How not to become a Millian heir

Abstract

Millianism is a highly contentious doctrine in the theory of meaning. It is the thesis that the contribution made by an ordinary proper name to securing the information content of, or the proposition expressed by, a declarative sentence in which the name occurs (outside of the scope of such nonextensional operators as quotation marks), as the sentence is used in a possible context, is simply the name's referent (bearer) in the given use.' The unpopularity of the doctrine stems heavily perhaps primarily from the fact that it leads to a serious philosophical difficulty discovered by Gottlob Frege, and which I have dubbed 'Frege's Puzzle': Let a and b be distinct but co-referential proper names such that the identity sentence 'a = b' contains information that is knowable only a posteriori, and can therefore be informative. Then how can this sentence 'a = b' differ at all in cognitive information (propositional) content from ra = a', which is a priori and uninformative? In Frege's Puzzle2 I proposed an analysis according to which the puzzle relies on three components: (i) a compositionality principle that propositions formed in the very same way from the very same components are the very same proposition; (ii) the principle, which I call 'Frege's Law', that declarative sentences sharing the same cognitive information (propositional) content do not differ in informativeness or epistemological status; and (iii) the observation that there are coreferential proper names a and b (for example, 'Hesperus' and 'Phosphorus') such that ra = b' is informative and a posteriori even though ra = a' is always uninformative and a priori. Together these assertions comprise the main premises of a powerful argument against Millianism. Most Millians, if forced to give direct response, would probably reject Frege's Law. And taken in one sense, I would agree. I argued, however,