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    Relevant logic's rejection of ex falso is therefore justi... — Carmelics
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    Challenges→The ex falso quodlibet — (A ∧ ¬A) → B — is not logically valid in relevant logic

    Relevant logic's rejection of ex falso is therefore justified on either dialetheist or paraconsistent grounds, but VSP as the stated mechanism is neither necessary nor sufficient for either justification.

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    Key Terms

    Dialetheist / Dialetheism(one possible justification for rejecting ex falso)
    The philosophical view that some statements can actually be both true and false at the same time, contradicting the usual logical rule that nothing can be both true and false.
    Ex falso (or ex falso quodlibet)(the specific logical rule that relevant logic rejects)
    A classical logic rule that says if you start with a contradiction (something both true and false), you can prove literally anything, no matter how unrelated.
    Paraconsistent(another possible justification for rejecting ex falso)
    A type of logic designed to handle contradictions without exploding into absurdity—it doesn't automatically let you prove anything from a contradiction.
    VSP(as a technical acronym in logic)
    An abbreviation for a specific logical principle or property (the exact name varies, but it's a formal rule that logicians debate).

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    necessary and sufficient conditions(in philosophical analysis)
    A 'necessary' condition is something that must be true for something else to happen; a 'sufficient' condition is something that guarantees it will happen. This phrase describes what must be true (and what's enough) for a definition to apply.
    relevant logic(Contrasted with classical monotonic logic where X ⊢ A implies X,Y ⊢ A for any Y)
    A logical system that restricts premise combination so that all premises must bear some relevance to the conclusion; adding irrelevant material does not preserve entailment

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    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    The ex falso quodlibet — (A ∧ ¬A) → B — is not logically valid in relevant logic

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