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Inverse View
It is not the case that Relevance logicians (Anderson and Belnap) argue that validity requires the premises to be genuinely relevant to the conclusion, not merely formally connected.
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Reasons For
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1.
Relevance is vague and context-dependent; no principled criterion exists for when premises are 'genuinely relevant' versus merely formally connected.
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2.
Classical logic's formal validity has worked successfully across mathematics, science, and philosophy; relevance logic gains no practical advantages.
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3.
Intuitions about 'relevance' are psychologically driven, not logically grounded; formality is what distinguishes logic from rhetoric or persuasion.
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Reasons Against
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Reason against
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1.
Classical logic permits 'explosion': from contradictions, anything follows formally, yet intuitively this seems invalid when premises lack connection to conclusion.
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2.
In real reasoning, we reject arguments where premises are logically unrelated to conclusions even if formally valid, suggesting relevance captures genuine validity.
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3.
Relevance logic explains why material conditionals with unrelated antecedents and consequents feel defective despite classical validity.
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