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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Thu, 3 Apr 2025 07:10:15 -0400
Organization: i2pn2 (i2pn.org)
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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.

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.