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    Classical logic's material conditional 'A → B' is truth-f... — Carmelics
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    Challenges→Logical validity requires that premises be relevant to the conclusion they support

    Classical logic's material conditional 'A → B' is truth-functional and has proven indispensable in mathematics and science without relevance constraints.

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    Reasons For

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    • 1.Material conditional enables proof by contradiction and reductio ad absurdum, which are foundational inference patterns in mathematics.
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    • 2.Truth-functionality allows mechanical computation: conditional validity depends only on truth values, not meanings, enabling automation.
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    • 3.Physics and engineering successfully use material conditionals in causal models without relevance constraints, yielding predictive accuracy.
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    Reasons Against

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    • 1.Material conditional validates 'true → false' as true when antecedent is false, but this contradicts how conditional reasoning actually works in natural language and cognition.
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    • 2.Relevant logic systems solve the paradoxes of material implication (like 'if pigs fly, then 2+2=5 is true') by requiring logical connection between premises and conclusions.
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    • 3.Scientific causal reasoning implicitly assumes relevance: we reject conditionals where antecedent and consequent are logically unrelated, suggesting relevance constraints are necessary.
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    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Logical validity requires that premises be relevant to the conclusion they suppo...Material conditional enables proof by contradiction and reductio ad absurdum, wh...Material conditional validates 'true → false' as true when antecedent is false, ...Physics and engineering successfully use material conditionals in causal models ...
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    Relevant logic systems solve the paradoxes of material implication (like 'if pig...Scientific causal reasoning implicitly assumes relevance: we reject conditionals...Truth-functionality allows mechanical computation: conditional validity depends ...

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