ABSTRACT. Saul A. Kripke, in his 1971 essay, “Identity and Necessity” (reprinted 2011, in Kripke, Philosophical Troubles, Collected Papers, Volume 1), argues on grounds of Leibnizian indiscernibility of identicals that identity relations are necessary. Kripke speaks here explicitly of the modality of identity statements, that are the linguistic expression of a metaphysical qualification. Beginning, in effect, with a true identity relation, a = b, Kripke considers the property of being necessarily identical to a. If a and b are identical, if, then, by Leibniz’s principle they must share all of their properties in common, and if reference to all properties shared by a and b on the assumption that a = b includes the property of being necessarily identical to a, then it follows that b must also be necessarily identical to a. The argument occurring previously in several forms in the philosophical literature is criticized in Kripke’s formalization. A telling objection is meant to be that the argument is circular because it works only for proper names or object constants construed as rigid designators in Kripke’s sense. The essential property of being necessarily identical to a lends itself to the similar definition of properties that simply falsify the Leibnizian principle on which Kripke’s argument depends. Considering all the possible choices, there is no closed sentence univocal reformulation of Kripke’s inherently equivocal concept of the property of being necessarily identical to a specific object that serves his argument’s needs. Kripke’s formalization of the argument for the necessity of identity overlooks identity relations involving nonrigidly designated relata, such as those expressed by means of definite descriptors, from which necessary identities cannot generally be inferred. The implications for Kripke’s metaphysics of modality are considered critically in light of these limitations of the formalization he considers in support of the necessity of identity relations, and by implication for the truth or falsehood of identity statements. pp. 7–26

Keywords: Identity; Kripke, Saul. A.; Leibnizian indiscernibility of identicals; Marcus, Ruth; modality, modal logic and semantics; Prior, Arthur; Quine, W.V.O.; rigid designation, designators; Wiggins, David