XPost: comp.theory, sci.logic   
   From: mikko.levanto@iki.fi   
      
   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.   
   It is actually quite obvious. But the halting problem as usually   
   formulated does not specify the input language for the halting   
   decider. Instead it requires that the solution inculdes the encoding   
   rules and that the input language can encode every possible Turing   
   machine with every possible input. If you don't have encodeing rules   
   that allow that then you don't have a solution to the halting   
   problem.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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