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From: Richard Damon <richard@damon-family.org>
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)
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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]
>>>>>>
>>>>>> <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]

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 
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