Mathematical entities must be accepted as part of our philosophical ontology

Putnam applied Quine’s naturalistic stance to mathematical ontology (Putnam 1972). At least since Galilei, our best theories from the natural sciences are mathematically expressed. Newton’s theory of gravitation, for instance, relies heavily on the classical theory of the real numbers. Thus an ontological commitment to mathematical entities seems inherent to our best scientific theories. This line of reasoning can be strengthened by appealing to the Quinean thesis of confirmational holism. Empir