Ontological commitment, on its face, is a relation between theories and entities, or kinds of entity. Before attempting to explicate and evaluate Quine's criterion of ontological commitment, it is important to specify more carefully the relata. A theory, for Quine, is just a set of sentences (or a single sentence) of some language. But what language? Strictly speaking, Quine's criterion is only to be applied to theories couched within the following especially austere form of first-order predicate logic: there are first-order existential and universal quantifiers but no other variable-binding operators; there are predicates, including identity, but no function symbols or individual constants. Thus, all names and definite descriptions have been eliminated from the language; reference rests entirely with the variables. The elimination of singular terms serves both to simplify the criterion and to avoid age-old confusions. Unlike bound variables, singular terms sometimes do and sometimes do not carry ontological commitment: ‘Socrates is wise’ presumably does; but ‘Pegasus does not exist’ presumably does not. Whenever singular terms do carry ontological commitment, it will be reflected in the assignment to the variables of the regimented theory. Thus, whenever a sentence containing a definite description is ontologically committed to some entity satisfying the description, so will be the regimented sentence that results from applying Russell's theory of descriptions (which was endorsed by Quine). Whenever a sentence containing a name is ontologically committed to some entity denoted by the name, so will be a regimented sentence that contains a predicate applying exclusively to that entity. For example, if instead of using the name ‘Socrates’ we use a predicate ‘Is-Socrates’ interpreted to mean is-identical-with-Socrates (sometimes abbreviated ‘Socratizes’), the ontological commitment incurred by the name is transferred without loss to the bound variable in ‘∃x Is‑Socrates(x)’ (or ‘∃x Socratizes(x)’).[3] 