Singular Terms

Abstract

In Frege: Philosophy of Language, ch.4, Michael Dummett argues, with great clarity and force, that it is “essential for Frege to be able to maintain that each expression may be recognised as belonging to its logical category or type from a knowledge of the way in which it is employed in the language” and, more specifically, that it is “essential, if Frege’s whole philosophy of language and the ontology that depends upon it are to be even viable, that it should be possible to give clear and exact criteria, relating to their functioning within language, for discriminating proper names from expressions of other kinds.”¹ With these claims I am in complete agreement; indeed, although I shall not defend it here, I would make a stronger claim provision of such criteria is an essential prerequisite, not only to any full defence of Frege’s own views, but to progress on a wide range of issues in the philosophies of language and mathematics and in general metaphysics. One important, and of course controversial, part of the dependent ontology in Frege’s case is his belief in the existence of a range of objects — (cardinal) numbers — to which simple numerals and other kinds of numerical expressions are to be understood as making reference. This belief may be seen as grounded in two claims: first, that such expressions function in certain statements as singular terms, and second, that the statements in which they so function are (some of them, anyway) true.