Quasi-Set Semantics and Ontological Compromise

Abstract

In this paper we will present a Tarski-like Semantics for first-orderlanguages by resorting to a theory of quasi-sets as meta-language. The objectiveis to allow that undistinguishable, though not identical, objects – in the sensedealt with by this theory –, appear in the domain of interpretation and may be values of variables in the Quinean sense. Thus, besides changing theinterpretation of symbols as the identity and the non-logical constants oflanguage, this Semantics will allow us to discuss – in a strict manner – thepossibility of relativizing the famous criterion of Quine’s OntologicalCompromise, according to which, without getting into minute details, a theoryexpressed in first-order language is compromised with the entities that oughtto be in the domain of interpretation so that the formula in question is trueand that such entities must ‘have identity’. As we shall see, by changing thismeta-language theory, we will change the kinds of objects that can belong tothe domain of interpretation.