  Thus formulated, the argument is valid. This forces the focus onto the two premises. In particular, a couple of important questions naturally arise. The first concerns how we are to understand the claim that mathematics is indispensable.  We address this in the next section. The second question concerns the first premise. It is nowhere near as self-evident as the second and it clearly needs some defense. We’ll discuss its defense in the following section. We’ll then present some of the more important objections to the argument, before considering the Quine-Putnam argument’s role in the larger scheme of things - where it stands in relation to other influential arguments for and against mathematical realism. 