• There exists a G such that G is logically equivalent to its own unprova

    From olcott@21:1/5 to All on Fri Apr 21 19:33:43 2023
    XPost: sci.logic, sci.math, alt.philosophy
    XPost: comp.theory

    ∃G ∈ F (G ↔ (G ⊬ F))

    There exists a G such that G is logically equivalent to its own
    unprovability in F

    *If we assume that there is such a G in F that means that*
    G is true means there is no sequence of inference steps that satisfies G
    in F.
    G is false means there is a sequence of inference steps that satisfies G
    in F.

    *Thus the above G simply does not exist 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

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