The first premise relies crucially on Quine's criterion of ontological commitment. After regimenting our best theories of the world in a first-order language, the ontological commitments of these theories can be read off as being the value of the existentially quantified variables. But how do we move from the ontological commitments of a theory to what we ought to be ontologically committed to? This is the point where the first premise of the indispensability argument emerges. If we are dealing with our best theories of the world, precisely those items that are indispensable to these theories amount to what we ought to be committed to. (Of course, a theory may quantify over more objects than those that are indispensable.) And by identifying the indispensable components invoked in the explanation of various phenomena, and noting that mathematical entities are among them, the platonist is then in a position to make sense of the success of applied mathematics.