Abstract
Deflationist approaches to abstract objects typically have a distinctive advantage over non-deflationist counterparts on the epistemological front, given the avoidance of commitment to the existence of these objects (Azzouni, Deflating existential consequence: a case for nominalism. Oxford University Press, 2004; Bueno, Stud Hist Phil Mod Phys, 36:465–490, 2005) or given the light-weight character that is assigned to them, as thin objects (Linnebo, Thin objects: an abstractionist account. Oxford University Press, 2018). But these approaches need to accommodate whatever use abstract objects are put to in mathematics, metaphysics, and in the sciences. Two deflationist approaches should be distinguished: (a) quantificational approaches, which explore the role of quantification in deflating ontological commitment (Azzouni, Deflating existential consequence: a case for nominalism. Oxford University Press, 2004; Bueno, Stud Hist Phil Mod Phys, 36:465–490, 2005), and (b) definitional approaches, which emphasize the role of suitable abstraction principles in the characterization of the relevant objects (Linnebo, Thin objects: an abstractionist account. Oxford University Press, 2018). In this paper, these views are contrasted and assessed. In the end, there is something to be said in favor of quantificational approaches and the thin access to objects they recommend.