XPost: comp.theory, sci.logic   
   From: richard@damon-family.org   
      
   On 7/20/25 10:33 AM, olcott wrote:   
   > On 7/20/2025 6:11 AM, joes wrote:   
   >> Am Sat, 19 Jul 2025 16:36:42 -0500 schrieb olcott:   
   >>> On 7/19/2025 4:26 PM, wij wrote:   
   >>>> On Sat, 2025-07-19 at 16:05 -0500, olcott wrote:   
   >>   
   >>>>> DD correctly simulated by HHH cannot reach past the "if" statement   
   >>>>> thus cannot reach the "return" statement.   
   >>>>   
   >>>> That is roughly what HP proof says.   
   >>>>   
   >>> Not at all. The HP proof claims that DD correctly simulated by HHH   
   >>> reaches the self-contradictory part of DD and thus forms a   
   >>> contradiction.   
   >>   
   >> No. It proves that the direct execution reaches the part that contra-   
   >> dicts HHH's return value.   
   >>   
   >   
   >    
   > Misrepresentation of Input:   
   > The standard proof assumes a decider   
   > H(M,x) that determines whether machine   
   > M halts on input x.   
   >   
   > But this formulation is flawed, because:   
   > Turing machines can only process finite   
   > encodings (e.g. ⟨M⟩), not executable entities   
   > like M.   
   >   
   > So the valid formulation must be   
   > H(⟨M⟩,x), where ⟨M⟩ is a string.   
   >    
   >   
   >   
      
   In other words, your explaination to Chat GPR was just in error, as the   
   decider *IS* given the representation of the program M.   
      
   Your problem is that because you don't understand how Turing Machine   
   work, you "reformuated" it into a case where program and representation   
   is blured (as is the actual defintion of "input").   
      
   The the error pointed out is actually in your setup, not the problem, as   
   the decider *IS* given   
      
   H  w  where  is the description of the machine, which is the   
   contray Turing Machine, and w is a copy of that description.   
      
   Thus, meeting the requirments that the AI said was needed.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)