Sorites and the Ship of Theseus: a logic of fuzzy identity

Graham Priest distinguishes between two kinds of Sorites paradoxes: standard Sorites, such as the paradox of the Heap, and non-standard Sorites, such as the Ship of Theseus. The former concerns properties of objects, whereas the latter concerns their identity conditions. Priest notes that the standard Sorites has been solved in fuzzy logic and proposes a logic of fuzzy identity to solve the non-standard Sorites in a similar way. Ideally, a definition of fuzzy identity would satisfy the fuzzy equivalents of the classical principles of identity: it should (i) be a fuzzy equivalence relation and (ii) validate a fuzzy version of the substitutivity of identicals. However, Priest’s definition fails to meet the latter requirement and only applies to a special case of the non-standard Sorites. I suggest an improvement on his logic that overcomes these shortcomings, provides the two Sorites with a unified solution, and also applies to reasoning about vague objects in general.