The logic of indexicals

Abstract

Since Kaplan (J Philos Logic 8(1): 81–98, 1979) first provided a logic for context-sensitive expressions, it has been thought that the only way to construct a logic for indexicals is to restrict it to arguments which take place in a single context— that is, instantaneous arguments, uttered by a single speaker, in a single place, etc. In this paper, I propose a logic which does away with these restrictions, and thus places arguments where they belong, in real world conversations. The central innovation is that validity depends not just on the sentences in the argument, but also on certain abstract relations between contexts. This enrichment of the notion of logical form leads to some seemingly counter-intuitive results: a sequence of sentences may make up a valid argument in one sequence of contexts, and an invalid one in another such sequence. I argue that this is an unavoidable result of context sensitivity in general, and of the nature of indexicals in particular, and that reflection on such examples will lead us to a better understanding of the idea of applying logic to context sensitive expressions, and thus to natural language in general.