Re: How a True(X) predicate can be defined for the set of analytic knowledge

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:
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On 4/1/2025 1:33 AM, Mikko wrote:

On 2025-03-31 18:33:26 +0000, olcott said:
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Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.

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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.

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Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).

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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.
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The proof is just another proof that some function is not Turing computable.
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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.
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Think of how many statements can be constructed from a finite alphabet of letters.
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Can you "test" every statement to see if it is consistant?
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Is "LKNSDFKLWRLKLKNKUKQWEEYIYWQFGFGH" consistent or inconsistent?
Try to come up with a better counter-example.

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It depends on what each of those letters mean.
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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