XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   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:   
   >>>>>>>   
   >>>>>>> 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   
   >>>>>>>   
      
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