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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: Wed, 13 Nov 2024 17:01:50 -0600
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On 11/13/2024 4:45 AM, Mikko wrote:
> On 2024-11-12 23:17:20 +0000, olcott said:
> 
>> On 11/10/2024 2:36 PM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 11/10/2024 1:04 PM, Alan Mackenzie wrote:
>>>
>>> [ .... ]
>>>
>>>>> 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.
>>>
>>> The details are unimportant.  Gödel's theorem is correct.  Your ideas
>>> contradict that theorem.  Therefore your ideas are incorrect.  Again, 
>>> the
>>> precise details are unimportant, and you wouldn't understand them
>>> anyway.  Your ideas are as coherent as 2 + 2 = 5.
>>>
>>
>> Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
> 
> That's correct (although T is usually used instead of L).
> Per this definition the first order group theory and the first order
> Peano arithmetic are incomplete.
> 

Every language that can by any means express self-contradiction
incorrectly shows that its formal system is incomplete.

>> When the above foundational definition ceases to exist then
>> Gödel's proof cannot prove incompleteness.
> 
> I doesn't cease to exist.
> 
> 
It becomes baseless.

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