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In this paper, I present a new semantics for demonstratives. Now some may think that David Kaplan (1989a,b) has already given a more than satisfactory semantics for demonstratives, and that there is no need for a new one. But I argue below that Kaplan's theory fails to describe the linguistic meanings of 'that' and other true demonstratives. My argument for this conclusion has nothing to do with cognitive value, belief sentences, or other such contentious matters in semantics and the philosophy of mind. Rather, it appeals to the obvious fact that there can be true utterances of certain sentences containing several occurrences of the same demonstrative (for instance, 'That is taller than that'). My argument can be answered by making a fairly modest revision in Kaplan's theory. But I believe that the resulting revised version of Kaplan's theory ignores or distorts various important semantic features of 'that'. Thus I ultimately argue in favor of a more substantial departure from Kaplan's theory. Perhaps the most remarkable feature of the theory I favor is that it ascribes three distinct sorts of meanings to demonstratives. 1. Preliminaries Indexicals are expressions whose reference varies from utterance to utterance, or from context to context: for example, 'I', 'today', 'you', 'that', 'there', and 'then'. Pure indexicals are (roughly) indexicals that refer automatically just in virtue of being uttered: the best examples are 'I', 'today', 'yesterday' and 'tomorrow'. ('Here' and 'now' are often included, though the spatial and temporal extents of their referents seem to be determined by something other than mere utterance.) True demonstratives are indexicals which require something more than mere utterance in order to acquire a referent. The paradigm example of a true
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