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Last Updated on May 6, 2015, by eNotes Editorial. Word Count: 2382

Article abstract: Kripke provided technical and conceptual advances in modal logic but is more widely known for his work in the philosophy of language, in particular for initiating the causal theory of reference.

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Early Life

Saul Aaron Kripke, son of Myer Samuel and Dorothy Evelyn (Karp) Kripke, attended Harvard University, where he received a B.A. degree in 1962. In 1959, as a student, he distinguished himself by publishing an influential paper in the prestigious Journal of Symbolic Logic. Upon graduation, he received a Fulbright scholarship. A member of the Society of Fellows at Harvard in philosophy and mathematical logic, he served his alma mater as a lecturer from 1963 to 1966, when he left to take an appointment at Rockefeller University, where he stayed for ten years. In 1976, he became the McCosh Professor of Philosophy at Princeton University.

Life’s Work

Kripke’s earliest writings and influence were in the field of modal logic. Where “standard” formal logic deals with the syntax and semantics of inference, modal logic extends these to characterize and systematize inferences involving the modalities of possibility and necessity. For example, “standard” logic does not allow the inference “If it is necessary that p, then p” or “If p, then it is possible that p.” Various systems of modal logic have been constructed to handle such inferences. One way of talking about such systems is to speak of “possible world semantics.” Although the world is the actual world, with a particular structure and history, things could have been different; facts could have been contrary to what they are. An intuitive way to speak of this is to talk of possible worlds, that is, worlds like the real world, but different in some respect or other.

To say that a proposition is possibly true simply means that, although it is false in the real world, it is true in some possible world. To say that a proposition is necessarily true simply means that it is true in all possible worlds (including the real world). Kripke’s first paper, “A Completeness Theorem in Modal Logic,” established that a formal modal system is complete: This means that any proposition p, either it or its negation, could be proven in that system (in other words, all valid inferences are shown to be valid in that system). This paper was followed by several others in the 1960’s, most notably “Semantical Considerations in Modal Logic,” in which Kripke elaborated on both technical aspects of modal logic and their wider implications and applications, including in the fields of ontology and philosophy of language.

It was these implications and applications of results in modal logic that brought Kripke his greatest renown. In 1972, he published Naming and Necessity, widely regarded as his most influential work and immediately considered a landmark in the philosophy of language. As the title indicates, he drew a connection between the modal element of necessity and the semantic issue of naming. The natural point of contact between these two, for Kripke, was the Leibnizian principle of the indiscernibility of identicals; that is, if two objects are identical, then they are indiscernible (or have all properties in common). If two objects really are identical, that is, if “a = b” is true, then, said Kripke, that identity would hold across all possible worlds (so that “a = b” would be necessarily true). From this starting point, Kripke questioned and ultimately rejected the view that names attach to objects in virtue of contingent properties associated with those names. For example, the name “Saul Kripke” attaches to a particular object not because of any contingent property that might be true of that particular object (for example, that he is the McCosh Professor of Philosophy). This is because there are possible worlds in which Saul Kripke is not the McCosh professor, but there are no possible worlds in which Saul Kripke is not Saul Kripke. Publication of Naming and Necessity, including its proposal of a new theory of reference and names, made Kripke a well-known figure not only in the community of logicians but also in the philosophical community at large.

His groundbreaking work in semantics continued throughout the 1970’s, highlighted by two more influential writings: one on truth, “Outline of a Theory of Truth,” and one on belief, “A Puzzle About Belief.” The former presented his attempt to provide a theory that both resolved paradoxes involving truth and captured basic intuitions about natural languages. Truth paradoxes have been long-standing in philosophy, the most famous being the liar paradox. This paradox is illustrated by the following sentence: “Everything I say is a lie.” If that sentence is true, then I am lying when I say that everything I say is a lie, which means that I am not lying. Another way to characterize this paradox is “This sentence is false.” If the sentence is false, then it must be true. A standard response to this paradox has been to speak of different levels of language, such that the content of that sentence is on one level, but when speaking about that sentence (for example, by calling it true or false), people are at a different level. The first level is often said to be the object language and the second level is said to be the metalanguage. Kripke, however, argued that with natural languages, people do not conceive of themselves as using different levels and do not speak of “truth-level-one,” “truth-level-two,” “truth-level-three,” and so on. A second concern for him was that, again with natural languages, people want to speak of truth-value gaps, times when we do not want to (or cannot) say that a given sentence is true or false. He addressed these problems using tools of mathematical logic to characterize what he calls a “fixed point” language. Critics of his outline claimed that certain truth paradoxes remain unexplained; however, supporters claimed that his approach, though incomplete, is more promising than other approaches.

The second influential paper (on belief) returned to issues of reference, truth, and what speakers have in mind. A legitimate intuition about the truth of sentences is that coreferential terms can be substituted in them without changing the truth value of those sentences. For example, if “Cicero was lazy” is true, then, if Cicero equals Tully, “Tully was lazy” also would be true. This sort of substitutivity, however, breaks down in belief contexts. That is, while it might be true that I believe Cicero was lazy, not knowing that Cicero equals Tully, I might not believe that Tully was lazy. Relating back to Kripke’s view that names are rigid designators and so should be interchangeable without affecting the truth value of the sentences in which they occur, belief contexts are problematic. The problem is not epistemological (I just don’t know that Cicero equals Tully), but semantic (the truth values of the sentences are different).

Kripke extends this problem beyond that of substitutivity of coreferential terms in belief contexts to simple, ordinary contexts of disquotation and translation. (The principle of disquotation is as follows: If a normal English speaker, on reflection, sincerely assents to p, then he believes that p. The principle of translation is that if a sentence of one language expresses a truth in that language, then any translation of it into any other language also expresses a truth in that other language.) Kripke’s puzzle is exemplified by the following case: Pierre, a normal French speaker who hears about the wonders of London, comes to believe “Londres est jolie” (London is pretty). However, if Pierre later learns English and visits London but sees only the seamy side of the city without realizing that this is the city he used to know as ‘Londres,’ Pierre comes to believe “London is not pretty.” Does Pierre, or does he not, believe that London is pretty? Remembering that the issue is semantic, not epistemological, Kripke insisted that “As any theory of truth must deal with the liar paradox, so any theory of belief and names must deal with this puzzle.”

Kripke’s work on these semantic problems and issues led to his second book, Wittgenstein on Rules and Private Language, which, like his earlier writings, generated enthusiasm and controversy. He suggested that the philosopher Ludwig Wittgenstein’s rejection of private languages revealed a much deeper concern with the very possibility of rule following in language, which, in turn, revealed concern about matters of meaning, truth, and knowledge.

In Philosophical Investigations (1956; bilingual English and German edition), Wittgenstein claimed that language was rule-governed and required publicity; there could be no private language. Obeying the rules of language entailed publicity. The very meaning of words requires rule-governedness, as does people’s ability to use and understand the meanings of words. Kripke asserted that Wittgenstein was actually addressing a “skeptical paradox,” namely, there was no way to properly account for what it is to follow a linguistic rule. If this is so, it strikes at the very core of meaning and language itself. How can one know if one is following a rule? It cannot just be based on the fact that one has followed, or believed that one has followed, a rule in the past, because past cases might not completely reveal the nature of the rule or correctly extrapolate that rule to new cases. (This is Scottish philosopher David Hume’s old problem of induction applied to linguistic rules.) If there is no way to account for rule following and if the meanings of words are dependent upon this, the very notion of meaning is in jeopardy.

Wittgenstein resolved his own paradox, said Kripke, by dropping the assumption that meaning is based on truth conditions and by adopting the view that meaning instead is based on assertability or justification conditions. Wittgenstein’s notions of language games and meaning as use, which require a sociality to both language and meaning, were part of this adopted view. As Kripke put it, “The solution turns on the idea that each person who claims to be following a rule can be checked by others.” This requirement of publicity was part and parcel of Kripke’s writings on semantics all along. Yet the apparent endorsement of Wittgenstein’s handling of this paradox, with its commitment to extrasemantic factors to account for meaning, suggests some movement on Kripke’s part away from his earlier separation of the semantics and pragmatics of language.


It is safe to say that in the second half of the twentieth century, Kripke was as influential in the fields of logic, ontology, and philosophy of language as any other philosopher. In particular, his nascent causal theory of reference became the dominant theory. Concepts that he introduced, such as rigid designators, became standard terminology. His early work in quantified modal logic was truly groundbreaking. His writings, often very technical but always clear and succinct, displayed the seriousness and rigor of twentieth century analytic philosophy. At a time when analytic philosophy as a whole came under criticism as being removed from the concerns of everyday people and even of other academic disciplines, Kripke maintained a seriousness of purpose and focus of thought to wrestle with perennial philosophical issues such as truth and meaning while demanding clarity of explanation. To understand contemporary philosophy of language, one must understand the work of Kripke.

Additional Reading

Davies, Martin. Meaning, Quantification, Necessity: Themes in Philosophical Logic. London: Routledge and Kegan Paul, 1981. Davies discusses Saul Kripke’s work in the context of modal logic and its connections with meaning, truth, and reference. Fairly technical.

Devitt, Michael. Designation. New York: Columbia University Press, 1981. Devitt extends Kripke’s views on reference by trying to flesh out his causal theory of reference.

Dummett, Michael. Truth and Other Enigmas. Cambridge, Mass.: Harvard University Press, 1978. Collection of essays on logic and language, including an influential critique of Kripke’s view of reference.

Forbes, Graeme. The Metaphysics of Modality. Oxford: Clarendon Press, 1985. A clear introduction to modal logic that includes explanations of Kripke’s contributions.

French, Peter A., Theodore E. Uehling, Jr., and Howard K. Wettstein, eds. Studies in the Philosophy of Language. Vol. 2 in Midwest Studies in Philosophy. Morris: University of Minnesota Press, 1977. Excellent anthology of papers on various issues related to meaning, reference, and names. Kripke’s “Speaker’s Reference and Semantic Reference” is included.

Humphreys, Paul, and James H. Fetzer, eds. The New Theory of Reference: Kripke, Marcus, and Its Origins. Dordrecht: Kluwer, 1998. This is a collection of papers that focuses on the controversy of whether, and to what extent, Kripke’s view of reference, especially its connections to quantified modal logic, was anticipated by the work of Ruth Barcan Marcus.

Katz, Jerold J. The Metaphysics of Meaning. Cambridge, Mass.: MIT Press, 1990. An introductory but sophisticated treatment of several philosophers on the nature of meaning, including Ludwig Wittgenstein, W. V. O. Quine, and Kripke.

Linsky, Leonard. Names and Descriptions. Chicago: University of Chicago Press, 1977. A clear, sophisticated introduction to issues of reference, existence, and modality, including a thorough discussion of Kripke’s notion of rigid designators and necessity of identity.

Linsky, Leonard. Referring. London: Routledge and Kegan Paul, 1967. Very clear survey of theories and concerns regarding reference before the publication of Kripke’s work.

McGinn, Colin. Wittgenstein on Meaning: An Interpretation and Evaluation. Oxford: Basil Blackwell, 1984. Clear and thorough introduction to Wittgenstein on meaning, including a critique of aspects of Kripke’s interpretation of Wittgenstein, particularly the role of community.

Salmon, Nathan U. Reference and Essence. Princeton, N.J.: Princeton University Press, 1981. Technical treatment of the theory of direct reference (causal theory) and its relation to essences.

Searle, John. Expression and Meaning: Studies in the Theory of Speech Acts. Cambridge, England: Cambridge University Press, 1979. This book responds to Kripke’s criticisms of Searle’s views on reference and proper names.

Searle, John. Intentionality: An Essay in the Philosophy of Mind. Cambridge, England: Cambridge University Press, 1983. This book includes Searle’s response to criticism by Kripke.

Searle, John. Speech Acts: An Essay in the Philosophy of Language. Cambridge, England: Cambridge University Press, 1969. This book contains several essays in which Searle elaborates on the theory of reference and proper names that Kripke rejects.

Teorema 17, no. 1 (Winter, 1998). This special issue commemorates the twenty-fifth anniversary of the publication of Kripke’s Naming and Necessity. Eight papers discuss and respond to various aspects of Kripke’s book.

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