What in our theoretical pronouncements commits us to objects? The Quinean standard for ontological commitment involves (nearly enough) commitments when we utter “there is” or “there are” statements without hope of eliminating these by paraphrase. Coupled with the indispensability of the truth of applied mathematical doctrine, the result is that the ontologically hard-nosed scientist is a Platonist—haplessly commited to abstracta. In this book Azzouni offers a way around the Quinean straitjacket: ontological commitment turns on how theories are (nearly enough) nailed to the world. The specifics of how theories are applied indicates which among the posits of a theory are mere mathematical garb and which are genuine connections to items out there. In the first part of the book Azzouni undercuts the arguments, both actual and possible, in support of Quine’s criterion. An alternative criterion for what exists—ontological independence—is offered, one in sturdy accord with ordinary folk views on the matter. In the second part of the book, a beginning is made of bringing this alternative to bear upon scientific theories with a rich mathematical component. Along the way, old philosophical issues about absolute space and time versus relative space and time, the status of mathematical posits, such as spatial and temporal points, and so on, are illuminated.