Identity and Necessity

The central argument is that if an identity statement between two proper names is true, it is necessarily true. Kripke derives this from the Leibnizian principle of the indiscernibility of identicals: if a is identical to b, then whatever is true of a is true of b, including the property of being necessarily identical to a . The essay rejects the received view that statements like 'Hesperus is Phosphorus' are contingently true—true as a matter of astronomical fact but possibly false. It also rejects the assumption that necessity and apriority are coextensive, arguing that some truths are both necessary and knowable only through experience.

A rigid designator is an expression that picks out the same object in every possible world where that object exists. Kripke argues that proper names are rigid designators, unlike definite descriptions such as 'the brightest object in the evening sky,' which may pick out different objects in different possible worlds . Rigid designation is essential because the necessity of identity follows only when both terms flanking the identity sign are rigid. If 'Hesperus' and 'Phosphorus' were disguised descriptions, the identity statement would be contingent. Because they are rigid names of the same object, the statement is necessary if true at all.

The essay establishes the necessary a posteriori through the Hesperus-Phosphorus example. That Hesperus is Phosphorus is a necessary truth (given rigid designation), but it was discovered empirically, through astronomical observation. Before the discovery, no one could have known it a priori . This matters because it overturns a Kantian assumption that necessary truths are knowable independently of experience and that a posteriori truths are merely contingent. Kripke's distinction between epistemic and metaphysical modality—between what could have been the case for all we knew and what could have been the case in reality—opens a new framework for modal metaphysics.

Identity and Necessity was delivered as a lecture in 1971 and published in Munitz's Identity and Individuation. Naming and Necessity, published in 1980 but based on lectures given in 1970, develops the same themes at much greater length, adding the causal-historical theory of reference and extended discussions of natural kind terms . The two works are complementary: Identity and Necessity is the compact, focused argument for the necessity of identity statements between names, while Naming and Necessity expands the framework to language, mind, and science. Readers often begin with Identity and Necessity as the clearer, more concentrated introduction to Kripke's modal revolution.

Dale Jacquette has argued that Kripke's formalization is circular: the argument works only if the terms are already construed as rigid designators, which is precisely what needs to be shown . Michael Wreen has advanced an argument that 'Hesperus is Phosphorus' is contingent, drawing on tensions in Kripke's views about how causal chains ground reference . Allan Gibbard and Andre Gallois have proposed purported counterexamples involving contingent identity, such as the statue and the lump of clay that coincide but could have diverged. Defenders of Kripke reply that these cases confuse identity with constitution, or that they trade on non-rigid descriptions rather than genuine rigid names.

A common misreading treats Kripke's claim that 'Hesperus is Phosphorus' is necessary as a claim that we could not have been wrong about it, or that it is a priori. Neither is correct. Kripke explicitly allows that we could have been wrong—before the astronomical discovery, it was epistemically possible that the evening star and morning star were different objects. The necessity is metaphysical, not epistemic: given that the names rigidly designate the same object, there is no possible world in which that object is not identical to itself . Another misreading assumes Kripke is a simple essentialist about all properties; his argument is specifically about the necessity of identity, not about which properties are essential to particular things.