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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Sat, 9 Nov 2024 17:17:26 -0600
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On 11/9/2024 4:35 PM, joes wrote:
> Am Sat, 09 Nov 2024 13:00:22 -0600 schrieb olcott:
>> On 11/9/2024 12:47 PM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 11/9/2024 11:58 AM, Alan Mackenzie wrote:
>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>> On 11/9/2024 10:03 AM, Alan Mackenzie wrote:
>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 11/9/2024 5:01 AM, joes wrote:
>>>>>>>>>>>>>>>>> On 11/8/24 12:25 PM, olcott wrote:
>>>
>>>>>>>>>>>>>>>>>> That formal systems that only apply truth preserving
>>>>>>>>>>>>>>>>>> operations to expressions of their formal language that
>>>>>>>>>>>>>>>>>> have been stipulated to be true cannot possibly be
>>>>>>>>>>>>>>>>>> undecidable is proven to be over-your-head on the basis
>>>>>>>>>>>>>>>>>> that you have no actual reasoning as a rebuttal.
>>>>>>>>> Gödel showed otherwise.
>>>>>>>> That is counter-factual within my precise specification.
>>>>>>> That's untrue - you don't have a precise specification.  And even
>>>>>>> if you did, Gödel's theorem would still hold.
>>>>>>>> When truth is only derived by starting with truth and applying
>>>>>>>> truth preserving operations then unprovable in PA becomes untrue
>>>>>>>> in PA.
>>>>>>> No.  Unprovable will remain.
>>>>>> *Like I said you don't pay f-cking attention*
>>>>> Stop swearing.  I don't pay much attention to your provably false
>>>>> utterances, no.  Life is too short.
>>>> That you denigrate what I say without paying attention to what I say
>>>> <is> the definition of reckless disregard for the truth that loses
>>>> defamation cases.
>>> Not at all.  I denigrate your lies, where by lies I mean the emphatic
>>> utterances of falsehood due to a lack of expertise in the subject
>>> matter.
>>> See the beginning of this subthread.
>> You are not doing that. I am redefining the foundation of the notion of
>> a formal system and calling this a lie can have your house confiscated
>> for defamation.
> 
> Go on, sue him, liar.
> 
>>> You are the one with reckless disregard for the truth.  You haven't
>>> even bothered to read the introductory texts which would help you
>>> understand what the truth is.
>>> I have no fear of you starting a defamation case against me.  For a
>>> start, you'd have to learn some German, and for another thing, I'd win
>>> on the merits.
>>>
>>>>> Hint: Gödel's theorem applies in any sufficiently powerful logical
>>>>> system, and the bar for "sufficiently powerful" is not high.
>>>> Unless it is stipulated at the foundation of the notion of formal
>>>> systems that ~Provable(PA, g) simply means ~True(PA, g).
> 
> That doesn’t make ~g provable.
> 
>>> If you're going to redefine the word provable to mean something else,
>>> you'll need some other word to mean what provable means to everybody
>>> else.
>> I am correcting the somewhat ill-founded notion of provable to only mean
>> applying truth preserving operations to finite string expressions of
>> language.
> 
> What else do you think it meant?
> 

https://en.wikipedia.org/wiki/Principle_of_explosion
Does not apply any truth preserving operations to
its premises.

If ~Provable in PA was understood to mean ~True
in PA then Gödel could not exist.


>>>>>> Unprovable(L,x) means Untrue(L,x)
>>>>>> Unprovable(L,~x) means Unfalse(L,x)
>>>>>> ~True(L,x) ^ ~True(L, ~x) means ~Truth-Bearer(L,x)
>>>>> If you're going to change the standard meaning of standard words,
>>>>> you'll find communicating with other people somewhat strained and
>>>>> difficult.
>>>> ZFC did the same thing and that was the ONLY way that Russell's
>>>> Paradox was resolved.
>>> No, they didn't do the same thing.  They stayed within the bounds of
>>> logic.
>> ZFC DID NOT STAY WITHIN THE BOUNDS OF NAIVE SET THEORY
>>
>>>   And yes, they resolved a paradox.  There is no paradox for your
>>> "system" to resolve, even if it were logically coherent.
>>>
>>>> When ~Provable(PA,g) means ~True(PA,g) then incompleteness cannot
>>>> exist.
>>> OK, That's a proof by contradiction that ~provable cannot mean ~true.
>> The assumption that ~Provable(PA, g) does not mean ~True(PA, g) cannot
>> correctly be the basis for any proof because it is only an assumption.

> It’s a very safe assumption, as it keeps both possibilities for the
> truth value of g open.
> 

It directly causes false conclusions by violating
the sound deductive inference model.

It is wasn't for stupid mistakes like this one
Nazi propaganda would have been put down as false
before it had a chance to take root in the USA
and swing the elections.

>>> We know, by Gödel's Theorem that incompleteness does exist.  So the
>>> initial proposition cannot hold, or it is in an inconsistent system.
>> Only on the basis of the assumption that ~Provable(PA, g) does not mean
>> ~True(PA, g)
>> Get rid of that single assumption AND EVERYTHING CHANGES
> 
> 


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer