Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: Unpartial Halt Deciders --- category error Date: Sat, 19 Apr 2025 16:02:53 -0500 Organization: A noiseless patient Spider Lines: 135 Message-ID: References: <87zfgdnufj.fsf@nosuchdomain.example.com> <0JxMP.1398486$cgs7.284882@fx14.ams4> <87sem5nu3q.fsf@nosuchdomain.example.com> <438052adf5074f27313bbb52c9f14c20fcfa2418@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 19 Apr 2025 23:02:55 +0200 (CEST) Injection-Info: dont-email.me; posting-host="08d11b4b162d6bbd305a554bf1d3c94a"; logging-data="2328833"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/dEoa/472RXF4tNVacZElK" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:3/SK4SArcVXhR6gK/9bX/jQ1DKo= In-Reply-To: X-Antivirus: Norton (VPS 250419-6, 4/19/2025), Outbound message X-Antivirus-Status: Clean Content-Language: en-US Bytes: 6974 On 4/19/2025 3:57 PM, Mr Flibble wrote: > On Sat, 19 Apr 2025 15:44:31 -0500, olcott wrote: > >> On 4/19/2025 1:06 PM, Mr Flibble wrote: >>> On Sat, 19 Apr 2025 13:34:40 -0400, Richard Damon wrote: >>> >>>> On 4/19/25 8:05 AM, Mr Flibble wrote: >>>>> On Sat, 19 Apr 2025 07:55:55 -0400, Richard Damon wrote: >>>>> >>>>>> On 4/18/25 11:52 PM, olcott wrote: >>>>>>> On 4/18/2025 2:32 PM, Keith Thompson wrote: >>>>>>>> Mr Flibble writes: >>>>>>>>> On Fri, 18 Apr 2025 12:25:36 -0700, Keith Thompson wrote: >>>>>>>>>> Mr Flibble writes: >>>>>>>>>>> I, aka Mr Flibble, have created a new computer science term, >>>>>>>>>>> the "Unpartial Halt Decider".  It is a Halt Decider over the >>>>>>>>>>> domain of all program-input pairs excluding pathological input >>>>>>>>>>> (a manifestation of the self referencial category error). >>>>>>>>>> [...] >>>>>>>>>> >>>>>>>>>> Do you have a rigorous definition of "pathological input"? >>>>>>>>>> >>>>>>>>>> Is there an algorithm to determine whether a given input is >>>>>>>>>> "pathological" or not? >>>>>>>>>> >>>>>>>>>> I could define an is_prime() function like this: >>>>>>>>>> >>>>>>>>>>      bool is_prime(int n) { >>>>>>>>>>          return n >= 3 && n % 2 == 1; >>>>>>>>>>          // returns true for odd numbers >= 3, false >>>>>>>>>>          for all others >>>>>>>>>>      } >>>>>>>>>> >>>>>>>>>> I'll just say that odd numbers that are not prime are >>>>>>>>>> pathological input, so I don't have to deal with them. >>>>>>>>> >>>>>>>>> Pathological input: >>>>>>>>> >>>>>>>>> Self-referencial to the decider. >>>>>>>> >>>>>>>> OK. >>>>>>>> >>>>>>>> Do you have a *rigorous* definition of "pathological input"? >>>>>>>> >>>>>>>> Is there an algorithm to determine whether a given input is >>>>>>>> "pathological" or not? >>>>>>>> >>>>>>>> >>>>>>> int DD() >>>>>>> { >>>>>>>   int Halt_Status = HHH(DD); >>>>>>>   if (Halt_Status) >>>>>>>     HERE: goto HERE; >>>>>>>   return Halt_Status; >>>>>>> } >>>>>>> >>>>>>> Patterns isomorphic to the above when simulated by HHH. >>>>>>> >>>>>>> >>>>>>> >>>>>> Examples are not definitions. >>>>>> >>>>>> And the problem is that the above example is itself a category error >>>>>> for the problem, as the DD provided above isn't a complete program, >>>>>> as it doesn't include the code for HHH as required, and when you >>>>>> include Halt7.c as part of the input, your HHH isn't a seperate >>>>>> program of its own, and thus doesn't have a Turing Complete range of >>>>>> inputs it can accept. >>>>>> >>>>>> Sorry, you are just showing you don't understand what it means to >>>>>> DEFINE something. >>>>> >>>>> Ah, the fundamental mistake you have been making all this time, >>>>> Damon! >>>>> The self-referencial category error doesn't magically disappear by >>>>> providing source code rather than a run-time function address to the >>>>> decider; you are simply transforming the same input without affecting >>>>> the result. >>>>> >>>>> /Flibble >>>> >>>> And WHAT is the category error? You stil can't show the difference in >>>> CATEGORY between what is allowed and what isn't, and in fact, you >>>> can't even precisely define what is and isn't allowed. >>>> >>>> Now, you also run into the issue that the "Olcott System" begins with >>>> an actual category error as we do not have the required two seperate >>>> programs of the "Decider" and the "Program to be decided on" given via >>>> representation as the input, as what you want to call that program to >>>> be decided isn't one without including the code of the decider it is >>>> using, >>>> and when you do include it, the arguments about no version of the >>>> decider being able to succeed is improper as it must always be that >>>> exact program that we started with, and thus it just FAILS to do a >>>> correct simulation, while a correct simulation of this exact input >>>> (which includes the ORIGINAL decider) will halt. >>>> >>>> Sorry, YOU are the one stuck with the fundamental mistake, or is it a >>>> funny mental mistake because you don't understand what you are talking >>>> about. >>> >>> The category error is extant over the domain of pathological inputs, no >>> matter what form those inputs take. >>> >>> /Flibble >> >> The category error in the halting problem proof is to define an input D >> that is able to actually do the opposite of whatever value that H >> reports. >> >> Now the question: Does the input D halt becomes self-contradictory for >> H. >> >> So it is asking a yes/no question where both yes and no are the wrong >> answer that is the category error. >> >> Objective and Subjective Specifications Eric C.R. Hehner Department of >> Computer Science, University of Toronto >> >> (6) Can Carol correctly answer “no” to this (yes/no) question? >> https://www.cs.toronto.edu/~hehner/OSS.pdf >> >> Richard Damon found a loophole in the original question. >> I inserted (yes/no) to close the loophole. > > No, the category error is conflating the decider with the input through > self-reference. > > /Flibble Yes that seems to be another way to say it. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer