Arbitrariness and the long road to permissivism

Abstract

Radically permissive ontologies like mereological universalism and material plenitude are typically motivated by concerns about arbitrariness or anthropocentrism: it would be objectionably arbitrary, the thought goes, to countenance only those objects that we ordinarily take there to be. Despite the prevalence of this idea, it isn't at all clear what it is for a theory to be “objectionably arbitrary”, or what follows from a commitment to avoiding arbitrariness in metaphysics. This paper aims to clarify both questions, and examines whether arguments from arbitrariness really are the proper foundations for one or both varieties of ontological permissivism. I argue that these considerations (even when made more precise) are far less successful at motivating radical forms of permissivism than we often take them to be. To do better, permissivists must either supply a much more developed metaphysics of material objects, or a controversial (but tempting) conception of what we're doing when we do metaphysics.

Explanation and Plenitude in Non-Well-Founded Set Theories

“…14 This argument for plenitude, while implicit in a lot of discussions, is most explicit in Bennett 15 (2004). See also Fairchild (2019Fairchild ( , 2022 for relevant discussion.…”