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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: Fri, 15 Nov 2024 07:05:31 -0500
Organization: i2pn2 (i2pn.org)
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On 11/14/24 9:58 PM, olcott wrote:
> On 11/14/2024 8:42 PM, Richard Damon wrote:
>> 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,
>>
> 
> Logic never has been free to override and supersede how
> truth itself fundamentally works.

Logic DEFINES how "Truth" works in the system.

You don't seem to understand that Formal Logic Systems are really 
independent universes with their own rules.

> 
> Logic confused itself by not breaking things down to
> their barest essence. There is no such thing as any
> analytic expression of language that is true having
> nothing that shows it is true.

Of course there is, that is what a stipulated axiom is.

> 
> If Goldbach conjecture is true then there is some
> finite or infinite sequence of truth preserving
> operations that shows this, otherwise it is not true.
> 

Right, but there may not be a finite sequence to allow that results to 
be proven.

You seem very unclear on the difference between Truth and Knowledge