What is priority monism?

In a series papers, Jonathan Schaffer defended priority monism, the thesis that the cosmos is the only fundamental material object, on which all other objects depend. A primitive notion of dependence plays a crucial role in Schaffer’s arguments for priority monism. The goal of this paper is to scrutinize this notion and also to shed new light on what is at stake in the debate. I present three familiar arguments for priority monism and point out that each relies on a connecting principle that ties dependence to other metaphysical relations. I then argue for two desiderata: the relation between dependence and other metaphysical relations needs to be strong enough to establish that other metaphysical relations are relevant to the direction of dependence but not so strong as to leave no room for revisionary versions of priority monism. I propose a particular way of meeting these desiderata, according to which the target notion of dependence is graded rather than all-or-nothing. One upshot is that we should be less preoccupied with priority monism itself and should instead focus on specific aspects of a broader monistic worldview.