Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: Disagreeing with tautologies is always incorrect -- mathematical induction Date: Sat, 31 May 2025 10:28:19 -0500 Organization: A noiseless patient Spider Lines: 186 Message-ID: <101f76j$173bb$2@dont-email.me> References: <1019v06$3u8nj$1@dont-email.me> <101at6j$4bga$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 17:28:20 +0200 (CEST) Injection-Info: dont-email.me; posting-host="c9a131a468f55446a50ed4b18f7c4193"; logging-data="1281387"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19OiZjmpCoUSfHe+qR4zD+P" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:R+hjFab+UFVhkfq6gBAZwjubZJc= Content-Language: en-US X-Antivirus: Norton (VPS 250531-2, 5/31/2025), Outbound message X-Antivirus-Status: Clean In-Reply-To: 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] Recursive Emulation Invariant (REI): DDD correctly emulated by HHH never reaches its own "ret" instruction (final halt state). Do you have any idea how to form a proper mathematical induction proof that when each HHH of an infinite set of HHH correctly simulates N steps of DDD the the REI holds? ========== REMAINDER OF ARTICLE TRUNCATED ==========