Competing semantics of vagueness: Many values versus super-truth

Synthese 33 (2-4):195--210 (1976)
A semantics of vagueness should reject the principle that every statement has a truth-value yet retain the classical tautologies. A many-value, non-truth-functional semantics and a semantics of super-valuations each have this result. According to the super-valuation approach, 'if a man with n hairs on his head is bald, then a man with n plus one hairs on his head is also bald' is false because it comes out false no matter how the vague predicate 'is bald' is appropriately made precise. But why should a sentence in which components actually remain imprecise be regarded as actually false just because it would be false if its components were precise? On one of the alternative treatments of quantification allowed by the many-value approach, the sentence in question is assigned an intermediate value closer to 'false' than to 'true'. Despite the elegance of the super-valuation approach, there are reasons to prefer the many-value approach.
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References found in this work BETA
Richmond Campbell (1974). The Sorites Paradox. Philosophical Studies 26 (3-4):175 - 191.
Michael Dummett (1975). Wang's Paradox. Synthese 30 (3-4):201--32.
David H. Sanford (1975). Borderline Logic. American Philosophical Quarterly 12 (1):29-39.
Citations of this work BETA
Bertil Rolf (1984). Sorites. Synthese 58 (2):219 - 250.
Ewa Orlowska (1984). Modal Logics in the Theory of Information Systems. Mathematical Logic Quarterly 30 (13‐16):213-222.
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