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    This consequence conflicts with classical logic's law of ... — Carmelics
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    Supports→Frege's refined view raises unresolved questions

    This consequence conflicts with classical logic's law of excluded middle and forces Frege into a three-valued or truth-value gap framework he never explicitly endorsed or systematically developed.

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    Key Terms

    Frege(as a major historical figure in philosophy)
    Gottlob Frege (1848-1925) was a German logician and philosopher who founded modern logic and did groundbreaking work on how language relates to meaning and existence.
    Three-valued logic(Kleene's version is one example of three-valued logic)
    A system of logic that allows for three possible truth states instead of the usual two: something can be true, false, or undefined (neither clearly true nor false).
    classical logic(Contrasted with Hegel's dialectical approach that accepts contradictions)
    Aristotelian logic that dominated during Hegel's lifetime
    consequence(Buridan's medieval logic)
    A logical relation with necessary truth-preservation (TP) as its fundamental component
    law of excluded middle

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    (Classical logic; shown to be incompatible with smooth infinitesimal analysis)
    The classical logical principle that for any proposition, either the proposition or its negation holds — applied here as: every real number is either equal to 0 or not equal to 0.
    truth-value gap(Used as the reductio assumption to generate a contradiction with (ES-sent) and (F-sent).)
    The situation in which a sentence is neither true nor false.

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    Philosophy of Language1 linkedSkepticism1 linked

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    Frege's refined view raises unresolved questions

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