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    C.I. Lewis demonstrated that any system preserving strict... — Carmelics
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    Challenges→A conditional is logically valid only if the antecedent and consequent share at least one sentential variable or parameter

    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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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
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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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    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    A conditional is logically valid only if the antecedent and consequent share at ...Allowing arbitrary consequents B to follow from fixed antecedents violates the r...From a logical truth, anything follows without incoherence: this is the principl...Lewis's own systems (S1-S5) were designed to restrict such inferences, suggestin...
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    Since contradictions are necessarily false, ¬◇(A ∧ ¬A) is a logical truth in any...Strict implication correctly formalizes necessary conditional: if A strictly imp...Variable-free validities like ¬◇(A ∧ ¬A) → B collapse distinctions between tauto...

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    Perspectives
    2 (1 for, 1 against)
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    1 edit