Bloomsbury Encyclopedia of Philosophers - Kripke, Saul Aaron (1940– )
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Kripke, Saul Aaron (1940– )

Kripke, Saul Aaron (1940– )
DOI: 10.5040/9781350052444-0544

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Saul Kripke was born on 13 November 1940 in Bay Shore, New York. He displayed prodigious mathematical talent as a child, and by age six he had acquired on his own a working knowledge of Hebrew. In the fourth grade Kripke read all of Shakespeare’s plays, and at age twelve he asked himself, “How do I know I am not dreaming?” His father, who was a rabbi and university teacher, told him that Descartes had written about this question, and Kripke responded by reading some philosophy as a teenager. Kripke studied at Harvard University, receiving a BA in 1962 but not before publishing his first contributions to logic. He then became a junior fellow at Harvard from 1963 to 1966, holding a concurrent position at Princeton as assistant professor of philosophy from 1964 to 1966. Kripke never received a doctorate, for the reason that no faculty at any of the universities with which he was associated felt qualified to examine him. He was lecturer at Harvard from 1966 to 1968, and then became associate professor at Rockefeller University in 1968 and full professor in 1972. Upon the dissolution of Rockefeller’s philosophy department, he went to Princeton University in 1977 as McCosh Professor of Philosophy. After becoming emeritus professor in 1997, he was a visiting professor at the Hebrew University of Jerusalem and the City University of New York. In 2003 he became a full-time professor of philosophy at the City University of New York Graduate Center, and his current title is Distinguished Professor of Philosophy. The Saul Kripke Center was founded there in 2007.

Kripke has been awarded honorary doctorates from the University of Nebraska, Johns Hopkins University, the University of Haifa and the University of Pennsylvania. In 1973 he gave the John Locke Lectures at the University of Oxford. At Princeton, Kripke won the Behrman Award for distinguished achievement in the humanities in 1988. Kripke’s work has been supported by the National Science and Guggenheim foundations, the American Council of Learned Societies, and National Endowment for the Humanities, among other institutions. He was the 2001 Winner of the Schock Prize in Philosophy, considered by many to be philosophy’s Nobel Prize. He was elected Fellow of the American Academy of Arts and Sciences (1978) and the American Philosophical Society (2005), and a Corresponding Fellow of the British Academy (1985)

Both Kripke’s books, Naming and Necessity (1980) and Wittgenstein on Rules and Private Language (1982), grew out of lectures he gave at Princeton. Both have been translated into several languages. He has also published many articles in logic and philosophy. He is probably the model for one of the main characters in Rebeccah Goldstein’s novel The Mind-Body Problem.

On the strength of his contributions to formal logic, semantics, metaphysics, the theory of truth, the mind–body problem, and Wittgenstein interpretation, Kripke is now regarded as one of the foremost philosophers and logicians. He combines extraordinary technical gifts with non-technical arguments of great intuitive force. Robert Nozick once referred to him as philosophy’s one uncontested genius. By virtue of his achievements in modal logic, semantics, and metaphysics, Kripke has helped forge a position – the so-called New Theory of Reference – as influential in the latter twentieth century as ordinary language philosophy was in the middle and logical positivism was in the early part of the twentieth century.

In spite of the great advances in logic made in the latter half of the nineteenth and first half of the twentieth century, the logic of modal notions remained relatively obscure until the late 1950s. It seems intuitively plausible that, for instance, if it is possible that P, for some proposition P, then it is necessary that it is possible that P. If it is necessary that “if P, then Q,” may we infer from the necessity of P to the necessity of Q? It is difficult to see how to resolve a question like this by just contemplating the meaning of the words used to express it. One could of course write down axioms to codify such inferences as these, and C. I. Lewis developed a number of axiomatic systems for this purpose. However, no formal demonstration was available to show that any such axiomatic system was consistent, or able to certify all inferences that are valid.

As a teenager Kripke developed a semantics for modal logic of just this sort. Related systems were studied independently by such logicians as Stig Kanger. The core idea is that one component of the model in terms of which semantics is given is a set of W or worlds, in the spirit of Leibniz’s notion of possible worlds. A formula of the language is then semantically analyzed in terms of that model’s set of worlds. A formula is necessarily true just in case it is true in all worlds in the model, while it is possibly true just in case it is true at some. The semantics of the modalities necessary and possible is then defined in terms of the familiar quantifiers all and some.

Our notions of possibility and necessity are not, however, univocal. In one use of the word, for instance, it is not possible for John, who is a monolingual adult English speaker, to speak Swahili; in another usage of that word it is, since he could take classes to learn that language. Kripke codifies this relative notion of possibility by defining an accessibility relation on worlds. For any given world W, there is some subset W’ of W such that each element of W’ is accessible from W. These, intuitively, are the worlds that are possible relative to W. Kripke shows that different restrictions on the accessibility relation (transitivity, symmetry, reflexivity, etc.) yield different theorems of modal logic, and correspond to different axiomatic systems already understood. The innovation led to an explosion in work on modal logic beginning in the middle 1960s, and had profound implications for semantics and metaphysics, described below.

In Naming and Necessity Kripke astounded the philosophical world by undermining the dominant theory, the Description Theory of Names, which holds that the meaning of a proper name such as “Aristotle” may be articulated using some description such as “The student of Plato who was tutor to Alexander the Great.” This theory also suggests a picture of how thoughts single out their objects, by containing a body of descriptive information, and they single out whatever object exemplifies that description.

Kripke’s alternative theory of names argues that proper names are rigid designators, where a name N rigidly designates object O just in case N refers to O, and N refers to O in every world in which O exists. Whereas the expression, “The tutor of Alexander” might not have referred to Aristotle (he might never have been hired for the job), the name “Aristotle” cannot but refer to Aristotle, at least in every world in which Aristotle exists. Hence “Aristotle” rigidly designates Aristotle. However, the descriptions that are plausible candidates for the putative descriptive meaning of “Aristotle” (the tutor of Alexander, the author of De Interpretatione, etc.), do not have the same modal profile as the name whose meaning they were thought to explicate. For example, Aristotle might never have gone into philosophy or pedagogy, but might have chosen a life as a lowly swineherd. He would still have been Aristotle, but none of the descriptions associated with his name would have applied to him. Hence an explanation of the name’s meaning in terms of descriptions seems untenable. Kripke offers other arguments against the Description Theory as well. Kripke reminds his readers of the power of intuitions as guides to philosophical knowledge, thereby challenging various orthodoxies. For instance, John Locke had held that insofar as alethic modalities such as necessity and possibility make sense at all, they do so only relative to how an object is described. Quine echoed this sentiment in contending that described as a mathematician, Jones is necessarily rational, whereas described as a cyclist, he is not. In Quine’s hands this was meant as an attack on the very coherence of the alethic modalities. Kripke argues that this doctrine that the only modality is verbal contradicts intuition. We have already seen that Aristotle, that very man, might have led an obscure life outside of philosophy. By contrast it seems quite dubious that this very piece of paper on which I write could have been made of vellum rather than wood pulp. Claims of this form concern so-called de re modality. As with many other great works of philosophy, in Naming and Necessity we find a number of major themes tightly interwoven, and one of the most significant is the centrality of our notion of de re modality.

From the premise that Hesperus is identical with Phosphorus, and the premise that both “Hesperus” and “Phosphorus” rigidly designate their bearer, it follows that Hesperus is necessarily identical with Phosphorus. Kripke remarks, however, that the identity of Hesperus and Phosphorus is only known a posteriori. Hence we may infer that “Hesperus is Phosphorus” is both necessary and a posteriori, a conclusion that disagrees with the longstanding doctrine that the necessary and the a priori coincide. Likewise, Kripke holds that natural kind terms such as “gold” and “water” have properties analogous to proper names construed rigidly: if “water” refers in the actual world to H2O then it refers in all counterfactual situations to stuff with that same molecular structure. If water is H2O, then it is necessarily but once again not a priori. Finally, consider the standard meter bar in Paris. We may stipulate from our armchairs that the expression “one meter” refers to the length of that bar. As a result it is a priori that the standard meter is one meter in length. On the other hand, that very bar might not have been one meter in length, since climatic perturbations might have changed its length due to a flaw in its protective casing. Consequently the claim that the standard meter is one meter is contingent if true. So that claim, if true, is contingent but also a priori.

Harmonizing with the work of Hilary Putnam , Keith Donnellan , and others, Kripke’s view of names and related locutions suggests a view of how our words mediate our relation to the world. In entertaining the name “Aristotle” I do not think about that man by associating a number of descriptions with his name that pick him out uniquely. Rather, by virtue of my familiarity with the name I stand at the receiving end of a causal–historical chain of users that can trace back its provenance to the original dubbing or baptism of Aristotle with the name “Aristotle” (possibly but not necessarily at his birth). Because I might be mistaken about some aspects of that historical provenance, I could be wrong about who are the referents of my names (and natural kind terms). The overall picture that emerges from the account of language that Kripke offers suggests our epistemic and semantic relation to the world to depend much less on what we know or believe about the meanings of our words, and much more about how we are causally situated in our social and physical environment than had commonly been acknowledged.

In Naming and Necessity Kripke also challenges a complacent acceptance of identity statements interpreted in such a way as to resolve philosophical problems. In philosophy of mind, many twentieth-century philosophers have contended that mental states are identical with states of the brain, or at least of the central nervous system. However, this identity is not thought to be a necessary truth; it seems conceivable that mental states could exist without any physical embodiment. Accordingly many philosophers held that mental states are identical to brain states, but only contingently so. Kripke attacks this notion of contingent identity on purely logical grounds. If A = B, then A and B share all their properties in common. Also, A has the “identity” property of being necessarily identical with A. But then B must have that same “identity” property, which is to say that B has the property of being necessarily identical with A as well. Hence any true identity statement, at least when the identity sign is flanked by genuine singular terms, must also be necessarily true.

Kripke then argued that mental states, such as the state of being in pain, are not identical to states of the central nervous system. As we have just seen, were they so identical they would necessarily be. However, Kripke argues, it certainly seems conceptually possible that there be a case of a pain that has no physical realization, or a physical state alleged to be identical to a sensation that is not in fact so. Perhaps, it might be replied, the sensation is necessarily identical to the brain state, but the sensation is not essentially a pain? Kripke responds by observing that if a sensation is in fact a pain, it is hard to see how that very sensation might have been anything other than a pain. Notice that all one need grant to Kripke is (1) the necessity of true identity statements, (2) that it is conceptually possible that there be disembodied states of mind, or states of the central nervous system not identical to sensations, and (3) that pains and other sensations are essentially the sensations that they are. These three premises together argue against the alleged contingent identity of sensations and brain states.

A conception of names as rigid designators, as espoused in Naming and Necessity, is only a partial characterization of their semantics. That conception is compatible with Direct Reference (the doctrine that the meaning of a name is given entirely by its having the bearer that it does), but is also compatible with a Fregean conception according to which a name’s meaning is not fully exhausted by its having the bearer that it does. (Nothing in principle rules out the set of descriptions alleged to be associated with a name being rigid in the way that the name is.) Although, as we have seen, in Naming and Necessity Kripke undermines one dominant position inspired by Frege, in that work and elsewhere Kripke scrupulously avoids espousing Direct Reference.

One familiar challenge to Direct Reference lies in the fact that attitude ascriptions seem to be sensitive to which of two co-referential names occur therein. Consider (1) Lois Lane thinks that Clark Kent is a reporter, and (2) Lois Lane thinks that Superman is a reporter. These last two sentences are exactly alike except for containing distinct but co-referring names. The first is true, the second is false. Assuming that the meaning of a sentence is a function of the meanings of its parts together with their mode of composition (the thesis of compositionality), if Direct Reference is true it will follow that (1) and (2) mean the very same thing, and so one must be true if the other is. This consideration, sometimes referred to as Frege’s Puzzle, is commonly invoked as a challenge to Direct Reference.

In his “A Puzzle About Belief” Kripke argues that Frege’s Puzzle lacks force against Direct Reference. His reason is that the very same puzzle can arise with a single name. Peter might take the name “Padewerski” to have two bearers. One is the Polish pianist. The other is the Polish statesman. Unbeknownst to Peter, the name “Padewerski” refers to just one man who is more versatile than Peter had imagined. Nevertheless, on one reading of that name, “Peter thinks that Padewerski is a statesman” is true, on another reading that sentence is false. Kripke takes this example to show that Frege’s Puzzle would arise even if every object had at most one name, and arises even if we accept a Fregean doctrine of sense as applied to names.

Kripke proposed a solution to the ancient Paradox of the Liar in his “Outline of a Theory of Truth” (1975). On one version of this paradox, the sentence, “This sentence is false” seems to be false if true, and if true, then false. If we assume further that every sentence is either true or false, and no sentence is both true and false, from the premise that “This sentence is false” is meaningful we may infer a contradiction. Kripke observes that an equally powerful paradox can be generated with a set of sentences considered in a situation in which some further facts hold. This de facto Liar paradox requires analysis just as much as the aforementioned de jure Liar paradox. Dominant solutions in the spirit of Bertrand Russell and Alfred Tarski had proposed that for a sentence to be meaningful it cannot refer to itself. Rather, a sentence can refer to a sentence in a distinct language (perhaps an object language) and say of it that it is true, or false, and so forth.

Kripke proposes an analysis in which sentences are indeed able to refer to themselves, but when they do so in such a way as to generate paradox, they are neither true nor false. He envisions a base-level language on which predicates have both extensions and anti-extensions (where not falling into an extension does not imply falling into an anti-extension), and on this basis constructs higher-level languages in ways constrained by the lower level. As the process of constructing these higher level languages proceeds, in some cases nothing new is added, with respect to what predicates fall into which extensions and which anti-extensions, from language level N to language level N+1. In that case we say that language level N is a fixed point. A sentence of language L lacks a truth value at level M just in case it lacks a truth value at a fixed point for L. Kripke shows that Liar-type sentences lack truth values under his fixed point construction. This approach does not shed light on the Strengthened Liar (one form of which is “This sentence is not true”), but has motivated others to build on Kripke’s work to find systems that do.

In 1982 Kripke published Wittgenstein On Rules and Private Language, which immediately gained considerable attention. In this book he argues that the force of Wittgenstein’s considerations about rule-following, as set forth primarily in the Philosophical Investigations, had not been fully appreciated. Kripke formulates a “skeptical paradox” to bring home the force of these considerations. Suppose a child is learning a mathematical operation such as addition (the example is generalizable to other rules such as those governing grammar, semantics, even etiquette). This child has only been exposed to a finite set of examples purporting to illustrate that operation of taking one number plus another number. For that reason, there is more than one way in which she might apply that operation to a new pair of numbers to be added, each of which is compatible with what she has observed thus far. For instance, having never seen a teacher add 1000 to 100,000, she might get the result 101,001 when she “adds” these numbers. This case of “addition” is compatible with what she has observed thus far, since her teachers had never covered this particular case for her. One might reply, “But then she didn’t understand any of her lessons about addition that she did observe!” Kripke counters, on Wittgenstein’s behalf, that this reply begs the very question at issue, which is what it means to grasp and conform to a putative rule.

Kripke’s skeptical paradox points out that there seems to be a clear difference between conforming to a rule such as “plus” and some other rule of “addition,” although there seems to be no substantive fact that makes one pattern of behavior conform to the “plus” rule more than any other pattern of behavior might. Kripke suggests that for there to be such a thing as a rule, and as a special case for an expression to be meaningful, there would have to be such a substantive fact in virtue of which one pattern of behavior conforms to a particular rule. Kripke then argues that no such substantive fact seems to be forthcoming. Any putative such fact is either insufficient to make it the case that one form of behavior conforms to a rule, or instead is simply a restatement of that very rule.

Some commentators, unconvinced that Kripke has properly interpreted Wittgenstein, have used “Kripkenstein” to denote that doctrine which Kripke claims to discern in Wittgenstein, leaving aside whether this claim is correct. Nonetheless, many commentators have found Kripkenstein’s skeptical paradox and related ideas worthy of discussion in their own right. It has also been argued that the above skeptical paradox rests upon the assumption that for there to be such facts as what an expression (“plus”, etc.) means, there must be some distinct, physical fact (including facts having to do with the agent’s dispositions to behavior) in virtue of which that expression means what it does. This reductionism about meaning may be challenged, and if it is we may be doubtful that the skeptical paradox raises an urgent problem.

Since Kripke’s publications on logic and reference, a controversy has arisen as to proper attribution of the original ideas for the New Theory of Reference. Philosophers such as Quentin Smith have claimed that Ruth Marcus anticipated some of the central ideas of Naming and Necessity without Kripke acknowledging her contribution. Kripke’s colleagues at Princeton from that time, John Burgess and Scott Soames, rallied to his defense. (Articles on both sides of the debate are collected in Humphreys and Fetzer 1998.) It cannot be denied that Kripke presented the main elements of the New Theory with unprecedented technical power and intuitive force.


“A Completeness Theorem in Modal Logic,” Journal of Symbolic Logic 24 (1959): 1–14.

“Identity and Necessity,” in Identity and Individuation , ed. Milton Munitz (New York, 1971), pp. 135–64.

“Naming and Necessity: Lectures Given to the Princeton University Philosophy Colloquium, January, 1970,” in Semantics of Natural Language , ed. Donald Davidson and Gilbert Harman (Dordrecht, 1972): 253–325, 763–9.

“Outline of a Theory of Truth,” Journal of Philosophy 72 (1975): 690–716.

“Is There a Problem about Substitutional Quantification?” in Truth and Meaning: Essays in Semantics , ed. Gareth Evans and John McDowell (Oxford, 1976), pp. 325–419.

“Speaker’s Reference and Semantic Reference,” Midwest Studies in Philosophy 2 (1977): 255–76.

“A Puzzle About Belief,” in Meaning and Use , ed. A. Margalit (Dordrecht, 1979), pp. 234–83.

Naming and Necessity , 2nd edn (Cambridge, Mass., 1980).

Wittgenstein On Rules and Private Language (Cambridge, Mass., 1982).

Philosophical Troubles: Collected Papers, Vol. 1 (Oxford, 2011). ISBN 9780199730155 Reference and Existence (Oxford, 2013).

Other Relevant Works

“Semantical Analysis of Modal Logic,” Journal of Symbolic Logic 24 (1959): 323–4.

“The Undecidability of Monadic Modal Quantification Theory,” Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 8 (1962): 113–6.

“Semantical Analysis of Modal Logic, I: Normal Propositional Calculi,” Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9 (1963): 67–96.

“Semantical Considerations on Modal Logic,” Acta Philosophica Fennica 16 (1963): 83–94.

“Semantical Analysis of Modal Logic, II: Non-Normal Propositional Calculi,” in The Theory of Models , ed. I. Addison, L. Henkin, and A. Tarski (Amsterdam, 1965), pp. 206–20.

“Semantical Analysis of Intuitionist Logic,” in Formal Systems and Recursive Functions , ed. M. Dummett and J. Crossley (Amsterdam, 1965), pp. 92–130.

“A Problem in the Theory of Reference,” in Philosophie et culture: actes du XVIIe Congrès mondial de philosophie , ed. V. Cauchy (Montréal, 1988), vol. 1, pp. 241–7.

“Russell's Notion of Scope,” Mind 114 (2005): 1005–1037.

“Yet Another Dogma of Empiricism,” Philosophy and Phenomenological Research 91 (2015): 381–385.

“Quantified Modality and Essentialism,” Noûs 51 (2017): 221–234.

Further Reading

Amer Phils 1950–2000 , Bio 20thC Phils, Blackwell Analytic Phil, Blackwell Comp Phils, Cambridge Dict Amer Bio, Oxford Comp Phil, Routledge Encycl Phil

Arif, Ahmed. Saul Kripke (London, 2007).

Berg, Jonathan, ed. Naming, Necessity and More: Explorations in the Philosophical Work of Saul Kripke (London, 2014).

Berger, Alan ed. Saul Kripke (Cambridge, UK, 2011).

Fitch, G. W. Saul Kripke (Chesham, UK, 2004).

Hughes, Christopher. Kripke: Names, Necessity, and Identity (Oxford, 2004).

Humphreys, Paul, and James Fetzer, eds. The New Theory of Reference: Kripke, Marcus, and Its Origins (Dordrecht, 1998).

Kusch, Martin. A Sceptical Guide to Meaning and Rules: Defending Kripke's Wittgenstein (Chesham, UK, 2006).

Noonan, Harold. Routledge Philosophy GuideBook to Kripke and Naming and Necessity (London and New York, 2013).

Norris, Christopher. Fiction, Philosophy and Literary Theory: Will the Real Saul Kripke Please Stand Up? (London, 2007).

Preti, Consuelo. On Kripke (Belmont, Cal., 2002).

Schwartz, Stephen, ed. Naming, Necessity, and Natural Kinds (Ithaca, N.Y., 1977).

Soames, Scott. Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity (Oxford, 2002).

Stanley, Jason. “Names and Rigid Designation,” in A Companion to Philosophy of Language , ed. Bob Hale and Crispin Wright (Oxford, 1998). van Fraassen, Bas, and J. C. Beall.

Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic (Oxford, 2003).

Wright, Crispin, and Alexander Miller, eds. Rule-Following and Meaning (Chesham, UK, 2002).