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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: Thu, 14 Nov 2024 17:40:19 -0600
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On 11/14/2024 2:39 AM, Mikko wrote:
> On 2024-11-13 23:01:50 +0000, olcott said:
> 
>> 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.
> 
> That "incorrectly shows" is non-sense. A language does not show,
> incorrectly or otherwise. A proof shows but not incorrectly. But
> for a proof you need a theory, i.e. more than just a language.
> 
> That a theory can't prove something is usually not provable in the
> theory itself but usually needs be proven in another theory, one
> that can be interpreted as a metatheory.
> 

*So in other words you just don't get it*
When you start with truth and only apply truth preserving
operations then you necessarily end up with truth.


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