Saul Kripke

Introduction

Saul Aaron Kripke is the American philosopher and logician whose contributions to modal logic (the Kripke semantics developed in his teenage and undergraduate years) and to the philosophy of language and metaphysics (especially through the lectures published as Naming and Necessity in 1980) reshaped late-twentieth-century analytic philosophy more deeply than any work since Quine's Word and Object (1960). The Kripke semantics gave the formal apparatus that has organized the philosophy of modality for sixty years; Naming and Necessity revived essentialist metaphysics, restructured the theory of reference, and produced what is widely treated as the most influential single body of lectures in twentieth-century philosophy.

Kripke's career was unusually concentrated. He produced his major technical work in modal logic before the age of twenty; he delivered the Naming and Necessity lectures at Princeton in 1970 (age twenty-nine); the Wittgenstein on Rules and Private Language lectures appeared in 1982. The published output is comparatively small relative to the size of the influence; many of Kripke's views were transmitted through unpublished lectures and through the network of students and colleagues he influenced directly.

Life

Saul Kripke was born on November 13, 1940, in Bay Shore, New York. His father was Rabbi Myer Kripke; his mother Dorothy Kripke wrote children's books on Jewish themes. The family moved to Omaha, Nebraska, when Saul was four; Rabbi Kripke became the leader of Beth El Synagogue, and Saul grew up in the Omaha Jewish community.

Kripke's mathematical and philosophical precocity was substantial. He taught himself ancient Hebrew at six, read portions of Shakespeare by nine, and was working through Descartes by twelve. His first paper on modal logic, A Completeness Theorem in Modal Logic (1959, published in the Journal of Symbolic Logic), was written when he was eighteen and is the founding statement of what became known as Kripke semantics. The follow-up papers — Semantical Analysis of Modal Logic I (1963), Semantical Analysis of Modal Logic II (1965), Semantical Analysis of Intuitionistic Logic (1965) — established him as the leading living modal logician.

Kripke took his BA at Harvard in 1962 (mathematics). He held positions at Harvard, the Rockefeller University, and Princeton, where he became the McCosh Professor of Philosophy in 1977 and remained until his retirement in 1998. From 2003 he served as Distinguished Professor of Philosophy at the CUNY Graduate Center.

Kripke died on September 15, 2022, in Plainsboro Township, New Jersey, at age eighty-one.

The problem he worked on

Kripke's project across the major works was the development of a rigorous treatment of necessity and possibility that could underwrite the substantive metaphysical claims that twentieth-century analytic philosophy had widely treated as suspect. The dominant logical positivist tradition through the 1950s had treated necessary truths as analytic (true in virtue of meaning alone) and had treated essentialist metaphysics (claims about the essential properties of objects, as distinct from their accidental properties) as metaphysically illegitimate. The Quinean attack on the analytic-synthetic distinction in Two Dogmas of Empiricism (1951) had appeared to extend the suspicion: if there are no analytic truths, then the analytic conception of necessary truth cannot be defended either.

Kripke's response is the substantive recovery of essentialist metaphysics through the formal apparatus of modal logic. The Kripke semantics provides a rigorous formal framework within which claims about necessity and possibility can be evaluated; the Naming and Necessity lectures show that this framework supports substantive essentialist claims that the prior tradition had ruled out. The recovery transformed analytic metaphysics from a marginal subfield into one of the most active areas of contemporary philosophy.

Contributions

Kripke semantics

The formal contribution that established Kripke's reputation: the development of a semantics for modal logic in terms of possible worlds and accessibility relations. The framework, developed in papers Kripke wrote as a teenager and undergraduate (the founding paper of 1959; the systematic statement in 1963 and 1965), provides the formal apparatus that has organized modal logic for sixty years.

The key innovation: instead of treating modal operators (necessarily, possibly) as primitive, the Kripke semantics analyzes them in terms of quantification over possible worlds. A proposition is necessarily true if it is true in every accessible possible world; possibly true if true in some accessible possible world. The accessibility relation between worlds determines which worlds count as accessible from a given world and which do not; different accessibility relations (reflexive, symmetric, transitive, equivalence) correspond to different modal logics (T, B, S4, S5).

The framework had immediate consequences. The completeness theorems Kripke proved (showing that the formal modal systems are sound and complete with respect to the appropriate Kripke models) provided the technical foundation for the subsequent work in modal logic. The framework has been extended to temporal logic, deontic logic, epistemic logic, conditional logic, and the broader family of intensional logics.

Kripke also developed the semantics for intuitionistic logic (the logic of constructive mathematics) using related techniques. The Kripke semantics for intuitionistic logic gives a possible-worlds interpretation of intuitionistic logical operators that has shaped the philosophy of constructive mathematics.

Naming and Necessity

The lectures Kripke delivered at Princeton in January 1970 and published as Naming and Necessity in 1980 (in Davidson and Harman's Semantics of Natural Language in 1972, then as a separate book) are widely treated as the most influential single body of lectures in twentieth-century philosophy. The lectures attack the description theory of reference (the dominant theory of how proper names refer, descended from Frege and Russell) and develop the alternative causal theory of reference together with substantive essentialist metaphysical conclusions.

The description theory, in its dominant form, held that a proper name (Aristotle, Cicero, Gödel) refers to whatever uniquely satisfies the descriptions speakers associate with the name. Kripke's attack: the description theory makes incorrect predictions about what we would say in counterfactual situations. The name Aristotle refers to the same individual even in worlds where Aristotle did not have the properties the descriptions ascribe to him (where he died young, where he did not teach Alexander). The reference is held fixed by something other than the descriptions.

The positive proposal: a name's reference is fixed by a causal-historical chain that begins with the original baptism in which the name was first attached to its bearer and is transmitted through subsequent uses by speakers who intend to refer to the same individual as those from whom they learned the name. The framework allows for divergence between what a speaker takes the name to mean and what the name actually refers to.

From this account of reference, Kripke derives substantive metaphysical conclusions. A proper name, on the causal theory, is a rigid designator — it refers to the same individual in every possible world in which that individual exists. Statements of identity between rigid designators (Hesperus is Phosphorus, water is H₂O) are therefore necessarily true if true at all, even when they are known empirically. The framework opens the space for necessary a posteriori truths (truths that are necessary but known only empirically) and for contingent a priori truths (truths that are contingent but knowable a priori).

The consequences for metaphysics are substantial. Essential properties (properties an object must have in every possible world in which it exists) are recovered as a legitimate subject of philosophical inquiry. Substantive claims about essences (Saul Kripke is essentially the person born of his actual biological parents; water is essentially H₂O) are defensible within the framework. The contemporary literature on essence, on natural kinds, on de re modality, and on contingent identity has been organized by Kripke's framework.

Wittgenstein on rules

Kripke's Wittgenstein on Rules and Private Language (1982) is his major work in the secondary literature on the late Wittgenstein. The book presents what Kripke calls Kripkenstein — an interpretation of Wittgenstein's rule-following discussion (Philosophical Investigations §§138–242) that develops a skeptical paradox about meaning.

The paradox: there is no fact about a speaker's past behavior or mental states that fixes what they mean by a word. The famous example: a speaker who has always given correct answers to addition problems below 57 might be following the rule plus (which gives 68 for 57 + 11) or the rule quus (which gives 5 for any problem involving numbers above 56). No fact about the speaker's past behavior or mental states settles which rule they have been following. The paradox is then extended: meaning in general cannot be grounded in facts about individual speakers; the skeptical solution is that meaning is grounded in the practices of the community of speakers.

The interpretation is widely contested. Many Wittgenstein scholars (especially Cora Diamond, James Conant, and the New Wittgenstein school) argue that Kripke's Kripkenstein is different from the actual Wittgenstein of the Investigations. Whatever the interpretive verdict, the book has been continuously generative in its own right; the Kripkenstein paradox has been the major contemporary engagement with rule-following and the foundations of meaning.

Key works

• A Completeness Theorem in Modal Logic (1959)
• Semantical Analysis of Modal Logic I (1963)
• Semantical Considerations on Modal Logic (1963)
• Naming and Necessity (1972/1980)
• Outline of a Theory of Truth (1975)
• Wittgenstein on Rules and Private Language (1982)
• Philosophical Troubles (Collected Papers Volume 1, 2011)

The Harvard University Press editions of Naming and Necessity and Wittgenstein on Rules are the standard texts. The Oxford University Press Collected Papers are publishing Kripke's body of papers and lectures (Volume 1 Philosophical Troubles appeared 2011; further volumes are in progress through the Saul Kripke Center at CUNY).

Influences and influenced

Influenced by: Frege (the founder of the analytic philosophy of language Kripke engages); Russell (the theory of descriptions Kripke critiqued); Wittgenstein (the subject of Wittgenstein on Rules); Quine (the immediate predecessor whose attack on essentialism Kripke reversed); Alonzo Church (the early formal-logical influence); Ruth Barcan Marcus (the predecessor in modal logic, whose Barcan formulas are studied within Kripke's framework); Hilary Putnam (the contemporary whose semantic externalism developed parallel to Kripke's).

Influenced: David Lewis (whose modal realism in On the Plurality of Worlds, 1986, takes Kripke's possible worlds with metaphysical seriousness); Hilary Putnam (whose Meaning and Reference parallels Kripke's framework); Alvin Plantinga (whose modal ontological argument uses Kripke's framework); the contemporary analytic metaphysics tradition through Kit Fine, Theodore Sider, David Chalmers, Timothy Williamson; the contemporary philosophy of mind through engagement with rigid designation and the mind-body problem; the contemporary philosophy of language through engagement with the causal theory of reference; the Kripkenstein literature in the contemporary philosophy of mind and language.

Reception

Kripke's reception was immediate and substantial. The technical papers on modal logic established him as the leading living modal logician within years of their publication; Naming and Necessity was widely regarded as a major event of postwar analytic philosophy and shaped multiple subfields; Wittgenstein on Rules and Private Language was immediately recognized as a major contribution to the contemporary engagement with the later Wittgenstein.

The institutional impact has been substantial. Almost every major analytic philosophy department teaches Naming and Necessity as a foundational text in the philosophy of language and metaphysics; the Kripke semantics is standard apparatus in graduate modal logic; the post-Kripkean tradition (David Lewis, Hilary Putnam, Alvin Plantinga, Kit Fine, the contemporary analytic metaphysics) operates within frameworks Kripke established.

Continuing engagement

Major recent scholarly work includes Scott Soames's Reference and Description (2005) and his broader work on the post-Kripkean philosophy of language, Nathan Salmon's Reference and Essence (1981, revised 2005), Stephen Schiffer's work on Kripkean themes, Alan Sidelle's Necessity, Essence, and Individuation (1989), and the Kripkenstein literature through John McDowell, Crispin Wright, Paul Boghossian, and others. The Saul Kripke Center at CUNY anchors the ongoing publication and scholarship. Active debates concern the precise scope of necessary a posteriori truths, the interpretation of the Kripkenstein paradox, the relation between Kripke's metaphysics and the broader essentialist tradition, and the contemporary status of two-dimensional semantics (developed by David Chalmers and Frank Jackson) as a response to Kripkean rigid designation.

Further reading

• Analytic Philosophy — the tradition Kripke transformed
• Quine — the immediate predecessor whose anti-essentialism Kripke reversed
• Russell — the predecessor whose theory of descriptions Kripke critiqued
• Frege — the founder of the analytic philosophy of language Kripke engages
• Wittgenstein — the subject of Wittgenstein on Rules and Private Language
• Essence and Existence — the metaphysical category Kripke's work revives in contemporary analytic philosophy

The American philosopher and logician whose contributions to modal logic and the philosophy of language reshaped late-twentieth-century analytic philosophy.