Many Many Problems

Supervaluationist solutions to 'the problem of the many' typically rely on two principles. First, the root of the problem is that singular terms can be vague, just as predicates can be. Secondly, the same resolution as the supervaluationist suggests for puzzles with vague predicates will resolve puzzles concerning vague singular terms. In recent years this second principle has been attacked from a number of fronts: it has been claimed that supervaluationist accounts of vague singular terms cannot explain the role of vague singular terms in propositional attitude reports, cannot explain penumbral connections between distinct singular terms, and cannot allow that vague singular terms are directly referential. While some of these arguments are successful against extant supervaluationist theories, I offer some natural modifications to supervaluationism which avoid the challenges.