The logic of indexicals

One of the central arguments in Strawson (1960) against the possibility of a formal semantics of natural language and of an associated logic was that indexicals cannot be dealt with formally.1 Kaplan’s “Demonstratives” provided a successful semantics and a logic for indexicals, and thus proved Strawson wrong about indexicals, and about context sensitive expressions in general.2 The present paper is motivated by the observation that Kaplan’s logic, and hence the whole tradition that grew out of it, is too limited: it only deals with monologues in a single context. The pervasive use of indexicals in conversations is beyond its scope. In a way, the situation with Kaplan’s restricted logic is as if Strawson had been right all along, except for a very small, and arbitrarily chosen, class of arguments. Furthermore, this restriction goes against the power of Kaplan’s semantics: indexicals are special precisely because they get different referents in different contexts, and we use this power in argumentation and conversation. Kaplan himself never said why he restricted logic in this way.3 The reason probably is that, historically, all forms of logic have assessed the premises and the conclusion in the same context, or as if they are not relative to any context. Soames (2010), in an argument reminiscent of Strawson’s, gives an explicit reason to follow Kaplan: if “I” can be used twice in an argument with different 1The core of his argument was already present in Strawson (1950). 2In this paper, I will be talking quite extensively about Kaplan’s work on indexicals. Since the two central papers were published in the same book, but written at least 12 years apart, I have found it useful to refer to them in a more descriptive manner than the usual citation conventions. I will use “[Demons]” for Kaplan (1989b) and “[Aft]” for Kaplan (1989a). 3However, some of Kaplan’s discussion about the difficulties of a logic of utterances can be taken to be reasons for the restrictions I am discussing (see, e.g. [Demons], pp. 584-585, where he talks about “verities of meaning” and “vagaries of action”). I am only claiming that Kaplan did not make this connection in the text.