• Changing the foundational basis to Proof Theoretic Semantics Tarski Undefinability is overcome

    From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Thu Feb 5 10:55:56 2026
    From Newsgroup: sci.math

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    Changing the foundation to proof theoretic semantics where
    truth is well-founded provability blocks TarskirCOs diagonal
    step most clearly seen on line (3)

    Here is the Tarski Undefinability Theorem proof
    (1) x ree Provable if and only if p
    (2) x ree True if and only if p
    (3) x ree Provable if and only if x ree True. // (1) and (2) combined
    (4) either x ree True or x|a ree True; // axiom: ~True(x) re? ~True(~x)
    (5) if x ree Provable, then x ree True; // axiom: Provable(x) raA True(x)
    (6) if x|a ree Provable, then x|a ree True; // axiom: Provable(~x) raA True(~x)
    (7) x ree True
    (8) x ree Provable
    (9) x|a ree Provable

    https://liarparadox.org/Tarski_275_276.pdf

    A proof theoretic prover rejects expressions that
    do not have "a well-founded justification tree within
    Proof theoretic semantics".

    The same way that Prolog does

    % This sentence is not true.
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.
    --
    Copyright 2026 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable for the entire body of knowledge.<br><br>

    This required establishing a new foundation<br>

    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Thu Feb 5 19:41:18 2026
    From Newsgroup: sci.math

    On 2/5/26 11:55 AM, olcott wrote:
    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    No, because you can't USE "Proof Theoretic Semantics" in a system that
    meets his rquirements, as they can't actually handle the semantics of mathematics.



    x ree Provable rco x ree True // proof theoretic semantics

    Changing the foundation to proof theoretic semantics where
    truth is well-founded provability blocks TarskirCOs diagonal
    step most clearly seen on line (3)

    And the Natural Numbers no longer exist.

    Sorry, you don't understand that the field has already DEFINED its truth definition, and thus you can't change it.


    Here is the Tarski Undefinability Theorem proof

    Your missing where that first statement comes from, it isn't an
    "assumption", but a statement that is proven to have a meaning in the
    system.

    (1) x ree Provable if and only if p
    (2) x ree True if and only if p
    (3) x ree Provable if and only if x ree True. // (1) and (2) combined
    (4) either x ree True or x|a ree True;-a-a-a-a // axiom: ~True(x) re? ~True(~x)
    (5) if x ree Provable, then x ree True;-a // axiom: Provable(x) raA True(x) (6) if x|a ree Provable, then x|a ree True;-a // axiom: Provable(~x) raA True(~x)
    (7) x ree True
    (8) x ree Provable
    (9) x|a ree Provable

    https://liarparadox.org/Tarski_275_276.pdf

    A proof theoretic prover rejects expressions that
    do not have "a well-founded justification tree within
    Proof theoretic semantics".

    The same way that Prolog does

    % This sentence is not true.
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.



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  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Thu Feb 5 18:44:54 2026
    From Newsgroup: sci.math

    On 2/5/2026 10:55 AM, olcott wrote:
    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    Changing the foundation to proof theoretic semantics where
    truth is well-founded provability blocks TarskirCOs diagonal
    step most clearly seen on line (3)

    Here is the Tarski Undefinability Theorem proof
    (1) x ree Provable if and only if p
    (2) x ree True if and only if p
    (3) x ree Provable if and only if x ree True. // (1) and (2) combined
    (4) either x ree True or x|a ree True;-a-a-a-a // axiom: ~True(x) re? ~True(~x)
    (5) if x ree Provable, then x ree True;-a // axiom: Provable(x) raA True(x) (6) if x|a ree Provable, then x|a ree True;-a // axiom: Provable(~x) raA True(~x)
    (7) x ree True
    (8) x ree Provable
    (9) x|a ree Provable

    https://liarparadox.org/Tarski_275_276.pdf

    A proof theoretic prover rejects expressions that
    do not have "a well-founded justification tree within
    Proof theoretic semantics".

    The same way that Prolog does

    % This sentence is not true.
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.



    With actual competent human review
    x ree Provable rco x ree True // proof theoretic semantics
    is changed to

    x ree Provable rcA x ree True // proof theoretic semantics
    This is Tarski's line (5)

    This overrules anything that contradicts it because
    it has now attained axiom status.

    Below I show how this overrules Tarski line (3)
    thus overcoming Tarski Undefinability when we
    change its foundation from truth conditional semantics
    to proof theoretic semantics. PTS was not available
    at the time That he wrote
    "The Concept of Truth in Formalized Languages"

    (3) x ree Provable if and only if x ree True.
    can be divided into
    (3)(a) if x ree Provable, then x ree True
    (3)(b) if x ree True, then x ree Provable
    (5) if x ree Provable, then x ree True
    (5) combined with (3)(b) becomes
    if x ree ProvablerCarCethen rCex ree Provable
    --
    Copyright 2026 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable for the entire body of knowledge.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Thu Feb 5 20:14:56 2026
    From Newsgroup: sci.math

    On 2/5/26 7:44 PM, olcott wrote:
    On 2/5/2026 10:55 AM, olcott wrote:
    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    Changing the foundation to proof theoretic semantics where
    truth is well-founded provability blocks TarskirCOs diagonal
    step most clearly seen on line (3)

    Here is the Tarski Undefinability Theorem proof
    (1) x ree Provable if and only if p
    (2) x ree True if and only if p
    (3) x ree Provable if and only if x ree True. // (1) and (2) combined
    (4) either x ree True or x|a ree True;-a-a-a-a // axiom: ~True(x) re? ~True(~x)
    (5) if x ree Provable, then x ree True;-a // axiom: Provable(x) raA True(x) >> (6) if x|a ree Provable, then x|a ree True;-a // axiom: Provable(~x) raA True(~x)
    (7) x ree True
    (8) x ree Provable
    (9) x|a ree Provable

    https://liarparadox.org/Tarski_275_276.pdf

    A proof theoretic prover rejects expressions that
    do not have "a well-founded justification tree within
    Proof theoretic semantics".

    The same way that Prolog does

    % This sentence is not true.
    ?- LP = not(true(LP)).
    LP = not(true(LP)).
    ?- unify_with_occurs_check(LP, not(true(LP))).
    false.



    With actual competent human review
    x ree Provable rco x ree True // proof theoretic semantics
    is changed to

    x ree Provable rcA x ree True // proof theoretic semantics
    This is Tarski's line (5)

    Which is a statement he PROVED was a statement with a meaning in the
    system, but you ignore that.


    This overrules anything that contradicts it because
    it has now attained axiom status.


    Nope, you don't "Overrule" things in logic, you just get a contradictioh
    which means you BROKE THE SYSTEM by asserting the contracdiction.


    Below I show how this overrules Tarski line (3)

    No such operation.

    All you are doing is proving you don't understand how real logic works.

    But then, you think you can make yourself God by just claiming it, and
    you will find out how wrong you are when you do meet him.

    thus overcoming Tarski Undefinability when we
    change its foundation from truth conditional semantics
    to proof theoretic semantics. PTS was not available
    at the time That he wrote
    "The Concept of Truth in Formalized Languages"

    (3) x ree Provable if and only if x ree True.
    can be divided into
    (3)(a) if x ree Provable, then x ree True
    (3)(b) if x ree True, then x ree Provable
    (5) if x ree Provable, then x ree True
    (5) combined with (3)(b) becomes
    if x ree ProvablerCarCethen rCex ree Provable



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  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 11:01:09 2026
    From Newsgroup: sci.math

    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define.
    --
    Mikko
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  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 09:30:53 2026
    From Newsgroup: sci.math

    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define.


    It is an axiom: reCx (Provable(x) rcA True(x))

    There are dozens of papers needed to verify this.
    It will take me quite a while to form proper citations
    of these papers. It is anchored in proof theoretic semantics.
    Generic PTS states that ~Provable(x) rco Meaningless(x).
    Model theory and truth conditional semantics are rejected.
    --
    Copyright 2026 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable for the entire body of knowledge.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 13:15:45 2026
    From Newsgroup: sci.math

    On 2/6/26 10:30 AM, olcott wrote:
    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define.


    It is an axiom: reCx (Provable(x) rcA True(x))

    But the axiom uses rcA which goes in just one direction, while you
    statements used rco which attempts to go both ways.



    There are dozens of papers needed to verify this.
    It will take me quite a while to form proper citations
    of these papers. It is anchored in proof theoretic semantics.
    Generic PTS states that ~Provable(x) rco Meaningless(x).
    Model theory and truth conditional semantics are rejected.


    And, I think your problem is you don't actually understand what you are reading. This shows in that you have been making the claim for years,
    but you are now admitting you can't ACTUALLY show why it is (yet).

    Your problem is it seems you fundamentally don't understand how
    semantics work, and why it is important to put things into context.

    This shows in part because you keep on trying to apply principles for
    general Philosophy to Formal Logic, where they do not apply.

    Sorry, you are just showing your fundamental ignorance of what you are
    talking about.
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  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 14:00:34 2026
    From Newsgroup: sci.math

    On 2/6/2026 12:15 PM, Richard Damon wrote:
    On 2/6/26 10:30 AM, olcott wrote:
    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define.


    It is an axiom: reCx (Provable(x) rcA True(x))

    But the axiom uses rcA which goes in just one direction, while you statements used rco which attempts to go both ways.


    This was corrected by an expert that seems
    to really know these things.

    This same expert agrees that with within PTS:
    "if x is provable, then it is true."



    There are dozens of papers needed to verify this.
    It will take me quite a while to form proper citations
    of these papers. It is anchored in proof theoretic semantics.
    Generic PTS states that ~Provable(x) rco Meaningless(x).
    Model theory and truth conditional semantics are rejected.


    And, I think your problem is you don't actually understand what you are reading. This shows in that you have been making the claim for years,
    but you are now admitting you can't ACTUALLY show why it is (yet).


    reCx (~Provable(x) rco Meaningless(x))
    Seems to be exactly and precisely what Proof Theoretic
    Semantics actually says. Since the SEP article was
    written by the guy that coined the term:
    "Proof Theoretic Semantics"
    It should be pretty definitive.

    https://plato.stanford.edu/entries/proof-theoretic-semantics/

    Your problem is it seems you fundamentally don't understand how
    semantics work, and why it is important to put things into context.


    Not at all. It all in "Proof Theoretic Semantics"

    This shows in part because you keep on trying to apply principles for general Philosophy to Formal Logic, where they do not apply.


    Try saying that after you spend three hours carefully studying
    the linked article. That article is not the end-all be-all
    of "Proof Theoretic Semantics", yet it does seem to be the
    most definitive single source.

    Sorry, you are just showing your fundamental ignorance of what you are talking about.
    --
    Copyright 2026 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable for the entire body of knowledge.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 18:18:18 2026
    From Newsgroup: sci.math

    On 2/6/26 3:00 PM, olcott wrote:
    On 2/6/2026 12:15 PM, Richard Damon wrote:
    On 2/6/26 10:30 AM, olcott wrote:
    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define.


    It is an axiom: reCx (Provable(x) rcA True(x))

    But the axiom uses rcA which goes in just one direction, while you
    statements used rco which attempts to go both ways.


    This was corrected by an expert that seems
    to really know these things.

    This same expert agrees that with within PTS:
    "if x is provable, then it is true."


    Right, Provable leads to Truth. But Not Provable does not mean not true,
    or Truth require provability by the axiom.

    I gues you are just admitting that you are just a pathetic liar.




    There are dozens of papers needed to verify this.
    It will take me quite a while to form proper citations
    of these papers. It is anchored in proof theoretic semantics.
    Generic PTS states that ~Provable(x) rco Meaningless(x).
    Model theory and truth conditional semantics are rejected.


    And, I think your problem is you don't actually understand what you
    are reading. This shows in that you have been making the claim for
    years, but you are now admitting you can't ACTUALLY show why it is (yet).


    reCx-a (~Provable(x) rco Meaningless(x))
    Seems to be exactly and precisely what Proof Theoretic
    Semantics actually says. Since the SEP article was
    written by the guy that coined the term:
    "Proof Theoretic Semantics"
    It should be pretty definitive.

    No, which is part of your problem. Proof-Theoretic Semantics say we
    can't talk about the truth of a statement we can not prove, NOT that the statement can't be true without the proof, just we can't talk about it.

    Proof-Theoretic Semantics limits our way of looking at things to what
    can be proven, and things outside of what can be proven are just outside
    the domain of discussion.

    The problem of using this Philosophical view in Formal Logic systems
    that have the power to create the Natural Number system is that we
    suddenly find we can't know if we can talk about a given statement until
    we solve it.


    https://plato.stanford.edu/entries/proof-theoretic-semantics/

    Your problem is it seems you fundamentally don't understand how
    semantics work, and why it is important to put things into context.


    Not at all. It all in "Proof Theoretic Semantics"

    Which you don't understand, as that is all discussion in PHILOSOPHY, not FORMAL LOGIC, particularly those systems that can create infinite
    domains of reguard.


    This shows in part because you keep on trying to apply principles for
    general Philosophy to Formal Logic, where they do not apply.


    Try saying that after you spend three hours carefully studying
    the linked article. That article is not the end-all be-all
    of "Proof Theoretic Semantics", yet it does seem to be the
    most definitive single source.

    Maybe you should notice how many times they talk about removing things
    like in standard logic. Since Formal Logic system include in there definitions, the mode of interpreation of the logic, you aren't allowed
    to change that and keep the system being "the same".

    In other words, if you want to change to your "Proof-Theoretic
    Semantics", you FIRST need to show how much of the system services the
    change of rules.

    Since the definition of arithmatic of Natural Numbers falls apart if you
    try to force this on it, all you are doing is saying that you logic
    can't handle mathematics.


    Sorry, you are just showing your fundamental ignorance of what you are
    talking about.



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  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 18:10:51 2026
    From Newsgroup: sci.math

    On 2/6/2026 5:18 PM, Richard Damon wrote:
    On 2/6/26 3:00 PM, olcott wrote:
    On 2/6/2026 12:15 PM, Richard Damon wrote:
    On 2/6/26 10:30 AM, olcott wrote:
    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define. >>>>>

    It is an axiom: reCx (Provable(x) rcA True(x))

    But the axiom uses rcA which goes in just one direction, while you
    statements used rco which attempts to go both ways.


    This was corrected by an expert that seems
    to really know these things.

    This same expert agrees that with within PTS:
    "if x is provable, then it is true."


    Right, Provable leads to Truth. But Not Provable does not mean not true,
    or Truth require provability by the axiom.

    I gues you are just admitting that you are just a pathetic liar.




    There are dozens of papers needed to verify this.
    It will take me quite a while to form proper citations
    of these papers. It is anchored in proof theoretic semantics.
    Generic PTS states that ~Provable(x) rco Meaningless(x).
    Model theory and truth conditional semantics are rejected.


    And, I think your problem is you don't actually understand what you
    are reading. This shows in that you have been making the claim for
    years, but you are now admitting you can't ACTUALLY show why it is
    (yet).


    reCx-a (~Provable(x) rco Meaningless(x))
    Seems to be exactly and precisely what Proof Theoretic
    Semantics actually says. Since the SEP article was
    written by the guy that coined the term:
    "Proof Theoretic Semantics"
    It should be pretty definitive.

    No, which is part of your problem. Proof-Theoretic Semantics say we
    can't talk about the truth of a statement we can not prove, NOT that the statement can't be true without the proof, just we can't talk about it.


    Lets try to say this exactly accurately.
    In PTS expressions that are unprovable are
    ungrounded in semantic meaning.

    When I refer to a formal system I am referring to
    Russell's atomic facts written down and placed in
    a simple Type Hierarchy.

    atomic facts, which consist either of a simple
    particular exhibiting a quality, or multiple
    simple particulars standing in a relation. https://plato.stanford.edu/entries/logical-atomism/

    Proof-Theoretic Semantics limits our way of looking at things to what
    can be proven, and things outside of what can be proven are just outside
    the domain of discussion.


    "true on the basis of meaning expressed in language"
    necessarily includes the entire body of knowledge
    expressed in language.

    The problem of using this Philosophical view in Formal Logic systems
    that have the power to create the Natural Number system is that we
    suddenly find we can't know if we can talk about a given statement until
    we solve it.


    https://plato.stanford.edu/entries/proof-theoretic-semantics/

    Your problem is it seems you fundamentally don't understand how
    semantics work, and why it is important to put things into context.


    Not at all. It all in "Proof Theoretic Semantics"

    Which you don't understand, as that is all discussion in PHILOSOPHY, not FORMAL LOGIC, particularly those systems that can create infinite
    domains of reguard.


    This shows in part because you keep on trying to apply principles for
    general Philosophy to Formal Logic, where they do not apply.


    Try saying that after you spend three hours carefully studying
    the linked article. That article is not the end-all be-all
    of "Proof Theoretic Semantics", yet it does seem to be the
    most definitive single source.

    Maybe you should notice how many times they talk about removing things
    like in standard logic. Since Formal Logic system include in there definitions, the mode of interpreation of the logic, you aren't allowed
    to change that and keep the system being "the same".

    In other words, if you want to change to your "Proof-Theoretic
    Semantics", you FIRST need to show how much of the system services the change of rules.

    Since the definition of arithmatic of Natural Numbers falls apart if you
    try to force this on it, all you are doing is saying that you logic
    can't handle mathematics.


    reCx (Provable(PA, x) rcA True(PA, x))
    reCx (Provable(PA, ~x) rcA False(PA, x))
    reCx (~True(PA, x) reo ~False(PA, x) rco ~Truth_Apt(PA, x))
    --
    Copyright 2026 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable for the entire body of knowledge.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 19:23:51 2026
    From Newsgroup: sci.math

    On 2/6/26 7:10 PM, olcott wrote:
    On 2/6/2026 5:18 PM, Richard Damon wrote:
    On 2/6/26 3:00 PM, olcott wrote:
    On 2/6/2026 12:15 PM, Richard Damon wrote:
    On 2/6/26 10:30 AM, olcott wrote:
    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define. >>>>>>

    It is an axiom: reCx (Provable(x) rcA True(x))

    But the axiom uses rcA which goes in just one direction, while you
    statements used rco which attempts to go both ways.


    This was corrected by an expert that seems
    to really know these things.

    This same expert agrees that with within PTS:
    "if x is provable, then it is true."


    Right, Provable leads to Truth. But Not Provable does not mean not
    true, or Truth require provability by the axiom.

    I gues you are just admitting that you are just a pathetic liar.




    There are dozens of papers needed to verify this.
    It will take me quite a while to form proper citations
    of these papers. It is anchored in proof theoretic semantics.
    Generic PTS states that ~Provable(x) rco Meaningless(x).
    Model theory and truth conditional semantics are rejected.


    And, I think your problem is you don't actually understand what you
    are reading. This shows in that you have been making the claim for
    years, but you are now admitting you can't ACTUALLY show why it is
    (yet).


    reCx-a (~Provable(x) rco Meaningless(x))
    Seems to be exactly and precisely what Proof Theoretic
    Semantics actually says. Since the SEP article was
    written by the guy that coined the term:
    "Proof Theoretic Semantics"
    It should be pretty definitive.

    No, which is part of your problem. Proof-Theoretic Semantics say we
    can't talk about the truth of a statement we can not prove, NOT that
    the statement can't be true without the proof, just we can't talk
    about it.


    Lets try to say this exactly accurately.
    In PTS expressions that are unprovable are
    ungrounded in semantic meaning.

    Right, which means you can't talk about them.


    When I refer to a formal system I am referring to
    Russell's atomic facts written down and placed in
    a simple Type Hierarchy.

    Then you aren't talking about a real Formal System.

    This is your problem, You don't understand what a Formal system actually is.

    You keep on thinking it is just a form of Philosophy, which it really isn't.


    -a atomic facts, which consist either of a simple
    -a particular exhibiting a quality, or multiple
    -a simple particulars standing in a relation. https://plato.stanford.edu/entries/logical-atomism/

    So, how do you fit Peano Arithmatic into that system?


    Proof-Theoretic Semantics limits our way of looking at things to what
    can be proven, and things outside of what can be proven are just
    outside the domain of discussion.


    "true on the basis of meaning expressed in language"
    necessarily includes the entire body of knowledge
    expressed in language.

    Try to do it.

    Since that body of knowledge expresses facts about mathematics and such system, it include things like the Pythagorean Theorem, which is *NOT*
    true just on the meaning of its words, or even as just "expressed in
    language" but as a logical deduction based on the axios of the system it
    is embedded into, processed to a conclusion.


    The problem of using this Philosophical view in Formal Logic systems
    that have the power to create the Natural Number system is that we
    suddenly find we can't know if we can talk about a given statement
    until we solve it.


    https://plato.stanford.edu/entries/proof-theoretic-semantics/

    Your problem is it seems you fundamentally don't understand how
    semantics work, and why it is important to put things into context.


    Not at all. It all in "Proof Theoretic Semantics"

    Which you don't understand, as that is all discussion in PHILOSOPHY,
    not FORMAL LOGIC, particularly those systems that can create infinite
    domains of reguard.


    This shows in part because you keep on trying to apply principles
    for general Philosophy to Formal Logic, where they do not apply.


    Try saying that after you spend three hours carefully studying
    the linked article. That article is not the end-all be-all
    of "Proof Theoretic Semantics", yet it does seem to be the
    most definitive single source.

    Maybe you should notice how many times they talk about removing things
    like in standard logic. Since Formal Logic system include in there
    definitions, the mode of interpreation of the logic, you aren't
    allowed to change that and keep the system being "the same".

    In other words, if you want to change to your "Proof-Theoretic
    Semantics", you FIRST need to show how much of the system services the
    change of rules.

    Since the definition of arithmatic of Natural Numbers falls apart if
    you try to force this on it, all you are doing is saying that you
    logic can't handle mathematics.


    reCx (Provable(PA, x)-a rcA True(PA, x))
    reCx (Provable(PA, ~x) rcA False(PA, x))
    reCx (~True(PA, x) reo ~False(PA, x) rco ~Truth_Apt(PA, x))



    Which isn't what Proof Theoretic says,

    As it doesn't introduce the concept of the predicate "True".

    It says if you CAN prove the statement in the system, then you can say
    the statement is true.

    And, if you CAN prove the converse of the statement in the system, then
    you can say the statement if false,

    And, if you CAN prove that the you can never do either of the above, you
    can say the statement is non-well-founded.

    You might not be able to do any of the above, in which case you can't
    talk about the statement and it truth.

    Since in mathematics, there ARE statements for which you can't do any of
    the above, Proof-Theoretic Semantic fall apart for it, as you start to
    run into the issue of not knowing if you can talk about the statements.
    It works better in simpler systems where there are many statements for
    which you can reduce it to one of the three cases you can talk about.


    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Fri Feb 6 19:13:50 2026
    From Newsgroup: sci.math

    On 2/6/2026 6:23 PM, Richard Damon wrote:
    On 2/6/26 7:10 PM, olcott wrote:
    On 2/6/2026 5:18 PM, Richard Damon wrote:
    On 2/6/26 3:00 PM, olcott wrote:
    On 2/6/2026 12:15 PM, Richard Damon wrote:
    On 2/6/26 10:30 AM, olcott wrote:
    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics
    Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics

    A definition in terms of an undefined symbol does not really define. >>>>>>>

    It is an axiom: reCx (Provable(x) rcA True(x))

    But the axiom uses rcA which goes in just one direction, while you
    statements used rco which attempts to go both ways.


    This was corrected by an expert that seems
    to really know these things.

    This same expert agrees that with within PTS:
    "if x is provable, then it is true."


    Right, Provable leads to Truth. But Not Provable does not mean not
    true, or Truth require provability by the axiom.

    I gues you are just admitting that you are just a pathetic liar.




    There are dozens of papers needed to verify this.
    It will take me quite a while to form proper citations
    of these papers. It is anchored in proof theoretic semantics.
    Generic PTS states that ~Provable(x) rco Meaningless(x).
    Model theory and truth conditional semantics are rejected.


    And, I think your problem is you don't actually understand what you >>>>> are reading. This shows in that you have been making the claim for
    years, but you are now admitting you can't ACTUALLY show why it is
    (yet).


    reCx-a (~Provable(x) rco Meaningless(x))
    Seems to be exactly and precisely what Proof Theoretic
    Semantics actually says. Since the SEP article was
    written by the guy that coined the term:
    "Proof Theoretic Semantics"
    It should be pretty definitive.

    No, which is part of your problem. Proof-Theoretic Semantics say we
    can't talk about the truth of a statement we can not prove, NOT that
    the statement can't be true without the proof, just we can't talk
    about it.


    Lets try to say this exactly accurately.
    In PTS expressions that are unprovable are
    ungrounded in semantic meaning.

    Right, which means you can't talk about them.


    Your way of saying it is way too weak.
    Is gibberish nonsense is more accurate.


    When I refer to a formal system I am referring to
    Russell's atomic facts written down and placed in
    a simple Type Hierarchy.

    Then you aren't talking about a real Formal System.

    This is your problem, You don't understand what a Formal system actually
    is.

    You keep on thinking it is just a form of Philosophy, which it really
    isn't.


    -a-a atomic facts, which consist either of a simple
    -a-a particular exhibiting a quality, or multiple
    -a-a simple particulars standing in a relation.
    https://plato.stanford.edu/entries/logical-atomism/

    So, how do you fit Peano Arithmatic into that system?


    Proof-Theoretic Semantics limits our way of looking at things to what
    can be proven, and things outside of what can be proven are just
    outside the domain of discussion.


    "true on the basis of meaning expressed in language"
    necessarily includes the entire body of knowledge
    expressed in language.

    Try to do it.

    Since that body of knowledge expresses facts about mathematics and such system, it include things like the Pythagorean Theorem, which is *NOT*
    true just on the meaning of its words,

    "true on the basis of meaning expressed in language"

    NOT THE MEANING OF WORDS
    NOT THE MEANING OF WORDS
    NOT THE MEANING OF WORDS
    NOT THE MEANING OF WORDS
    NOT THE MEANING OF WORDS
    NOT THE MEANING OF WORDS

    *THE MEANING IN ALL FORMAL MATHEMATICAL AND NATURAL LANGUAGES*
    *THE MEANING IN ALL FORMAL MATHEMATICAL AND NATURAL LANGUAGES*
    *THE MEANING IN ALL FORMAL MATHEMATICAL AND NATURAL LANGUAGES*

    I spent 25 years coming up with that you could
    take two minutes to pay COMPLETE ATTENTION.
    <snip>


    Since the definition of arithmatic of Natural Numbers falls apart if
    you try to force this on it, all you are doing is saying that you
    logic can't handle mathematics.


    reCx (Provable(PA, x)-a rcA True(PA, x))
    reCx (Provable(PA, ~x) rcA False(PA, x))
    reCx (~True(PA, x) reo ~False(PA, x) rco ~Truth_Apt(PA, x))



    Which isn't what Proof Theoretic says,

    As it doesn't introduce the concept of the predicate "True".

    It says if you CAN prove the statement in the system, then you can say
    the statement is true.

    And, if you CAN prove the converse of the statement in the system, then
    you can say the statement if false,

    And, if you CAN prove that the you can never do either of the above, you
    can say the statement is non-well-founded.


    *Good job, you got the most important point exactly correctly*
    Non-well-founded means not truth-apt.

    You might not be able to do any of the above, in which case you can't
    talk about the statement and it truth.


    The key thing is that PTS rejects cases of pathological
    self-reference as lacking a well-founded justification
    tree thus semantically ill-formed within PTS.

    Since in mathematics, there ARE statements for which you can't do any of
    the above, Proof-Theoretic Semantic fall apart for it, as you start to
    run into the issue of not knowing if you can talk about the statements.
    It works better in simpler systems where there are many statements for
    which you can reduce it to one of the three cases you can talk about.



    You are conflating mathematics within the foundation of
    Truth Conditional Semantics with mathematics itself.

    Mathematics within Proof Theoretic Semantics cannot
    be incomplete.
    --
    Copyright 2026 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable for the entire body of knowledge.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Mon Feb 9 07:51:34 2026
    From Newsgroup: sci.math

    On 2/7/26 11:59 PM, olcott wrote:
    On 2/7/2026 8:47 PM, Tristan Wibberley wrote:
    On 07/02/2026 00:10, olcott wrote:
    When I refer to a formal system I am referring to
    Russell's atomic facts written down and placed in
    a simple Type Hierarchy.

    Is that, in effect, the conventional meaning of "formal system"? It is
    not normally expressed so, see Curry and Feys.


    It is the axiomatic foundation of this:
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.


    No, because that doesn't exist.

    The problem is "True" can't be computable in a system that handles all knowledge, as you have been shown.

    Your problem is you just don't understand what you are talking about, as
    truth is a concept you, as a pathological liar, can't understand.
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math on Mon Feb 9 07:51:36 2026
    From Newsgroup: sci.math

    On 2/8/26 12:07 AM, olcott wrote:
    On 2/7/2026 9:49 PM, Richard Damon wrote:
    On 2/7/26 8:10 PM, olcott wrote:
    On 2/7/2026 2:56 PM, Richard Damon wrote:
    On 2/7/26 11:46 AM, olcott wrote:
    On 2/7/2026 10:33 AM, Richard Damon wrote:
    On 2/7/26 10:10 AM, olcott wrote:
    On 2/7/2026 8:46 AM, Richard Damon wrote:
    On 2/7/26 9:22 AM, olcott wrote:
    On 2/7/2026 7:50 AM, Richard Damon wrote:
    On 2/7/26 8:10 AM, olcott wrote:
    On 2/7/2026 4:25 AM, Mikko wrote:
    On 06/02/2026 17:30, olcott wrote:
    On 2/6/2026 3:01 AM, Mikko wrote:
    On 05/02/2026 18:55, olcott wrote:

    Changing the foundational basis to Proof Theoretic Semantics >>>>>>>>>>>>>>> Tarski Undefinability is overcome

    x ree Provable rco x ree True // proof theoretic semantics >>>>>>>>>>>>>>
    A definition in terms of an undefined symbol does not >>>>>>>>>>>>>> really define.

    It is an axiom: reCx (Provable(x) rcA True(x))

    There are theories where every sentence is provable but it >>>>>>>>>>>> is not
    possiible to interprete any theory so that every sentence is >>>>>>>>>>>> true.


    Proof Theoretic Semantics enables
    "true on the basis of meaning expressed in language"
    to be reliably computable for the entire body of knowledge. >>>>>>>>>>>


    No it doesn't, but then you never understood what truth is, or >>>>>>>>>> really what knowledge is.


    "true on the basis of meaning expressed in language"
    expressions of language are defined in terms of other
    expressions of language thus truth is computed on the
    basis of relations between finite strings.

    In other words, you admit your definition is self-referenetial, >>>>>>>> and by your own claims, not a basis for logic.


    It is an acyclic directed graph.

    So, what part of language has meaning without reference to
    anything else?

    You just said that your expressions are defined in terms of other >>>>>> expressions. Which ones are definable without reference to
    anything else?


    It is all a huge semantic tautology, even the
    stipulated "atomic facts" specify relations
    between finite strings.

    In other words, NO, you can't explain what you mean and need to keep
    changing it because you don't understand what you are talking about.

    A system that is one bing semantic tautology means it is basically
    worthless as everything is just redundently true


    When we understand that every expression that is "true on the basis
    of meaning expressed in language" derives all of its meaning by its
    relation to other expressions of language then we can see that the
    expressions PTS rejects really are semantically meaningless. We can
    anchor this even more by stipulating that these relations are
    semantic entailment specified syntactically.



    But the problem is too many true statements are NOT "True on the basis
    of meaning expressed in language", like the Pythagorean Theorem.


    Those ate atomic facts in the system, stipulated to be true.
    Russell's atomic facts are complete.

    So, your system tries to take everything that is true as stipulated?

    Then it isn't a logic system, and is just inconsistant.

    You have as a axiom then that Goldbach's conjecture is either True or False.

    You also apperently have no way currently to decide it, but you also
    insist it must be decidable.

    You have as an axiom that Godel's G is a True Statement that can not be
    proven in its system (that= *IS* part of our body of knowledge,
    expressible in our language) but then say that all true thihgs can be
    proven.

    You system is just proven to be self-inconsistant.


    Thus, your system based on just things that are, is woefully
    underpowered.


    The complete body of all knowledge that can be written
    down is not underpowered.

    But you keep on changing what you are talking about.

    Is it just expressible in language, or it is things fully defined to
    their truth by the language.

    The problem is that "meaning" in language allows for infinite chains of
    logic, but computation and proof do not.



    Until you can show how you can show the Pythogorean Theorem fits into
    you system, you are just showing that you are just an idiotic liar.


    You you are going to be disrespectful I will stop talking to you.



    What is "disrespetful" about pointing out that you can't prove your claim.

    That *IS* just showing that you are just a liar.

    Part of your problem is that youy don't understand that trying to
    express everything "known" will tend to cause an INFINITE operation, as
    trying to actually write out that knowledge over arithmatic is unbounded
    if you insist on "unwinding" the induction rule that creates it. we get:

    0 + 1 = 1
    1 + 1 = 2
    2 + 1 = 3
    3 + 1 = 4
    ...
    To infinity. Thus your axiom set is not finite, and thus can't actually
    be fully expressed in finite language.

    If you allow yourself to "compress" that with inductive properties, then
    you have admitted that infinite (technically "unbounded") operation of
    the formulas ARE allowed to determine truth, and thus some truth is
    beyond bounded proof or calculation.

    Of course, you are just to ignorant to understand that fact.
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Mon Feb 9 08:02:39 2026
    From Newsgroup: sci.math

    On 2/9/2026 6:51 AM, Richard Damon wrote:
    On 2/7/26 11:59 PM, olcott wrote:
    On 2/7/2026 8:47 PM, Tristan Wibberley wrote:
    On 07/02/2026 00:10, olcott wrote:
    When I refer to a formal system I am referring to
    Russell's atomic facts written down and placed in
    a simple Type Hierarchy.

    Is that, in effect, the conventional meaning of "formal system"? It is
    not normally expressed so, see Curry and Feys.


    It is the axiomatic foundation of this:
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.


    No, because that doesn't exist.

    The problem is "True" can't be computable in a system that handles all knowledge, as you have been shown.

    Your problem is you just don't understand what you are talking about, as truth is a concept you, as a pathological liar, can't understand.

    I warned you about disrespect
    --
    Copyright 2026 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable for the entire body of knowledge.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Python@python@cccp.invalid to sci.math on Mon Feb 9 14:37:07 2026
    From Newsgroup: sci.math

    Le 09/02/2026 |a 15:02, olcott a |-crit :
    On 2/9/2026 6:51 AM, Richard Damon wrote:
    On 2/7/26 11:59 PM, olcott wrote:
    On 2/7/2026 8:47 PM, Tristan Wibberley wrote:
    On 07/02/2026 00:10, olcott wrote:
    When I refer to a formal system I am referring to
    Russell's atomic facts written down and placed in
    a simple Type Hierarchy.

    Is that, in effect, the conventional meaning of "formal system"? It is >>>> not normally expressed so, see Curry and Feys.


    It is the axiomatic foundation of this:
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.


    No, because that doesn't exist.

    The problem is "True" can't be computable in a system that handles all
    knowledge, as you have been shown.

    Your problem is you just don't understand what you are talking about, as
    truth is a concept you, as a pathological liar, can't understand.

    I warned you about disrespect

    You deserve NO respect. Dishonest crank.
    --- Synchronet 3.21b-Linux NewsLink 1.2
  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,sci.lang,comp.lang.prolog on Mon Feb 9 22:47:26 2026
    From Newsgroup: sci.math

    On 2/9/26 9:02 AM, olcott wrote:
    On 2/9/2026 6:51 AM, Richard Damon wrote:
    On 2/7/26 11:59 PM, olcott wrote:
    On 2/7/2026 8:47 PM, Tristan Wibberley wrote:
    On 07/02/2026 00:10, olcott wrote:
    When I refer to a formal system I am referring to
    Russell's atomic facts written down and placed in
    a simple Type Hierarchy.

    Is that, in effect, the conventional meaning of "formal system"? It is >>>> not normally expressed so, see Curry and Feys.


    It is the axiomatic foundation of this:
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.


    No, because that doesn't exist.

    The problem is "True" can't be computable in a system that handles all
    knowledge, as you have been shown.

    Your problem is you just don't understand what you are talking about,
    as truth is a concept you, as a pathological liar, can't understand.

    I warned you about disrespect


    What is disrespectful about calling out your lies.

    Show me how you are actually defining your terms without using
    duplicious definitions.

    Either "meaning" comes from the classical definitions in logic, which
    allows for the infinte applicaiton of logical operations, which means
    that, since computations that give answers are always finite, that not
    all truth is computable, or you system just can't HAVE mathematics.

    Since you refuse to answer that question, the only thing remaining is
    that you are just admitting to being a liar.
    --- Synchronet 3.21b-Linux NewsLink 1.2