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It is not the case that Supervaluationism violates classical inference rules: under supervaluational semantics, 'A or not-A' can be supertrue while neither 'A' nor 'not-A' is true.
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Reasons For
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1.
If classical inference rules fail at the object level, supervaluationism undermines the distinction between validity and invalidity itself.
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2.
Distinguishing 'truth' from 'supertruth' creates a hierarchy of semantic notions; ordinary logical reasoning operates at the basic truth level, not metalevel.
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3.
Vagueness can be adequately modeled using degree-theoretic semantics or epistemic approaches without abandoning classical logic's inference rules.
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Reasons Against
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1.
Supervaluationism correctly models vagueness: borderline cases lack determinate truth-values, making classical bivalence inappropriate for vague predicates.
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2.
Classical logic assumes a complete, determinate world; but vagueness is a genuine semantic phenomenon requiring non-classical frameworks.
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3.
The law of excluded middle ('A or not-A') can be supertrue without either disjunct being true, preserving logical validity at the metalevel.
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