The chapter aims to clarify the metaphysical picture underlying the so-called Quine-Putnam Indispensability Argument (IA) by proposing an alternative reading that allows for minimal notions of object and existence (in Linnebo’s 2013 sense). In such a framework, the conclusion of the revised IA is not that mathematical entities exist, as existence comes with reference and objecthood and is, therefore, quite easy to establish. Rather, this revised version of the argument claims that mathematical entities make a demand on the world, thus asserting that mathematical entities are heavyweight entities. The chapter begins by introducing the debate over the metaphysical picture underlying the IA and goes on to present Linnebo’s notions of minimal object, existence, and the distinction between thick versus thin objects. It then shows that it is possible to take some of Quine’s theses on ontological commitment, existence, and reference to formulate a notion of existence that is minimal in nature. Furthermore, the chapter explores what is required to characterize light and heavyweight objects in a Quinean manner. Finally, the Quine-Putnam IA is reformulated in terms of the light versus heavy distinction, with the aim of uncovering the metaphysical assumptions underpinning the original argument and demonstrating that its conclusion is implausible by Quine’s naturalistic standards.