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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Wed, 13 Nov 2024 20:09:18 -0500
Organization: i2pn2 (i2pn.org)
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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.

Until then, you are just a blatering idiot who shows he is a liar by 
ignoring the fundamental definitions of the system he is stuck in.

> 
>>>> As for your attempts to pretend that unprovable statements are the same
>>>> as false statements,
>>> I never said that ~True(L,x) == False(L,x).
>> Neither did Alan claim that you did.
>>
>>> I have been saying the direct opposite of your claim for
>>> years now. False(L, x) == True(L, ~x)
>> Then if G is false, ~G must be true, 
> 
> Is: "What time is it?" false?
> Is: "What time is it?" true?
> If neither true nor false then not a truth bearer.
> 
>> but you want it to also be false.
>> That's a contradiction.
>>
>>>> Mark Twain got it right when he asked "How many legs does a dog have if
>>>> you call a tail a leg?".  To which the answer is "Four: calling a tail
>>>> a leg doesn't make it one.".
> 
>