A Semantic Solution to Frege's Puzzle

Abstract

Gottlob Frege observed that a sentence of the form 'a = b' has a different cognitive value (Erkenntniswert) from a sentence of the form 'a = a,' where 'a' and 'b' are co-referential proper names; 'a = b' is informative, one might say, and 'a = a' is not. From this he inferred that (proper) names have senses (Sinne) and that the sense of a name may be different from the sense of another co-referential name.1 It follows from this that the sense of a name is not determined by its referent. Frege thought that the sense of a name is analogous to the sense of a definite description on three counts: (i) it is the descriptive content of the term; (ii) it determines the reference of the term; and (iii) it contributes to the cognitive value of any expression in which the term occurs. Although the exact nature of Fregean senses might be open to endless debate, it is clear that the postulation for each name of a sense satisfying (i), (ii), and especially (iii) would provide an explanation of the informativeness of 'a = b.' This is the strength of a Fregean theory of names. However, Saul A. Kripke has convinced many philosophers that names do not have Fregean senses, or any descriptive contents, in terms of which their reference is determined.2 Kripke resurrected John Stuart Mill's idea that names are connotationless tags. Kripke's arguments were novel and ingenious. He taught us a great deal about names and modality. And yet, Kripke has not completely dispelled the Fregean reason for postulating descriptive contents for names. Or so it appears. If, as Kripke has us believe, names are thoroughly nondescriptive, then we seem to have a problem; the informativeness of 'a = b' seems to defy explanation. If names have no descriptive contents, co-referential names seem not to differ from each other in any way semantic. But if so, it