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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct
Date: Thu, 14 Nov 2024 10:52:23 +0200
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On 2024-11-14 01:09:18 +0000, Richard Damon said:

> On 11/13/24 11:50 AM, olcott wrote:
>> On 11/13/2024 10:33 AM, joes wrote:
>>> Am Wed, 13 Nov 2024 09:11:13 -0600 schrieb olcott:
>>>> On 11/13/2024 5:57 AM, Alan Mackenzie wrote:
>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>> 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)) When the above
>>>>>> foundational definition ceases to exist then Gödel's proof cannot
>>>>>> prove incompleteness.
>>> 
>>>>> What on Earth do you mean by a definition "ceasing to exist"?  Do you
>>>>> mean you shut your eyes and pretend you can't see it?
>>>>> Incompleteness exists as a concept, whether you like it or not.
>>>>> Gödel's theorem is proven, whether you like it or not (evidently the
>>>>> latter).
>>>>> 
>>>> When the definition of Incompleteness:
>>>> Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
>>>>     becomes
>>>> ¬TruthBearer(L,x) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
>>>> Then meeting the criteria for incompleteness means something else
>>>> entirely and incompleteness can no longer be proven.
>> 
>>> What does incompleteness mean then?
>>> 
>> 
>> Incompleteness ceases to exist the same way that Russell's
>> Paradox ceases to exist in ZFC.
> 
> Not until your create your logic system like Z & F did to make ZFC.

It wouldn't be that simple. Zermelo and Fraenkel accepted ordinary logic
but Olcott wants to reject that so he would need to start with building
a new logical foundation.

-- 
Mikko