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  • Truth Bearer or Truth Maker

    From Mild Shock@21:1/5 to olcott on Wed Jul 24 22:34:59 2024
    But truth bearer has another meaning.
    The more correct terminology is anyway
    truth maker, you have to shift away the

    focus from the formula and think it is
    a truth bearer, this is anyway wrong,
    since you have two additional parameters
    your "True" and your language "L".

    So all that we see here in expression such as:

    [~] True(L, [~] A)

    Is truth making, and not truth bearing.
    In recent years truth making has received
    some attention, there are interesting papers
    concerning truth makers. And it has

    even a SEP article:

    Truthmakers
    https://plato.stanford.edu/entries/truthmakers/

    A world of truthmakers? https://philipp.philosophie.ch/handouts/2005-5-5-truthmakers.pdf

    olcott schrieb:

    The key difference is that we no long use the misnomer
    "undecidable" sentence and instead call it for what it
    really is an expression that is not a truth bearer, or
    proposition in L.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mild Shock@21:1/5 to All on Thu Jul 25 12:27:00 2024
    Sometimes conjectures become theorems
    when we move into a different model,
    like when we leave arithmetic, and

    go into set theory or analysis. A typical
    example is the Goodstein sequence, which
    becomes provable terminating in ZFC:

    Goodstein's theorem is a statement about the
    natural numbers, proved by Reuben Goodstein in 1944 https://en.wikipedia.org/wiki/Goodstein's_theorem

    Because ZFC has stronger induction principles.
    So maybe Goldbach's conjecture will
    have the same fate, and sometime become

    provable? Don't know. Isn't Terrence Tao
    expert on everything prime numbers. He
    had some success with the weak conjecture:

    In 2012, Terence Tao proved this without
    the Riemann Hypothesis; this improves both results. https://en.wikipedia.org/wiki/Goldbach's_weak_conjecture

    But its even not necessary to follow such
    a strict program to regain the "finite"
    character of logic. Even if we stick to

    classical logic, Gödels incompleteness
    theorem shows that this classical logic
    stil has some "finite" limitations,

    in that a axiomatization of arithmetic,
    will still not fully capture the intended
    model of arithmetic, in that the axiomatization

    will necessarily have at least one sentences
    which is not truth bearing in Olcotts words:

    https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

    Putting another Olcott label on the bottle
    doesn't change the content of the bottle.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mild Shock@21:1/5 to Mild Shock on Thu Jul 25 12:30:04 2024
    Obviously the current Artificial Intelligence
    wave, with its incarnations such as ChatGPT
    isn't that good, otherwise we might have heard

    of some break through. Were some conjectures
    meanwhile proved with the help of Artificial
    Intelliegence, or is the current AI only

    good at halucinating undirected nonsense from
    existing knowledge, not able to complete an
    unsolved conjecture?

    Mild Shock schrieb:
    Sometimes conjectures become theorems
    when we move into a different model,
    like when we leave arithmetic, and

    go into set theory or analysis. A typical
    example is the Goodstein sequence, which
    becomes provable terminating in ZFC:

    Goodstein's theorem is a statement about the
    natural numbers, proved by Reuben Goodstein in 1944 https://en.wikipedia.org/wiki/Goodstein's_theorem

    Because ZFC has stronger induction principles.
    So maybe Goldbach's conjecture will
    have the same fate, and sometime become

    provable? Don't know. Isn't Terrence Tao
    expert on everything prime numbers. He
    had some success with the weak conjecture:

    In 2012, Terence Tao proved this without
    the Riemann Hypothesis; this improves both results. https://en.wikipedia.org/wiki/Goldbach's_weak_conjecture

    But its even not necessary to follow such
    a strict program to regain the "finite"
    character of logic. Even if we stick to

    classical logic, Gödels incompleteness
    theorem shows that this classical logic
    stil has some "finite" limitations,

    in that a axiomatization of arithmetic,
    will still not fully capture the intended
    model of arithmetic, in that the axiomatization

    will necessarily have at least one sentences
    which is not truth bearing in Olcotts words:

    https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

    Putting another Olcott label on the bottle
    doesn't change the content of the bottle.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)