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On 5/28/2024 10:38 PM, Richard Damon wrote:What makes you think that? I understand how Prolog works, and why it only models relatively simple logic systems, because it just can't handle the higher order logical primitives. It can't even handle full first order logic.On 5/28/24 10:39 PM, olcott wrote:The fact that you assert that you know the underlying details ofOn 5/28/2024 9:04 PM, Richard Damon wrote:>On 5/28/24 10:59 AM, olcott wrote:>On 5/28/2024 1:59 AM, Mikko wrote:>On 2024-05-27 14:34:14 +0000, olcott said:>
>?- LP = not(true(LP)).>
LP = not(true(LP)).
>
?- unify_with_occurs_check(LP, not(true(LP))).
false.
>
In other words Prolog has detected a cycle in the directed graph of the
evaluation sequence of the structure of the Liar Paradox. Experts seem
to think that Prolog is taking "not" and "true" as meaningless and is
only evaluating the structure of the expression.
The words "not" and "true" of Prolog are meaningful in some contexts
but not above. The word "true" is meaningful only when it has no arguments.
>
That Prolog construes any expression having the same structure as the
Liar Paradox as having a cycle in the directed graph of its evaluation
sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it must
be rejected.
But Prolog doesn't support powerful enough logic to handle the system like Tarski and Godel are talking about.
>
The fact that Prolog just rejects it shows that.
>
Your ignorance is no excuse.
What ignorance?
>
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
without even glancing at the documentation and write-up in Clocksin and
Mellish seems to be willful ignorance.
Why is it ridiculous?The fact that I understand the limitation of Prolog and what forms of logic it can do, which seems to be beyond your understanding?Utterly Ridiculous (and you probably don't know it).
>
Claiming that Prolog rejects a statement because it doesn't fit its grammer is meaningless for more complicated logics that don't have that same grammer restricition.
>
IF you want to limit the logic you use to what Prolog can handle, go ahead, the rest of the world likes its mathematics.
>>>>>>You could try>
?- LP = not(true(LP), true(LP).
>
or
?- LP = not(true(LP), not(true(LP)).
>
The predicate unify_with_occurs_check checks whether the resulting
sructure is acyclic because that is its purpose. Whether a simple
Yes exactly. If I knew that Prolog did this then I would not have
created Minimal Type Theory that does this same thing. That I did
create MTT that does do this same thing makes my understanding much
deeper.
>unification like LP = not(true(LP)) does same is implementation>
dependent as Prolog rules permit but do not require that. In a
typical implementation a simple unification does not check for
cycles.
>
ISO Prolog implementations have the built-in predicate
unify_with_occurs_check/2 for sound unification
https://en.wikipedia.org/wiki/Occurs_check#Sound_unification
>
Alternatively such expressions crash or remain stuck in infinite loops.
>
>Anyway, none of this is relevant to the topic of this thread or>
topics of sci.logic.
>
...14 Every epistemological antinomy can likewise be used for
a similar undecidability proof...(Gödel 1931:40)
>
Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
>
https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
>
It would
then be possible to reconstruct the *antinomy of the liar* in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
>
CONCEPT OF TRUTH IN FORMALIZED LANGUAGES, Tarski
https://liarparadox.org/Tarski_247_248.pdf
>
The Liar Paradox and other such {epistemological antinomies} must be
rejected as type mismatch errors for any system of bivalent logic thus
cannot be correctly used for any undecidability or undefinability proof.
>
But you just don't don't understand what was done in those proofs.
>
Neither of them assumed the Liar's paradox had a truth value. Only statements formed from VALID logical sequences in the field.
>
Please try to show what step in Godel's or Tarski's proof where they made a logical error (not just came up with a statement you think can't be valid).
>
Tarski's Liar Paradox from page 248
It would then be possible to reconstruct the antinomy of the liar
in the metalanguage, by forming in the language itself a sentence
x such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
Right, He has SHOWN that the logic system, when given the assumption of the existance of the Truth Predicate, can construct the liar as a truth-bearing statement.
>
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