The Criterion of Ontological Commitment as a Logical Tester in Ontology

This is the first of three chapters on ontology in \(\lambda \) -philosophy. The chapter contains a didactic introduction to ontology and the problem of universals from the point of view of Quine’s criterion of ontological commitment ( \(=\) COC). A didactic analogy is proposed: the COC is like an electrical tester for ontology. So, the COC is a piece of logico-philosophical test equipment used to detect the presence or absence of entities of a certain kind among the range of values of the bound variables of a theory/language. Moreover, a programming extension of the COC based on compiler output also provides a way to determine the presence or absence of a certain kind of entity in a programming language. Ontology in the \(\lambda \) -calculus is very important because it suggests a concise and powerful functional ontology implemented in both  logic and programming, which is an integral part of our everyday digital life. Furthermore, the \(\lambda \) -calculus suggests a remarkable ontological reduction: It only reifies functions and the powerful operations of the \(\lambda \) -calculus are able to generate sets, numbers, and other abstract entities required by science. Finally, R. M. Martin’s metalinguistic analysis of the COC and an account of nominalistic constructions are also discussed.