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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Wed, 2 Apr 2025 22:33:00 -0500
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On 4/2/2025 10:11 PM, Richard Damon wrote:
> On 4/2/25 10:57 PM, olcott wrote:
>> On 4/2/2025 8:58 PM, Richard Damon wrote:
>>> On 4/2/25 9:33 PM, olcott wrote:
>>>> On 4/2/2025 5:07 PM, Richard Damon wrote:
>>>>> On 4/2/25 12:03 PM, olcott wrote:
>>>>>> On 4/2/2025 4:32 AM, Mikko wrote:
>>>>>>> On 2025-04-01 17:56:25 +0000, olcott said:
>>>>>>>
>>>>>>>> On 4/1/2025 1:33 AM, Mikko wrote:
>>>>>>>>> On 2025-03-31 18:33:26 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Anything the contradicts basic facts or expressions
>>>>>>>>>> semantically entailed from these basic facts is proven
>>>>>>>>>> false.
>>>>>>>>>
>>>>>>>>> Anything that follows from true sentences by a truth preserving
>>>>>>>>> transformations is true. If you can prove that a true sentence
>>>>>>>>> is false your system is unsound.
>>>>>>>>
>>>>>>>> Ah so we finally agree on something.
>>>>>>>> What about the "proof" that detecting inconsistent
>>>>>>>> axioms is impossible? (I thought that I remebered this).
>>>>>>>
>>>>>>> A method that can always determine whether a set of axioms is 
>>>>>>> inconsistent
>>>>>>> does not exist. However, there are methods that can correctly 
>>>>>>> determine
>>>>>>> about some axiom systems that they are inconsistent and fail on 
>>>>>>> others.
>>>>>>>
>>>>>>> The proof is just another proof that some function is not Turing 
>>>>>>> computable.
>>>>>>>
>>>>>>
>>>>>> A finite set of axioms would seem to always be verifiable
>>>>>> as consistent or inconsistent.  This may be the same for
>>>>>> a finite list of axiom schemas.
>>>>>>
>>>>>
>>>>> Think of how many statements can be constructed from a finite 
>>>>> alphabet of letters.
>>>>>
>>>>> Can you "test" every statement to see if it is consistant?
>>>>>
>>>>
>>>> Is "LKNSDFKLWRLKLKNKUKQWEEYIYWQFGFGH" consistent or inconsistent?
>>>> Try to come up with a better counter-example.
>>>
>>> It depends on what each of those letters mean.
>>>
>>
>> So say what they mean to form your counter-example
>> showing that consistency across a finite set of axioms
>> is undecidable. PUT UP OR SHUT UP.
> 
> No. You are just going off on a Red Herring.
> 
> Show where your system defeats Godel's proof of the inability to prove 
> consistancy.
> 
> PUT UP OR SHUT UP.
> 

*I am proved categorically correct*
A system that begins with A consistent set of
basic facts and only derives expressions from
this set by semantic logical entailment cannot
possibly have inconsistency.

If such a system could possibly have inconsistency
then at least one valid counter-example could
be provided showing this.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer