Modality, Weights, and Inconsistent Premise Sets

It is a commonplace that some of our desires are stronger than others; that certain values and norms are more important than others; and that states of affairs can be more likely than others. Some authors have claimed that the classic premise semantics for modals in linguistic semantics fails to capture how the truth-conditions of modal sentences can be sensitive to such differences in strength and priority. I develop an interpretation of the classic premise semantic framework that captures various ways in which weights and priorities can affect the interpretation of modals. Modals, on the standard semantics, receive their interpretation from contextually supplied functions from worlds to premise sets (“conversational backgrounds”). I propose that we understand these functions as encoding the content of an intuitively relevant body of considerations (conditional norms, preferences, expectations, etc.). The resulting world-indexed premise sets that figure in the truth-conditions of modal sentences represent what follows from these considerations given the relevant circumstances in the evaluation world. Facts about weights and priorities are encoded not in the individual premise sets (or in additional operations defined on them), but in how premise sets are assigned across worlds by the given conversational background. Next I offer one way of extending the account to certain comparative modal sentences. The proposed analysis captures various inference patterns involving modal auxiliaries, comparatives, and equatives, improving on certain previous approaches to graded modality within the classic framework. The paper concludes with several theoretical reflections on the relation between the semantics of modals and the logic of weights and priorities. The account developed in this paper locates a crucial role for research on proper reasoning involving weights and priorities without building the findings of this research into the conventional meaning of modal language.