• Re: Rejecting expressions of formal language having pathologicalself-reference

    From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Thu Nov 27 10:20:46 2025
    From Newsgroup: comp.ai.philosophy

    olcott kirjoitti 26.11.2025 klo 17.27:
    On 11/26/2025 4:30 AM, Mikko wrote:
    olcott kirjoitti 14.11.2025 klo 16.42:
    On 11/14/2025 3:01 AM, Mikko wrote:
    On 2025-11-13 16:00:58 +0000, olcott said:

    On 11/13/2025 3:05 AM, Mikko wrote:
    On 2025-11-12 14:45:34 +0000, olcott said:

    Rejecting expressions of formal language
    having pathological self-reference

    Explained how expressions with pathological self
    reference can simply be rejected as semantically/
    syntactically unsound thus preventing undefinability,
    and undecidability.

    This sentence is not true: "This sentence is not true"
    is true only because the inner sentence is semantically
    unsound. The inner sentence is formalized in Minimal
    Type Theory as LP := ~True(LP).
    (where A := B means A is defined as B).

    https://philpapers.org/rec/OLCREO

    Can someone review my actual reasoning
    elaborated in the paper?

    If you want to use the term "formal language" you must prove that
    there is a Turing machine that can determine whether a string is a >>>>>> valid sentence of your language. If no such Turing machine exists
    you have no justifiction for the use of the word "formal".

    Been there done that and provided all the details.

    Where? At least not where the above pointer points to.


    In the paper that you failed to read.
    https://www.researchgate.net/
    publication/397533139_Rejecting_expressions_of_formal_language_having_pathological_self-reference

    In that article there is no proof that there is no proof that there is a
    Turing machine that can determine whether a string is a valid sentence
    of your lanugage. The article does not even mention Turing machine.


    It is all the deep meaning of unify_with_occurs_check()
    that rejects an expression as semantically unsound
    because its evaluation is stuck in an infinite loop.


    The Liar Paradox formalized in the Prolog Programming language

    This sentence is not true.
    It is not true about what?
    It is not true about being not true.
    It is not true about being not true about what?
    It is not true about being not true about being not true.
    Oh I see you are stuck in a loop!

    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Failing an occurs check seems to mean that the resolution of an
    expression remains stuck in an infinite loop. Just as the formalized
    Prolog determines that there is a cycle in the directed graph of the evaluation sequence of LP the simple English proves that the Liar
    Paradox never gets to the point. It has merely been semantically unsound
    all these years.

    All ot that is irrelevant to your lie about where the proof is.
    That you chose to lie about it and then to distract is a strong
    indication that you have no proof but prefer to lie otherwise.
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Thu Nov 27 10:22:40 2025
    From Newsgroup: comp.ai.philosophy

    Tristan Wibberley kirjoitti 26.11.2025 klo 21.46:
    On 26/11/2025 15:27, olcott wrote:
    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Why do you keep posting that?

    In order to distract from the facts he doesn't want to face.
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Chris M. Thomasson@chris.m.thomasson.1@gmail.com to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Thu Nov 27 00:39:24 2025
    From Newsgroup: comp.ai.philosophy

    On 11/27/2025 12:22 AM, Mikko wrote:
    Tristan Wibberley kirjoitti 26.11.2025 klo 21.46:
    On 26/11/2025 15:27, olcott wrote:
    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Why do you keep posting that?

    In order to distract from the facts he doesn't want to face.


    ditto.
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Thu Nov 27 09:49:41 2025
    From Newsgroup: comp.ai.philosophy

    On 11/27/2025 2:20 AM, Mikko wrote:
    olcott kirjoitti 26.11.2025 klo 17.27:
    On 11/26/2025 4:30 AM, Mikko wrote:
    olcott kirjoitti 14.11.2025 klo 16.42:
    On 11/14/2025 3:01 AM, Mikko wrote:
    On 2025-11-13 16:00:58 +0000, olcott said:

    On 11/13/2025 3:05 AM, Mikko wrote:
    On 2025-11-12 14:45:34 +0000, olcott said:

    Rejecting expressions of formal language
    having pathological self-reference

    Explained how expressions with pathological self
    reference can simply be rejected as semantically/
    syntactically unsound thus preventing undefinability,
    and undecidability.

    This sentence is not true: "This sentence is not true"
    is true only because the inner sentence is semantically
    unsound. The inner sentence is formalized in Minimal
    Type Theory as LP := ~True(LP).
    (where A := B means A is defined as B).

    https://philpapers.org/rec/OLCREO

    Can someone review my actual reasoning
    elaborated in the paper?

    If you want to use the term "formal language" you must prove that >>>>>>> there is a Turing machine that can determine whether a string is a >>>>>>> valid sentence of your language. If no such Turing machine exists >>>>>>> you have no justifiction for the use of the word "formal".

    Been there done that and provided all the details.

    Where? At least not where the above pointer points to.


    In the paper that you failed to read.
    https://www.researchgate.net/
    publication/397533139_Rejecting_expressions_of_formal_language_having_pathological_self-reference

    In that article there is no proof that there is no proof that there is a >>> Turing machine that can determine whether a string is a valid sentence
    of your lanugage. The article does not even mention Turing machine.


    It is all the deep meaning of unify_with_occurs_check()
    that rejects an expression as semantically unsound
    because its evaluation is stuck in an infinite loop.


    The Liar Paradox formalized in the Prolog Programming language

    This sentence is not true.
    It is not true about what?
    It is not true about being not true.
    It is not true about being not true about what?
    It is not true about being not true about being not true.
    Oh I see you are stuck in a loop!

    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Failing an occurs check seems to mean that the resolution of an
    expression remains stuck in an infinite loop. Just as the formalized
    Prolog determines that there is a cycle in the directed graph of the
    evaluation sequence of LP the simple English proves that the Liar
    Paradox never gets to the point. It has merely been semantically
    unsound all these years.

    All ot that is irrelevant to your lie about where the proof is.
    That you chose to lie about it and then to distract is a strong
    indication that you have no proof but prefer to lie otherwise.


    Formalized in Olcott's Minimal Type Theory
    LP := ~True(LP) // LP {is defined as} ~True(LP)
    that expands to ~True(~True(~True(~True(~True(~True(...)))))) https://philarchive.org/archive/PETMTT-4v2

    The Liar Paradox fails because its specifies
    infinite recursion.
    --
    Copyright 2025 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning" computable.

    This required establishing a new foundation
    for correct reasoning.
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Thu Nov 27 12:27:11 2025
    From Newsgroup: comp.ai.philosophy

    On 11/27/25 10:49 AM, olcott wrote:
    On 11/27/2025 2:20 AM, Mikko wrote:
    olcott kirjoitti 26.11.2025 klo 17.27:
    On 11/26/2025 4:30 AM, Mikko wrote:
    olcott kirjoitti 14.11.2025 klo 16.42:
    On 11/14/2025 3:01 AM, Mikko wrote:
    On 2025-11-13 16:00:58 +0000, olcott said:

    On 11/13/2025 3:05 AM, Mikko wrote:
    On 2025-11-12 14:45:34 +0000, olcott said:

    Rejecting expressions of formal language
    having pathological self-reference

    Explained how expressions with pathological self
    reference can simply be rejected as semantically/
    syntactically unsound thus preventing undefinability,
    and undecidability.

    This sentence is not true: "This sentence is not true"
    is true only because the inner sentence is semantically
    unsound. The inner sentence is formalized in Minimal
    Type Theory as LP := ~True(LP).
    (where A := B means A is defined as B).

    https://philpapers.org/rec/OLCREO

    Can someone review my actual reasoning
    elaborated in the paper?

    If you want to use the term "formal language" you must prove that >>>>>>>> there is a Turing machine that can determine whether a string is a >>>>>>>> valid sentence of your language. If no such Turing machine exists >>>>>>>> you have no justifiction for the use of the word "formal".

    Been there done that and provided all the details.

    Where? At least not where the above pointer points to.


    In the paper that you failed to read.
    https://www.researchgate.net/
    publication/397533139_Rejecting_expressions_of_formal_language_having_pathological_self-reference

    In that article there is no proof that there is no proof that there
    is a
    Turing machine that can determine whether a string is a valid sentence >>>> of your lanugage. The article does not even mention Turing machine.


    It is all the deep meaning of unify_with_occurs_check()
    that rejects an expression as semantically unsound
    because its evaluation is stuck in an infinite loop.


    The Liar Paradox formalized in the Prolog Programming language

    This sentence is not true.
    It is not true about what?
    It is not true about being not true.
    It is not true about being not true about what?
    It is not true about being not true about being not true.
    Oh I see you are stuck in a loop!

    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Failing an occurs check seems to mean that the resolution of an
    expression remains stuck in an infinite loop. Just as the formalized
    Prolog determines that there is a cycle in the directed graph of the
    evaluation sequence of LP the simple English proves that the Liar
    Paradox never gets to the point. It has merely been semantically
    unsound all these years.

    All ot that is irrelevant to your lie about where the proof is.
    That you chose to lie about it and then to distract is a strong
    indication that you have no proof but prefer to lie otherwise.


    Formalized in Olcott's Minimal Type Theory
    LP := ~True(LP)    // LP {is defined as} ~True(LP)
    that expands to ~True(~True(~True(~True(~True(~True(...)))))) https://philarchive.org/archive/PETMTT-4v2

    The Liar Paradox fails because its specifies
    infinite recursion.


    In other words, Olcott's Minimal Type Theory is insufficient to express
    some statements that have logical values.

    Sorry, all you are doing is proving that you don't know what you are
    talking about.
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Fri Nov 28 10:45:01 2025
    From Newsgroup: comp.ai.philosophy

    olcott kirjoitti 27.11.2025 klo 17.49:
    On 11/27/2025 2:20 AM, Mikko wrote:
    olcott kirjoitti 26.11.2025 klo 17.27:
    On 11/26/2025 4:30 AM, Mikko wrote:
    olcott kirjoitti 14.11.2025 klo 16.42:
    On 11/14/2025 3:01 AM, Mikko wrote:
    On 2025-11-13 16:00:58 +0000, olcott said:

    On 11/13/2025 3:05 AM, Mikko wrote:
    On 2025-11-12 14:45:34 +0000, olcott said:

    Rejecting expressions of formal language
    having pathological self-reference

    Explained how expressions with pathological self
    reference can simply be rejected as semantically/
    syntactically unsound thus preventing undefinability,
    and undecidability.

    This sentence is not true: "This sentence is not true"
    is true only because the inner sentence is semantically
    unsound. The inner sentence is formalized in Minimal
    Type Theory as LP := ~True(LP).
    (where A := B means A is defined as B).

    https://philpapers.org/rec/OLCREO

    Can someone review my actual reasoning
    elaborated in the paper?

    If you want to use the term "formal language" you must prove that >>>>>>>> there is a Turing machine that can determine whether a string is a >>>>>>>> valid sentence of your language. If no such Turing machine exists >>>>>>>> you have no justifiction for the use of the word "formal".

    Been there done that and provided all the details.

    Where? At least not where the above pointer points to.


    In the paper that you failed to read.
    https://www.researchgate.net/
    publication/397533139_Rejecting_expressions_of_formal_language_having_pathological_self-reference

    In that article there is no proof that there is no proof that there
    is a
    Turing machine that can determine whether a string is a valid sentence >>>> of your lanugage. The article does not even mention Turing machine.


    It is all the deep meaning of unify_with_occurs_check()
    that rejects an expression as semantically unsound
    because its evaluation is stuck in an infinite loop.


    The Liar Paradox formalized in the Prolog Programming language

    This sentence is not true.
    It is not true about what?
    It is not true about being not true.
    It is not true about being not true about what?
    It is not true about being not true about being not true.
    Oh I see you are stuck in a loop!

    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Failing an occurs check seems to mean that the resolution of an
    expression remains stuck in an infinite loop. Just as the formalized
    Prolog determines that there is a cycle in the directed graph of the
    evaluation sequence of LP the simple English proves that the Liar
    Paradox never gets to the point. It has merely been semantically
    unsound all these years.

    All ot that is irrelevant to your lie about where the proof is.
    That you chose to lie about it and then to distract is a strong
    indication that you have no proof but prefer to lie otherwise.


    Formalized in Olcott's Minimal Type Theory
    LP := ~True(LP)    // LP {is defined as} ~True(LP)
    that expands to ~True(~True(~True(~True(~True(~True(...)))))) https://philarchive.org/archive/PETMTT-4v2

    The Liar Paradox fails because its specifies
    infinite recursion.

    Irrelevant to your lie about where the proof is. That you chose to lie
    about it and then to distract is a strong indication that you have no
    proof but prefer to lie otherwise.
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Fri Nov 28 09:22:00 2025
    From Newsgroup: comp.ai.philosophy

    On 11/28/2025 2:45 AM, Mikko wrote:
    olcott kirjoitti 27.11.2025 klo 17.49:
    On 11/27/2025 2:20 AM, Mikko wrote:
    olcott kirjoitti 26.11.2025 klo 17.27:
    On 11/26/2025 4:30 AM, Mikko wrote:
    olcott kirjoitti 14.11.2025 klo 16.42:
    On 11/14/2025 3:01 AM, Mikko wrote:
    On 2025-11-13 16:00:58 +0000, olcott said:

    On 11/13/2025 3:05 AM, Mikko wrote:
    On 2025-11-12 14:45:34 +0000, olcott said:

    Rejecting expressions of formal language
    having pathological self-reference

    Explained how expressions with pathological self
    reference can simply be rejected as semantically/
    syntactically unsound thus preventing undefinability,
    and undecidability.

    This sentence is not true: "This sentence is not true"
    is true only because the inner sentence is semantically
    unsound. The inner sentence is formalized in Minimal
    Type Theory as LP := ~True(LP).
    (where A := B means A is defined as B).

    https://philpapers.org/rec/OLCREO

    Can someone review my actual reasoning
    elaborated in the paper?

    If you want to use the term "formal language" you must prove that >>>>>>>>> there is a Turing machine that can determine whether a string is a >>>>>>>>> valid sentence of your language. If no such Turing machine exists >>>>>>>>> you have no justifiction for the use of the word "formal".

    Been there done that and provided all the details.

    Where? At least not where the above pointer points to.


    In the paper that you failed to read.
    https://www.researchgate.net/
    publication/397533139_Rejecting_expressions_of_formal_language_having_pathological_self-reference

    In that article there is no proof that there is no proof that there >>>>> is a
    Turing machine that can determine whether a string is a valid sentence >>>>> of your lanugage. The article does not even mention Turing machine.


    It is all the deep meaning of unify_with_occurs_check()
    that rejects an expression as semantically unsound
    because its evaluation is stuck in an infinite loop.


    The Liar Paradox formalized in the Prolog Programming language

    This sentence is not true.
    It is not true about what?
    It is not true about being not true.
    It is not true about being not true about what?
    It is not true about being not true about being not true.
    Oh I see you are stuck in a loop!

    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Failing an occurs check seems to mean that the resolution of an
    expression remains stuck in an infinite loop. Just as the formalized
    Prolog determines that there is a cycle in the directed graph of the
    evaluation sequence of LP the simple English proves that the Liar
    Paradox never gets to the point. It has merely been semantically
    unsound all these years.

    All ot that is irrelevant to your lie about where the proof is.
    That you chose to lie about it and then to distract is a strong
    indication that you have no proof but prefer to lie otherwise.


    Formalized in Olcott's Minimal Type Theory
    LP := ~True(LP)    // LP {is defined as} ~True(LP)
    that expands to ~True(~True(~True(~True(~True(~True(...))))))
    https://philarchive.org/archive/PETMTT-4v2

    The Liar Paradox fails because its specifies
    infinite recursion.

    Irrelevant to your lie about where the proof is. That you chose to lie
    about it and then to distract is a strong indication that you have no
    proof but prefer to lie otherwise.


    In other words you are simply ignoring this ~True(~True(~True(~True(~True(~True(...))))))
    --
    Copyright 2025 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning" computable.

    This required establishing a new foundation
    for correct reasoning.
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Sat Nov 29 12:28:04 2025
    From Newsgroup: comp.ai.philosophy

    olcott kirjoitti 28.11.2025 klo 17.22:
    On 11/28/2025 2:45 AM, Mikko wrote:
    olcott kirjoitti 27.11.2025 klo 17.49:
    On 11/27/2025 2:20 AM, Mikko wrote:
    olcott kirjoitti 26.11.2025 klo 17.27:
    On 11/26/2025 4:30 AM, Mikko wrote:
    olcott kirjoitti 14.11.2025 klo 16.42:
    On 11/14/2025 3:01 AM, Mikko wrote:
    On 2025-11-13 16:00:58 +0000, olcott said:

    On 11/13/2025 3:05 AM, Mikko wrote:
    On 2025-11-12 14:45:34 +0000, olcott said:

    Rejecting expressions of formal language
    having pathological self-reference

    Explained how expressions with pathological self
    reference can simply be rejected as semantically/
    syntactically unsound thus preventing undefinability,
    and undecidability.

    This sentence is not true: "This sentence is not true"
    is true only because the inner sentence is semantically
    unsound. The inner sentence is formalized in Minimal
    Type Theory as LP := ~True(LP).
    (where A := B means A is defined as B).

    https://philpapers.org/rec/OLCREO

    Can someone review my actual reasoning
    elaborated in the paper?

    If you want to use the term "formal language" you must prove that >>>>>>>>>> there is a Turing machine that can determine whether a string >>>>>>>>>> is a
    valid sentence of your language. If no such Turing machine exists >>>>>>>>>> you have no justifiction for the use of the word "formal".

    Been there done that and provided all the details.

    Where? At least not where the above pointer points to.


    In the paper that you failed to read.
    https://www.researchgate.net/
    publication/397533139_Rejecting_expressions_of_formal_language_having_pathological_self-reference

    In that article there is no proof that there is no proof that
    there is a
    Turing machine that can determine whether a string is a valid
    sentence
    of your lanugage. The article does not even mention Turing machine. >>>>>>

    It is all the deep meaning of unify_with_occurs_check()
    that rejects an expression as semantically unsound
    because its evaluation is stuck in an infinite loop.


    The Liar Paradox formalized in the Prolog Programming language

    This sentence is not true.
    It is not true about what?
    It is not true about being not true.
    It is not true about being not true about what?
    It is not true about being not true about being not true.
    Oh I see you are stuck in a loop!

    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Failing an occurs check seems to mean that the resolution of an
    expression remains stuck in an infinite loop. Just as the
    formalized Prolog determines that there is a cycle in the directed
    graph of the evaluation sequence of LP the simple English proves
    that the Liar Paradox never gets to the point. It has merely been
    semantically unsound all these years.

    All ot that is irrelevant to your lie about where the proof is.
    That you chose to lie about it and then to distract is a strong
    indication that you have no proof but prefer to lie otherwise.


    Formalized in Olcott's Minimal Type Theory
    LP := ~True(LP)    // LP {is defined as} ~True(LP)
    that expands to ~True(~True(~True(~True(~True(~True(...))))))
    https://philarchive.org/archive/PETMTT-4v2

    The Liar Paradox fails because its specifies
    infinite recursion.

    Irrelevant to your lie about where the proof is. That you chose to lie
    about it and then to distract is a strong indication that you have no
    proof but prefer to lie otherwise.

    In other words you are simply ignoring this ~True(~True(~True(~True(~True(~True(...))))))

    Your new lie is irrelevant to your earlier lie about where the proof is.
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Tristan Wibberley@tristan.wibberley+netnews2@alumni.manchester.ac.uk to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Mon Dec 1 14:45:27 2025
    From Newsgroup: comp.ai.philosophy

    On 26/11/2025 20:07, olcott wrote:
    On 11/26/2025 1:46 PM, Tristan Wibberley wrote:
    On 26/11/2025 15:27, olcott wrote:
    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Why do you keep posting that?


    Until it is accepted or someone correctly shows
    how it does not once-and-for-all resolve
    the Liar Paradox I will keep posting it.

    Can you show how it /does/ ?
    --
    Tristan Wibberley

    The message body is Copyright (C) 2025 Tristan Wibberley except
    citations and quotations noted. All Rights Reserved except that you may,
    of course, cite it academically giving credit to me, distribute it
    verbatim as part of a usenet system or its archives, and use it to
    promote my greatness and general superiority without misrepresentation
    of my opinions other than my opinion of my greatness and general
    superiority which you _may_ misrepresent. You definitely MAY NOT train
    any production AI system with it but you may train experimental AI that
    will only be used for evaluation of the AI methods it implements.

    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Mon Dec 1 09:18:03 2025
    From Newsgroup: comp.ai.philosophy

    On 12/1/2025 8:45 AM, Tristan Wibberley wrote:
    On 26/11/2025 20:07, olcott wrote:
    On 11/26/2025 1:46 PM, Tristan Wibberley wrote:
    On 26/11/2025 15:27, olcott wrote:
    This is formalized in the Prolog programming language
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.

    Why do you keep posting that?


    Until it is accepted or someone correctly shows
    how it does not once-and-for-all resolve
    the Liar Paradox I will keep posting it.

    Can you show how it /does/ ?


    Been there done that many times no one cares.

    BEGIN:(Clocksin & Mellish 2003:254)
    Finally, a note about how Prolog matching sometimes differs from the unification used in Resolution. Most Prolog systems will allow you to
    satisfy goals like:

    equal(X, X).
    ?- equal(foo(Y), Y).

    that is, they will allow you to match a term against an uninstantiated
    subterm of itself. In this example, foo(Y) is matched against Y,
    which appears within it. As a result, Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
    and so on. So Y ends up standing for some kind of infinite structure. END:(Clocksin & Mellish 2003:254)

    LP = not(true(LP)).
    not(true(not(true(not(true(not(true(LP)))))))).
    expands to not(true(not(true(not(true(not(true(...)))))))).
    --
    Copyright 2025 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning" computable.

    This required establishing a new foundation
    for correct reasoning.
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