Re: Mathematical incompleteness has always been a misconception --- Tarski

On 2/22/25 12:24 PM, olcott wrote:

On 2/22/2025 3:12 AM, Mikko wrote:

On 2025-02-21 23:22:23 +0000, olcott said:
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On 2/20/2025 3:01 AM, Mikko wrote:

On 2025-02-18 13:50:22 +0000, olcott said:
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There is nothing like that in the following concrete example:
LP := ~True(LP)
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In other words you are saying the Prolog is incorrect
to reject the Liar Paradox.
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Above translated to Prolog
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?- LP = not(true(LP)).
LP = not(true(LP)).

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According to Prolog rules LP = not(true(LP)) is permitted to fail.
If it succeeds the operations using LP may misbehave. A memory
leak is also possible.
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?- unify_with_occurs_check(LP, not(true(LP))).
false

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This merely means that the result of unification would be that LP conains
itself. It could be a selmantically valid result but is not in the scope
of Prolog language.
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It does not mean that. You are wrong.

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It does in the context where it was presented. More generally,
unify_with_occurs_check also fails if the arguments are not
unfiable. But this possibility is already excluded by their
successfull unification.
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 IT CANNOT POSSIBLY BE SEMANTICALLY VALID
YOU ARE 100% COMPLETELY WRONG ABOUT THIS

Sure it is, unless your system can't express the properties of the Natural Numbers.

 prolog spots and rejects expressions that have the
"some kind of infinite structure" Liar Paradox
form of pathological self-reference. See page 3.

And Prologs logic can't express the properties of the Natural Numbers.

 https://www.researchgate.net/ publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
 

I am not going bother to quote Clocksin and Mellish
proving that you are wrong.

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You are right, a quote that does not support your claim
is not a good idea.
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