Vagueness and domain restriction

In the introduction to their vagueness reader, Rosanna Keefe and Peter Smith clas-sified accounts of vagueness with respect to how they handle the sorites paradox. The sorites paradox is set out in the standard way with reference to a sorites se-quence s of objects s1,..., sn and an associated vague predicate F. In S, there is a very small and seemingly negligible difference between any two adjacent ele-ments si and si+1 with respect to the dimension that is relevant to satisfying F (for instance, if F is ‘... is tall’, then the dimension is height). This suggests that if si satisfies F, then so does si+1. Since S is a sorites sequence for F it is also stipulated that s1 satisfies F and that sn does not. Let ti denote si, 1 ≤ i ≤ n. Then the sorites argument is set up a