance is merely the Liar Paradox in disguise.   
   >>   
   >> No, it isn't.   
   >>   
   >> You're not even smart enough to keep straight in your head   
   >> what is part of the /problem/ and what is a /result/   
   >> of investigating the problem.   
   >>   
   >> The Halting Problem is literally a sentence of the form: "can   
   >> a Turing machine calculate whether any Turing Machine halts".   
   >>   
   >   
   > When the halting problem instance defines and input   
   > that does the opposite of whatever its decider reports   
   > this is structurally the same as the set of sentences   
   > that are true only when they are false and false only   
   > when they are true.   
      
   Only in the mind of an imbecile who can't think outside of the box.   
      
   Specifically, the [75, 95] box on the IQ scale.   
      
   The instance does not refer to any part of itself and assert   
   its negation. An external observer is required in order to   
   recognize a contradiction. There is a self-reference, but not   
   one that causes an infinite evaluation issue.   
      
   It is simulatenously true in that case that a certain decision   
   is being made, and that the program is behasving opposite to that.   
      
   These two situations easily coexist.   
      
   The contradiction between them is something that is externally   
   recognized; it doesn't threaten the well-formedness of the   
   case.   
      
   > All pathological self-reference is inherently   
   > semantically unsound.   
      
   Not all self-reference is "pathological". Liar Paradox? I would   
   say so. It has an obvious problem of not being evaluable, and so   
   if we adopt the word "pathological" for any such a problem,   
   it is pathological.   
      
      
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