XPost: comp.theory, sci.logic   
   From: flibble@red-dwarf.jmc.corp   
      
   On Wed, 06 Aug 2025 07:01:18 -0500, olcott wrote:   
      
   > On 8/6/2025 6:29 AM, Richard Damon wrote:   
   >> On 8/6/25 7:15 AM, olcott wrote:   
   >>> On 8/6/2025 6:01 AM, Richard Damon wrote:   
   >>>> On 8/5/25 10:56 PM, olcott wrote:   
   >>>>>   
   >>>>> It is a requirement of the aspect of Ĥ named Ĥ.embedded_H.   
   >>>>>   
   >>>>>   
   >>>> Depends on which system you are working in.   
   >>>>   
   >>>> IF you are talking about Linz system, where H *IS* a Halt Decider,   
   >>> If H *is* a halt decider then the proof that no halt decider exists is   
   >>> done.   
   >>   
   >> Nope, because while in that system, H *IS* a Halt Decider, but might   
   >> not actually exist.   
   >>   
   >>   
   > A lack of sufficient precision in your words again.   
   > H *is* a halt decider that may not exist is a contradiction.   
      
   No, the proofs are asking if such a halt decider exists so it is a   
   *premise* (a statement that is provisionally accepted as true for the   
   purpose of the argument) that a *hypothetical* H exists and the proofs   
   then go on to show that such an H cannot exist.   
      
   /Flibble   
      
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