What is the role of model theory in the study of meaning?

Abstract

One of the most important events in the development of modern linguistics was the break-through of model-theoretic semantics in the 1970s which is so intimately connected with the works of Richard Montague (1974). But ever since its first applications to linguistics, the adequacy of model theory for the study of natural language semantics has been doubted (cf. Jardine 1975; Potts 1975 and with special reference to Montague’s version of that approach Potts 1976), and although model theory is a well-established subdiscipline of mathematical logic, its proper role for the foundations of logic is as much debated as its adequacy in the study of natural language meaning. Constructivists (Kamlah and Lorenzen 1967: 1933195; Martin-Liif 1984: 3) and finitists (Hilbert and Bernays 1934: 125-131), as well as logicians who, like Hinst (1982) conceive of logical rules as based on pragmatic principles, are more often sceptical about the explanatory value of model theory as an account of meaning. Admittedly, also these critics may use model-theoretic means as technical tools in their formal work, and there is something like a constructive model theory. But what is at issue here is not the technical apparatus of model theory but its status as an explanatory account to meaning. When the eminent logician A. Mostowski (1965), in his lectures on the development of mathematical logic from 1930 to 1964, opens his lecture on the theory of models1 with the statement, ‘the modern form of semantics is the theory of models’, this seems to represent a problem as settled which is still being discussed. This is even more true for linguistics than for logic and metamathematics. So, Bickhard and Campbell’s (B&C’s) foundational article on the application