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    Carmelics

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

    It is not the case that C.I. Lewis demonstrated that any system preserving strict implication's modal character licenses variable-free validities like ¬◇(A ∧ ¬A) → B without logical incoherence.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Variable-free validities like ¬◇(A ∧ ¬A) → B collapse distinctions between tautologies and contingent truths.
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    • 2.Allowing arbitrary consequents B to follow from fixed antecedents violates the relevance principle: conclusion should relate to premises.
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    • 3.Lewis's own systems (S1-S5) were designed to restrict such inferences, suggesting his framework rejects, not licenses, this claim.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Strict implication correctly formalizes necessary conditional: if A strictly implies B, then ¬◇(A ∧ ¬B) holds necessarily.
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    • 2.Since contradictions are necessarily false, ¬◇(A ∧ ¬A) is a logical truth in any consistent modal system.
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    • 3.From a logical truth, anything follows without incoherence: this is the principle of explosion applied at the modal level.
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