On formal versus commonsense semantics
David Israël · 1987
There is semantics and, on the other hand, there is seraan~ics.And then there is the theory of meaning or content.I shall speak of pure mathematical semantics and real semantics.I have very little idea what "formal" means in "formal semantics"--unless it simply means semantics done rigorously and systematically.1 I have even less idea what is meant by "commonsense semantics".I shall not speak much of the theory of meaning.The distinction between these two modes of semantics, the mathematical and the real, is not meant to be a hard and fast distinction--nor, most assuredly, is it intended to be rigorous or systematic.As I see it, the distinction has primarily to do with purposes or goals, derivatively, with constraints on the tools or conceptual resources considered available to realize those goals.In particular, real semantics is simply pure mathematical semantics with certain goals in mind and thus operating under certain additional constraints.Another way to put the point: some work in pure mathematical semantics is in fact a contribution to real semantics; however, it does not have to be such to make a genuine contribution to pure mathematical semantics.2 Hence, since real semantics can be executed with the same degree of rigor and systematicity as must all of pure mathematical semantics, it should be.Have I made myself clear?Not entirely, perhaps.Let's try a more systematic approach.Pure mathematical semantics is either a part of or an application of mathematical logic.Real semantics, even though an application of mathematical logic, is a part of the theory of meaning or content.Contributions to real semantics had better cast some light on naturally occurring phenomena within the purview of a theory of meaning--on such properties and relations as truth analyticity, necessity, implication.Traditionally (indeed, until Montague, almost undeviatingly) the techniques of pure mathematical semantics were deployed for formal or artificial languages.But this by itself is of no importance.These languages were invented, and are of interest only because, or insofar as, they are plausible and illuminating models, in the intuitive sense, of real phenomena in thought and in informal language.Consequently, the nature of the languages studied need not make an essential difference.3 What does make a difference is the purpose 1This is mildly disingenuous; talk of "formal semantics" is usually grounded in one or another idea of "logical (or, more generally syntactic) form".But one should beware the overly eager application of such notions to the semantics of natural languages.20f course, problems pursued for purely technical, mathematical reasons often turn out to be related to important questions and issues in real semantics.3Indeed, the two examples I shall consider concern the semantics of formal languages.