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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 21:57:59 -0500
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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.

> You should know better than that, but you don't, because you really are 
> too stupid.
> 

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