Three-Valued Plurivaluationism: A Reply to Williamson's Criticisms on the Three-Valued Approach to the Sorites Paradox

In the past 40 years, philosophers have proposed a large number of solutions to the sorites paradox, aiming at both pinpointing the problem(s) of these arguments and giving a plausible explanation of why we are taken in by them. However, one kind of these solutions, namely, the three-valued solutions, has often been thought to be implausible. There are two main objections to the three-valued approach to vagueness in the literature. One of them focuses on the fact that the approach is truth-functional and thereby cannot do justice to the phenomenon of penumbral connection. The other objection is that the three-valued approach falls foul of "the problem of higher-order vagueness" by imposing sharp cut-off points on a sorites series where there should be none. Since the second one it often thought to be more serious than the first one, I will elaborate on it first.