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computers / comp.ai.philosophy / Re: Concise refutation of halting problem proofs V62 [ my legacy ]( the nature of truth )

Re: Concise refutation of halting problem proofs V62 [ my legacy ]( the nature of truth )

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Subject: Re: Concise refutation of halting problem proofs V62 [ my legacy ](
the nature of truth )
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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Fri, 18 Feb 2022 21:03 UTC

On 2/18/2022 2:46 PM, Richard Damon wrote:
> On 2/18/22 2:33 PM, olcott wrote:
>> On 2/18/2022 1:12 PM, Richard Damon wrote:
>>> On 2/18/22 1:41 PM, olcott wrote:
>>>> On 2/18/2022 11:49 AM, Richard Damon wrote:
>>>>> On 2/18/22 12:18 PM, olcott wrote:
>>>>>> On 2/18/2022 11:08 AM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 2/18/22 11:55 AM, olcott wrote:
>>>>>>>> On 2/18/2022 10:38 AM, Richard Damon wrote:
>>>>>>>>> On 2/18/22 11:02 AM, olcott wrote:
>>>>>>>>>> On 2/18/2022 9:52 AM, Richard Damon wrote:
>>>>>>>>>>> On 2/18/22 9:55 AM, olcott wrote:
>>>>>>>>>>>> On 2/17/2022 10:21 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 2/17/22 11:06 PM, olcott wrote:
>>>>>>>>>>>>>> On 2/17/2022 9:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 2/17/22 10:30 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 2/17/2022 9:12 PM, Python wrote:
>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>> On 2/17/2022 9:02 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 2/17/22 1:44 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 2/17/2022 12:16 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>>>>>> On Thu, 17 Feb 2022 07:00:26 -0500
>>>>>>>>>>>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> On 2/17/22 12:36 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2/16/2022 11:33 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/16/2022 10:54 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/16/22 11:22 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/16/2022 10:17 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/16/22 11:09 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2/16/2022 9:56 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Every simulating halt decider that must
>>>>>>>>>>>>>>>>>>>>>>>>>>>> abort the simulation
>>>>>>>>>>>>>>>>>>>>>>>>>>>> of its input to prevent its infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation correctly
>>>>>>>>>>>>>>>>>>>>>>>>>>>> transitions to its reject state.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> WRONG. You aren't following the right
>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Try to actually PROVE your statement.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Try to prove that a baby kitten is an animal
>>>>>>>>>>>>>>>>>>>>>>>>>> and not the windows
>>>>>>>>>>>>>>>>>>>>>>>>>> of an office building. It is all in the simple
>>>>>>>>>>>>>>>>>>>>>>>>>> meaning of the
>>>>>>>>>>>>>>>>>>>>>>>>>> words.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> RED HERRING.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> You just don't understand the difference
>>>>>>>>>>>>>>>>>>>>>>>>> betweeen FORMAL logic
>>>>>>>>>>>>>>>>>>>>>>>>> systems and informal ones.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> You have FAILED, but are too dumb to know it.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Halting problem undecidability and infinitely
>>>>>>>>>>>>>>>>>>>>>>>>>> nested simulation
>>>>>>>>>>>>>>>>>>>>>>>>>> (V3)
>>>>>>>>>>>>>>>>>>>>>>>>>> https://www.researchgate.net/publication/358009319_Halting_problem_undecidability_and_infinitely_nested_simulation_V3
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Your monument to your stupidity.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Not ONE bit of formal prpof.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> FAIL.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Maybe you can convince yourzelf that you have
>>>>>>>>>>>>>>>>>>>>>>>>> proven something,
>>>>>>>>>>>>>>>>>>>>>>>>> but if you want anyone who means anything to
>>>>>>>>>>>>>>>>>>>>>>>>> agree with you, you
>>>>>>>>>>>>>>>>>>>>>>>>> have a VERY long wait.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> I think that you understand this deep in your
>>>>>>>>>>>>>>>>>>>>>>>>> heart, which is why
>>>>>>>>>>>>>>>>>>>>>>>>> you just peddle your garbage on forums that
>>>>>>>>>>>>>>>>>>>>>>>>> don't require peer
>>>>>>>>>>>>>>>>>>>>>>>>> review to make statements.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Every simulating halt decider that must abort
>>>>>>>>>>>>>>>>>>>>>>>> the simulation of its
>>>>>>>>>>>>>>>>>>>>>>>> input to prevent its infinite simulation
>>>>>>>>>>>>>>>>>>>>>>>> correctly transitions to
>>>>>>>>>>>>>>>>>>>>>>>> its reject state.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> You all know that what I say is self-evidently
>>>>>>>>>>>>>>>>>>>>>>>> true.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> The fact that no counter-example exists proves
>>>>>>>>>>>>>>>>>>>>>>>> that I am correct.
>>>>>>>>>>>>>>>>>>>>>>>> The fact that no counter-example exists proves
>>>>>>>>>>>>>>>>>>>>>>>> that I am correct.
>>>>>>>>>>>>>>>>>>>>>>>> The fact that no counter-example exists proves
>>>>>>>>>>>>>>>>>>>>>>>> that I am correct.
>>>>>>>>>>>>>>>>>>>>>>>> The fact that no counter-example exists proves
>>>>>>>>>>>>>>>>>>>>>>>> that I am correct.
>>>>>>>>>>>>>>>>>>>>>>>> The fact that no counter-example exists proves
>>>>>>>>>>>>>>>>>>>>>>>> that I am correct.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Example:
>>>>>>>>>>>>>>>>>>>>>>> A simulating halt decider that must abort the
>>>>>>>>>>>>>>>>>>>>>>> simulation of its
>>>>>>>>>>>>>>>>>>>>>>> input to prevent its infinite simulation where
>>>>>>>>>>>>>>>>>>>>>>> this input halts on
>>>>>>>>>>>>>>>>>>>>>>> its own without being aborted.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> How about our H and the H" built from it.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> You have shown the H must abort its simulation of
>>>>>>>>>>>>>>>>>>>>>> H" or H will never
>>>>>>>>>>>>>>>>>>>>>> halt. That is accepted.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> BUT, When we look at the actual behavoir of H <H">
>>>>>>>>>>>>>>>>>>>>>> we see that we
>>>>>>>>>>>>>>>>>>>>>> have the following trace:
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> We start at H".Q0 <H">
>>>>>>>>>>>>>>>>>>>>>> We go to H".Qx <H"> <H">
>>>>>>>>>>>>>>>>>>>>>> since H".Qx has a copy of H at it, and we have
>>>>>>>>>>>>>>>>>>>>>> said that H has
>>>>>>>>>>>>>>>>>>>>>> supposedly correctly decided that H" <H"> is a
>>>>>>>>>>>>>>>>>>>>>> non-halting
>>>>>>>>>>>>>>>>>>>>>> computation, and thus aborts its simulation of its
>>>>>>>>>>>>>>>>>>>>>> input and goes to
>>>>>>>>>>>>>>>>>>>>>> H.Qn, we know that at  H" will go to H".Qn
>>>>>>>>>>>>>>>>>>>>>> When H" goes to H".Qn, it Halts.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> THus we have shown that H" <H"> is non-halting
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Thus we have shown that H <H"> <H"> was wrong.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Thus we HAVE the counter example that you claim
>>>>>>>>>>>>>>>>>>>>>> does not exist.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> H is WRONG about H <H"> <H"> because if H goes to
>>>>>>>>>>>>>>>>>>>>>> H.Qn for this
>>>>>>>>>>>>>>>>>>>>>> input, BY DEFINITION, it means that the simple
>>>>>>>>>>>>>>>>>>>>>> running opf H" applied
>>>>>>>>>>>>>>>>>>>>>> to <H"> must never halt, but we have just shown
>>>>>>>>>>>>>>>>>>>>>> that BECAUSE H <H">
>>>>>>>>>>>>>>>>>>>>>> <H"> goes to H.Qn, that H"<H"> will also go to
>>>>>>>>>>>>>>>>>>>>>> H".Qn and Halt, and
>>>>>>>>>>>>>>>>>>>>>> thus H has violated its requirements, and thus is
>>>>>>>>>>>>>>>>>>>>>> not correct.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> FAIL.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> You have just shown that you don't understand
>>>>>>>>>>>>>>>>>>>>>> anything about formal
>>>>>>>>>>>>>>>>>>>>>> logic or how to prove something.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> A claim that because someone hasn't produced a
>>>>>>>>>>>>>>>>>>>>>> counter example means
>>>>>>>>>>>>>>>>>>>>>> your statement must be true is just plain unsond
>>>>>>>>>>>>>>>>>>>>>> logic.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> TTo claim something follows, 'by the meaning of
>>>>>>>>>>>>>>>>>>>>>> the words' and not
>>>>>>>>>>>>>>>>>>>>>> being able to show the actual FORMAL definitions
>>>>>>>>>>>>>>>>>>>>>> being used to make
>>>>>>>>>>>>>>>>>>>>>> that claim, is just unsound logic.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> FORMAL LOGIC doesn't accept crude rhetorical
>>>>>>>>>>>>>>>>>>>>>> arguments, but only
>>>>>>>>>>>>>>>>>>>>>> formal step by step proofs.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> All you have done is PROVED that you don't
>>>>>>>>>>>>>>>>>>>>>> understand what you are
>>>>>>>>>>>>>>>>>>>>>> doing, and you don't understand how to use formal
>>>>>>>>>>>>>>>>>>>>>> logic.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> This is sort of understandable since you have
>>>>>>>>>>>>>>>>>>>>>> revealed that you goal
>>>>>>>>>>>>>>>>>>>>>> is just to try to establish an Epistemological
>>>>>>>>>>>>>>>>>>>>>> statement, which isn't
>>>>>>>>>>>>>>>>>>>>>> even a field of "Formal Logic', but Philosophy, so
>>>>>>>>>>>>>>>>>>>>>> if that is the
>>>>>>>>>>>>>>>>>>>>>> field you are used to talking in, you just don't
>>>>>>>>>>>>>>>>>>>>>> have a background to
>>>>>>>>>>>>>>>>>>>>>> handle Formal Logic, which Computation Theory uses.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> So, you have just FAILED to understand what you
>>>>>>>>>>>>>>>>>>>>>> need to do to show
>>>>>>>>>>>>>>>>>>>>>> something in COmputation Theory, which also shows
>>>>>>>>>>>>>>>>>>>>>> that you don't
>>>>>>>>>>>>>>>>>>>>>> really understand Epistimology, as you clearly
>>>>>>>>>>>>>>>>>>>>>> don't undstand the
>>>>>>>>>>>>>>>>>>>>>> concept of the Knowing of the Truth of
>>>>>>>>>>>>>>>>>>>>>> Propositions, the idea of
>>>>>>>>>>>>>>>>>>>>>> actual 'Facts'.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> FAIL.
>>>>>>>>>>>>>>>>>>>>> Have you really got nothing better to do with your
>>>>>>>>>>>>>>>>>>>>> time?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> According to medical science I have terminal cancer
>>>>>>>>>>>>>>>>>>>> with little time left. I intend my HP proof rebuttal
>>>>>>>>>>>>>>>>>>>> to be my legacy.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Since you already agreed that the pathological
>>>>>>>>>>>>>>>>>>>> self-reference of the halting problem proofs makes
>>>>>>>>>>>>>>>>>>>> these proof illegitimate I have no idea why you
>>>>>>>>>>>>>>>>>>>> would be reversing course now.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Excpe that you HAVEN'T shown the proofs to be
>>>>>>>>>>>>>>>>>>> illegitimate.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Here is Flibble's reply:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Flibble is a well known crank and troll.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You are wasting your time acting as a crank and looking
>>>>>>>>>>>>>>>>> for support
>>>>>>>>>>>>>>>>> from other cranks.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I have boiled the error of the incompleteness theorem
>>>>>>>>>>>>>>>> down to a single simple sentence. Try and find a single
>>>>>>>>>>>>>>>> error of substance in my paper:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Even a bot can be a mere naysayer it doesn't even take a
>>>>>>>>>>>>>>>> moron.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Your logic is incorrect because you assume your
>>>>>>>>>>>>>>> conclusion as a premise.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You use the WRONG definition of Truth, and assume that
>>>>>>>>>>>>>>> Truth can only be something that is proven, and then from
>>>>>>>>>>>>>>> that try to prove that Truth is only something that csn
>>>>>>>>>>>>>>> be proven.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> This is incorrect, and thus your whole arguement is invalid.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> For example, in mathematics, there are a number of
>>>>>>>>>>>>>>> statements that must either be True of False, there is no
>>>>>>>>>>>>>>> possible middle ground, but these statements have not
>>>>>>>>>>>>>>> been shown to be provable or disprovable. An example of
>>>>>>>>>>>>>>> this is the 3x+1 problem.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Every expression of language does not count as true until
>>>>>>>>>>>>>> after it has been proven. There are only two ways to
>>>>>>>>>>>>>> determine if an analytical expression of language is true.
>>>>>>>>>>>>>> It is an axiom that assigned the value of Boolean true. It
>>>>>>>>>>>>>> is derived by sound deduction that is ultimately anchored
>>>>>>>>>>>>>> in axioms.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Can you PROVE that statement? or is this just a axiom you
>>>>>>>>>>>>> need to assume.
>>>>>>>>>>>>
>>>>>>>>>>>> Analytical expressions of language are verified to be true
>>>>>>>>>>>> entirely on the basis of their meaning.
>>>>>>>>>>>
>>>>>>>>>>> WRONG. Formal;
>>>>>>>>>> That is a stipulated definition just like a "given" in geometry.
>>>>>>>>>> In these cases all disagreement is simply incorrect.
>>>>>>>>>>
>>>>>>>>>> If I say that a cat is an animal and you disagree and say that
>>>>>>>>>> a cat is the windows of an office building you are simply wrong.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Except that you can't 'stipulate' a definition for something
>>>>>>>>> already defined in the system, especially to something wrong.
>>>>>>>>> That violates the rules of Formal Logic.
>>>>>>>> (1) That is already what analytical truth means:
>>>>>>>> "Analytic propositions are true or not true solely by virtue of
>>>>>>>> their meaning"
>>>>>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>>>>>
>>>>>>>
>>>>>>> Which is a definition in PHILOSOPHY, not FORMAL LOGIC.
>>>>>> logic is a branch of philosophy
>>>>>>
>>>>>> https://www.theedadvocate.org/need-know-education-understanding-4-main-branches-philosophy/#:~:text=The%20four%20main%20branches%20of%20philosophy%20are,epistemology%2C%20axiology%2C%20and%20logic.
>>>>>>
>>>>>>
>>>>>
>>>>> But is a different branch than your Epistemology with different
>>>>> rules. Formal Logic, which mathematics uses defines things
>>>>> differently than what you want to use.
>>>>
>>>> Yes and when formal logic diverges from applying truth preserving
>>>> operations to premises that are known to be true (sound deductive
>>>> inference) on the basis of the semantic relevance that is maintained
>>>> in the syllogism:
>>>>
>>>> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>> then formal logic errs and diverges from truth.
>>>>
>>>> Logical entailment does not require premises to be true yet still
>>>> requires true preserving operations to be applied on the basis of
>>>> semantic relevance.
>>>> Which just says that YOU don't agree with what the whole world
>>>> agrees is
>>> the truth.
>>>
>>> Find, you are on your own.
>>>
>>
>> Things an ignoramus would say:
>>> YOU have shown yourself to be incapable of understanding the basic
>>> principles of Formal Logic, and are thus unqualified to discuss it.
>> When everything that you learn you learn by only rote understanding
>> cannot possibly get any more shallow.
>>
>> I am discussing the philosophical underpinnings upon which correct
>> reasoning is based.
>>
>
> Then you are doing it at the wrong place.
>
> If you disagree with the fundamental logic underpinnings of all of
> Formal Logic, you don't start in a peripheral field. That is useless.
>

Philosophical foundationalism is the ultimate basis and ground-of-being
of correct reasoning and logic, thus 100% directly opposite of
peripheral. It cannot possibly be any less peripheral.

The reason that Gödel's 1931 Incompleteness is incorrect is that true
and unprovable cannot possibly co-occur because analytical true always
requires a connected set of true statements, which is its proof.

Try and find any analytical expression of language that it known with
100% logical certainty to be true that has no proof that it is true.

That is like trying to find a cat that is 100% dog.

> You need to either talk in the epistemological groups to get them to
> just reject out of hand that the Formal Logic systems are valid and that
> they just need to ignore everything that comes out of it (good luck) or
> you find a group on fundamental Formal Logic and discuss your issues there.
>
> At the level of Computation Theory, there CAN'T be a change in definiton
> of 'Truth', except as it trickles up, as Field is based on so much that
> derives from more fundamental fields, which would need to work on
> changing first.
>
> You are basically being the guy looking under the street lamp for your
> keys, and when someone asks you where you dropped them you point to the
> other side of the lot where it is dark, but explain that you are looking
> here because there is light.
>
> I will warn you, that from what I am seeing, for you to go into those
> areas you will need to be prepared to fight a Battle of Wits, even
> though it seems you are unarmed.
>
>
>

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

SubjectRepliesAuthor
o Concise refutation of halting problem proofs V62 [ Linz Proof ]

By: olcott on Sun, 6 Feb 2022

57olcott
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