 Independently of the paradoxes (Bealer &amp; Mönnich 1989: 198 ff.), there is the issue of providing identity conditions for properties, specifying when it is the case that two properties are identical. If one thinks of properties as meanings of natural language predicates and tries to account for intensional contexts, one will be inclined to assume rather fine-grained identity conditions, possibly even allowing that [\(\lambda x(R(x) \amp S(x))\)] and [\(\lambda x(S(x) \amp R(x))\)] are distinct (see Fox &amp; Lappin 2015 for an approach based on operational distinctions among computable functions). On the other hand, if one thinks of properties as causally operative entities in the physical world, one will want to provide rather coarse-grained identity conditions. For instance, one might require that [\(\lambda x A\)] and [\(\lambda x B\)] are the same property iff it is physically necessary that \(\forall x(A \leftrightarrow B)\). Bealer (1982) tries to combine the two approaches (see also Bealer &amp; Mönnich  1989)[15].