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    One must either relax the condition for being 'purely inf... — Carmelics
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    One must either relax the condition for being 'purely inferential' or add more structure to accommodate the natural deduction introduction rule for negation.

    Philosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

    2 perspectives
    Reason against 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 against 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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    Philosophy of Language

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    Related

    Bilateral proof systems, as developed by Rumfitt, assign assertoric and rejectiv...If denial is a primitive speech act coordinate with assertion, the negation intr...Prawitz and Dummett's harmony criterion accommodates introduction rules that app...Proof-theoretic semantics can treat negation as defined via absurdity, making fa...
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    The natural deduction introduction rule for negation requires either the falsum ...The strictest criterion for purely inferential rules cannot be met by the natura...

    Similar

    The strictest criterion for purely inferential rules cannot be met by ...92%The strictest criterion for 'purely inferential' rules—requiring every...87%The natural deduction introduction rule for negation must employ eithe...85%The natural deduction introduction rule for negation requires either t...84%

    Source

    AI-extracted1/3 agreementValid
    SEP: logical-constants
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    We would have to say when an introduction or elimination rule counts as “purely inferential,” to exclude rules like these: \begin{equation*} \frac{a~\text{is red}}{Ra} \quad \frac{A, B, \text{water is}~H_{2}O}{A * B} \end{equation*} The strictest criterion would allow only rules in which every sign, besides a single instance of the constant being characterized, is either structural (like the comma) or schematic (like \(\dq{A}\)). But although this condition is met by the standard rules for con
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

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    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit