 In the mid-1970s, Dummett raised the issue of the proper place of lexical meaning in a semantic theory. If the job of a theory of meaning is to make the content of semantic competence explicit—so that one could acquire semantic competence in a language L by learning an adequate theory of meaning for L—then the theory ought to reflect a competent speaker’s knowledge of circumstances in which she would assert a sentence of L, such as “The horse is in the barn”, as distinct from circumstances in which she would assert “The cat is on the mat”. This, in turn, appears to require that the theory yields explicit information about the use of ‘horse’, ‘barn’, etc., or, in other words, that it includes information which goes beyond the logical type of lexical units. Dummett identified such information with a word’s Fregean sense. However, he did not specify the format in which word senses should be expressed in a semantic theory, except for words that could be defined (e.g., ‘aunt’ = “sister of a parent”): in such cases, the definiens specifies what a speaker must understand in order to understand the word (Dummett 1991). But of course, not all words are of this kind. For other words, the theory should specify what it is for a speaker to know them, though we are not told how exactly this should be done. Similarly, Grandy (1974) pointed out that by identifying the meaning of a word such as ‘wise’ as a function from possible worlds to the sets of wise people in those worlds, Montague semantics only specifies a formal structure and eludes the question of whether there is some possible description for the functions which are claimed to be the meanings of words. Lacking such descriptions, possible worlds semantics is not really a theory of meaning but a theory of logical form or logical validity. Again, aside from suggesting that “one would like the functions to be given in terms of computation procedures, in some sense”, Grandy had little to say about the form of lexical descriptions.