XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 10/23/2025 1:48 PM, dbush wrote:   
   > On 10/23/2025 2:40 PM, olcott wrote:   
   >> On 10/23/2025 1:31 PM, dbush wrote:   
   >>> On 10/23/2025 2:17 PM, olcott wrote:   
   >>>> On 10/23/2025 1:09 PM, dbush wrote:   
   >>>>> On 10/23/2025 2:06 PM, olcott wrote:   
   >>>>>> On 10/23/2025 1:00 PM, dbush wrote:   
   >>>>>>> On 10/23/2025 1:58 PM, olcott wrote:   
   >>>>>>>> On 10/23/2025 12:03 PM, dbush wrote:   
   >>>>>>>>> On 10/23/2025 12:49 PM, olcott wrote:   
   >>>>>>>>>> On 10/23/2025 10:48 AM, dbush wrote:   
   >>>>>>>>>>> On 10/23/2025 11:46 AM, olcott wrote:   
   >>>>>>>>>>>> On 10/23/2025 4:15 AM, Mikko wrote:   
   >>>>>>>>>>>>> On 2025-10-22 12:35:14 +0000, olcott said:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>> On 10/22/2025 4:07 AM, Mikko wrote:   
   >>>>>>>>>>>>>>> On 2025-10-21 15:04:58 +0000, olcott said:   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> On 10/21/2025 3:45 AM, Mikko wrote:   
   >>>>>>>>>>>>>>>>> On 2025-10-20 16:17:07 +0000, olcott said:   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>> On 10/20/2025 3:42 AM, Mikko wrote:   
   >>>>>>>>>>>>>>>>>>> On 2025-10-19 16:21:42 +0000, olcott said:   
   >>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>> On 10/19/2025 4:24 AM, Mikko wrote:   
   >>>>>>>>>>>>>>>>>>>>> On 2025-10-18 13:16:50 +0000, olcott said:   
   >>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>> On 10/18/2025 7:16 AM, olcott wrote:   
   >>>>>>>>>>>>>>>>>>>>>>>    
   >>>>>>>>>>>>>>>>>>>>>>> Please think this all the way through without   
   >>>>>>>>>>>>>>>>>>>>>>> making any guesses   
   >>>>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>>> Simulating Termination Analyzer HHH correctly   
   >>>>>>>>>>>>>>>>>>>>>>> simulates its input until:   
   >>>>>>>>>>>>>>>>>>>>>>> (a) Detects a non-terminating behavior pattern:   
   >>>>>>>>>>>>>>>>>>>>>>> abort simulation and return 0.   
   >>>>>>>>>>>>>>>>>>>>>>> (b) Simulated input reaches its simulated   
   >>>>>>>>>>>>>>>>>>>>>>> "return" statement: return 1.   
   >>>>>>>>>>>>>>>>>>>>>>> (c) If HHH must abort its simulation to prevent   
   >>>>>>>>>>>>>>>>>>>>>>> its own non- termination   
   >>>>>>>>>>>>>>>>>>>>>>>      then HHH is correct to abort this simulation   
   >>>>>>>>>>>>>>>>>>>>>>> and return 0.   
   >>>>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>>> typedef int (*ptr)();   
   >>>>>>>>>>>>>>>>>>>>>>> int HHH(ptr P);   
   >>>>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>>> int DD()   
   >>>>>>>>>>>>>>>>>>>>>>> {   
   >>>>>>>>>>>>>>>>>>>>>>>   int Halt_Status = HHH(DD);   
   >>>>>>>>>>>>>>>>>>>>>>>   if (Halt_Status)   
   >>>>>>>>>>>>>>>>>>>>>>>     HERE: goto HERE;   
   >>>>>>>>>>>>>>>>>>>>>>>   return Halt_Status;   
   >>>>>>>>>>>>>>>>>>>>>>> }   
   >>>>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>>> int main()   
   >>>>>>>>>>>>>>>>>>>>>>> {   
   >>>>>>>>>>>>>>>>>>>>>>>   HHH(DD);   
   >>>>>>>>>>>>>>>>>>>>>>> }   
   >>>>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>>> What value should HHH(DD) correctly return?   
   >>>>>>>>>>>>>>>>>>>>>>>    
   >>>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>>> When the halting problem requires a halt decider   
   >>>>>>>>>>>>>>>>>>>>>> to report   
   >>>>>>>>>>>>>>>>>>>>>> on anything besides the behavior that its input   
   >>>>>>>>>>>>>>>>>>>>>> actually   
   >>>>>>>>>>>>>>>>>>>>>> specifies this is just like requiring a silk purse   
   >>>>>>>>>>>>>>>>>>>>>> be made   
   >>>>>>>>>>>>>>>>>>>>>> from a sow's ear.   
   >>>>>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>>>>> The way halting problem is usally presented the   
   >>>>>>>>>>>>>>>>>>>>> input to the   
   >>>>>>>>>>>>>>>>>>>>> problem is a Truing machine   
   >>>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>>> The input to the problem is never ever a Turing   
   >>>>>>>>>>>>>>>>>> machine it is always a finite string generally   
   >>>>>>>>>>>>>>>>>> assumed to be a machine description.   
   >>>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>>> The input to the problem as usually presented is a pair   
   >>>>>>>>>>>>>>>>> of a   
   >>>>>>>>>>>>>>>>> Turing machine and an input to it.   
   >>>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>>> Wrong again. It is always a finite string Turing Machine   
   >>>>>>>>>>>>>>>> description and never an actual Turing machine.   
   >>>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>> As the problem is presented in Wikipedia the input to the   
   >>>>>>>>>>>>>>> proble   
   >>>>>>>>>>>>>>> is a program and an input to it. Both can be regareded as   
   >>>>>>>>>>>>>>> finite   
   >>>>>>>>>>>>>>> strings.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> The behavior of the caller of HHH(DD) is not encoded in   
   >>>>>>>>>>>>>> its input.   
   >>>>>>>>>>>>>> HHH has no way to tell who its caller is.   
   >>>>>>>>>>>>>> This is what makes the halting problem a category error.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> No, it does not. Nothing in the problem statement "Present   
   >>>>>>>>>>>>> a method   
   >>>>>>>>>>>>> to determine whether a given program halts or runs forwever   
   >>>>>>>>>>>>> when   
   >>>>>>>>>>>>> started with a given input to that program" says that the   
   >>>>>>>>>>>>> behaviour   
   >>>>>>>>>>>>> of the caller of HHH(DD) is not encoded to in the input to   
   >>>>>>>>>>>>> HHH.   
   >>>>>>>>>>>>> It merely requires that the required method produces the   
   >>>>>>>>>>>>> correct   
   >>>>>>>>>>>>> answer for any program and any input.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Sure and equally the pure mental object of a Turing   
   >>>>>>>>>>>> machine is limited in this same sort of way that it   
   >>>>>>>>>>>> cannot bake a birthday cake.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Turing machine deciders only compute the mapping   
   >>>>>>>>>>>> from their finite string inputs to an accept state   
   >>>>>>>>>>>> or reject state on the basis that this input finite   
   >>>>>>>>>>>> string specifies a semantic or syntactic property.   
   >>>>>>>>>>>   
   >>>>>>>>>>> And you agreed that this means they are allowed to report on   
   >>>>>>>>>>> the halt status of the machine described by the input:   
   >>>>>>>>>>>   
   >>>>>>>>>>> On 10/20/2025 11:51 PM, olcott wrote:   
   >>>>>>>>>>>  > On 10/20/2025 10:45 PM, dbush wrote:   
   >>>>>>>>>>>  >> And it is a semantic tautology that a finite string   
   >>>>>>>>>>> description of a   
   >>>>>>>>>>>  >> Turing machine is stipulated to specify all semantic   
   >>>>>>>>>>> properties of the   
   >>>>>>>>>>>  >> described machine, including whether it halts when   
   >>>>>>>>>>> executed directly.   
   >>>>>>>>>>>  >   
   >>>>>>>>>>>  > Yes that is all correct   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> That is all a correct statement of the false   
   >>>>>>>>>> assumption that derives the category error.   
   >>>>>>>>>>   
   >>>>>>>>>> Turing machine deciders only compute the mapping   
   >>>>>>>>>> from their finite string inputs to an accept state   
   >>>>>>>>>> or reject state on the basis that this input finite   
   >>>>>>>>>> string specifies a semantic or syntactic property.   
   >>>>>>>>>   
   >>>>>>>>> Repeat of previously refuted point where you explicitly agreed   
   >>>>>>>>> with the refutation:   
   >>>>>>>>>   
      
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