  Regimented theory contains no abstract objects other than sets. Many abstracta, however, can be defined in terms of sets: numbers, functions, and other mathematical entities being the most obvious. Quine excludes other alleged abstracta, such as properties, propositions (as distinct from sentences), and merely possible entities. The chief reason for this is that he finds the identity-criteria for such entities unclear. He holds, quite generally, that we should not postulate entities without having clear identity-criteria for them. (This is the view that he sums up in the slogan “no entity without identity”; see (1969, 23) and elsewhere.) Doing so would threaten the clarity and definiteness which the notion of identity brings to theory; local gains from postulating, say, propositions are not worth this global loss. (For a contrary view about properties, see Armstrong 1980.)