The full necessitation principle Nec is inapplicable to f... — Carmelics

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The full necessitation principle Nec is inapplicable to formulas containing free terms in Q

Modality & Possibility

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1 reason for

2 reasons against

Reasons For

1 perspective

Reason for

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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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Reasons Against

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Reason against 1 of 2

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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 against 2 of 2

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