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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: comp.theory Subject: Re: Halting Problem: How my refutation differs to Peter Olcott's Date: Mon, 12 May 2025 10:19:03 +0300 Organization: - Lines: 111 Message-ID: References: <3bc01824e1d95a30b9784942a8b7ef3bc9ec8ff8@i2pn2.org> <445621fd6d6864f68b1c6e2040cff818c336600f@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 12 May 2025 09:19:04 +0200 (CEST) Injection-Info: dont-email.me; posting-host="d66022cf12555db523e1c5ad57a06eab"; logging-data="1036509"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/XYcVhyZFbWROokMv/4TV6" User-Agent: Unison/2.2 Cancel-Lock: sha1:MrLk8rkzpnuT2eF4OrKbr90izSc= On 2025-05-11 03:11:43 +0000, Mr Flibble said: > On Sat, 10 May 2025 22:00:26 -0500, olcott wrote: > >> On 5/10/2025 9:51 PM, Mr Flibble wrote: >>> On Sat, 10 May 2025 21:49:41 -0400, Richard Damon wrote: >>> >>>> On 5/10/25 9:18 PM, Mr Flibble wrote: >>>>> On Sat, 10 May 2025 21:07:34 -0400, Richard Damon wrote: >>>>> >>>>>> On 5/10/25 9:00 PM, olcott wrote: >>>>>>> On 5/10/2025 6:56 PM, Mr Flibble wrote: >>>>>>>> On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote: >>>>>>>> >>>>>>>>> On 5/10/25 4:38 PM, Mr Flibble wrote: >>>>>>>>>> How my refutation differs to Peter's: >>>>>>>>>> >>>>>>>>>> * Peter refutes the halting problem based on pathological input >>>>>>>>>> manifesting in a simulating halt decider as infinite recursion, >>>>>>>>>> this being treated as non-halting. >>>>>>>>>> * Flibble refutes the halting problem based on patholgical input >>>>>>>>>> manifesting as decider/input self-referencial conflation, >>>>>>>>>> resulting in the contradiction at the heart of the halting >>>>>>>>>> problem being a category (type) error, i.e. ill-formed. >>>>>>>>>> >>>>>>>>>> These two refutations are related but not exactly the same. >>>>>>>>>> >>>>>>>>>> /Flibble >>>>>>>>> >>>>>>>>> And the problem is that you use incorrect categories. >>>>>>>>> >>>>>>>>> The decider needs to be of the category "Program". >>>>>>>>> >>>>>>>>> The input also needs to be of the category "Program", but >>>>>>>>> provided via a representation. The act of representation lets us >>>>>>>>> convert items of category Program to the category of Finite >>>>>>>>> String which can be an input. >>>>>>>> >>>>>>>> Those two categories you have identified are different hence the >>>>>>>> category error. >>>>>>>> >>>>>>>> >>>>>>> That is correct. A running program and an input finite string ARE >>>>>>> NOT THE SAME. >>>>>> >>>>>> But there is a direct relationship between the two. >>>>>> >>>>>> >>>>>> >>>>>>>>> The "Pathological Input" *IS* a Program, built by the simple >>>>>>>>> rules of composition that are allowed in the system. >>>>>>>> >>>>>>>> Such composition is invalid. >>>>>>>> >>>>>>>> >>>>>>> Richard is trying to get away with saying that a finite string THAT >>>>>>> IS NOT A RUNNING PROGRAM A RUNNING PROGRAM >>>>>>> >>>>>>> >>>>>> But they are related to each other, >>>>> >>>>> Even if there is some perceived relationship between the two >>>>> different categories it doesn't mean there still isn't a category >>>>> error. >>>> >>>> So, what is the error, since the input *IS* the finite string that was >>>> built by the program representation operation, and thus *IS* what an >>>> input needs to be. >>>> >>>> >>>>> Why relationship doesn’t rescue the mistake: >>>>> >>>>> * Shared context ≠ shared type. >>>>> – A pupil and a teacher are clearly related (one teaches, one >>>>> learns), but the question “Who is taller, the lesson?” commits a >>>>> category error because a lesson isn’t the kind of thing that has >>>>> height, regardless of its pedagogical ties to people. >>>> >>>> Which doesn't apply here, and you are just indicationg you don't >>>> understand what a representation is. >>>> >>>> The input is a finite string that represents a program. >>> >>> A program and a finite string representing a program are different >>> categories ergo we have a category error. >>> >>> /Flibble >> >> This made no difference difference until my simulating termination >> analyzer discovered they they don't always have the same behavior as was >> merely presumed for 90 years. >> >> A halt decider was "defined" to report on the behavior of the direct >> execution of the input ONLY because no one knew that it could possibly >> be different behavior than what the input finite string specifies. >> >> Everyone here takes this false assumption as the infallible word of God. >> A textbook says it therefore it must be infallible. > > Yes, the reason why these two different categories cause a category error > is because of the self-referential dependency between them, which > manifests as infinite recursion in your simulating halt decider case. That is contradicto in adiecto: a refertial dependncy between two entities of different categories cannot be self-referential. An entity can have a self-referential dependncy only to itself and it is always of the same category as it is itself. -- Mikko