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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 18:53:53 -0500
Organization: i2pn2 (i2pn.org)
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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.

The fact that something is satisfied by NO numbers, mightg require 
testing EVERY number, which might make it true, but since we CAN'T test 
ourselves physically test every number, it isn't knowable.

This is your fundamental error, that you don't see the difference 
between something becoming Truth and it being able to be known.