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It is not the case that Relevant logic requires that antecedent and consequent share propositional variables for a conditional to be valid, which p→q need not satisfy.
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Reasons For
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Reason for
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1.
Relevance conditions lack a precise, universally accepted definition, making relevant logic technically underdeveloped compared to classical approaches.
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2.
Material conditional p→q is justified by truth-conditions alone; adding relevance requirements imports extra metaphysical commitments without semantic justification.
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3.
Even unrelated conditionals (e.g., 'if snow is white, then grass is green') seem perfectly meaningful and evaluable, suggesting relevance isn't necessary.
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Reasons Against
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Reason against
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1.
Classical logic validates p→q even when p and q are completely unrelated, producing counterintuitive 'paradoxes of material implication.'
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2.
Relevant logic better captures how conditionals function in natural language and reasoning, where connection between antecedent and consequent matters.
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3.
Scientific and mathematical arguments require genuine connections between premises and conclusions, not merely true antecedents and consequents.
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