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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Classical logic's material conditional 'A → B' is truth-functional and has proven indispensable in mathematics and science without relevance constraints.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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