XPost: comp.theory, sci.logic   
   From: mikko.levanto@iki.fi   
      
   On 15/12/2025 01:39, olcott wrote:   
   > On 12/14/2025 4:12 AM, Mikko wrote:   
   >> On 13/12/2025 17:47, olcott wrote:   
   >>> On 12/13/2025 4:46 AM, Mikko wrote:   
   >>>> olcott kirjoitti 12.12.2025 klo 16.27:   
   >>>>> On 12/12/2025 2:56 AM, Mikko wrote:   
   >>>>>> olcott kirjoitti 12.12.2025 klo 6.01:   
   >>>>>>> Principle 1: Turing machine deciders compute functions   
   >>>>>>> from finite strings to {accept, reject} according to   
   >>>>>>> whether the input has a syntactic property or specifies   
   >>>>>>> a semantic property.   
   >>>>>>   
   >>>>>>> The halting problem requires that a halt decider   
   >>>>>>> report on the direct execution of a Turing machine,   
   >>>>>>> thus category error.   
   >>>>>>   
   >>>>>> The last thus is false. What clause before it claims is irrelevant to   
   >>>>>> the meaning of the term "category error". Therefore the conclusion is   
   >>>>>> not proven.   
   >>>>>   
   >>>>> The halting problem requires reporting on the behavior   
   >>>>> of an executing Turing machine. Turing machines only   
   >>>>> take finite string inputs and not Turing machine inputs.   
   >>>>> *This is the category error*   
   >>>>>   
   >>>>> Turing machine deciders only report on the behavior   
   >>>>> of Turing machines indirectly through the proxy of   
   >>>>> finite strings. *This key detail has been ignored*   
   >>>>>   
   >>>>> Principle 2: We measure the semantic property that   
   >>>>> the finite string specifies by a UTM-based halt   
   >>>>> decider that simulates its input finite string   
   >>>>> step-by-step and watches the execution trace of   
   >>>>> this behavior.   
   >>>>>   
   >>>>> This eliminates the category error.   
   >>>>   
   >>>> You can't elminate what didn't ever exist. Instead that simply   
   >>>> declares that you are not talking about the halting problem.   
   >>>   
   >>> When you carefully evaluate my reasoning you   
   >>> will see that no decider can possibly report   
   >>> on anything that is not directly encoded in   
   >>> its finite string input input according to   
   >>> the semantics of its encoding language.   
   >>   
   >> I don't need your reasoning in order to know that. I knew it already.   
   >   
   > Then you would know that the behavior of DD   
   > simulated by HHH overrules the behavior of   
   > DD executed from main as the behavior that the   
   > input finite string specifies.   
      
   That is irrelevan to my comment that your "thus" is false.   
      
   --   
   Mikko   
      
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