RULES AND REFERENCE

What is the network of properties and relations in virtue of which a word refers to a thing? What turns one object in the world into a representation of other objects? We shall say very little about this matter: it would take us too far into cognitive science and away from the ontological concerns which are the topic of this book. Our sympathies are with a broadly causal, or functionalist, account of the nature of representation and reference. We shall simply assume that there is such a thing as reference, to be elucidated sooner or later, but not here.

Taking reference for granted, we then ask: what things in the world are the referents of words in language? More specifically, what are the referents of the symbols used in science? Having defended scientific, metaphysical, and modal realism, the answer a realist must give is determined. Clearly, the referents of scientific language include individuals, universals, and possibilia. Included among universals are higher–level properties and relations, like quantities and vectors and structural universals, relations of proportion (real numbers), and – let us not forget – sets. Sets are especially important in semantics, for reasons which we shall explain.

A crucial question for semantics is: what, if anything, do predicates correspond to? Given a true sentence, with a name in it which refers to an individual, say, we may divide the sentence into two parts: the name and the rest.