 Thus, the ordinary objects include all the concrete objects (since \(E!x\) implies \(\Diamond E!x\)), as well as possible objects that aren’t in fact concrete but might have been. On this theory, therefore, being abstract is not the negation of being concrete. Instead, the definition validates an intuition that numbers, sets, etc., aren’t the kind of thing that could be concrete. Though Zalta’s definition of abstract seems to comport with the way of primitivism—take concrete as primitive, and then define abstract as not possibly concrete—it differs in that (a) axioms are stated that govern the conditions under which abstract objects exist (see below), and (b) the features commonly ascribed to abstract objects are derived from principles that govern the property of being concrete. For example, Zalta accepts principles such as: necessarily, anything with causal powers is concrete (i.e., \(\Box \forall x(Cx \to E!x)\)). Then since abstract objects are, by definition, concrete at no possible world, they necessarily fail to have causal powers.