Lessons from the Logic of Demonstratives : What indexicality teaches us about logic, and vice versa

Logic and linguistically-informed philosophy of language are becoming increasingly specialised disciplines. I think this is a consequence of the fact that each is making rapid progress, but it has as a consequence that it has become less routine for someone who is doing cutting-edge work on central topics in the one to also be doing cutting-edge work on central topics in the other. As a result, the topics which receive a lot of attention from logicians may be things that the average philosopher of language regards as fringe topics—e.g. logics of belief or substructural logics—and some central topics in linguistically informed philosophy of language—e.g. the structure of propositions, adverbs or contextualism— may be largely ignored in logic. The aim of the present paper is to provide some contamination in both directions. I will take one seminal idea from the philosophy of language and explore some consequences for logic (or at the very least, for the philosophy of logic) and then take one method from logic, and use it to prove a theorem that can help to explain and clarify some ideas in the philosophy of language.