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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Disagreeing with tautologies is always incorrect -- mathematical
 induction
Date: Sat, 31 May 2025 10:28:19 -0500
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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]
>>>>>
>>>>> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>>>>>      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?

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