XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 10/23/2025 1:59 PM, dbush wrote:   
   > On 10/23/2025 2:55 PM, olcott wrote:   
   >> 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.   
   >>>>>>>>>>>>   
      
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