To most mathematical logicians working in the 1980s, first-order logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician named Thoralf Skolem argued that set theory should be based on first-order logic, it was a radical and unprecedented proposal. The radical nature of what Skolem proposed resulted, above all, from its e...

W. V. Quine splits the fundamental question of ontology—What is there?—into two questions: What does a theory say that there is? and What theories ought we adopt? Of these, only the former seems amenable to philosophical treatment. Quine thus attempts to formulate an adequate criterion of ontological commitment. Syntactically, the initially existentially quantified sentences of a theory appear ...