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computers / comp.theory / Re: To understand the misconception of mathematical incompleteness...

Re: To understand the misconception of mathematical incompleteness...

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https://news.novabbs.org/computers/article-flat.php?id=53178&group=comp.theory#53178

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From: richard@damon-family.org (Richard Damon)
Newsgroups: sci.logic,comp.theory
Subject: Re: To understand the misconception of mathematical incompleteness...
Date: Sun, 4 Feb 2024 18:49:51 -0500
Organization: i2pn2 (i2pn.org)
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 by: Richard Damon - Sun, 4 Feb 2024 23:49 UTC

On 2/4/24 4:01 PM, olcott wrote:
> On 2/4/2024 12:16 PM, Richard Damon wrote:
>> On 2/4/24 1:08 PM, olcott wrote:
>>> On 2/4/2024 11:45 AM, Richard Damon wrote:
>>>> On 2/4/24 9:06 AM, olcott wrote:
>>>>> On 2/4/2024 6:36 AM, Richard Damon wrote:
>>>>>> On 2/3/24 11:36 PM, olcott wrote:
>>>>>>> On 2/3/2024 9:48 PM, Richard Damon wrote:
>>>>>>>> On 2/3/24 10:28 PM, olcott wrote:
>>>>>>>>> On 2/3/2024 8:32 PM, Richard Damon wrote:
>>>>>>>>>> On 2/3/24 9:01 PM, olcott wrote:
>>>>>>>>>>> On 2/3/2024 6:43 PM, Richard Damon wrote:
>>>>>>>>>>>> On 2/3/24 7:34 PM, olcott wrote:
>>>>>>>>>>>>> On 2/3/2024 6:20 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 2/3/24 7:03 PM, olcott wrote:
>>>>>>>>>>>>>>> In order to see exactly where arithmetic truth correctly
>>>>>>>>>>>>>>> plugs into
>>>>>>>>>>>>>>> analytic truth we must first understand that this is true:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> An analytic expression is: Any expression of language
>>>>>>>>>>>>>>> verified as
>>>>>>>>>>>>>>> completely true entirely on the basis of its relation to
>>>>>>>>>>>>>>> other
>>>>>>>>>>>>>>> expressions of language that derive their meaning from truth
>>>>>>>>>>>>>>> conditional semantics. (AKA stipulated truth).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> *Truth-conditional semantics* is an approach to semantics
>>>>>>>>>>>>>>> of natural
>>>>>>>>>>>>>>> language that sees meaning (or at least the meaning of
>>>>>>>>>>>>>>> assertions) as
>>>>>>>>>>>>>>> being the same as, or reducible to, their truth conditions.
>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Truth-conditional_semantics
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> *Analytic truth is*
>>>>>>>>>>>>>>> (a) Expressions stipulated to be true thus giving
>>>>>>>>>>>>>>> semantic meaning to terms. *similar to axioms*
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> (b) Expressions derived by applying truth preserving
>>>>>>>>>>>>>>> finite string
>>>>>>>>>>>>>>> transformations to elements of (a) *similar to proofs
>>>>>>>>>>>>>>> from axioms*
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Note, the ABOVE is NOT from your refernce, and the
>>>>>>>>>>>>>> definition normally used does not include your end note of
>>>>>>>>>>>>>> "similar to proof from axioms", but allows for the
>>>>>>>>>>>>>> application of an INFINITE sequence to establish truth,
>>>>>>>>>>>>>> while proofs require a finite sequences.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Note also, your reference is almost exclusively about why
>>>>>>>>>>>>>> "Truth-Condition Semantics" are not used/valid, so trying
>>>>>>>>>>>>>> to use it to support your position is counter-productive.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This has been pointed out to you many times, and your
>>>>>>>>>>>>>> refusal to learn it just shows your total ignorance and
>>>>>>>>>>>>>> stupidity with regard to logic.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 'True in Russell's system' means, as was said:
>>>>>>>>>>>>>>> proved in Russell's system; and
>>>>>>>>>>>>>>> 'false in Russell's system' means:
>>>>>>>>>>>>>>> the opposite has been proved in Russell's system
>>>>>>>>>>>>>>> https://www.liarparadox.org/Wittgenstein.pdf
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> AKA  True(RS, P) ≡ (RS ⊢ P)
>>>>>>>>>>>>>>> AKA False(RS, P) ≡ (RS ⊢ ¬P)
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Which isn't actually a true statement, and others have
>>>>>>>>>>>>>> show that to be true.
>>>>>>>>>>>>>
>>>>>>>>>>>>> *This <is> what Wittgenstein is saying*
>>>>>>>>>>>>>   True(RS, P) ≡ (RS ⊢ P)
>>>>>>>>>>>>> False(RS, P) ≡ (RS ⊢ ¬P)
>>>>>>>>>>>>
>>>>>>>>>>>> WHICH ISN'T THE DEFINITION OF TRUE in Russel's system.
>>>>>>>>>>>>
>>>>>>>>>>>> So, an ERROR.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I know that Wittgenstein is correct because I came up with
>>>>>>>>>>>>> his same reasoning before I ever herd of him.
>>>>>>>>>>>>
>>>>>>>>>>>> And you are BOTH WRONG.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> *This <is> the generic way that ALL analytical truth really
>>>>>>>>>>>>> works*
>>>>>>>>>>>>> *thus when math and logic diverge from this THEY ARE WRONG*
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Nope, just shows you are a stupid ignroant pathological
>>>>>>>>>>>> lying idiot.
>>>>>>>>>>>
>>>>>>>>>>> *It is really stupid to rely on ad hominem so much*
>>>>>>>>>>
>>>>>>>>>> I don't use ad hominem, and your claim just shows you don't
>>>>>>>>>> know what it means.
>>>>>>>>>>
>>>>>>>>>> ad-hominem would be to say you are wrong because you are
>>>>>>>>>> "stupid" (or some other attribute).
>>>>>>>>>>
>>>>>>>>>> I say you are stupid because you are constistantly WRONG, and
>>>>>>>>>> point out why you are wrong.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> An actual rebuttal requires a valid counter-example.
>>>>>>>>>>
>>>>>>>>>> Which you fail to do.
>>>>>>>>>>
>>>>>>>>>> YOU are the one claiming that the Halting Proof is wrong, and
>>>>>>>>>> claim to do so by claiming to show a counter example.
>>>>>>>>>>
>>>>>>>>>> I point out the errors in your definitions, That dosn't need a
>>>>>>>>>> counter-example.
>>>>>>>>>>
>>>>>>>>>> I show that your counter-example fails to meet the definitions,
>>>>>>>>>>
>>>>>>>>>> The DEFINITION of Halting is based the behavior of the actual
>>>>>>>>>> machine, not some unsound logic based on a partial
>>>>>>>>>> simulation.] That behavior is to reach a final state.
>>>>>>>>>>
>>>>>>>>>> In EVERY case where you propose an H that actually gives an
>>>>>>>>>> answer, I show that the answer it gives is wrong.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> That you and others simply don't believe me is not any
>>>>>>>>>>> sort of valid counter-example.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It isn't "beleive" we PROVE you are using the WRONG
>>>>>>>>>> definitions, by looking at your own words.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Try and find any expression of language that must be true or
>>>>>>>>>>> false
>>>>>>>>>>> that has no sequence of steps infinite or otherwise that derive
>>>>>>>>>>> its truth or falsity.
>>>>>>>>>>
>>>>>>>>>> So, more Strawmen and lies of altering statements.
>>>>>>>>>>
>>>>>>>>>> I NEVER said that something could be true with NO sequence of
>>>>>>>>>> steps, not even infinite.
>>>>>>>>>>
>>>>>>>>>> I have ALWAYS said that Truth is establisheb by a chain,
>>>>>>>>>> either finite or infinite, from the truth makers of the system.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> *That aspect of your reasoning seems superior to most*
>>>>>>>>>
>>>>>>>>> What you don't seem to understand is that some expressions
>>>>>>>>> are unprovable and irrefutable because there is something
>>>>>>>>> wrong with them such as:
>>>>>>>>>
>>>>>>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>>>>>>> similar undecidability proof... (Gödel 1931:43)
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Yes, there are statements which are unprovable or irrefutable
>>>>>>>> because the statement has not truth value. The Liar is one of them.
>>>>>>>>
>>>>>>>> But, you do not understand what Godel did, so your argument
>>>>>>>> there is just invalid.
>>>>>>>>
>>>>>>>
>>>>>>> He does not matter what Gödel did nearly as much that he did not
>>>>>>> understand that epistemological antinomies are erroneous. You
>>>>>>> seem to understand this thus putting you above him.
>>>>>>
>>>>>> Then it doesn't matter what you claim, it is just enough to know
>>>>>> that Truth is Truth and some Truth is unprovbable, so your claim
>>>>>> otherwise is just noise.
>>>>>>
>>>>>> You err when you claim someone is wrong for doing something they
>>>>>> did not to.
>>>>>>
>>>>>> THAT is Libel.
>>>>>>
>>>>>
>>>>> That Gödel did not understand that epistemological antinomies must
>>>>> be rejected as erroneous is factual. This by itself proves that he
>>>>> did not correctly understand undecidability, the key element of
>>>>> his proof.
>>>>>
>>>>
>>>> But he didn't do what you claim, showing that YOU are the stupid and
>>>> ignorant one.
>>>
>>> Whether or not he did or did not do what I claim, he did assert
>>> that he intended to do what I claim.
>>> ...We are therefore confronted with a proposition which asserts its
>>> own unprovability...(Gödel 1931:43-44)
>>
>> Nope.
>>
>> So, you ADMIT you are just making up your claims.
>>
>> Good that you are honest about something
>>
>>>
>>> and proved that he failed to understand that epistemological antinomies
>>> must be rejected as incorrect thus not the basis for any proof.
>>> ...14 Every epistemological antinomy can likewise be used for a
>>> similar undecidability proof...(Gödel 1931:43)
>>>
>>> Gödel did not say I am going to use something in a proof that I
>>> already know cannot correctly be used in a proof. He thought
>>> that he could use it in a proof and HE WAS WRONG.
>>>
>>
>> Nope, YOU are wrong, because you don't understand what he did.
>
> ...14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof...(Gödel 1931:43)
> WRONG !!!
>
> ...14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof...(Gödel 1931:43)
> WRONG !!!
>
> ...14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof...(Gödel 1931:43)
> WRONG !!!
>
> ...14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof...(Gödel 1931:43)
> WRONG !!!
>
> ...14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof...(Gödel 1931:43)
> WRONG !!!
>
>

Which doesn't meen he built the proof of an assumption that the
epistemological antinomy was anything other than an epistemological
antinomy, and thus didn't drive any statement truth from such a statement.

You don't seem to understand the morphological operations he used.

You have admitted that what he did isn't a problem, as you can't find
the spot he actually did what you claim

Thus, you are admitting that you yourself is the liar.

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o To understand the misconception of mathematical incompleteness...

By: olcott on Sun, 4 Feb 2024

26olcott
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