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Math Help - Excluded middle

  1. #1
    Junior Member
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    Excluded middle

    Hi all,

    Could anyone please explain what an excluded middle from the following derivation is?

    Many thanks

    ssharish
    Attached Thumbnails Attached Thumbnails Excluded middle-excluded-middle.png  
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  2. #2
    MHF Contributor
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    Re: Excluded middle

    The excluded middle is an axiom schema A\lor\neg A. This means that A can be replaced by any formula to get an axiom. Equivalently, it is an inference rule with no assumptions.
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  3. #3
    MHF Contributor
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    Re: Excluded middle

    I should add that the law of excluded middle is just a name for formulas of the form A\lor\neg A. It does not automatically mean that it has to be used as an axiom. In fact, in natural deduction it is usually derivable using the inference rule of double-negation elimination. Pure natural deduction does not have axioms.
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