How did Quine use formal language to identify a scientific theory’s ontological commitments?

To identify a scientific theory’s ontological commitments, W.V.O. Quine proposed that the theory must first be expressed in the formal language of predicate calculus. In this canonical logical framework, a theory is ontologically committed to those entities that must be capable of serving as the values of its bound variables for the theory’s statements to be true.123

Quine summarized this approach with his famous criterion: "To be is to be the value of a bound variable". By translating a theory into this formal structure, one can determine what the theory asserts to exist by examining the range of its existential quantifiers—specifically, the entities that must exist for the quantified statements to hold.312

While Quine personally advocated for a "sparse" ontology consisting only of concrete physical objects and abstract sets, his method provides a systematic way to reveal the commitments inherent in any theory. By requiring that theories be represented in a well-understood logical language, Quine sought to clarify exactly what a theory claims to be real, rather than relying on ambiguous natural language references.412