 Following Geach, call a two-place predicate with these properties in a theory an “I-predicate” in that theory. Relative to another, richer, theory the same predicate, interpreted in the same way, may not be an I-predicate. If so it will not, and did not even in the poorer theory, express identity. For example, “having the same income as” will be an I-predicate in a theory in which persons with the same income are indistinguishable, but not in a richer theory.