The English language is rife with expressions that involve the word might. For example, you are reading this abstract, but you might have decided to read something else instead. Although this claim is undoubtedly true, it is not clear what makes it to be true: what fact it happens to express.
Counterpart theory is a formal language designed to express the meanings of claims involving the word might. According to the counterpart theorist, the claim “You might have read something else instead of this abstract” in fact means, "There is a non-actual person who is similar to (but not identical to) you and this person read something else instead of this abstract." Although the language of counterpart theory is technically impressive and is easy to use with precision, many philosophers are incredulous that it accurately portrays what speakers mean when they use the expression might.
Hoping to sooth the incredulous, Ulrich Meyer (forthcoming) proves that his language of counterpart theory has expressive superiority over all known rivals. Since his version of counterpart theory is able to express more than its rivals can, this is a reason to think that it does capture the meanings of our English modal claims despite its initial implausibility. In my talk, I object to Meyer by showing that his proof of expressive superiority ultimately depends on yet another implausible claim: that English speakers are, without their awareness, talking about a certain kind of mathematical object – a (sometimes empty) set. Since you cannot successfully defend an implausible idea by appealing to other implausible ideas, Meyer’s proof, however technically impressive, fails to demonstrate anything about the meaning of English claims. I conclude by considering some strategies that are analogous to Meyer’s, but avoid appealing to mathematical objects.