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excluded middle law

Law of excluded middle:

One of the traditional three laws of thought (along with the laws of identity and contradiction).

Every proposition is either true or not true.

This is weaker than the law of bivalence (every proposition is true or false), since if there is a third truth value excluded middle can still hold, though bivalence will fail. (However, bivalence is sometimes treated as a version of excluded middle).

For classical logic, excluded middle follows from the law of contradiction. Intuitionist logic accepts the latter but not excluded middle (also see: double negation), for reasons connected with the ‘Jones was brave’ example (see bivalence).

Also see: degrees of truth

Source:
P T Geach and W F Bednarowski, “The Law of Excluded Middle’ (symposium), Proceedings of the Aristotelian Society, supplementary volume (1956)

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    • 2.5 Why Mathematics Lacks Rigor: And all of Infinite Set Theory is Wrong
    • 2.6 Notebook: Contradiction , Journal for Writing, College Ruled Size 6" x 9", 110 Pages

Related:

  • bivalence law or principle
  • contradiction law
  • identity law
  • three laws of thought
  • dialetheism

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    contextualism

    subjective idealism

    innate ideas

    degrees of truth

    language of thought

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