We may wonder about the status of logical accounts of the meaning of language. When does a particular proposal count as a theory? How do we judge a theory to be correct? What criteria can we use to decide whether one theory is ?better? than another? Implicitly, many accounts attribute a foundational status to set theory, and set-theoretic characterisations of possible worlds in par-ticular. The goal of a semantic theory is then to find a translation of the phenomena of interest into a set-theoretic model. Such theories may be deemed to have ?explanatory? or ?predictive? power if a map-ping can found into expressions of set-theory that have the appropri-ate behaviour by virtue of the rules of set-theory. This can be con-trasted with an approach in which we can help ourselves to ?new? primitives and ontological categories, and devise logical rules and axioms that capture the appropriate inferential behaviour. This alter-native approach can be criticised as being mere ?descriptivism?, lack-ing predictive or explanatory power. Here we will seek to defend the ?descriptivist? approach. Any formal account must assume some normative interpretation, but there is a sense in which descriptivist theories can provide a more honest cha-racterisation. In contrast, the set-theoretic approach tends to conflate distinct ontological notions. Mapping a pattern of semantic behaviour into some pre-existing set-theoretic behaviour may lead to certain aspects of that behaviour being overlooked, or ignored. Arguments about the explanatory and predictive power of set-theoretic interpre-tations can also be questioned. We aim to provide alternative notions for evaluating the quality of a formalisation, and the role of formal theory. Ultimately, claims about the inadequacies of ?descriptivist? accounts compared to set-theoretic reductions must rely on criteria and assumptions that lie outside the domain of formal semantics as such
