Abstract

This is a dissertation of philosophy of mathematics, in the analytical tradition, about the Quine-Putnam mathematical indispensability argument, that we ought to have ontological commitment to mathematical entities that are indispensable to our best scientific theories. It is an argument for the metaphysical mathematical realism supported by Quinean doctrines such as naturalism and holism. My overall aim is to make a discussion of the argument. The argument will be defended against generic objections or some of its detractors such as Azzouni, Maddy, Cheyne and Balaguer. Matters connected with the indispensability of mathematics, such as the epistemic problem of Benacerraf and the agnosticist view of Balaguer, will be discussed. Primarily, the discussion is ontological; secondarily, the discussion is epistemological and metaphysical.