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    Relevant logic's variable-sharing condition (VSP) conflat... — Carmelics
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    Challenges→The ex falso quodlibet — (A ∧ ¬A) → B — is not logically valid in relevant logic

    Relevant logic's variable-sharing condition (VSP) conflates syntactic topic-overlap with semantic relevance, rejecting valid inferences on purely formal grounds that have no metaphysical basis.

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    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.VSP rejects A∨¬A→B solely because B shares no propositional variable with the antecedent, ignoring that this is logically valid in classical logic.
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    • 2.Semantic relevance requires a meaningful connection in truth-conditions, not mere syntactic overlap—two logically independent propositions can be relevantly connected.
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    • 3.Requiring variable-sharing conflates relevance with entailment; A can be relevant to B's truth without B appearing in A's truth-functional structure.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.VSP captures genuine intuitions about relevance: 'snow is white' and 'Paris is pretty' seem irrelevant premises for any mixed-topic conclusion.
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    • 2.Without VSP-like restrictions, explosion and disjunctive syllogism permit deriving any conclusion from contradictions, abandoning meaningful constraint on inference.
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    • 3.Variable-sharing is a principled, checkable criterion for relevance; rejecting it requires a better formal account of what makes premises semantically relevant.
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    Key Terms

    Formal grounds(the basis the statement says VSP uses to reject arguments)
    Rules based purely on the structure and shape of statements, without considering what they actually mean or represent in reality.
    Metaphysical basis(what the statement claims relevant logic is missing)
    A reason based on how reality actually is—the fundamental nature of things that exist, rather than just rules on paper.
    Semantic relevance(what the statement argues VSP fails to capture)
    Whether one statement actually matters to another based on what they really mean—not just whether they use similar words or symbols.
    Syntactic(as used in linguistics)
    Related to the rules and structure of how words are arranged in language, rather than their meaning.
    Topic-overlap(what syntactic analysis can measure)
    When two statements are about the same subject or contain the same basic elements, just looking at their form without considering their actual meaning.
    Variable-sharing condition (VSP)(a specific rule within relevant logic)
    A rule in relevant logic that says: for an argument to be valid, the basic building blocks (variables) in the starting statements must appear somewhere in the ending statement.
    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
    valid inference(Used within informal logic's definition of a good argument)
    A conclusion that follows from the premises

    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Requiring variable-sharing conflates relevance with entailment; A can be relevan...Semantic relevance requires a meaningful connection in truth-conditions, not mer...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    The ex falso quodlibet — (A ∧ ¬A) → B — is not logically valid in relevant logic
    VSP captures genuine intuitions about relevance: 'snow is white' and 'Paris is p...
    +3 moreShow less
    VSP rejects A∨¬A→B solely because B shares no propositional variable with the an...Variable-sharing is a principled, checkable criterion for relevance; rejecting i...Without VSP-like restrictions, explosion and disjunctive syllogism permit derivi...