Kripke Saul A(aron) (b.1940), American mathematician and philosopher, considered one of the most deeply influential contemporary figures in logic and philosophy. While a teenager, he formulated a semantics for modal logic (the logic of necessity and possibility) based on Leibniz’s notion of a possible world, and, using the apparatus, proved completeness for a variety of systems (1959, 1963). Possible world semantics (due in part also to Carnap and others) has proved to be one of the most fruitful developments in logic and philosophy. Kripke’s 1970 Princeton lectures, Naming and Necessity (1980), were a watershed. The work primarily concerns proper names of individuals (e.g., ‘Aristotle’) and, by extension, terms for natural kinds (‘water’) and similar expressions. Kripke uses his thesis that any such term is a rigid designator – i.e., designates the same thing with respect to every possible world in which that thing exists (and does not designate anything else with respect to worlds in which it does not exist) – to argue, contrary to the received Fregean view, that the designation of a proper name is not semantically secured by means of a description that gives the sense of the name. On the contrary, the description associated with a particular use of a name will frequently designate something else entirely. Kripke derives putative examples of necessary a posteriori truths, as well as contingent a priori truths. In addition, he defends essentialism – the doctrine that some properties of things are properties that those things could not fail to have (except by not existing) – and uses it, together with his account of natural-kind terms, to argue against the identification of mental entities with their physical manifestations (e.g., sensations with specific neural events). In a sequel, ‘A Puzzle about Belief’ (1979), Kripke addresses the problem of substitution failure in sentential contexts attributing belief or other propositional attitudes. Kripke’s interpretation of the later Wittgenstein as a semantic skeptic has also had a profound impact (Wittgenstein on Rules and Private Language, 1980, 1982). His semantic theory of truth (‘Outline of a Theory of Truth,’ 1975) has sparked renewed interest in the liar paradox (‘This statement is false’) and related paradoxes, and in the development of non-classical languages containing their own truth predicates as possible models for natural language. In logic, he is also known for his work in intuitionism and on his theory of transfinite recursion on admissible ordinals. Kripke, McCosh Professor of Philosophy (emeritus) at Princeton, frequently lectures on numerous further significant results in logic and philosophy, but those results have remained unpublished. See also A PRIORI , CAUSAL THEORY OF PROPER NAMES , MEANING , PHILOSOPHY OF LANGUAGE , WITTGENSTEI. N.S.