• Re: Introducing the foundation of correct reasoning

    From Richard Damon@21:1/5 to olcott on Sat Mar 18 19:57:23 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/18/23 7:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X in
    L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between premises
    P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese




    You understand that your "Provable" doesn't match at all the normal
    concept of Provable.

    In normal logic, Provable is more like your "True" operator, except that
    it include the restriction that the chain of semantic connections is
    finite in length, i.e. actually expressible.

    We talk about a Statement being Provable or not, not with respect to a
    given premise, but the logic system as a whole.

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  • From olcott@21:1/5 to All on Sat Mar 18 18:17:26 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X in
    L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between premises
    P and X in L. *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese



    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

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  • From olcott@21:1/5 to olcott on Sat Mar 18 19:32:48 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X in
    L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between premises
    P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that
    is why I opened up this discussion.


    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
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  • From Richard Damon@21:1/5 to olcott on Sat Mar 18 20:54:25 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/18/23 8:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X in
    L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that
    is why I opened up this discussion.



    First, let me clarify, your requirment of "Semantic Connection" isn't
    just you "by the meaning of the words" is it, because at that point you
    can't prove the Pythagorean theorem since there is nothing about the sm
    of the squares of the two sides that would imply that it would
    neccesarily be the square of the hypotenuse, so your seem to be using
    the classical logic meaning which is connected via a series of logical inferences.

    Next, does you logic system include a "Not" operator. and is it true
    that either X or NOT X is true. (I think this is one of your points, but
    state it clearly). If your system isn't "Binary", what are all the
    logical truth values, and what is the COMPLETE truth table of ALL your
    basic operators with inputs of ALL possible Truth Values? (like And, Or,
    Not)

    That may be one of the issue you are going to need to think about. This
    is one of the big points of non-binary logic system.

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  • From olcott@21:1/5 to olcott on Sun Mar 19 01:00:49 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X in
    L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that
    is why I opened up this discussion.



    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
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  • From Richard Damon@21:1/5 to olcott on Sun Mar 19 06:48:57 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/23 2:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X
    in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    L can be any natural or formal language as long as it has the above interfaces.

    ???? That seems out of context, maybe if you actually reply to the
    message you want to respond to, you might be more understandable.

    Of course, that might be the issue, it makes you more understandable and
    the errors obvious.


    Now, are you talking about "Languages", or "Logic Systems". They are
    different you know.


    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that
    is why I opened up this discussion.




    --- SoupGate-Win32 v1.05
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  • From olcott@21:1/5 to olcott on Sun Mar 19 10:45:32 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X
    in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    L can be any natural or formal language as long as it has the above interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese

    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to olcott on Sun Mar 19 10:52:49 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property >>>> of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X
    in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)

    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sun Mar 19 12:58:13 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/23 11:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property >>>>> of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X
    in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>

    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that >>>> is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    So, statements don't actually have "Truth Values" in your system, you
    need to use predicates about them?

    Is "FALSE" an actual predicate, or is it a logical value?

    How about "TRUE".

    Your ⊨□ operator was defined on predicates, not values, so how was FALSE
    or TRUE used with it?

    Seems you don't actually have a system that handles actual logic.

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  • From olcott@21:1/5 to olcott on Sun Mar 19 12:30:09 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property >>>>> of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and X
    in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>

    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system that >>>> is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions of language L that are stipulated to be true to X.

    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sun Mar 19 13:42:20 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/23 1:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the
    property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and
    X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>

    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from >>>>> correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system
    that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions of language L that are stipulated to be true to X.


    Except until you can show how to actually DEFINE true within the system
    (so it can be evaluated) you haven't done it.

    Your "True" predicate isn't defined IN THE FIELD, but by natural language.

    It just makes it clear you don't understand what he is talking about,
    which sort of points out the worthlessness of your system.

    --- SoupGate-Win32 v1.05
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  • From olcott@21:1/5 to olcott on Sun Mar 19 12:55:24 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the
    property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and
    X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>

    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from >>>>> correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system
    that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to
    Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong to T
    we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also correspond
    to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.



    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sun Mar 19 14:33:31 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/23 1:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the
    property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and >>>>>>> X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>

    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from >>>>>> correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system >>>>>> that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict Tarski's
    conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions
    of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong to T
    we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also correspond
    to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.




    Unresponsive.
    '
    Also, shows you don't understand what you are talking about.

    And, as an example, it is shown that Godel's sentence, that there does
    not exist any natural number which meets a specific primative recursive relationship, is True in F (but not provable in F), As we can show that
    for ANY number n, it doesn't meet that relationship, and that can be
    determine just by running the relationship on the number, all these
    steps being in F.

    The actual proof that this is the result for all number can't be done in
    F, but that doesn't affect the truth of the statement. It IS a fact that
    for every natural number n, it can be shown, just within F, that it
    doesn't meet the requirements of the relationship.

    Thus, G is proved true by a semantic connection from the elementary
    theorems of F to the statment G. The set of connection needed just
    happens to be infinite, and the definition of a PROOF, is an expressible
    finite set of connections with in the Field.


    You dont seem to understand that by the definition, it is quite possibe
    to prove in meta-F that there exist within the theory F, a connection
    within F, from its axioms to the conclusion.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to olcott on Sun Mar 19 13:22:13 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 12:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the
    property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary
    consequence of others.

    True(L,X) means that a semantic connection exists between (a) and >>>>>>> X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between
    premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>

    L can be any natural or formal language as long as it has the above
    interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges from >>>>>> correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

    I am not sure what aspect of logic would be changed by this system >>>>>> that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every
    element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict Tarski's
    conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions
    of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong to T
    we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also correspond
    to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.

    If a semantic connection exists then this semantic connection can be
    specified syntactically.

    If G states that there is no syntactic connection from the elementary
    theorems of F to G in F, then G is stating that G is untrue in F.



    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to olcott on Sun Mar 19 14:21:13 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 1:22 PM, olcott wrote:
    On 3/19/2023 12:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary >>>>>>>> consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the
    property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary >>>>>>>> consequence of others.

    True(L,X) means that a semantic connection exists between (a)
    and X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between >>>>>>>> premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>>

    L can be any natural or formal language as long as it has the
    above interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its
    operations on the basis of this system or such a system diverges >>>>>>> from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this
    foundation. https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>
    I am not sure what aspect of logic would be changed by this
    system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every >>>>> element of the entire body of analytical truth, whether it be facts
    about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict Tarski's
    conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions
    of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to
    Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong to T
    we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true.
    https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also correspond
    to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.

    If a semantic connection exists then this semantic connection can be specified syntactically.

    If G states that there is no syntactic connection from the elementary theorems of F to G in F, then G is stating that G is untrue in F.

    The conventional proof that G is true is not a proof that G is true in
    F, it is a proof that G is true in meta-F.

    LP = "This sentence is not true"
    is not true because LP is not a truth bearer

    This sentence is not true: "This sentence is not true"
    is true because LP is not a truth bearer.

    G = "this sentence cannot be proven in F"
    cannot be proven in F because G has a vacuous truth object.

    ?- G = not(provable(F, G)).

    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false.

    Proves that G has a vacuous truth object.

    This sentence cannot be proven: "this sentence cannot be proven in F"
    is true because G has a vacuous truth object.

    TT = "This sentenced is true"
    is not true because TT has a vacuous truth object.

    This sentence is true.
    What is it true about?
    It is true about being true.
    What is it true about being true about?
    It is true about being true about being true...



    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sun Mar 19 15:33:52 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/23 3:21 PM, olcott wrote:
    On 3/19/2023 1:22 PM, olcott wrote:
    On 3/19/2023 12:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary >>>>>>>>> consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the >>>>>>>>> property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary >>>>>>>>> consequence of others.

    True(L,X) means that a semantic connection exists between (a) >>>>>>>>> and X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between >>>>>>>>> premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    L can be any natural or formal language as long as it has the
    above interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its >>>>>>>> operations on the basis of this system or such a system diverges >>>>>>>> from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this >>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>
    I am not sure what aspect of logic would be changed by this
    system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every >>>>>> element of the entire body of analytical truth, whether it be facts >>>>>> about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict
    Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions
    of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to
    Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong to T >>> we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true.
    https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also correspond >>> to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.

    If a semantic connection exists then this semantic connection can be
    specified syntactically.

    If G states that there is no syntactic connection from the elementary
    theorems of F to G in F, then G is stating that G is untrue in F.

    The conventional proof that G is true is not a proof that G is true in
    F, it is a proof that G is true in meta-F.


    Which, because of the nature of the statement, also makes it true it F.

    if we prove that 2+2 = 4 in one mathematical field, it is also true in
    all field with the same mathematics.

    LP = "This sentence is not true"
    is not true because LP is not a truth bearer

    But that isn't the Statment of G.


    This sentence is not true: "This sentence is not true"
    is true because LP is not a truth bearer.

    So?


    G = "this sentence cannot be proven in F"
    cannot be proven in F because G has a vacuous truth object.

    Which isn't the statement of G, but only a statement provable in Meta-F
    to have the same truth value as G.

    G IS a truth bearer, as it asks about the existance of a natural number matching a computable result.


    ?- G = not(provable(F, G)).

    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false.

    Proves that G has a vacuous truth object.


    Nope, proves you are a LIAR.

    Since that isn't G.

    This sentence cannot be proven: "this sentence cannot be proven in F"
    is true because G has a vacuous truth object.

    Not G, so just proving your ignorance.


    TT = "This sentenced is true"
    is not true because TT has a vacuous truth object.

    Irrelevent


    This sentence is true.
    What is it true about?
    It is true about being true.
    What is it true about being true about?
    It is true about being true about being true...




    Just prove that you don;t know what you are talking about.

    And, have the emotional level of a three-year old.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to olcott on Wed Mar 22 00:05:17 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 2:21 PM, olcott wrote:
    On 3/19/2023 1:22 PM, olcott wrote:
    On 3/19/2023 12:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary >>>>>>>>> consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the >>>>>>>>> property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary >>>>>>>>> consequence of others.

    True(L,X) means that a semantic connection exists between (a) >>>>>>>>> and X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between >>>>>>>>> premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    L can be any natural or formal language as long as it has the
    above interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its >>>>>>>> operations on the basis of this system or such a system diverges >>>>>>>> from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this >>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>
    I am not sure what aspect of logic would be changed by this
    system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every >>>>>> element of the entire body of analytical truth, whether it be facts >>>>>> about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict
    Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions
    of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to
    Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong to T >>> we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true.
    https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also correspond >>> to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.

    If a semantic connection exists then this semantic connection can be
    specified syntactically.

    If G states that there is no syntactic connection from the elementary
    theorems of F to G in F, then G is stating that G is untrue in F.

    The conventional proof that G is true is not a proof that G is true in
    F, it is a proof that G is true in meta-F.

    LP = "This sentence is not true"
    is not true because LP is not a truth bearer

    This sentence is not true: "This sentence is not true"
    is true because LP is not a truth bearer.

    G = "this sentence cannot be proven in F"
    cannot be proven in F because G has a vacuous truth object.

    ?- G = not(provable(F, G)).

    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false.

    Proves that G has a vacuous truth object.

    This sentence cannot be proven: "this sentence cannot be proven in F"
    is true because G has a vacuous truth object.

    G has a vacuous truth object
    G has a vacuous truth object
    G has a vacuous truth object
    G has a vacuous truth object


    TT = "This sentenced is true"
    is not true because TT has a vacuous truth object.

    This sentence is true.
    What is it true about?
    It is true about being true.
    What is it true about being true about?
    It is true about being true about being true...




    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Wed Mar 22 10:53:54 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/22/23 1:05 AM, olcott wrote:
    On 3/19/2023 2:21 PM, olcott wrote:
    On 3/19/2023 1:22 PM, olcott wrote:
    On 3/19/2023 12:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary >>>>>>>>>> consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the >>>>>>>>>> property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary >>>>>>>>>> consequence of others.

    True(L,X) means that a semantic connection exists between (a) >>>>>>>>>> and X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists
    between premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from >>>>>>>>>> cheese


    L can be any natural or formal language as long as it has the
    above interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its >>>>>>>>> operations on the basis of this system or such a system
    diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this >>>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>>
    I am not sure what aspect of logic would be changed by this
    system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to
    every
    element of the entire body of analytical truth, whether it be facts >>>>>>> about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict
    Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from
    expressions of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to >>>> Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong
    to T
    we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true.
    https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also
    correspond
    to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.

    If a semantic connection exists then this semantic connection can be
    specified syntactically.

    If G states that there is no syntactic connection from the elementary
    theorems of F to G in F, then G is stating that G is untrue in F.

    The conventional proof that G is true is not a proof that G is true in
    F, it is a proof that G is true in meta-F.

    LP = "This sentence is not true"
    is not true because LP is not a truth bearer

    This sentence is not true: "This sentence is not true"
    is true because LP is not a truth bearer.

    G = "this sentence cannot be proven in F"
    cannot be proven in F because G has a vacuous truth object.

    ?- G = not(provable(F, G)).

    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false.

    Proves that G has a vacuous truth object.

    This sentence cannot be proven: "this sentence cannot be proven in F"
    is true because G has a vacuous truth object.

    G has a vacuous truth object
    G has a vacuous truth object
    G has a vacuous truth object
    G has a vacuous truth object

    SO you think that the existance of a Natural Number that satisfies a
    computable relationship can br vacuoud?

    That is like saying if we are asked if 2 + 2 = 4, there is no answer.


    Of course, your problem is you don't undertand what G actually is, just
    what FROM G can be proved in Meta-F, namely that any number that
    satisfies the relationship proves that G is true (that there is no
    number that satisfies it), and the lack of such a number means that G
    can't be proved within F.



    TT = "This sentenced is true"
    is not true because TT has a vacuous truth object.

    This sentence is true.
    What is it true about?
    It is true about being true.
    What is it true about being true about?
    It is true about being true about being true...





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  • From Richard Damon@21:1/5 to olcott on Wed Mar 22 15:35:44 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/22/23 3:25 PM, olcott wrote:
    On 3/19/2023 2:21 PM, olcott wrote:
    On 3/19/2023 1:22 PM, olcott wrote:
    On 3/19/2023 12:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary >>>>>>>>>> consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the >>>>>>>>>> property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary >>>>>>>>>> consequence of others.

    True(L,X) means that a semantic connection exists between (a) >>>>>>>>>> and X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists
    between premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from >>>>>>>>>> cheese


    L can be any natural or formal language as long as it has the
    above interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its >>>>>>>>> operations on the basis of this system or such a system
    diverges from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this >>>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>>
    I am not sure what aspect of logic would be changed by this
    system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to
    every
    element of the entire body of analytical truth, whether it be facts >>>>>>> about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict
    Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from
    expressions of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to >>>> Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong
    to T
    we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true.
    https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also
    correspond
    to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.

    If a semantic connection exists then this semantic connection can be
    specified syntactically.

    If G states that there is no syntactic connection from the elementary
    theorems of F to G in F, then G is stating that G is untrue in F.

    The conventional proof that G is true is not a proof that G is true in
    F, it is a proof that G is true in meta-F.

    LP = "This sentence is not true"
    is not true because LP is not a truth bearer

    This sentence is not true: "This sentence is not true"
    is true because LP is not a truth bearer.

    G = "this sentence cannot be proven in F"
    cannot be proven in F because G has a vacuous truth object.

    ?- G = not(provable(F, G)).

    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false.

    Proves that G has a vacuous truth object.



    We are therefore confronted with a proposition which asserts its own unprovability. (Gödel 1931:39-41)

    Right, which isn't G itself, but something derived from it in Meta-F

    Read the proof you have posted, keep track of what system he is talking
    about.

    Your just PROVING that you don't actually understand what the proof is
    about.


    Thus Gödel's G is simplified to this:
    G = ¬(F ⊢ G)

    Nope, it says that G is true if and only if it is not true that F proves
    G, as proven in Meta-F


    Translated into Prolog like this:
    ?- G = not(provable(F, G)).


    Nop,e as that ISN'T G, only the statment PROVEN to have and equivalent
    truth value ot G.

    Note, Prolog is incapable of handling this level of Logic.

    Can you use Prolog to prove the Pythagorean Theorem?


    Found to be incorrect by this:
    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false

    Which just means that it is beyond Prolog

    Also, since you LIED to Prolog, doesn't mean anything.


    Because the Prolog G has an “uninstantiated subterm of itself” we can know that unification will fail because it specifies “some kind of
    infinite structure.”The quotes come from: (Clocksin and Mellish 2003:255)

    Right, because the logic of the system exceeds the capabilities of Prolog.


    So G is unprovable in F because G is incorrect, thus not because F is incomplete.

    Nope, Since you have shown you don't understand what G actually is, your
    logic is incorret.

    IF G is incorrect, then there must exist a number that matches the
    Primative Recursive Relationship, and thus from the proof in Meta-F, we
    know that G is provable, so by your logic, you logic system can prove an incorrect statement, and thus is shown to be inconsistent.

    Of course, since you don't understand what G is, even though you have
    presented the paper (translated) of the proof, you are showing that this
    is above your head, just shows how little you understand about logic.


    This sentence cannot be proven: "this sentence cannot be proven in F"
    is true because G has a vacuous truth object.

    TT = "This sentenced is true"
    is not true because TT has a vacuous truth object.

    This sentence is true.
    What is it true about?
    It is true about being true.
    What is it true about being true about?
    It is true about being true about being true...





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  • From olcott@21:1/5 to olcott on Wed Mar 22 14:25:16 2023
    XPost: comp.theory, sci.logic, alt.philosophy

    On 3/19/2023 2:21 PM, olcott wrote:
    On 3/19/2023 1:22 PM, olcott wrote:
    On 3/19/2023 12:55 PM, olcott wrote:
    On 3/19/2023 12:30 PM, olcott wrote:
    On 3/19/2023 10:52 AM, olcott wrote:
    On 3/19/2023 10:45 AM, olcott wrote:
    On 3/19/2023 1:00 AM, olcott wrote:
    On 3/18/2023 7:32 PM, olcott wrote:
    On 3/18/2023 6:17 PM, olcott wrote:
    Just like with syllogisms conclusions a semantically necessary >>>>>>>>> consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the >>>>>>>>> property
    of Boolean true.

    (b) Some expressions of language L are a semantically necessary >>>>>>>>> consequence of others.

    True(L,X) means that a semantic connection exists between (a) >>>>>>>>> and X in L. *Axiom(P) ⊨□ X*

    Provable(L,P,X) means that a semantic connection exists between >>>>>>>>> premises P and X in L.   *P ⊨□ X*

    The Moon is made from green cheese ⊨□ The Moon is made from cheese


    L can be any natural or formal language as long as it has the
    above interfaces.

    When this is called the foundation of correct reasoning
    *and indeed is the actual foundation of correct reasoning*
    that means that every system of logic either derives all of its >>>>>>>> operations on the basis of this system or such a system diverges >>>>>>>> from
    correct reasoning into incorrect thus erroneous reasoning.

    The kludge of the principle of explosion is eradicated by this >>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>
    I am not sure what aspect of logic would be changed by this
    system that
    is why I opened up this discussion.




    The foundation of correct reasoning is just that and applies to every >>>>>> element of the entire body of analytical truth, whether it be facts >>>>>> about the world or mathematical relationships.

    (A & ~A) ⊨□ FALSE
    FALSE ⊨□ FALSE
    TRUE  ⊨□ TRUE
    A & B ⊨□ A
    A & B ⊨□ B
    The Moon is made from green cheese ⊨□ The Moon is made from cheese >>>>>>

    False(X) ⊨□ True(~X)

    X = "this sentence is not true"
    (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)


    The predicate True(L,X) is provided to explicitly contradict
    Tarski's conclusion that no such predicate can possibly exist.

    True(L,X) means that there is a semantic connection from expressions
    of language L that are stipulated to be true to X.


    expressions of language L that are stipulated to be true correspond to
    Haskell Curry elementary theorems of T.

    Let T be such a theory. Then the elementary statements which belong to T >>> we shall call the elementary theorems of T; we also say that these
    elementary statements are true for T. Thus, given T, an elementary
    theorem is an elementary statement which is true.
    https://www.liarparadox.org/Haskell_Curry_45.pdf

    expressions of language L that are stipulated to be true also correspond >>> to the basic facts of natural language such as cats are animals thus
    cats are not ten story office buildings.

    That it is true in F that G is unprovable in F requires a semantic
    connection from elementary theorems of F to G in F, otherwise G is
    untrue in F.

    If a semantic connection exists then this semantic connection can be
    specified syntactically.

    If G states that there is no syntactic connection from the elementary
    theorems of F to G in F, then G is stating that G is untrue in F.

    The conventional proof that G is true is not a proof that G is true in
    F, it is a proof that G is true in meta-F.

    LP = "This sentence is not true"
    is not true because LP is not a truth bearer

    This sentence is not true: "This sentence is not true"
    is true because LP is not a truth bearer.

    G = "this sentence cannot be proven in F"
    cannot be proven in F because G has a vacuous truth object.

    ?- G = not(provable(F, G)).

    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false.

    Proves that G has a vacuous truth object.



    We are therefore confronted with a proposition which asserts its own unprovability. (Gödel 1931:39-41)

    Thus Gödel's G is simplified to this:
    G = ¬(F ⊢ G)

    Translated into Prolog like this:
    ?- G = not(provable(F, G)).

    Found to be incorrect by this:
    ?- unify_with_occurs_check(G, not(provable(F, G))).
    false

    Because the Prolog G has an “uninstantiated subterm of itself” we can
    know that unification will fail because it specifies “some kind of
    infinite structure.”The quotes come from: (Clocksin and Mellish 2003:255)

    So G is unprovable in F because G is incorrect, thus not because F is incomplete.

    This sentence cannot be proven: "this sentence cannot be proven in F"
    is true because G has a vacuous truth object.

    TT = "This sentenced is true"
    is not true because TT has a vacuous truth object.

    This sentence is true.
    What is it true about?
    It is true about being true.
    What is it true about being true about?
    It is true about being true about being true...




    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

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  • From olcott@21:1/5 to All on Sat Apr 1 16:14:42 2023
    XPost: sci.logic, sci.math, comp.theory
    XPost: alt.philosophy

    The following foundation of correct reasoning simultaneously gets rid of
    Gödel Incompleteness Tarski Undefinability the principle of explosion
    and every other divergence from correct reasoning that is allowed by
    logic systems since the syllogism.

    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.
    (b) Some expressions of language L are a semantically necessary
    consequence of others.
    P is a subset of expressions of language L
    T is a subset of (a)

    Provable(P,X) means P ⊨□ X
    True(T,X) means X ∈ (a) or T ⊨□ X
    False(T,X) means T ⊨□ ~X

    The above system only applies to the analytic side of the analytic
    synthetic distinction which includes all of math and logic yet excludes expressions of language that can only be verified as true with input
    from the sense organs.

    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

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  • From olcott@21:1/5 to olcott on Sat Apr 1 16:58:23 2023
    XPost: sci.logic, sci.math, comp.theory
    XPost: alt.philosophy

    On 4/1/2023 4:14 PM, olcott wrote:
    The following foundation of correct reasoning simultaneously gets rid of Gödel Incompleteness Tarski Undefinability the principle of explosion
    and every other divergence from correct reasoning that is allowed by
    logic systems since the syllogism.

    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.
    (b) Some expressions of language L are a semantically necessary
    consequence of others.
    P is a subset of expressions of language L
    T is a subset of (a)

    Provable(P,X)   means P ⊨□ X
    True(T,X)       means X ∈ (a) or T ⊨□ X
    False(T,X)      means T ⊨□ ~X

    The above system only applies to the analytic side of the analytic
    synthetic distinction which includes all of math and logic yet excludes expressions of language that can only be verified as true with input
    from the sense organs.


    When this is called the foundation of correct reasoning it is called
    that because this is the actual way that analytic truth really works.

    When any existing formal system violates the way that analytic truth
    really works then it is incorrect in the absolute sense because all
    formal systems and mathematics are instances of analytic truth.

    When other formal systems are requited to inherit True(x), Provable(x)
    and False(x) from this foundation then only their divergence is
    abolished.

    Semantic relations that are specified syntactically are still allowed
    and long as they are semantically coherent.

    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

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  • From Richard Damon@21:1/5 to olcott on Sat Apr 1 17:39:17 2023
    XPost: sci.logic, sci.math, comp.theory
    XPost: alt.philosophy

    On 4/1/23 5:14 PM, olcott wrote:
    The following foundation of correct reasoning simultaneously gets rid of Gödel Incompleteness Tarski Undefinability the principle of explosion
    and every other divergence from correct reasoning that is allowed by
    logic systems since the syllogism.

    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.
    (b) Some expressions of language L are a semantically necessary
    consequence of others.
    P is a subset of expressions of language L
    T is a subset of (a)

    Provable(P,X)   means P ⊨□ X

    Which differs from classical logic, so you have lost all ability to
    refer to ANYTHING from classical logic until you reestablih it, since
    classical logic requries that Provable means a FINITE chain of logic
    from P to X, not just "any" chain.

    Also, Provable tends to be based not a arbitrary subset of expressions
    of languge (which doesn't even require them to be known true) but is
    provable in a "Theory" where we start from a subset of the truth-makers
    (a). of the Theory.

    True(T,X)       means X ∈ (a) or T ⊨□ X
    False(T,X)      means T ⊨□ ~X

    The above system only applies to the analytic side of the analytic
    synthetic distinction which includes all of math and logic yet excludes expressions of language that can only be verified as true with input
    from the sense organs.


    But since you disagree on key points to the existing system, you need to
    start at the bottom of the logic tree, you don't even have 1+1 = 2
    anymore until you actually prove it.

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  • From Richard Damon@21:1/5 to olcott on Sat Apr 1 18:52:50 2023
    XPost: sci.logic, sci.math, comp.theory
    XPost: alt.philosophy

    On 4/1/23 5:58 PM, olcott wrote:
    On 4/1/2023 4:14 PM, olcott wrote:
    The following foundation of correct reasoning simultaneously gets rid of
    Gödel Incompleteness Tarski Undefinability the principle of explosion
    and every other divergence from correct reasoning that is allowed by
    logic systems since the syllogism.

    Just like with syllogisms conclusions a semantically necessary
    consequence of their premises

    Semantic Necessity operator: ⊨□

    (a) Some expressions of language L are stipulated to have the property
    of Boolean true.
    (b) Some expressions of language L are a semantically necessary
    consequence of others.
    P is a subset of expressions of language L
    T is a subset of (a)

    Provable(P,X)   means P ⊨□ X
    True(T,X)       means X ∈ (a) or T ⊨□ X
    False(T,X)      means T ⊨□ ~X

    The above system only applies to the analytic side of the analytic
    synthetic distinction which includes all of math and logic yet excludes
    expressions of language that can only be verified as true with input
    from the sense organs.


    When this is called the foundation of correct reasoning it is called
    that because this is the actual way that analytic truth really works.


    And, since you are changing the foundations of the existing logic
    system, you need to throw them ALL out and start fresh.

    When any existing formal system violates the way that analytic truth
    really works then it is incorrect in the absolute sense because all
    formal systems and mathematics are instances of analytic truth.

    And since you have made a change at the fundamental level, you need to
    throw out ALL previous work in logic and start over. PERIOD.


    When other formal systems are requited to inherit True(x), Provable(x)
    and False(x) from this foundation then only their divergence is
    abolished.

    And since you are changing the base of ALL formal systems, you need to
    verify EVERY proposition proven in them is still valid under your new
    rules. Depending on your meaning of "Semantic" it may be easy to move
    through many of them, or it may be very slow.

    YOU need to do this before you can processed.

    Show us that in your system 1 + 1 is still 2, remember, you need to go
    back to the full set of first principles in each system it is based on,
    not just assume you can use the existing logical results.

    This means you are first going to need to start at basic logic and
    deteremine what can actually be shown to still work.


    Semantic relations that are specified syntactically are still allowed
    and long as they are semantically coherent.


    You like throwing out the words, what do you actually MEAN.

    I think you don't understand the actual problem, because you don't
    actually underestand what you are doing.

    Is "Semantic", based on "The Meaning of the Word", (and how can a
    syntactically defined relationship be coherent for all meaning of the
    words?)

    Or, is "Semantic" what is classically defined, which basically negates
    all your meaning as it basically means that which can be shown as
    necessity by the syntactic rules.

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