 Which set could make [the clay that was on the desk on July 1st] = [the clay that was on the table on July 2nd] true? What about the set of all minimal parts of clay, i.e., the set of all the instances of clay that have no other instance of clay as part?  However, with mass nouns like garbage, it is not clear what the minimal parts would be (cf. Pelletier &amp; Schubert 2003). And more crucially, one cannot exclude a priori the possibility that what a given mass noun applies to may be indefinitely divisible. So the semantics should not require mass nouns to have minimal parts (cf. Bunt 1985; Gillon 1992). (See section 9 for a solution to this problem within the framework of non-singular logic; see Steen 2012, section 2.3, for various metaphysical considerations concerning the purely set-theoretic approach.)