Disimplicature

Speranza

A mainstay assumption in natural-language semantics is that \emph{if}-clauses bind indexical argument-places in \emph{then}-clauses. Unfortunately, recent work (compare \citealt{santorio12}) suggests that \emph{if}-clauses can somehow act to `shift the context'. On the framework of Kaplan's `Demonstratives' \citep{kaplan77}, that would be `monstrous' and somehow impossible `in English'. The superseding framework of Lewis's `Index, context, and content' \citep{lewis80icc} instead maintains that an indexical argument-place is just one that is bindable (compare~\citealt[ch.~1]{stalnaker14}), but maintains that these are rare---whereas the lesson of recent work is that they are pervasive.

This brief technical note observes that it is possible to `hack' the Lewis framework to make use of a resource that is doing little work: the `postsemantic' stage, whereby nonpropositional semantic values are transformed into propositional contents. I provide a semantics for \emph{if}-clauses on which they \emph{restrict} the domain of definedness of their operanda to those in which the antecedent is correct, and then \emph{test} for the correctness of the consequent: postsemantically, then, we `seek out' the closest context in which the antecedent is correct; if it is one in which the consequent is correct, the conditional is correct in our context. The result has the structure of a Stalnaker-conditional, but over contexts rather than worlds.

The `hack' has the radical consequence that this the mainstay assumption in natural-language semantics is wrong: if \emph{if}-clauses act postsemantically rather than in the course of semantic composition, then nothing about their behavior can teach us anything about the distribution of indexical argument-places