 But it remains that it is not guaranteed that a two-place predicate that is an I-predicate in the theory to which it belongs expresses identity. In fact, no condition can be stated in a first-order language for a predicate to express identity, rather than mere indiscernibility by the resources of the language. However, in a second-order language, in which quantification over all properties (not just those for which the language contains predicates) is possible and Leibniz’s Law is therefore statable, identity can be uniquely characterised. Identity is thus not first-order, but only second-order definable.