• Re: This is how I overturn the Tarski Undefinability theorem

    From Richard Damon@21:1/5 to olcott on Sat Aug 31 15:11:13 2024
    On 8/31/24 2:48 PM, olcott wrote:
    *This is how I overturn the Tarski Undefinability theorem*
    An analytic expression of language is any expression of formal or
    natural language that can be proven true or false entirely on the basis
    of a connection to its semantic meaning in this same language.

    This connection must be through a sequence of truth preserving
    operations from expression x of language L to meaning M in L. A lack of
    such connection from x or ~x in L is construed as x is not a truth
    bearer in L.

    Right, so when x in L is defined to be !True(L,x) does such a connetion
    exist?



    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 *SHOWS* that in the system, it is possible to create the
    statement that

    x (in L) is defined to be ~True(L, x)

    PERIOD.

    Try to show where is proof of such a statement is wrong.
    Your problem is you don't understand what Tarski is doing at all, so you
    can't point to a statement that is in error, just that you think the
    answer must be wrong. THAT is not a "refuation", just proof that it is
    likely that the error is in *YOUR* ideas,

    So, if you claim that such a statement x can neither be established or
    refuted in L, then BY THE DEFINITION of the "True" prediciate, that is
    that True is TRUE if the statement is actually true, while FALSE for all
    other cases, either being refutable, or being a non-truth bearer, then
    True(L, x) must be FALSE, but that means that !True(L, x) must be TRUE,
    and thus x *IS* establish as a TRUE statement, derivable from the fact
    that True(L, x) was FALSE, and the definition of negation.

    This means that there exist a statement (x) which is TRUE, but True(L,x)
    is FALSE, and thus the predicate True can not meet its definition.

    This shows that no such predicate can meet that definition.

    Unless you can resolve THAT contradiciton somehow, you have to accept
    the conclusion, or just admit you don't understand how logic works.


    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*

    But that is invalid, as Prolog doesn't support the needed degree of logic.

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

    As Prolog admits here. All you have done here is proven that you don't
    actually understand how logic works.


    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Which is meaningless as Prolog doesn't support the needed level of
    logic, and proves that YOU don't support the needed level of logic, and
    thus your "arguement" is just invalid, and you claims just lies.


    The purpose of this work was to show that algorithmic
    undecidability is a misconception providing more details
    than Wittgenstein's rebuttal of Gödel.

    https://www.liarparadox.org/Wittgenstein.pdf


    Which was a statement taken from unpublished papers, and was apparently
    from before Wittgenstein had even read the actual Godel paper.

    We don't know if Wittgenstein even continued to believe this, with the question, if he did, why did he not publish it?

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  • From Mikko@21:1/5 to olcott on Sun Sep 1 15:52:47 2024
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem*
    An analytic expression of language is any expression of formal or
    natural language that can be proven true or false entirely on the basis
    of a connection to its semantic meaning in this same language.

    This connection must be through a sequence of truth preserving
    operations from expression x of language L to meaning M in L. A lack of
    such connection from x or ~x in L is construed as x is not a truth
    bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct
    response.

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

    To the extend Prolog formalizes anything, that only formalizes
    the condept of self-reference. I does not say anything about
    int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.

    The purpose of this work was to show that algorithmic
    undecidability is a misconception providing more details
    than Wittgenstein's rebuttal of Gödel.

    Which it didn't show.

    https://www.liarparadox.org/Wittgenstein.pdf

    --
    Mikko

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  • From Mikko@21:1/5 to olcott on Mon Sep 2 10:54:06 2024
    On 2024-09-01 13:47:00 +0000, olcott said:

    On 9/1/2024 7:52 AM, Mikko wrote:
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem*
    An analytic expression of language is any expression of formal or
    natural language that can be proven true or false entirely on the basis
    of a connection to its semantic meaning in this same language.

    This connection must be through a sequence of truth preserving
    operations from expression x of language L to meaning M in L. A lack of
    such connection from x or ~x in L is construed as x is not a truth
    bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x
    https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct
    response.

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

    To the extend Prolog formalizes anything, that only formalizes
    the condept of self-reference. I does not say anything about
    int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.


    It may seem that way if you have no idea what
    (a) a directed is
    (b) what cycles in a directed graph are
    (c) What an evaluation sequence is

    More relevanto would be what a "truth-maker" is.
    Anyway, it seems that Prolog does not say anything about
    truth-bearers because Prolog does not say anything about
    truth-bearers.

    If you do know these things then Prolog proved that LP
    has no truth-maker and thus cannot be a truth-bearer.

    Prolog does not prove anythng about truth bearers. Certain kind
    of Prolog programs can be regarded as proofs in a weak formal
    system but that does not include those that end with "false".
    Even then the proof is not a proof about anything, just a
    formal proof.

    The purpose of this work was to show that algorithmic
    undecidability is a misconception providing more details
    than Wittgenstein's rebuttal of Gödel.

    Which it didn't show.

    I showed it to everyone knowing (a)(b)(c)

    No, you did not.

    --
    Mikko

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  • From Mikko@21:1/5 to olcott on Tue Sep 3 13:38:04 2024
    On 2024-09-02 13:01:23 +0000, olcott said:

    On 9/2/2024 2:54 AM, Mikko wrote:
    On 2024-09-01 13:47:00 +0000, olcott said:

    On 9/1/2024 7:52 AM, Mikko wrote:
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem*
    An analytic expression of language is any expression of formal or
    natural language that can be proven true or false entirely on the basis >>>>> of a connection to its semantic meaning in this same language.

    This connection must be through a sequence of truth preserving
    operations from expression x of language L to meaning M in L. A lack of >>>>> such connection from x or ~x in L is construed as x is not a truth
    bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x
    https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct
    response.

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

    To the extend Prolog formalizes anything, that only formalizes
    the condept of self-reference. I does not say anything about
    int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.


    It may seem that way if you have no idea what
    (a) a directed is
    (b) what cycles in a directed graph are
    (c) What an evaluation sequence is

    More relevanto would be what a "truth-maker" is.
    Anyway, it seems that Prolog does not say anything about
    truth-bearers because Prolog does not say anything about
    truth-bearers.


    When Prolog derives expression x from Facts and Rules
    by applying the truth preserving operations of Rules to
    Facts is the truthmaker for truth-bearer x.

    A Prolog impementation applies Prolog operations. For some cases
    Prolog offers several operations letting the implementation to
    choose which one to apply. Consequently some goals may evaluate
    to true in some implementations and false in others, for example

    L = [L].

    --
    Mikko

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  • From Richard Damon@21:1/5 to olcott on Tue Sep 3 22:28:07 2024
    On 9/3/24 8:44 AM, olcott wrote:
    On 9/3/2024 5:38 AM, Mikko wrote:
    On 2024-09-02 13:01:23 +0000, olcott said:

    On 9/2/2024 2:54 AM, Mikko wrote:
    On 2024-09-01 13:47:00 +0000, olcott said:

    On 9/1/2024 7:52 AM, Mikko wrote:
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem*
    An analytic expression of language is any expression of formal or >>>>>>> natural language that can be proven true or false entirely on the >>>>>>> basis of a connection to its semantic meaning in this same language. >>>>>>>
    This connection must be through a sequence of truth preserving
    operations from expression x of language L to meaning M in L. A
    lack of such connection from x or ~x in L is construed as x is
    not a truth bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x
    https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct
    response.

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

    To the extend Prolog formalizes anything, that only formalizes
    the condept of self-reference. I does not say anything about
    int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.


    It may seem that way if you have no idea what
    (a) a directed is
    (b) what cycles in a directed graph are
    (c) What an evaluation sequence is

    More relevanto would be what a "truth-maker" is.
    Anyway, it seems that Prolog does not say anything about
    truth-bearers because Prolog does not say anything about
    truth-bearers.


    When Prolog derives expression x from Facts and Rules
    by applying the truth preserving operations of Rules to
    Facts is the truthmaker for truth-bearer x.

    A Prolog impementation applies Prolog operations.

    Which are (like logic) for the most part truth preserving.
    If (A & B) then A

    But Prolog can not express ALL logical statement.


    For some cases
    Prolog offers several operations letting the implementation to
    choose which one to apply.

    I don't thing so. Once the Facts and Rules are specified
    Prolog chooses whatever Facts and Rules to prove x or not.
    It is back-chained inference.

    But the set of Prolog operations are limited compared to logic.


    Consequently some goals may evaluate
    to true in some implementations and false in others, for example

      L = [L].




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  • From Mikko@21:1/5 to olcott on Fri Sep 6 14:55:29 2024
    On 2024-09-03 12:44:00 +0000, olcott said:

    On 9/3/2024 5:38 AM, Mikko wrote:
    On 2024-09-02 13:01:23 +0000, olcott said:

    On 9/2/2024 2:54 AM, Mikko wrote:
    On 2024-09-01 13:47:00 +0000, olcott said:

    On 9/1/2024 7:52 AM, Mikko wrote:
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem*
    An analytic expression of language is any expression of formal or >>>>>>> natural language that can be proven true or false entirely on the basis >>>>>>> of a connection to its semantic meaning in this same language.

    This connection must be through a sequence of truth preserving
    operations from expression x of language L to meaning M in L. A lack of >>>>>>> such connection from x or ~x in L is construed as x is not a truth >>>>>>> bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x
    https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct
    response.

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

    To the extend Prolog formalizes anything, that only formalizes
    the condept of self-reference. I does not say anything about
    int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.


    It may seem that way if you have no idea what
    (a) a directed is
    (b) what cycles in a directed graph are
    (c) What an evaluation sequence is

    More relevanto would be what a "truth-maker" is.
    Anyway, it seems that Prolog does not say anything about
    truth-bearers because Prolog does not say anything about
    truth-bearers.


    When Prolog derives expression x from Facts and Rules
    by applying the truth preserving operations of Rules to
    Facts is the truthmaker for truth-bearer x.

    A Prolog impementation applies Prolog operations.

    Which are (like logic) for the most part truth preserving.
    If (A & B) then A

    Logic where the infoerence rules are for the most part truth prserving
    is not useful. They all must be.

    For some cases
    Prolog offers several operations letting the implementation to
    choose which one to apply.

    I don't thing so. Once the Facts and Rules are specified
    Prolog chooses whatever Facts and Rules to prove x or not.
    It is back-chained inference.

    Standard Prolog is what the Prolog standard says. Conforming implementations may vary if the standard allows. If you think otherwise you are wrong.
    There are also non-starndard Prlongs that vary even more.

    Consequently some goals may evaluate
    to true in some implementations and false in others, for example

     L = [L].

    No matter what you think this is an example. It is outside of the intended application area but not prohibited.

    --
    Mikko

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  • From Mikko@21:1/5 to olcott on Sat Sep 7 11:35:00 2024
    On 2024-09-06 12:22:04 +0000, olcott said:

    On 9/6/2024 6:55 AM, Mikko wrote:
    On 2024-09-03 12:44:00 +0000, olcott said:

    On 9/3/2024 5:38 AM, Mikko wrote:
    On 2024-09-02 13:01:23 +0000, olcott said:

    On 9/2/2024 2:54 AM, Mikko wrote:
    On 2024-09-01 13:47:00 +0000, olcott said:

    On 9/1/2024 7:52 AM, Mikko wrote:
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem*
    An analytic expression of language is any expression of formal or >>>>>>>>> natural language that can be proven true or false entirely on the basis
    of a connection to its semantic meaning in this same language. >>>>>>>>>
    This connection must be through a sequence of truth preserving >>>>>>>>> operations from expression x of language L to meaning M in L. A lack of
    such connection from x or ~x in L is construed as x is not a truth >>>>>>>>> bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x
    https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct
    response.

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

    To the extend Prolog formalizes anything, that only formalizes >>>>>>>> the condept of self-reference. I does not say anything about
    int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.


    It may seem that way if you have no idea what
    (a) a directed is
    (b) what cycles in a directed graph are
    (c) What an evaluation sequence is

    More relevanto would be what a "truth-maker" is.
    Anyway, it seems that Prolog does not say anything about
    truth-bearers because Prolog does not say anything about
    truth-bearers.


    When Prolog derives expression x from Facts and Rules
    by applying the truth preserving operations of Rules to
    Facts is the truthmaker for truth-bearer x.

    A Prolog impementation applies Prolog operations.

    Which are (like logic) for the most part truth preserving.
    If (A & B) then A

    Logic where the infoerence rules are for the most part truth prserving
    is not useful. They all must be.

    For some cases
    Prolog offers several operations letting the implementation to
    choose which one to apply.

    I don't thing so. Once the Facts and Rules are specified
    Prolog chooses whatever Facts and Rules to prove x or not.
    It is back-chained inference.

    Standard Prolog is what the Prolog standard says. Conforming implementations >> may vary if the standard allows. If you think otherwise you are wrong.
    There are also non-starndard Prlongs that vary even more.


    The fundamental architectural overview of all Prolog implementations
    is the same True(x) means X is derived by applying Rules (AKA truth preserving operations) to Facts.

    The details are permitted to differ.

    --
    Mikko

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  • From Richard Damon@21:1/5 to olcott on Sat Sep 7 09:19:10 2024
    On 9/7/24 9:06 AM, olcott wrote:
    On 9/7/2024 3:35 AM, Mikko wrote:
    On 2024-09-06 12:22:04 +0000, olcott said:

    On 9/6/2024 6:55 AM, Mikko wrote:
    On 2024-09-03 12:44:00 +0000, olcott said:

    On 9/3/2024 5:38 AM, Mikko wrote:
    On 2024-09-02 13:01:23 +0000, olcott said:

    On 9/2/2024 2:54 AM, Mikko wrote:
    On 2024-09-01 13:47:00 +0000, olcott said:

    On 9/1/2024 7:52 AM, Mikko wrote:
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem* >>>>>>>>>>> An analytic expression of language is any expression of
    formal or natural language that can be proven true or false >>>>>>>>>>> entirely on the basis of a connection to its semantic meaning >>>>>>>>>>> in this same language.

    This connection must be through a sequence of truth
    preserving operations from expression x of language L to >>>>>>>>>>> meaning M in L. A lack of such connection from x or ~x in L >>>>>>>>>>> is construed as x is not a truth bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x
    https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct >>>>>>>>>> response.

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

    To the extend Prolog formalizes anything, that only formalizes >>>>>>>>>> the condept of self-reference. I does not say anything about >>>>>>>>>> int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.


    It may seem that way if you have no idea what
    (a) a directed is
    (b) what cycles in a directed graph are
    (c) What an evaluation sequence is

    More relevanto would be what a "truth-maker" is.
    Anyway, it seems that Prolog does not say anything about
    truth-bearers because Prolog does not say anything about
    truth-bearers.


    When Prolog derives expression x from Facts and Rules
    by applying the truth preserving operations of Rules to
    Facts is the truthmaker for truth-bearer x.

    A Prolog impementation applies Prolog operations.

    Which are (like logic) for the most part truth preserving.
    If (A & B) then A

    Logic where the infoerence rules are for the most part truth prserving >>>> is not useful. They all must be.

    For some cases
    Prolog offers several operations letting the implementation to
    choose which one to apply.

    I don't thing so. Once the Facts and Rules are specified
    Prolog chooses whatever Facts and Rules to prove x or not.
    It is back-chained inference.

    Standard Prolog is what the Prolog standard says. Conforming
    implementations
    may vary if the standard allows. If you think otherwise you are wrong. >>>> There are also non-starndard Prlongs that vary even more.


    The fundamental architectural overview of all Prolog implementations
    is the same True(x) means X is derived by applying Rules (AKA truth
    preserving operations) to Facts.

    The details are permitted to differ.


    Instead of using any single order of logic we simultaneously
    represent an arbitrary number of orders of logic in a type
    hierarchy knowledge ontology.


    Doesn't work, and just shows that you don't understand what you are
    talking about.

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  • From Mikko@21:1/5 to olcott on Sun Sep 8 11:45:42 2024
    On 2024-09-07 13:06:52 +0000, olcott said:

    On 9/7/2024 3:35 AM, Mikko wrote:
    On 2024-09-06 12:22:04 +0000, olcott said:

    On 9/6/2024 6:55 AM, Mikko wrote:
    On 2024-09-03 12:44:00 +0000, olcott said:

    On 9/3/2024 5:38 AM, Mikko wrote:
    On 2024-09-02 13:01:23 +0000, olcott said:

    On 9/2/2024 2:54 AM, Mikko wrote:
    On 2024-09-01 13:47:00 +0000, olcott said:

    On 9/1/2024 7:52 AM, Mikko wrote:
    On 2024-08-31 18:48:18 +0000, olcott said:

    *This is how I overturn the Tarski Undefinability theorem* >>>>>>>>>>> An analytic expression of language is any expression of formal or >>>>>>>>>>> natural language that can be proven true or false entirely on the basis
    of a connection to its semantic meaning in this same language. >>>>>>>>>>>
    This connection must be through a sequence of truth preserving >>>>>>>>>>> operations from expression x of language L to meaning M in L. A lack of
    such connection from x or ~x in L is construed as x is not a truth >>>>>>>>>>> bearer in L.

    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

    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x
    https://liarparadox.org/Tarski_275_276.pdf

    *Formalized as Prolog*
    ?- LP = not(true(LP)).
    LP = not(true(LP)).

    According to Prolog semantics "false" would also be a correct >>>>>>>>>> response.

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

    To the extend Prolog formalizes anything, that only formalizes >>>>>>>>>> the condept of self-reference. I does not say anything about >>>>>>>>>> int.

    When formalized as Prolog unify_with_occurs_check()
    detects a cycle in the directed graph of the evaluation
    sequence proving the LP is not a truth bearer.

    Prolog does not say anything about truth-bearers.


    It may seem that way if you have no idea what
    (a) a directed is
    (b) what cycles in a directed graph are
    (c) What an evaluation sequence is

    More relevanto would be what a "truth-maker" is.
    Anyway, it seems that Prolog does not say anything about
    truth-bearers because Prolog does not say anything about
    truth-bearers.


    When Prolog derives expression x from Facts and Rules
    by applying the truth preserving operations of Rules to
    Facts is the truthmaker for truth-bearer x.

    A Prolog impementation applies Prolog operations.

    Which are (like logic) for the most part truth preserving.
    If (A & B) then A

    Logic where the infoerence rules are for the most part truth prserving >>>> is not useful. They all must be.

    For some cases
    Prolog offers several operations letting the implementation to
    choose which one to apply.

    I don't thing so. Once the Facts and Rules are specified
    Prolog chooses whatever Facts and Rules to prove x or not.
    It is back-chained inference.

    Standard Prolog is what the Prolog standard says. Conforming implementations
    may vary if the standard allows. If you think otherwise you are wrong. >>>> There are also non-starndard Prlongs that vary even more.


    The fundamental architectural overview of all Prolog implementations
    is the same True(x) means X is derived by applying Rules (AKA truth
    preserving operations) to Facts.

    The details are permitted to differ.


    Instead of using any single order of logic we simultaneously
    represent an arbitrary number of orders of logic in a type
    hierarchy knowledge ontology.

    The type system of Prolog is different.

    --
    Mikko

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  • From Mikko@21:1/5 to olcott on Sun Sep 8 17:31:23 2024
    On 2024-09-08 12:44:56 +0000, olcott said:

    On 9/8/2024 3:45 AM, Mikko wrote:
    On 2024-09-07 13:06:52 +0000, olcott said:

    On 9/7/2024 3:35 AM, Mikko wrote:
    On 2024-09-06 12:22:04 +0000, olcott said:

    The fundamental architectural overview of all Prolog implementations >>>>> is the same True(x) means X is derived by applying Rules (AKA truth
    preserving operations) to Facts.

    The details are permitted to differ.


    Instead of using any single order of logic we simultaneously
    represent an arbitrary number of orders of logic in a type
    hierarchy knowledge ontology.

    The type system of Prolog is different.


    Yes I know that. The architecture of Prolog is used
    the implementation details are scrapped.

    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false. // LP is rejected as cyclic

    Even with Prolog just the way it is it is not as stupid
    as Tarski's system that doesn't know to reject the Liar
    Paradox.

    https://liarparadox.org/Tarski_247_248.pdf

    Most Prolog implementations don't reject L = not(ture(LP)).

    --
    Mikko

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  • From Mikko@21:1/5 to olcott on Mon Sep 9 12:05:06 2024
    On 2024-09-08 14:38:51 +0000, olcott said:

    On 9/8/2024 9:31 AM, Mikko wrote:
    On 2024-09-08 12:44:56 +0000, olcott said:

    On 9/8/2024 3:45 AM, Mikko wrote:
    On 2024-09-07 13:06:52 +0000, olcott said:

    On 9/7/2024 3:35 AM, Mikko wrote:
    On 2024-09-06 12:22:04 +0000, olcott said:

    The fundamental architectural overview of all Prolog implementations >>>>>>> is the same True(x) means X is derived by applying Rules (AKA truth >>>>>>> preserving operations) to Facts.

    The details are permitted to differ.


    Instead of using any single order of logic we simultaneously
    represent an arbitrary number of orders of logic in a type
    hierarchy knowledge ontology.

    The type system of Prolog is different.


    Yes I know that. The architecture of Prolog is used
    the implementation details are scrapped.

    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false. // LP is rejected as cyclic

    Even with Prolog just the way it is it is not as stupid
    as Tarski's system that doesn't know to reject the Liar
    Paradox.

    https://liarparadox.org/Tarski_247_248.pdf

    Most Prolog implementations don't reject L = not(ture(LP)).


    ?- unify_with_occurs_check(LP, not(true(LP))).
    Prolog just gets stuck in an infinite loop
    when a cyclic term is unified.

    You can ask "unify_with_occurs_check(LP, not(true(LP)))" but you
    needn't. If you don't ask it doen't reject. You can say that
    "LP = not(true(LP))" and most Prolog implementations simply
    assign not(true(LP) to LP. Whether your program gets stuck in
    an infinite loop depends on what you try to do with LP.

    --
    Mikko

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  • From Mikko@21:1/5 to olcott on Tue Sep 10 12:12:48 2024
    On 2024-09-09 13:12:13 +0000, olcott said:

    On 9/9/2024 4:05 AM, Mikko wrote:
    On 2024-09-08 14:38:51 +0000, olcott said:

    On 9/8/2024 9:31 AM, Mikko wrote:
    On 2024-09-08 12:44:56 +0000, olcott said:

    On 9/8/2024 3:45 AM, Mikko wrote:
    On 2024-09-07 13:06:52 +0000, olcott said:

    On 9/7/2024 3:35 AM, Mikko wrote:
    On 2024-09-06 12:22:04 +0000, olcott said:

    The fundamental architectural overview of all Prolog implementations >>>>>>>>> is the same True(x) means X is derived by applying Rules (AKA truth >>>>>>>>> preserving operations) to Facts.

    The details are permitted to differ.


    Instead of using any single order of logic we simultaneously
    represent an arbitrary number of orders of logic in a type
    hierarchy knowledge ontology.

    The type system of Prolog is different.


    Yes I know that. The architecture of Prolog is used
    the implementation details are scrapped.

    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false. // LP is rejected as cyclic

    Even with Prolog just the way it is it is not as stupid
    as Tarski's system that doesn't know to reject the Liar
    Paradox.

    https://liarparadox.org/Tarski_247_248.pdf

    Most Prolog implementations don't reject L = not(ture(LP)).


    ?- unify_with_occurs_check(LP, not(true(LP))).
    Prolog just gets stuck in an infinite loop
    when a cyclic term is unified.

    You can ask "unify_with_occurs_check(LP, not(true(LP)))" but you
    needn't. If you don't ask it doen't reject.

    It gets stuck in an infinite loop.

    You can say that
    "LP = not(true(LP))" and most Prolog implementations simply
    assign not(true(LP) to LP. Whether your program gets stuck in
    an infinite loop depends on what you try to do with LP.


    ?- LP. % Gets stuck in an infinite loop

    As I already said, some operations with LP get stuck in an infinite loop.
    That does not prevent the use of LP in other operations. For example,
    LP = not(LP) does not get stuck but simply evaluates to false.

    --
    Mikko

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  • From Richard Damon@21:1/5 to olcott on Tue Sep 10 21:37:01 2024
    On 9/10/24 9:10 AM, olcott wrote:
    On 9/10/2024 4:12 AM, Mikko wrote:
    On 2024-09-09 13:12:13 +0000, olcott said:

    On 9/9/2024 4:05 AM, Mikko wrote:
    On 2024-09-08 14:38:51 +0000, olcott said:

    On 9/8/2024 9:31 AM, Mikko wrote:
    On 2024-09-08 12:44:56 +0000, olcott said:

    On 9/8/2024 3:45 AM, Mikko wrote:
    On 2024-09-07 13:06:52 +0000, olcott said:

    On 9/7/2024 3:35 AM, Mikko wrote:
    On 2024-09-06 12:22:04 +0000, olcott said:

    The fundamental architectural overview of all Prolog
    implementations
    is the same True(x) means X is derived by applying Rules (AKA >>>>>>>>>>> truth preserving operations) to Facts.

    The details are permitted to differ.


    Instead of using any single order of logic we simultaneously >>>>>>>>> represent an arbitrary number of orders of logic in a type
    hierarchy knowledge ontology.

    The type system of Prolog is different.


    Yes I know that. The architecture of Prolog is used
    the implementation details are scrapped.

    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false. // LP is rejected as cyclic

    Even with Prolog just the way it is it is not as stupid
    as Tarski's system that doesn't know to reject the Liar
    Paradox.

    https://liarparadox.org/Tarski_247_248.pdf

    Most Prolog implementations don't reject L = not(ture(LP)).


    ?- unify_with_occurs_check(LP, not(true(LP))).
    Prolog just gets stuck in an infinite loop
    when a cyclic term is unified.

    You can ask "unify_with_occurs_check(LP, not(true(LP)))" but you
    needn't. If you don't ask it doen't reject.

    It gets stuck in an infinite loop.

    You can say that
    "LP = not(true(LP))" and most Prolog implementations simply
    assign not(true(LP) to LP. Whether your program gets stuck in
    an infinite loop depends on what you try to do with LP.


    ?- LP. % Gets stuck in an infinite loop

    As I already said, some operations with LP get stuck in an infinite loop.
    That does not prevent the use of LP in other operations. For example,
    LP = not(LP) does not get stuck but simply evaluates to false.


    LP == "this sentence is not true"
    True(LP)
    "LP is rejected an invalid input"


    Not a valid answer for a predicate.

    Sorry, you are just proving your stupidity.

    If you want to make your own system, DO SO, and do it FULLY, not just
    your half-ass incorrect method of trying to band-aid onto an existing
    system after presuming to pull out the foundation, that just doesn't
    work and shows that you just don't have the skills needed to even try
    what you are claiming to do.

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  • From Mikko@21:1/5 to olcott on Wed Sep 11 10:29:46 2024
    On 2024-09-10 13:10:27 +0000, olcott said:

    On 9/10/2024 4:12 AM, Mikko wrote:
    On 2024-09-09 13:12:13 +0000, olcott said:

    On 9/9/2024 4:05 AM, Mikko wrote:
    On 2024-09-08 14:38:51 +0000, olcott said:

    On 9/8/2024 9:31 AM, Mikko wrote:
    On 2024-09-08 12:44:56 +0000, olcott said:

    On 9/8/2024 3:45 AM, Mikko wrote:
    On 2024-09-07 13:06:52 +0000, olcott said:

    On 9/7/2024 3:35 AM, Mikko wrote:
    On 2024-09-06 12:22:04 +0000, olcott said:

    The fundamental architectural overview of all Prolog implementations
    is the same True(x) means X is derived by applying Rules (AKA truth >>>>>>>>>>> preserving operations) to Facts.

    The details are permitted to differ.


    Instead of using any single order of logic we simultaneously >>>>>>>>> represent an arbitrary number of orders of logic in a type
    hierarchy knowledge ontology.

    The type system of Prolog is different.


    Yes I know that. The architecture of Prolog is used
    the implementation details are scrapped.

    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false. // LP is rejected as cyclic

    Even with Prolog just the way it is it is not as stupid
    as Tarski's system that doesn't know to reject the Liar
    Paradox.

    https://liarparadox.org/Tarski_247_248.pdf

    Most Prolog implementations don't reject L = not(ture(LP)).


    ?- unify_with_occurs_check(LP, not(true(LP))).
    Prolog just gets stuck in an infinite loop
    when a cyclic term is unified.

    You can ask "unify_with_occurs_check(LP, not(true(LP)))" but you
    needn't. If you don't ask it doen't reject.

    It gets stuck in an infinite loop.

    You can say that
    "LP = not(true(LP))" and most Prolog implementations simply
    assign not(true(LP) to LP. Whether your program gets stuck in
    an infinite loop depends on what you try to do with LP.


    ?- LP. % Gets stuck in an infinite loop

    As I already said, some operations with LP get stuck in an infinite loop.
    That does not prevent the use of LP in other operations. For example,
    LP = not(LP) does not get stuck but simply evaluates to false.

    LP == "this sentence is not true"
    True(LP)
    "LP is rejected an invalid input"

    If you can't say anything you needn't babble.

    --
    Mikko

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