• Re: Undecidable decision problems are abolished [Ross Finlayson]

    From Richard Damon@21:1/5 to olcott on Tue Dec 12 07:31:10 2023
    On 12/11/23 11:54 PM, olcott wrote:
    On 12/11/2023 10:07 PM, Ross Finlayson wrote:
    On Monday, December 11, 2023 at 4:59:55 PM UTC-8, Richard Damon wrote:
    On 12/11/23 11:43 AM, olcott wrote:
    On 12/11/2023 5:37 AM, Mikko wrote:
    On 2023-12-10 15:09:28 +0000, olcott said:

    On 12/10/2023 4:10 AM, Mikko wrote:
    On 2023-12-09 15:27:08 +0000, olcott said:

    On 12/9/2023 3:53 AM, Mikko wrote:
    On 2023-12-08 17:10:15 +0000, olcott said:

    On 12/8/2023 1:52 AM, Mikko wrote:
    On 2023-12-05 19:26:20 +0000, olcott said:

    The way that is works for the entire body of analytic
    knowledge:
    True(x) ≡ (⊢ x)
    False(x) ≡ (⊢ ¬x)

    Note that those don't define the semantical thruth, which is the >>>>>>>>>>> usual meaning of "true".


    ∀L ∈ Formal_System ∀x ∈ Language(L)
    True(L,x) ≡ (T ⊢ x)
    False(L,x) ≡ (T ⊢ ¬x)

    Yes they do:
    (1) The notions of True and False are inherently semantic.

    The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>>
    (2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>>>       logic to diverge from the model of the syllogism is a huge
    mistake.

    A syllogism is a formal inference that does not depend on
    semantics.


    https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    It always depends on defined sets providing its semantics as
    Categorical propositions
    https://en.wikipedia.org/wiki/Categorical_proposition

    Not for purposes that do not need any semantics.

    Mikko


    *Yes for all purposes. I am changing logic into correct reasoning* >>>>>>
    The only way that we can tell the the principle of explosion
    is nonsense is by plugging semantics into it and then see
    that this semantics is not semantically carried though.

    That does not show that the principle of explosion is nonsense.

    Ross Finlayson said that the principle of explosion cannot exist in
    relevance logic, thus making my point.
    Ye, *IF* you accept the logical limitations of "Relevence Logic", you
    can avoid the problems of the Principle of Explosion. But then you need
    to accept that you logic system is "weaker" as there will be statements
    that can not be proven in it (or even stated) then in "Classical" logic. >>>>
    The principle of explosion "proves" nonsense when semantics are
    required.
    (a) Cat are dogs
    (b) Cats are not dogs
    (c) Therefore the Moon is made from green cheese
    But


    The cow jumped over the Moon and The cow did not jump over the Moon >>>>>> therefore the Moon is made from green cheese.

    Have you ever met the cow that both jumped over the Moon and did not >>>>> jump over the Moon?


    It has always been the case that contradictions only proof falsehood.
    The principle of explosion violates
    https://en.wikipedia.org/wiki/Law_of_noncontradiction
    No, Contradictions prove that something is incorrect. If you get to a
    Contradicition in your logic, you KNOW that something prior was
    incorreect (or your logical system is just inherently broken)

    The correct way to process the principle of explosion is:
    (A ∧ ¬A) ⊢ False

    That does not process the principle of explosion.


    That is what a contradiction actually semantically entails.
    People that only learn these things by rote never notice
    errors that are discerned by the coherent philosophical foundation.
    Nope.

    Your never ever learned attitude means you just naturally speak
    incorrect statements, which when you repeat them after being told
    otherwise, make you into a habitual patholgocial liar.

    You can't refute climate change because your native tongue is lies an
    illogic, so of course you don't know how to show that.

    One way to interprete the situation where False is proven is that
    instead of the usual two truth values (False and True) there is only >>>>> one that has two names, i.e., False is the same as True.

    Nonsense gibberish. Bivalent formal systems inherently have a set of
    immutable properties. This is not merely a game, unless we formalize
    True(L,x) defeating Tarski dangerous lies will cause climate change
    to destroy all life on Earth by the time we hit +8C as early as 2100.

    https://phys.org/news/2023-12-million-year-history-carbon-dioxide-comfort.html?fbclid=IwAR3paozWIzEXvRp0swQVLRO8cbjXADWmSNZw8r5w41ULyYElSxNLqccDxXU
    So, you don't understand that "Bivalent" isn't the only type of Logic?
    or Formal System?

    What does Tarski have to do with disproving Lies?

    Tarski says that there are SOME statements which we can not determine
    their Truth Value, he does NOTHING to limit the ability to show that
    some things are just false.

    That you think it does, just shows how little you understand about what
    you pontificate on.

    Then every
    True sentence is False and every False sentence is True. If there
    are no other truth values then every sentence is both True and False. >>>>> Not very useful but coherent.

    Mikko







    Everything Zen?  Yes, I think so.



    Actually a bunch of times here I've also written little extensions to
    classical logic
    that just leave out material implication and ex falso quodlibet.

    It's not like you need it for free will or speculation of any sort,
    absurd or not,
    you can have your own private language of things, though it results not
    equi-interpretability as far as there's interpretability.

    Mostly this was recently when it was for "D.C.'s linear editor of
    syllogistic
    constructs, what D.C. says", where long ago I put down material
    implication
    as flawed, that a model from the universe of models is different than
    a bit-set
    of state-flags.

    Or, you know, "chucks" and "jigs", bits and their states.



    You perfectly agree with my assessment of the two key issues of
    classical logic. When we encode the entire body of human knowledge using Higher Order Logic such that the meaning of the terms is fully
    integrated into this logic using a knowledge ontology then it seems that
    we have a logic much more powerful than classical logic that excludes
    the above two issues.

    When we hypothesize that all human knowledge is formalized syntactically
    then provable does entail true. To simplify the idea of a knowledge
    ontology we can call this a tree of knowledge arranged as an inheritance hierarchy of sound deductions. We don't have to build this tree we
    merely imagine that it exists as the architecture of the notion of
    True(L,x).


    Nope. One point, by restricting the domain of your logic, you need to
    eliminate much of the "knowledge" you had, as it was based on logic that
    you have now prohibited.

    Remember, every statement shown to be true in a Formal System is based
    on the properties of that Formal System, including the rules of logic
    that it used.

    The "Logic" isn't more powerful, as it can, by definition, do less
    things. Perhaps you can claim that the meaning of being Known is "More Powerful", as what is known has passed a stronger test, but if that
    comes at the cost of having to unknow a lot of what is known, is that
    what you want?

    Note, your statement:

    When we hypothesize that all human knowledge is formalized syntactically
    then provable does entail true.


    Just isn't true, as formalizing knowledge, even all of it, doesn't, in
    itself, change the definition of "True".

    It is a well accepted given that we don't, and can't, know everything
    that is actually true, because Truth is independent of Knowledge even if Knowledge is made dependent on Truth.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Tue Dec 12 20:44:06 2023
    On 12/12/23 1:32 AM, olcott wrote:
    On 12/12/2023 12:08 AM, Ross Finlayson wrote:
    On Monday, December 11, 2023 at 8:54:26 PM UTC-8, olcott wrote:
    On 12/11/2023 10:07 PM, Ross Finlayson wrote:
    On Monday, December 11, 2023 at 4:59:55 PM UTC-8, Richard Damon wrote: >>>>> On 12/11/23 11:43 AM, olcott wrote:
    On 12/11/2023 5:37 AM, Mikko wrote:
    On 2023-12-10 15:09:28 +0000, olcott said:

    On 12/10/2023 4:10 AM, Mikko wrote:
    On 2023-12-09 15:27:08 +0000, olcott said:

    On 12/9/2023 3:53 AM, Mikko wrote:
    On 2023-12-08 17:10:15 +0000, olcott said:

    On 12/8/2023 1:52 AM, Mikko wrote:
    On 2023-12-05 19:26:20 +0000, olcott said:

    The way that is works for the entire body of analytic >>>>>>>>>>>>>> knowledge:
    True(x) ≡ (⊢ x)
    False(x) ≡ (⊢ ¬x)

    Note that those don't define the semantical thruth, which >>>>>>>>>>>>> is the
    usual meaning of "true".


    ∀L ∈ Formal_System ∀x ∈ Language(L)
    True(L,x) ≡ (T ⊢ x)
    False(L,x) ≡ (T ⊢ ¬x)

    Yes they do:
    (1) The notions of True and False are inherently semantic. >>>>>>>>>>>
    The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>>>> semantics of T, so True as defined above is not a semantic >>>>>>>>>>> notion.

    (2) I am saying that dividing semantics from syntax thus >>>>>>>>>>>> enabling
    logic to diverge from the model of the syllogism is a huge >>>>>>>>>>>> mistake.

    A syllogism is a formal inference that does not depend on >>>>>>>>>>> semantics.


    https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    It always depends on defined sets providing its semantics as >>>>>>>>>> Categorical propositions
    https://en.wikipedia.org/wiki/Categorical_proposition

    Not for purposes that do not need any semantics.

    Mikko


    *Yes for all purposes. I am changing logic into correct reasoning* >>>>>>>>
    The only way that we can tell the the principle of explosion
    is nonsense is by plugging semantics into it and then see
    that this semantics is not semantically carried though.

    That does not show that the principle of explosion is nonsense.

    Ross Finlayson said that the principle of explosion cannot exist in >>>>>> relevance logic, thus making my point.
    Ye, *IF* you accept the logical limitations of "Relevence Logic", you >>>>> can avoid the problems of the Principle of Explosion. But then you
    need
    to accept that you logic system is "weaker" as there will be
    statements
    that can not be proven in it (or even stated) then in "Classical"
    logic.

    The principle of explosion "proves" nonsense when semantics are
    required.
    (a) Cat are dogs
    (b) Cats are not dogs
    (c) Therefore the Moon is made from green cheese
    But


    The cow jumped over the Moon and The cow did not jump over the Moon >>>>>>>> therefore the Moon is made from green cheese.

    Have you ever met the cow that both jumped over the Moon and did not >>>>>>> jump over the Moon?


    It has always been the case that contradictions only proof falsehood. >>>>>> The principle of explosion violates
    https://en.wikipedia.org/wiki/Law_of_noncontradiction
    No, Contradictions prove that something is incorrect. If you get to a >>>>> Contradicition in your logic, you KNOW that something prior was
    incorreect (or your logical system is just inherently broken)

    The correct way to process the principle of explosion is:
    (A ∧ ¬A) ⊢ False

    That does not process the principle of explosion.


    That is what a contradiction actually semantically entails.
    People that only learn these things by rote never notice
    errors that are discerned by the coherent philosophical foundation. >>>>> Nope.

    Your never ever learned attitude means you just naturally speak
    incorrect statements, which when you repeat them after being told
    otherwise, make you into a habitual patholgocial liar.

    You can't refute climate change because your native tongue is lies an >>>>> illogic, so of course you don't know how to show that.

    One way to interprete the situation where False is proven is that >>>>>>> instead of the usual two truth values (False and True) there is only >>>>>>> one that has two names, i.e., False is the same as True.

    Nonsense gibberish. Bivalent formal systems inherently have a set of >>>>>> immutable properties. This is not merely a game, unless we formalize >>>>>> True(L,x) defeating Tarski dangerous lies will cause climate change >>>>>> to destroy all life on Earth by the time we hit +8C as early as 2100. >>>>>>
    https://phys.org/news/2023-12-million-year-history-carbon-dioxide-comfort.html?fbclid=IwAR3paozWIzEXvRp0swQVLRO8cbjXADWmSNZw8r5w41ULyYElSxNLqccDxXU
    So, you don't understand that "Bivalent" isn't the only type of Logic? >>>>> or Formal System?

    What does Tarski have to do with disproving Lies?

    Tarski says that there are SOME statements which we can not determine >>>>> their Truth Value, he does NOTHING to limit the ability to show that >>>>> some things are just false.

    That you think it does, just shows how little you understand about
    what
    you pontificate on.

    Then every
    True sentence is False and every False sentence is True. If there >>>>>>> are no other truth values then every sentence is both True and
    False.
    Not very useful but coherent.

    Mikko







    Everything Zen? Yes, I think so.



    Actually a bunch of times here I've also written little extensions
    to classical logic
    that just leave out material implication and ex falso quodlibet.

    It's not like you need it for free will or speculation of any sort,
    absurd or not,
    you can have your own private language of things, though it results not >>>> equi-interpretability as far as there's interpretability.

    Mostly this was recently when it was for "D.C.'s linear editor of
    syllogistic
    constructs, what D.C. says", where long ago I put down material
    implication
    as flawed, that a model from the universe of models is different
    than a bit-set
    of state-flags.

    Or, you know, "chucks" and "jigs", bits and their states.


    You perfectly agree with my assessment of the two key issues of
    classical logic. When we encode the entire body of human knowledge using >>> Higher Order Logic such that the meaning of the terms is fully
    integrated into this logic using a knowledge ontology then it seems that >>> we have a logic much more powerful than classical logic that excludes
    the above two issues.

    When we hypothesize that all human knowledge is formalized syntactically >>> then provable does entail true. To simplify the idea of a knowledge
    ontology we can call this a tree of knowledge arranged as an inheritance >>> hierarchy of sound deductions. We don't have to build this tree we
    merely imagine that it exists as the architecture of the notion of
    True(L,x).
    --
    Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
    hits a target no one else can see." Arthur Schopenhauer

    No, where here there's a sort of "pure logic" with "first-order
    formalizability".


    No we are assuming Higher Order Logic.

    You know that HOL largely is incompatible with Relevence theory, as part
    of the nature of Relevence logic is a restriction on the form of the
    antecedent and consequence of the operations, which makes the broad
    operation of the qualifiers hard to work in, thus Higher Order Logics
    (or even First Order Logic) which are based on them, hard (if not
    impossible) to work into the logic.


    You describe what seems a correspondence theory of truth.


    Not at all. It is all part of the coherence theory of truth.

    I suppose there was that "debate of Sowa" a while ago.

    What's "sensible, fungible, and tractable", results of course that
    there still remains all of Godel's and Tarski's results, they don't need
    "Russell's Boole's Comte's logical positivism's not-quite-classical
    logic".

    That there's an extra-ordinary and a theory for a pure logic with
    first-order-formalizability, and "zero-eth order", is just a bit above
    that.

    Data access and contemplation are two different things,
    to distinguish "large data structures" from "profound realizings".

    I.e., here there's that for being counter to Goedel, puts the
    extra-ordinary in the theory, not that it's closed well-founded again.

    ~Provable(L,x) ≡ ~True(L,x)
    Gödel's PA and his metamathematics at the next higher order of logic

    So, it is not true the the number g doesn't exist and also that it is
    not true that it does?

    After all, Godel proved that it doesn't actually exist, and we can't
    prove that.

    I guess your logic system fails the property of the excluded middle for
    simple existance.


    There's a well-founded fragment, ..., but it's undecideable in
    ZF - Axiom of Ordinary Infinity whether there's even a standard
    model of integers, at all, or just fragments and extensions.

    This helps make for things like Borel vs. Combinatorics,
    number theory with a prime or composite at infinity, the
    undecideability or for stronger-leaning alternatives in
    number-theoretic conjectures, and for such purposes
    as axiomless natural deduction resulting "a theory", "A Theory".

    Zen, I think not.



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