A model-theoretic criterion of ontology

Conclusion My aim has been to adapt Quine's criterion of the ontological commitment of theories couched in standard quantificational idiom to a much broader class of theories by focusing on the set-theoretic structure of the models of those theories. For standard first-order theories, the two criteria coincide on simple entities. Divergences appear as they are applied to higher-order theories and as composite entities are taken into account. In support of the extended criterion, I appeal to its fruits in treating the various examples considered above and to the healthy intuitions of the non-noneists among us. Don't O(m) and E(m) comprise just the things we should have though existed according to a particular interpretation m of a language or a theory? Whatever the answer (and it will hardly be unanimous), I hope to have pointed the way towards a recognition of ontology as a worthwhile branch of modern theory.Earlier versions of parts of this paper were read at New York University, at the Australasian Association of Philosophy, and at the University of Sydney. I am very grateful to William Barrett, Keith Campbell, Gregory Currie, Kenneth Gemes, Toomas Karmo, and Stephen Read for comments and criticisms.