Borderline Logic

American Philosophical Quarterly 12 (1):29-39 (1975)
To accommodate vague statements and predicates, I propose an infinite-valued, non-truth-functional interpretation of logic on which the tautologies are exactly the tautologies of classical two-valued logic. iI introduce a determinacy operator, analogous to the necessity operator in alethic modal logic, to allow the definition of first-order and higher-order borderline cases. On the interpretation proposed for determinacy, every statement corresponding to a theorem of modal system T is a logical truth, and I conjecture that every logical truth on the interpretation corresponds to a theorem of T. the interpretation is extended to predicate logic. A borderline case of a predicate 'F’ is neither determinately F nor determinately not-F. Traditional sorites arguments are seen to fall apart early in their gradual stepwise passage from truth to falsity.
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    Elia Zardini (2013). Higher-Order Sorites Paradox. Journal of Philosophical Logic 42 (1):25-48.
    Graeme Forbes (1986). In Defense of Absolute Essentialism. Midwest Studies in Philosophy 11 (1):3-31.
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    Diana Raffman (2009). Demoting Higher-Order Vagueness. In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press. 509--22.
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    Elia Zardini (2013). Higher-Order Sorites Paradox. Journal of Philosophical Logic 42 (1):25-48.

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