 This view, as Linnebo himself admits, faces some problems. One of them is that the methodologies used by working mathematicians, such as classical logic, impredicative definitions, and taking arbitrary subcollections of infinite domains, seem to presuppose objects that are more independent, i.e., objects that don’t have a shallow nature (2018, 197; for a discussion of independence, see  Section 4.1 of the entry on  platonism in mathematics).  Another problem (2018, 195) is that in order for an object to count as having a shallow nature, an intrinsic unity relation has to be available. An investigation is required to establish that there is such an intrinsic unity relation in each case. It is far from clear that a conditional principle with an intrinsic unity relation is available for each of problematic cases mentioned in this entry, such as chess, legal institutions or the English language. Finally, Linnebo doesn’t discuss the question of whether sets of concrete urelements are themselves abstract or concrete. At present, there may be an important question left open by his theory that other theories of abstract objects answer.