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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: Thu, 14 Nov 2024 21:42:23 -0500
Organization: i2pn2 (i2pn.org)
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On 11/14/24 9:26 PM, olcott wrote:
> On 11/14/2024 5:53 PM, Richard Damon wrote:
>> On 11/14/24 6:40 PM, olcott wrote:
>>> 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.
>>>
>>>
>>
>> Right, but that truth might not be PROVABLE (by a finite proof that 
>> establishes Knowledge) as Truth is allowed to be established by 
>> infinite chains.
>>
> 
> All of analytic truth is specified as relations between
> expressions of language. When these relations do not exist
> neither does the truth of these expressions.

But in FORMAL LOGIC, that analytic Truth is specified as the axioms of 
the system, and the approved logical operations for the system.

You confuse "Formal Logic" with "Philosophy" due to your ignorance of them.

> 
> I am looking at this on the basis of how truth itself
> actually works. You are looking at this on the basis
> of memorized dogma.
> 

No, because you logic is based on LIES, because you are trying to 
redefine fundamental terms within the system, as opposed to doiing the 
work to make a system the way you want, likely because you are just to 
ignorant to do the work,


Sorry, but you are doing a very good job of showing your utter ignorance 
of the fields that you are trying to talk about.