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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: Sun, 10 Nov 2024 14:10:37 -0600
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On 11/10/2024 1:04 PM, Alan Mackenzie wrote:
> olcott <polcott333@gmail.com> wrote:
>> On 11/10/2024 10:37 AM, Alan Mackenzie wrote:
>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>> On 11/10/2024 4:03 AM, Alan Mackenzie wrote:
>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>> On 11/9/2024 4:28 PM, Alan Mackenzie wrote:
>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 11/9/2024 3:45 PM, Alan Mackenzie wrote:
> 
>>>>> [ .... ]
> 
>>>>>>>>> Gödel understood mathematical logic full well (indeed, played a
>>>>>>>>> significant part in its development),
> 
>>>>>>>> He utterly failed to understand that his understanding
>>>>>>>> of provable in meta-math cannot mean true in PA unless
>>>>>>>> also provable in PA according to the deductive inference
>>>>>>>> foundation of all logic.
> 
>>>>>>> You're lying in your usual fashion, namely by lack of expertise.  It
>>>>>>> is entirely your lack of understanding.  If Gödel's proof was not
>>>>>>> rigorously correct, his result would have been long discarded.  It
>>>>>>> is correct.
> 
>>>>>> Even if every other detail is 100% correct without
>>>>>> "true and unprovable" (the heart of incompleteness)
>>>>>> it utterly fails to make its incompleteness conclusion.
> 
>>>>> You are, of course, wrong here.  You are too ignorant to make such a
>>>>> judgment.  I believe you've never even read through and verified a proof
>>>>> of Gödel's theorem.
> 
>>>> If you had a basis in reasoning to show that I was wrong
>>>> on this specific point you could provide it.
> 
>>> I have read through and understood a proof of Gödel's theorem, and it was
>>> correct.  Therefore you are wrong in what you assert.  You have never
>>> read such a proof, otherwise you would have said so.  Therefore, on this
>>> matter, you are ignorant, certainly when compared with me.
> 
>>>> You have no basis in reasoning on this specific point all you have is
>>>> presumption.
> 
>>> It is you who is lacking any basis in what you say.  I have already given
>>> my bases for calling out your falsehoods.
> 
>>>>>> Perhaps you simply don't understand it at that level
>>>>>> thus will never have any idea that I proved I am correct.
> 
>>>>> More lies.  You don't even understand what the word "proved" means.
> 
>>>> Here is what Mathworld construes as proof ....
> 
>>> I didn't say you couldn't search the web and find descriptions of what a
>>> proof is.  I said that you, you personally, don't understand those
>>> descriptions.
> 
>>> I would furthermore propose you have never read and understood a
>>> mathematical proof, and I also propose you have never constructed such a
>>> proof yourself.  If I am wrong here, feel free to counter these
>>> propositions.
> 
>>> A thorough understanding of mathematical proof is a prerequisite for
>>> talking meaningfully about things like Gödel's therem.  You lack that
>>> prerequisite, therefore all your false statements about it are lies by
>>> lack of expertise.
> 
>> In other words you can only dodge and thus not address my
>> specific point ....
> 
> I have addressed your point perfectly well.  Gödel's theorem is correct,
> therefore you are wrong.  What part of that don't you understand?

YOU FAIL TO SHOW THE DETAILS OF HOW THIS DOES
NOT GET RID OF INCOMPLETENESS.

When C is a necessary consequence of the Haskell Curry
elementary theorems of L (Thus stipulated to be true in L)
then and only then is C is True in L.
https://www.liarparadox.org/Haskell_Curry_45.pdf

(Haskell_Curry_Elementary_Theorems(L) □ C) ≡ True(L, C)

This simple change does get rid of incompleteness because
Incomplete(L) is superseded and replaced by Incorrect(L,x).

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