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

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:
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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.

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No. You are just going off on a Red Herring.
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Show where your system defeats Godel's proof of the inability to prove consistancy.
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PUT UP OR SHUT UP.
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*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.
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If such a system could possibly have inconsistency
then at least one valid counter-example could
be provided showing this.
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 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