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

On 2025-02-22 17:24:59 +0000, olcott said:

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

On 2025-02-21 23:22:23 +0000, olcott said:
 

On 2/20/2025 3:01 AM, Mikko wrote:

On 2025-02-18 13:50:22 +0000, olcott said:
 

There is nothing like that in the following concrete example:
LP := ~True(LP)
 In other words you are saying the Prolog is incorrect
to reject the Liar Paradox.
 Above translated to Prolog
 ?- LP = not(true(LP)).
LP = not(true(LP)).

 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.
 

?- unify_with_occurs_check(LP, not(true(LP))).
false

 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.
 

 It does not mean that. You are wrong.

 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.
 

 IT CANNOT POSSIBLY BE SEMANTICALLY VALID

Of course it is. Its semantics is well defined by the Prolog standard.
Whether you like that semantics or not is irrelevant.
--
Mikko