• =?UTF-8?Q?Re=3A_G=C3=B6del=27s_1931_incompleteness_fails_HOL?=

    From Richard Damon@21:1/5 to olcott on Sun Dec 10 08:11:16 2023
    On 12/9/23 9:55 PM, olcott wrote:
    On 12/9/2023 7:22 PM, Jim Burns wrote:
    On 12/8/2023 12:29 AM, olcott wrote:
    On 12/7/2023 6:11 PM, olcott wrote:
    On 12/7/2023 10:20 AM, olcott wrote:
    On 12/6/2023 9:56 PM, olcott wrote:
    On 12/6/2023 4:35 PM, Jim Burns wrote:

    [...]

    ...14
    Every epistemological antinomy can likewise
    be used for a similar undecidability proof...
    (Gödel 1931:43-44)

    Thus Gödel really screwed up.
    Epistemological antinomies

    The epistemological antinomy
    | This sentence is false
    |
    is not in Gödel's proof.

    | This sentence is false
    |
    is the blueprint, which guides
    Gödel placement of (metaphorically) actual
    bricks and mortar.

    You live in a building of some kind, I'd bet.
    What odds would you give on whether
    that building's blueprints are incorporated
    into its construction?
    If you ripped plaster off walls,
    would you find particular sheets paper
    holding up waterlines?

    In note 14, Gödel is mentioning that
    other blueprints can guide the placement of
    (metaphorically) actual bricks and mortar
    for other proofs.
    Nor are those other blueprints incorporated
    into those other proofs.

    Epistemological antinomies
    are neither

    ...here nor there.

    Since no epistemological antinomy can ever be used for
    any proof at all Gödel proved that it didn't have a clue
    about the subject matter of his paper.

    But he didn't, not in the way you are talking about.

    By your own logic, YOU are "using" an epistemological antinomy in your
    "proof" that Godel is incorrect, so your own proof is shown to be invalid.


    https://liarparadox.org/Tarski_247_248.pdf
    Tarski said that he used Gödel as a basis
    and in the above link shows that he anchored
    his whole proof in the actual Liar Paradox.

    Right, and again, not in the way you are assuming it was done.


    *Here is his actual proof*
    https://liarparadox.org/Tarski_275_276.pdf


    Right, and where did he assume that the Liar was a true statement?

    What he has shown is that the assumption that we can algorithmically
    determine the truth value of a sentence (his "Definition of Truth") then
    it would be possible to logically prove the Truth of the Liar. Since
    this is impossible, the assumption can't be true.

    You just don't understand how logic works.

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