Truths Containing Empty Names

1. A problem for direct reference. According to the thesis of Direct Reference (or the DR-thesis for short), the propositions expressed by sentences containing the proper names and indexical pronouns of natural language are a strict function of the semantic referents of the names and indexicals, as opposed to being a function of any Fregean descriptive senses or contents that the names and indexicals might be alleged to possess. Another way of expressing this idea is to say that the sole semantic contribution that a proper name or indexical can make to the propositions expressed by sentences containing the term is the term’s semantic referent. Bertrand Russell called terms of this sort ‘names in the logical sense’ (1918, 201). I will call them ‘genuine terms’. Following standard practice, I will call the propositions expressed by sentences containing genuine terms, ‘singular propositions’. Like many others, I endorse the DR-thesis. In my case, the primary reason for endorsing the thesis lies in the modal considerations first briefly introduced by John Searle (1958) and later clarified and forcefully applied by Saul Kripke (1972a), considerations which show that proper names do not have the meanings of contingent definite descriptions. David Kaplan (1989) raised related points to support the conclusion that indexical pronouns are also genuine terms. In recent work I have argued at some length that the DR-thesis entails both that (a) a sentence containing a non-referring name or indexical can express no proposition, and hence that (b) such sentences can have no truth value, that is, can be neither true or false. (See McKinsey 2006 and (manuscript).) Following Braun (1993), we can call (a) the ‘noproposition’ view. It certainly seems that the no-proposition view follows immediately from the DR-thesis. After all, if the proposition expressed by a sentence containing a genuine term is a function of the term’s referent, and yet the term has no referent, then the sentence can express no proposition: a function without an argument can have no value.