In the by now well known talks he gave at Princeton, Saul Kripke claimed that “[t]heoretical identities … are generally identities involving two rigid designators and therefore are examples of the necessary a posteriori.” (Published as “Naming and Necessity,” in G. Harmon and D. Davidson, eds., Semantics of Natural Language (Dordrecht, 1972) 253-355; (hereafter referred to as “NN”; this quote p. 331.) A rigid designator is an expression that designates the same object in all possible worlds when it is used. So Kripke is claiming that ‘Water is H20’ and ‘Heat is the motion of molecules’ are generally identities involving expressions like ‘water’ and ‘the motion of molecules’ which designate the same objects in all possible worlds. If the identity statement is true, both sides designate the same object rigidly, i.e., in all possible worlds, and therefore the statement is necessarily true. On the other hand, whether it is true is determined ultimately by appeal to experience. It follows that if true, the identity is necessary a posteriori.