Propositions and Multiple Indexing

It is argued that propositions cannot be the compositional semantic values of sentences (in context) simply due to issues stemming from the compositional semantics of modal operators (or modal quantifiers). In particular, the fact that the arguments for double indexing generalize to multiple indexing exposes a fundamental tension in the default philosophical conception of semantic theory. This provides further motivation for making a distinction between two sentential semantic contents—what (Dummett 1973) called “ingredient sense” and “assertoric content”.