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Synthese

, Volume 192, Issue 6, pp 1839–1860 | Cite as

The logic of indexicals

  • Alexandru RadulescuEmail author
Article

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.

Keywords

Indexicals Context sensitivity Validity Semantics 

Notes

Acknowledgments

Earlier versions of this paper were presented in 2011 at the UCLA Philosophy of Language Workshop, at the 3rd Semantic Content Workshop, Barcelona, Spain, and the 11th International Workshop on Semantics, Pragmatics, and Rhetoric, Donostia, Spain; in 2012 at the APA Central, Chicago, at the Society for Exact Philosophy, Ohio State University, at the University of Rochester, and at the University of Illinois, Chicago; and in 2013 at Colorado State University, University of Missouri, Columbia, and at Carnegie Mellon University. I would like to thank all those audiences for good discussions, and very good objections. Special thanks are due to several anonymous referees, Sam Cumming, Marina Folescu, Geoff Georgi, Andrew Hsu, Tony Martin, Eliot Michaelson, Terry Parsons, Scott Soames, Lynsey Wolter, and Henk Zeevat. And the most special thanks are due to David Kaplan, who talked to me about these ideas for a good number of years, who read and amply commented on versions of this text for almost as many years, and who usually agrees with parts of this paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MissouriColumbiaUSA

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