Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory Subject: Re: Disagreeing with tautologies is always incorrect -- mathematical induction Date: Sat, 31 May 2025 14:39:50 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <85d94d54bba7ac2794f4e0be9cee83056c295a71@i2pn2.org> References: <1019v06$3u8nj$1@dont-email.me> <101at6j$4bga$2@dont-email.me>

<101f76j$173bb$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 31 May 2025 18:48:19 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2723957"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: <101f76j$173bb$2@dont-email.me> X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US On 5/31/25 11:28 AM, olcott wrote: > On 5/31/2025 9:57 AM, Ross Finlayson wrote: >> On 05/30/2025 07:26 AM, Richard Damon wrote: >>> On 5/29/25 8:13 PM, olcott wrote: >>>> On 5/29/2025 7:05 PM, Ross Finlayson wrote: >>>>> On 05/29/2025 08:37 AM, olcott wrote: >>>>>> HHH is a simulating termination analyzer that uses >>>>>> an x86 emulator to emulate its input. HHH is capable >>>>>> of emulating itself emulating DDD. >>>>>> >>>>>> HHH is executed within the x86utm operating system >>>>>> that enables any C function to execute another C >>>>>> function in debug step mode. >>>>>> >>>>>> *Here is the fully operational code* >>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c >>>>>> >>>>>> void DDD() >>>>>> { >>>>>> HHH(DDD); >>>>>> return; >>>>>> } >>>>>> >>>>>> _DDD() >>>>>> [00002192] 55 push ebp >>>>>> [00002193] 8bec mov ebp,esp >>>>>> [00002195] 6892210000 push 00002192 >>>>>> [0000219a] e833f4ffff call 000015d2 // call HHH >>>>>> [0000219f] 83c404 add esp,+04 >>>>>> [000021a2] 5d pop ebp >>>>>> [000021a3] c3 ret >>>>>> Size in bytes:(0018) [000021a3] >>>>>> >>>>>> >>>>>> If simulating halt decider H correctly simulates its >>>>>> input D until H correctly determines that its simulated D >>>>>> would never stop running unless aborted then >>>>>> >>>>>> It is a tautology that any input D to termination >>>>>> analyzer H that *would never stop running unless aborted* >>>>>> DOES SPECIFY NON-TERMINATING BEHAVIOR. >>>>>> >>>>>> Simulating Termination Analyzer H is Not Fooled by Pathological >>>>>> Input D >>>>>> https://www.researchgate.net/ >>>>>> publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D >>>>>> >>>>>> >>>>>> >>>>> >>>>> No it's not. >>>>> >>>>> (Was, "disagreeing with tautologies is always incorrect".) >>>>> >>>>> It's the _deductive_ analysis that makes for the >>>>> "analytical bridges" to escape an "inductive impasse". >>>>> >>>> >>>> If by inductive impasse you are referring to mathematical >>>> induction you might be right. If you are referring to logical >>>> induction then you are wrong. >>> >>> But "Inductive Logic" isn't actually logic in the formal sense, but ways >>> to try to approximate a correct answer when deductive logic can't get >>> one. Since Deductive Logic DOES determine the correct answer, just one >>> you don't like, you are just rejecting actual logic and adopting a >>> system that you can lie in. >>> >>> >>> >>>> >>>> So far I have not been able to make a proof by mathematical >>>> induction that I am correct. >>> >>> Because it is impossible to correctly prove a wrong statement. >>> >>>> >>>> The closest that I got is that for any value of N when >>>> N steps of DDD are correctly emulated by HHH the emulated >>>> DDD never reaches its own "ret" instruction final halt state. >>>> >>> >>> But the problmm here is that your system, when properly defined for H to >>> actually be that series of programs, and D to be the programs built on >>> those H, it becomes immediately apparant that you aren't talking about >>> hte SAME D in each of those steps, so just talking about D as a singular >>> entity is just a category error. >>> >>> Making D to be a program fragment which is completed in each instance to >>> try and make D be something singular, just runs afoul of the >>> requirements that it be a program, and then H needs to not be the >>> required computation (which can only operate on what it in the input, >>> and not other outside resource, like other things in memory) as it looks >>> outside to code of the input to "correctly simulate" it. >>> >>> Thus, what you have proven is not that any of those D are non-halting >>> (since every D was different), but that no H can prove such a D to be >>> halting by thing method, even though we CAN, outside of the code of H, >>> make that proof. >> >> The "inductive" is very much like the "empirical", >> and "deduction" isn't only about "elimination". >> >> >> "There is no but: only yet", reflects that the >> modal and temporally modal relevance logic is >> not about contradictions, instead change. >> >> >> The very idea of a Principle of Contradiction >> instead of a Principle of Inversion leads to >> a very simple obstinacy and fallacies like >> those of, "material implication", that aren't so. >> >> Then a principle of inversion can help arrive >> at a Principle of Sufficient Reason: yet a >> more "Principle of Sufficient, and Thorough, Reason". >> >> >> >> The analytical bridges for abduction about the >> deduction about the impasses of induction, help >> make for the "classical superclassical" reason >> usually attributes to Zeno with the most, "paradoxes", >> that there are none or that there is one a paradox, >> make for a, "wider, fuller dialectic", what makes >> for why "axiomless natural deduction" arrives at >> being the only true theory of Truth, capital Truth. >> >> >> Then, that requires a bit of a complete ontological >> commitment, yet at least it's true so won't be wrong. >> >> >> This was, "disagreeing with tautologies is always incorrect", >> yet, "disagreeing with tautologies is always correct". >> >> Just a bit longer, ..., for the _sufficient_ reason, >> and, the _sufficient, and thorough_, reason. >> >> Here's a bunch of podcasts where this is detailed further, >> mostly under that "Logos 2000" section, >> https://www.youtube.com/@rossfinlayson . >> >> >> Won't be wrong, ..., and has a true logic and mathematics. >> Not much else, though it does give a science. >> >> Then the idea of physics itself arising from that also occurs. >> >> Reason, Rationality, Reality: Nature >> >> > > I wish that I could understand that. > > _DDD() > [00002192] 55 push ebp > [00002193] 8bec mov ebp,esp > [00002195] 6892210000 push 00002192 > [0000219a] e833f4ffff call 000015d2 // call HHH > [0000219f] 83c404 add esp,+04 > [000021a2] 5d pop ebp > [000021a3] c3 ret > Size in bytes:(0018) [000021a3] Not a program, so not a valid input to program decider. > > Recursive Emulation Invariant (REI): > DDD correctly emulated by HHH never reaches its own > "ret" instruction (final halt state). Since your DDD can't be correctly emulated, your "Invarient" is just ========== REMAINDER OF ARTICLE TRUNCATED ==========