Pragmatics and Semantics of Free Choice Disjunction

Abstract

A disjunction is an expression using ‘or’, such as ‘Anne has a Ford or a Tesla’. From such a statement, we cannot usually infer either disjunct, for example, that ‘Anne has a Ford’. However, in choice situations like ‘You may have coffee or tea’ we can infer either option. The problem of free choice disjunction is to determine why these choice inferences are legitimate (von Wright 1968, Kamp 1973, Meyer 2016).

Central to this discussion is the observation that a modal possibility operator ranging over a disjunction sometimes implies a conjunction of possibilities. In the case of permission, we express this as the choice principle ‘May (P or Q)’ entails ‘May P and May Q’ (Zimmerman 2000). Unfortunately, this inference cannot hold in a logical language without significant modification of the systems involved.

I explore the history of proposed solutions to this problem, including semantic solutions that assign a distinctive meaning to free choice disjunctions and pragmatic solutions that use features of their utterance to solve the problem. I draw connections between semantics and pragmatics and, using the tools of dynamic logic (Baltag et al. 1998, van Benthem 2010), I present a formal account of one major (Gricean) approach to the problem (Kratzer & Shimoyama 2002).

Ultimately, I explore the role of logic in this debate and argue that we should formally represent the meaning of these expressions directly as conjunctions of possibilities. Thus, rather than trying to account for the choice principle within a logical system, we must instead account for the fact that, in choice situations, the meaning of ‘May (P or Q)’ translates into logical formalism as (May P & May Q).