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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The full necessitation principle Nec is inapplicable to formulas containing free terms in Q

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Kripke's completeness proofs for modal logic apply Nec to open formulas by treating free variables as implicitly universally bound, preserving soundness.
      ?

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    • 2.The inapplicability of Nec to formulas with free terms confuses the semantic role of free variables with the metaphysical contingency of named individuals.
      ?

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    • 3.Hughes and Cresswell demonstrate that restricting Nec to closed formulas undermines the derivability of key theorems in standard modal systems like S5.
      ?

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    Reason for 2 of 2
    ?
    • 1.Free terms in formal systems can be treated as schematic variables ranging over all possible values, not as designators of contingent particulars.
      ?

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    • 2.If a formula holds universally across all substitution instances, necessitation is warranted regardless of whether specific referents are necessary beings.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Q cannot prove the existence of any necessary beings
      ?

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    • 2.Some free terms in Q might refer to contingent beings
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    • 3.Applying Nec to formulas with free terms referring to contingent beings would be unjustified without provable necessary existence
      ?

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