Mass nouns and non-singular logic
Résumé
A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but non-singular logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets when characterizing their semantics, we arrive at a Russellian paradox. Likewise, a semantics based upon predicate logic and mereological sums is too weak, since it cannot characterize the “intermediary” construals that sentences containing mass nouns may receive. We then develop an account where mass nouns are treated as non-singular terms. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: "The silverware that is on the table comes from Italy." We show that this account provides a satisfactory semantics for a wide range of sentences, including cases often seen as difficult, like "The clay that made up those three bowls is identical with the clay that now makes up these two statues" (cf. Cartwright 1965) and "All phosphorus is either red or black" (Roeper 1983).