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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that One must either relax the condition for being 'purely inferential' or add more structure to accommodate the natural deduction introduction rule for negation.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Proof-theoretic semantics can treat negation as defined via absurdity, making falsum a legitimate logical primitive rather than a structural addition.
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    • 2.Prawitz and Dummett's harmony criterion accommodates introduction rules that appeal to absurdity without violating inferentialist purity, since falsum carries no non-inferential content.
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    Reason for 2 of 2
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    • 1.Bilateral proof systems, as developed by Rumfitt, assign assertoric and rejective forces to sentences, allowing negation introduction to be stated purely in terms of denial without invoking falsum.
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    • 2.If denial is a primitive speech act coordinate with assertion, the negation introduction rule gains a purely inferential formulation that requires no relaxation of the purity condition.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.The strictest criterion for purely inferential rules cannot be met by the natural deduction introduction rule for negation.
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    • 2.The natural deduction introduction rule for negation requires either the falsum constant or an additional instance of the negation sign.
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