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  • Re: Most generically exactly what is a proof?

    From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math on Wed Dec 3 12:47:42 2025
    From Newsgroup: comp.theory

    olcott kirjoitti 2.12.2025 klo 16.49:
    On 12/2/2025 3:15 AM, Mikko wrote:
    olcott kirjoitti 1.12.2025 klo 14.27:

    A prove is any sequence of steps that shows
    that its conclusion is necessarily true.
    That depends on the exact meaning of "shows". The usual meaning of
    "show" is to make something visible. But merely making some sequence
    of some steps visible does not make it a proof.

    What I usually mean by proof is any kind of correct
    semantic logical entailment anchored in the basis
    of expressions of language that are certainly true.

    What others mean by "proof" does not include anything that cannot
    be checked without a proof that it is a "proof".
    --
    Mikko
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  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math on Wed Dec 3 10:06:12 2025
    From Newsgroup: comp.theory

    On 12/3/2025 4:47 AM, Mikko wrote:
    olcott kirjoitti 2.12.2025 klo 16.49:
    On 12/2/2025 3:15 AM, Mikko wrote:
    olcott kirjoitti 1.12.2025 klo 14.27:

    A prove is any sequence of steps that shows
    that its conclusion is necessarily true.
    That depends on the exact meaning of "shows". The usual meaning of
    "show" is to make something visible. But merely making some sequence
    of some steps visible does not make it a proof.

    What I usually mean by proof is any kind of correct
    semantic logical entailment anchored in the basis
    of expressions of language that are certainly true.

    What others mean by "proof" does not include anything that cannot
    be checked without a proof that it is a "proof".


    When we know that "cats" <are> "mammals"
    and that "mammals" <are> "animals" then
    we certainly know that "cats" <are> "animals".

    The entire body of general knowledge can be
    encoded this same way. We could do this same
    thing for situation specific knowledge on a
    case-by-case basis. General knowledge is finite.
    The entire set of situation specific knowledge
    is infinite.
    --
    Copyright 2025 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning" computable.

    This required establishing a new foundation
    for correct reasoning.
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