XPost: comp.theory, sci.logic, sci.math   
   From: dbush.mobile@gmail.com   
      
   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   
   >>>>>>   
   >>>>>> This means you agree that the finite string input to HHH(DD),   
   >>>>>> which is the description of machine DD and therefore specifies all   
   >>>>>> semantic properties of that machine, specifies halting behavior.   
   >>>>>>   
   >>>>>>   
   >>>>> That is a perfectly correct statement of the   
   >>>>> halting problems false assumption   
      
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