ABSTRACT
This chapter develops an argument for realism along roughly the following lines: quantification over mathematical entities is indispensable for science, both formal and physical; therefore it should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. If "numbers exist" and "sets exist" are true by convention, then considerations of dispensability or indispensability are irrelevant. In sum, fictionalism has on the whole been rejected for a bad reason: because verificationism has made the perfectly sound and elementary distinction between truth of scientific theory and truth of its observational consequences unpopular, and thereby dismissed just the point that worried the fictionalists. A theological fictionalist like Duhem maintained that Thomistic metaphysics could establish propositions about reality as true; science could only show that certain propositions are useful for prediction and systematization of data.
