Semantics

To the mathematician encountering linguistic semantics for the first time, the whole area appears as a random collection of loosely connected philosophical puzzles, held together somewhat superficially by terminology and tools borrowed from logic. In Section 6.1 we will discuss some of the puzzles that played a significant role in the development of linguistic semantics from a narrow utilitarian perspective: suppose an appropriate technique of mathematical logic can be found to deal with the philosophical puzzle — how much does it help us in dealing with the relationship between grammatical expressions and their meaning? Since the task is to characterize this relationship, we must, at the very least, provide a theory capable of (A) characterizing the set of expressions and (B) characterizing the set of meanings. By inspecting the Liar (Section 6.1.1), opacity (Section 6.1.2), and the Berry paradox (Section 6.1.3), we will gradually arrive at a more refined set of desiderata, distinguishing those that we see as truly essential for semantics from those that are merely nice to have. These will be summarized in Section 6.1.4.