A Note on Interpreting Theories
Michael D. Resnik · Noûs · 1974
Quine's criterion applies to theories (in canonical notation), that is, interpreted sets of sentences. A theory T thus consists of a set of sentences r and an ordered (n + I)-tuple (D, P1, ..., Pn), where D is the domain of the interpretation of T and P1, ..., Pn are the interpretations of the predicates of the sentences in r. However, the bound variables of T range over D. Thus, in order to specify a theory T to which Quine's criterion is to be applied, one must specify D, and, consequently, Quine's criterion for determining the ontology of T, i.e., D, is superfluous if applicable.'