A requirement on any theory of vagueness is that it solve the sorites paradox. It is generally agreed that there are two aspects to such a solution. One task is to locate the error in the sorites argument. The second task is to explain why the argument is nevertheless compelling: why the sorites reasoning constitutes a paradox rather than a simple mistake. I argue for a further constraint on approaches to the second task: they should conform to the standard modus operandi in formal semantics, in which the semantic theory one develops is taken to be implicit in the usage and/or intuitions of competent speakers. I then argue that, out of the current main contenders for a theory of vagueness, only certain theories that posit degrees of truth can meet this further constraint. Thus, while many have claimed to have solutions to the paradox, only certain kinds of degree theory can actually solve the sorites.
