A solution to the sorites paradox is obtained by distinguishing three formats of the sorites argument and appraising them in the light of four fundamental considerations: (i) the appropriate notion of truth for the application of vague predicates to their borderline cases, (ii) a certain construal of borderline cases, (iii) a certain freedom of use of vague terms not enjoyed by non-Vague terms and (iv) the revocation of that freedom by deductive contexts.

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. (shrink)