Skolem fragments

W. V. Quine splits the fundamental question of ontology—What is there?—into two questions: What does a theory say that there is? and What theories ought we adopt? Of these, only the former seems amenable to philosophical treatment. Quine thus attempts to formulate an adequate criterion of ontological commitment. Syntactically, the initially existentially quantified sentences of a theory appear to constitute the locus of its ontological commitments (cf. [5], [2], [3], and [1]). Semantically, however, Quine offers at least three criteria of commitment: a theory is committed to (1) the objects in the domain of its intended model (cf. [4]); (2) the objects in the domain of its intended model that cannot be eliminated by means of proxy functions (cf. [6]); or (3) the objects in the domain of every model of it (or to objects of kinds such that some objects of those kinds are in each of its models) (cf. [7]). In this paper I shall show that Quine's syntactic criterion corresponds to and, indeed, follows from the third semantic criterion. Any philosopher using a syntactic criterion of ontological commitment such as Quine's that determines commitments according to sentences of the form