In Defense of Indispensability Argument

In the debate between mathematical realism and nominalism, Quine’s indispensability argument maintains an important status. It is widely regarded as the most potent argument supporting mathematical realism. However, it also faces various nominalists’ challenges.
Although it has never been explicitly formulated by Quine himself, Quine’s indispensability argument is often assumed to include three main premises: (1) indispensability thesis – mathematics is indispensable to natural science; (2) naturalism – there is no first philosophy and philosophy is continuous to science; (3) confirmational holism – the confirmation of scientific theories confirms not only its physical but also its mathematical components.
In chapter one, I try to give a preliminary form of QIA and discuss each premise in light of Quine’s general philosophical views. In chapter two, I consider Field’s challenge to the indispensability thesis and conclude that it is most likely Field’s nominalistic program is deemed to fail, or at least not completely successful. Chapter three discusses naturalism and confirmational holism theses in QIA, by reviewing Maddy’s view on naturalism and Sober’s objection to confirmational holism, I conclude that the preliminary version of QIA introduced in the beginning is too strong to be an ontological argument and an adequate version of QIA is put forward – RQIA (a version of QIA without confirmational holism). In chapter four, I try to give a way to deal with a variety of separation objections, which may be a challenge to RQIA.