A Ratiocinative Study and Assessment of W. V. O. Quine's "Criterion of Ontological Commitment"

Abstract

Purpose: This work has three main objectives: Firstly, it offers an elucidation of the notion of ontological commitment. Secondly, it assesses the adequacy of the criterion of ontological commitment for different languages. Thirdly, it offers some speculative and evaluative remarks regarding the significance of Quine's criterion of ontological commitment. Many ontologists, within the analytic tradition, often appeal to Quine's criterion of ontological commitment, when debating whether an assertion or theory implies the existence of a certain entity. Regarding his goal in formulating this criterion, he says that the criterion does not aim to help us discover what it is that there is, but only what a theory says there is: "I look to variables and quantification for evidence as to what a theory says that there is, not for evidence as to what there is" (Quine, 1960: 225). Its most popular formulation, using textual evidence from Quine's oeuvre, is: "To be is to be the value of a bound variable," (Quine, 1961: 15). However, this formulation is susceptible to gross misunderstanding, especially if one is influenced by the formalities and technical maneuvers of model theory. In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). Model theory is a branch of mathematical logic where we study mathematical structures by considering the first-order sentences true in those structures and the sets definable by first-order formulas. Model theory studies the relations between sentences of a formal language and the interpretations (or "˜structures') which make these sentences true or false. It offers precise definitions of truth, logical truth and consequence, meanings and modalities.

Methodology: This work is expository, analytic, critical and evaluative in its methodology. Of course, there are familiar philosophical problems which are within the discursive framework of "˜ontology,' often phrased by asking if something or some category of things are "real," or whether "they exist," concretely. An outstanding example is provided by the traditional problem of universals, which issues in the nominalist-realist controversy, as to the real existence of universals, or of abstract entities such as classes (in the mathematical sense) or propositions (in the abstract sense, referring to the content of an assertion in abstraction from the particular words used to convey it).

Results: In as much as one might agree with Quine's Criterion of Ontological Commitment, one might also opine that it is nonetheless a feature of first-order language (i.e. the language embodied in first-order logic; a symbolized reasoning process comprising relations, functions and constants, in which each sentence or statement is broken down into a subject and a predicate. In this regard, the predicate modifies or defines the properties of the subject) that there should be an exact correspondence between the ontological commitments carried by a sentence and the objects that must be counted among the values of the variables in order for the sentence to be true. However, this in itself is not a reason for thinking that such a feature will generalize beyond first-order languages. It is possible for Quine's Criterion to degenerate, when the language contains atomic predicates expressing extrinsic properties.

Unique Contribution to theory, practice and policy: Based on Quine's analysis, a theory is committed to those and only those entities that in the last analysis serve as the values of its bound variables. Thus, ordinary first-order theory commits one to an ontology only of individuals (particulars), whereas higher order logic commits one to the existence of sets, i.e. of collections of definite and distinct entities (or, alternatively, of properties and relations). Likewise, if bound first-order variables are assumed to range over sets (as they do in set theory), a commitment to the existence of these sets is incurred. Admittedly, the precise import of Quine's criterion of ontological commitment, however, is not completely clear, nor is it clear in what other sense one is perhaps committed by a theory to those entities that are named or otherwise referred to in it, but not quantified over in it. However, it despite its limitations, it has made is possible for one to measure the ontological cost of theories, an important component in deciding which theories to accept, thus offering a partial foundation for theory choice.