Abstract. Austere modal metaphysicians advocate that some individuals, propositions and properties could have been nothing, that there could have been some individuals, propositions and properties that are actually nothing, and that necessarily, whatever stands in a relation is identical to something. Their metaphysics is thus not only contingentist about individuals, propositions and properties but also seriously actualist. The absence of a plausible account of the compositional semantics of first-order modal languages consistent with austere modal theories constitutes an abductive consideration against these. In reply, Stalnaker (2012) has sketched an account of the compositional semantics of first-order modal languages – formulated in terms of a generalisation of the Russellian notion of a propositional function -, which, according to him, is consistent with an austere modal metaphysics. In this paper Stalnaker’s sketched account is rigorously developed. Pace Stalnaker, it is shown in the paper that this account and Stalnaker’s views on which it