Mathematical Indispensability Argument

The mathematical indispensability argument is the central objection to mathematical nominalism, most famously formulated by W.V.O. Quine and Hilary Putnam. The argument runs: (1) we ought to believe in the entities that are indispensable to our best scientific theories; (2) mathematics is indispensable to our best scientific theories; (3) therefore, we ought to believe in mathematical entities. The nominalist's only escape is to show that mathematics is not indispensable — that every scientific theory employing mathematics can be reformulated without it. This is the project of nominalization, and its success or failure determines the fate of abstract ontology.