A consequence of Quine’s celebrated critique of the analytic-synthetic distinction-a consequence drawn by Quine himself-is that the existence of mathematical entities is to be justified in the way in which one justifies the postulation of theoretical entities in physics. As Quine himself once put it,2

Certain things we want to say in science may compel us to admit into the range of variables of quantification not only physical objects but also classes and relations of them; also numbers, functions, and other objects of pure mathematics. For mathematics-not uninterpreted mathematics, but genuine set theory, logic, number theory, algebra of real and complex numbers, and so on-is best looked upon as an integral part of science, on a par with the physics, economics, etc. in which mathematics is said to receive its applications.