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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Wed, 13 Nov 2024 16:33:11 -0000 (UTC)
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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?

>> 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, 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.".
-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.