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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: Thu, 3 Apr 2025 16:44:06 -0500
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On 4/3/2025 6:10 AM, Richard Damon wrote:
> On 4/2/25 11:33 PM, olcott wrote:
>> 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.
>>
> 
> But how do you know that you began with a consistent set of basic facts. 
> That is the question. You just set yourself up with a circular definition.
> 

(a) Test them against each other (finite set)
(b) Test them against each other (finite set in a hierarchy of types)

> You can't just define that a given set of facts are, in fact, consistant.
> 
> Note, that "Consistency" of the facts is only defined through the logic 
> system they create and it being consistent, so you are just showing that 
> if you assume the answer, you should be able to prove it.
> 
> Sorry, you are just showing you fundamentally don't understand what you 
> are talking about.


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