The Logic of Indexicals
The semantics of indexicals, at least in their most basic uses, was convincingly developed in David Kaplan's "Demonstratives'', and his views are widely accepted today. Having proposed a formal semantics of indexicals, Kaplan also worked out a logic of indexicals. Most of the features of his logic come from the formal semantics; these I will accept, and even defend when prompted. But one feature goes against the grain of the semantics: arguments are forced to have all their steps within a single context of utterance. My central goal in this dissertation is to argue that this limitation is incorrect, and to provide a logic that does without it. This requires a new definition of validity, to take into account not just the logical form of sentences, but also certain abstract, relational properties of the sequence of contexts that the argument takes place in.
The logic I propose is designed for indexicals; traditionally, these are contrasted with demonstratives. I propose a new way to make this distinction, based on the observation that typical utterances have a speaker and an addressee, irrespective of the words being uttered, and, most importantly, whether or not the words "I'' or "you'' are used. By contrast, demonstratives need personal assistance from the speaker: utterances don't have demonstrata unless the sentences used contain demonstratives. I then argue that the traditional distinction, which is also inherited from "Demonstratives'', along with other criteria proposed in the literature, are mistaken. The main study case is the second person singular pronoun, which has been commonly, and wrongly, thought to be a demonstrative.
Finally, I discuss the ways in which the logic of indexicals differs conceptually both from classical first order logic, and from Kaplan's logic. By looking not just at sentences and their parts, but also at the contexts, and the relations between them, we discover new and unexpected ways in which we can get valid arguments and logical truths.