Extensional vs. Intensional Logic

The German mathematician and one of the founding fathers of modern logic, Gottlob Frege (1848-1925), was the first to clearly realize that semantics has little to do with psychology, and that it could be usefully explicated in mathematical terms (see Dummett, 1973; 1981). His depsychologization of semantics followed from his depsychologization of logic. Frege understood how crucial it was for the development of logic to draw a sharp boundary separating it from psychology: to make it clear that logic is not a matter of what is going on in some person’s head, in the sense that psychology is. This is because logic is concerned with what is true and consequently what follows from what — and whether something is true, or whether something follows from something else, is an objective matter independent of what is going on in the head of a particular person. As a consequence, Frege realized that if logic must be separated from psychology, then the same is true for semantics — at least insofar as semantics underlies truth and entailment. It is clear that the truth value of a sentence depends on the meaning of the sentence: the sentence “Penguins eat fish” is true not only due to the fact that penguins do eat fish, but of course also due to the fact that the words of which it consists mean what they do in English. Hence, if meaning were a matter of what is going on in somebody’s head, then truth would have to be too — hence meaning must not, in pain of the subjectivization of truth, be a psychological matter. But what, then, is meaning? Frege started from the prima facie obvious fact that names stand for objects of the world. Unprecedentedly, he assimilated indicative sentences to names as well: he saw them as specific kinds of names denoting the two truth values: truth and falsity. The reason for this move was that he divided expressions into two sharply separated groups: into “saturated” — i.e. self-standing — and “unsaturated” — i.e. incomplete — ones. He took names and sentences as species of the former kind, whereas he took predicates as paradigmatic examples of the latter one; and he came to use the word “name” as a synonym of “saturated expression”. The reason why he identified the entities named by sentences with truth values was articulated by Frege in the form of what has later become known as the slingshot argument1. This argument itself rests on what has subsequently come to be called the principle of compositionality and what Frege tacitly, but unambiguously assumed2. The principle