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    The inconsistency is provable in a finite number of steps... — Carmelics
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    Supports→The addition of Basic Law V to second-order logic implies a contradiction.

    The inconsistency is provable in a finite number of steps within the combined system, satisfying Frege's own standard of rigorous gapless proof that he applied throughout Grundgesetze.

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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.
    Grundgesetze(as the specific work being discussed)
    The title of Frege's major work, meaning 'Basic Laws' in German; it was his attempt to create a complete logical system that would serve as the foundation for all mathematics.
    Inconsistency(as used in logic)
    When a system contains statements that contradict each other—like saying 'this is true' and 'this is false' at the same time.
    Provable(describing what can be established within a system)
    Able to be proven true using the accepted rules and starting points of a logical system.
    Rigorous

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    (as used in academic and philosophical discourse)
    Careful, thorough, and following strict rules—the opposite of loose or casual reasoning.
    gapless proof(Illustrated by the traditional syllogism 'All men are mortal; Socrates is a man; hence Socrates is mortal')
    A proof in which every inferential step is explicit and no steps are skipped

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    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

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    The addition of Basic Law V to second-order logic implies a contradiction.

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