Saul Aaron Kripke (born 1940) is an American philosopher and logician now emeritus from Princeton and professor of philosophy at CUNY Graduate Center. He has been immensely influential in a number of fields related to logic and philosophy of language. Much of his work remains unpublished or exists only as tape-recordings and privately circulated manuscripts. He is nonetheless widely considered one of the most significant philosophers alive, and was the winner of the 2001 Schock Prize in Logic and Philosophy.
Kripke, is best known for four contributions to philosophy: semantics for modal (and related) logics, published in several essays beginning while he was in his teens; his 1972 Princeton lectures Naming and Necessity, which significantly restructured philosophy of language and, as some have put it, "made metaphysics respectable again"; for a controversial and influential interpretation of Wittgenstein; for his contribution to developing formal theories of truth designed to handle the liar paradox.
Two of Kripke's earlier works (A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic) were very influential to modal logic. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke because of his contributions to modal logic.
In Semantical Considerations on Modal Logic, published in 1963, Kripke responded to a difficulty with classical quantification theory. The whole motivation for the world-relative approach was to reflect the idea that objects in one world may fail to exist in another. If standard quantifier rulers are used, however, every term must refer to something that exists in all the possible worlds. This seems incompatible with our ordinary practice of using terms to refer to things that only exist contingently.
Kripke's response to this difficulty was to eliminate terms. He gave an example of a system that uses the world-relative interpretation and preserves the classical rules. However, the costs are severe. First, his language is artificially impoverished, and second, the rules for the propositional modal logic must be weakened.
Naming and Necessity
Kripke's three lectures constitute an attack on the descriptivist (Fregean, Russellian) theory of reference with respect to proper names, according to which a name refers to an object by virtue of the name's being associated with a description that the object in turn satisfies. He gave several examples purporting to render descriptivism implausible (e.g., surely Aristotle could have died at age two and so not satisfied any of the descriptions we associate with his name). Kripke proposed instead a causal theory of reference, according to which a name refers to an object by virtue of a causal connection with the object as mediated through communities of speakers. In this way, names are rigid designators: it refers to the named object in every possible world in which the object exists. Causal theories of reference have since been elaborated and developed by Hilary Putnam, Keith Donnelan , Gareth Evans, and others, and are perhaps more widely held than descriptivist theories now. Notable holdouts include John Searle.
Kripke also raised the prospect of a posteriori necessities—facts that are necessarily true, though they can be known only through empirical investigation. Examples include “Hesperus is Phosphorus”, “Cicero is Tully”, and other identity claims where two names refer to the same object.
There is controversy as to whether Kripke was in turn echoing earlier work by Ruth Barcan Marcus in both these ideas.
Finally, Kripke gave an argument against identity materialism in the philosophy of mind, the view that every mental fact is identical with some physical fact (See talk). Kripke argued that the only way to defend this identity is as an a posteriori necessary identity, but that such an identity—e.g., pain is C-fibers firing—could not be necessary, given the possibility of real honest-to-goodness pain that has nothing to do with C-fibers firing. Similar arguments are defended today by David Chalmers.
Kripke also made interesting contributions to the study of the later Wittgenstein in lectures published as Wittgenstein on Rules and Private Language, although his work here has been faulted for being not particularly true to the historical Wittgenstein. Indeed, many philosophers refer to the subject of Kripke's book as "Kripkenstein," on the grounds that whoever the text is about, it's not about Wittgenstein. (For alternative readings of Wittgenstein, see for Colin McGinn's Wittgenstein on Meaning.) Kripke's book has also been faulted for not giving credit to other authors who interpreted Wittgenstein similarly (see Robert J. Fogelin's Wittgenstein). Kripke's influence has been substantial, but much of his work, unfortunately, exists only in tape-recorded or transcript form.
In his 1975 article "Outline of a Theory of Truth", Kripke showed that a language can consistently contain its own truth predicate, which was deemed impossible by Alfred Tarski, a pioneer in the area of formal theories of truth. The trick involves letting truth be a partially defined property over the set of grammatically well-formed sentences in the language. Kripke showed how to do this recursively by starting from the set of expressions in a language which do not contain the truth predicate, defining a truth predicate over just that segment: this adds new sentences to the language, and truth is in turn defined for all of them. Unlike Tarski's approach, however, Kripke lets "truth" be the union of all of these definition-stages; after a denumerable infinity of steps the language reaches a "fixed point" such that using Kripke's method to expand the truth-predicate does not change the language any further. Such a fixed point can then be taken as the basic form of a natural language containing its own truth predicate. But this predicate is undefined for any sentences that do not, so to speak, "bottom out" in simpler sentences not containing a truth predicate. That is, "'Snow is white'is true" is well-defined, as is "'"Snow is white" is true' is true," and so forth, but neither "This sentence is true" nor "This sentence is not true" receive truth-conditions; they are, in Kripke's terms, "ungrounded."