Saul Kripke

Saul Aaron Kripke (/sɔːl ˈkrɪpki/; born November 13, 1940) is an American philosopher and logician. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Since the 1960s, Kripke has been a central figure in a number of fields related to mathematical logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and set theory. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts. Kripke was the recipient of the 2001 Schock Prize in Logic and Philosophy.

Kripke has made influential and original contributions to logic, especially modal logic. His work has profoundly influenced analytic philosophy; his principal contribution is a semantics for modal logic involving possible worlds, now called Kripke semantics.[6] Another of his most important contributions is his argument that necessity is a "metaphysical" notion that should be separated from the epistemic notion of a priori, and that there are necessary truths that are a posteriori truths, such as that water is H2O. He has also contributed an original reading of Wittgenstein, referred to as "Kripkenstein." A 1970 Princeton lecture series, published in book form in 1980 as Naming and Necessity, is considered one of the most important philosophical works of the twentieth century.

Saul Kripke
BornNovember 13, 1940 (age 78)
EducationHarvard University (B.A., 1962)
AwardsRolf Schock Prizes in Logic and Philosophy (2001)
EraContemporary philosophy
RegionWestern philosophy
InstitutionsPrinceton University
CUNY Graduate Center
Main interests
Logic (particularly modal)
Philosophy of language
Set theory
Philosophy of mind
History of analytic philosophy
Notable ideas
Kripke–Platek set theory
Work on theory of reference (causal theory of reference, causal-historical theory of reference,[1] direct reference theory, criticism of the Frege–Russell view)
Admissible ordinal
Kripke structure
Rigid vs. flaccid designator
A posteriori necessity
The possibility of analytic a posteriori judgments[2][3]
Semantic theory of truth (Kripke's theory)
Non-analytic, a posteriori necessary truths[4]
Contingent a priori[5]
Kripke semantics
Disquotational principle
Accessibility relation
Rule-following paradox (Kripkenstein)
Humphrey objection

Life and career

Saul Kripke is the oldest of three children born to Dorothy K. Kripke and Rabbi Myer S. Kripke.[7] His father was the leader of Beth El Synagogue, the only Conservative congregation in Omaha, Nebraska; his mother wrote educational Jewish books for children. Saul and his two sisters, Madeline and Netta, attended Dundee Grade School and Omaha Central High School. Kripke was labeled a prodigy, teaching himself Ancient Hebrew by the age of six, reading Shakespeare's complete works by nine, and mastering the works of Descartes and complex mathematical problems before finishing elementary school.[8][9] He wrote his first completeness theorem in modal logic at 17, and had it published a year later. After graduating from high school in 1958, Kripke attended Harvard University and graduated summa cum laude in 1962 with a bachelor's degree in mathematics. During his sophomore year at Harvard, he taught a graduate-level logic course at nearby MIT. Upon graduation he received a Fulbright Fellowship, and in 1963 was appointed to the Society of Fellows. Kripke later said, "I wish I could have skipped college. I got to know some interesting people but I can't say I learned anything. I probably would have learned it all anyway just reading on my own."[10]

After briefly teaching at Harvard, in 1968 Kripke moved to Rockefeller University in New York City, where he taught until 1976. In 1978 he took a chaired professorship at Princeton University.[11] In 1988 he received the university's Behrman Award for distinguished achievement in the humanities. In 2002 Kripke began teaching at the CUNY Graduate Center, and in 2003 he was appointed a distinguished professor of philosophy there.

Kripke has received honorary degrees from the University of Nebraska, Omaha (1977), Johns Hopkins University (1997), University of Haifa, Israel (1998), and the University of Pennsylvania (2005). He is a member of the American Philosophical Society and an elected Fellow of the American Academy of Arts and Sciences, and in 1985 was a Corresponding Fellow of the British Academy.[12] He won the Schock Prize in Logic and Philosophy in 2001.[13]

Kripke was married to philosopher Margaret Gilbert. He is the second cousin once removed of television writer, director, and producer Eric Kripke.


LTL model
Example Kripke model for linear temporal logic, a particular modal logic

Kripke's contributions to philosophy include:

  1. Kripke semantics for modal and related logics, published in several essays beginning in his teens.
  2. His 1970 Princeton lectures Naming and Necessity (published in 1972 and 1980), which significantly restructured philosophy of language.
  3. His interpretation of Wittgenstein.
  4. His theory of truth.

He has also contributed to set theory (see admissible ordinal and Kripke–Platek set theory).

Modal logic

Two of Kripke's earlier works, A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic, the former written when he was a teenager, were on modal logic. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke. Kripke introduced the now-standard Kripke semantics (also known as relational semantics or frame semantics) for modal logics. Kripke semantics is a formal semantics for non-classical logic systems. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The discovery of Kripke semantics was a breakthrough in the making of non-classical logics, because the model theory of such logics was absent before Kripke.

A Kripke frame or modal frame is a pair , where W is a non-empty set, and R is a binary relation on W. Elements of W are called nodes or worlds, and R is known as the accessibility relation. Depending on the properties of the accessibility relation (transitivity, reflexivity, etc.), the corresponding frame is described, by extension, as being transitive, reflexive, etc.

A Kripke model is a triple , where is a Kripke frame, and is a relation between nodes of W and modal formulas, such that:

  • if and only if ,
  • if and only if or ,
  • if and only if implies .

We read as "w satisfies A", "A is satisfied in w", or "w forces A". The relation is called the satisfaction relation, evaluation, or forcing relation. The satisfaction relation is uniquely determined by its value on propositional variables.

A formula A is valid in:

  • a model , if for all w ∈ W,
  • a frame , if it is valid in for all possible choices of ,
  • a class C of frames or models, if it is valid in every member of C.

We define Thm(C) to be the set of all formulas that are valid in C. Conversely, if X is a set of formulas, let Mod(X) be the class of all frames which validate every formula from X.

A modal logic (i.e., a set of formulas) L is sound with respect to a class of frames C, if L ⊆ Thm(C). L is complete with respect to C if L ⊇ Thm(C).

Semantics is useful for investigating a logic (i.e., a derivation system) only if the semantical entailment relation reflects its syntactical counterpart, the consequence relation (derivability). It is vital to know which modal logics are sound and complete with respect to a class of Kripke frames, and for them, to determine which class it is.

For any class C of Kripke frames, Thm(C) is a normal modal logic (in particular, theorems of the minimal normal modal logic, K, are valid in every Kripke model). However, the converse does not hold generally. There are Kripke incomplete normal modal logics, which is unproblematic, because most of the modal systems studied are complete of classes of frames described by simple conditions.

A normal modal logic L corresponds to a class of frames C, if C = Mod(L). In other words, C is the largest class of frames such that L is sound wrt C. It follows that L is Kripke complete if and only if it is complete of its corresponding class.

Consider the schema T : . T is valid in any reflexive frame : if , then since w R w. On the other hand, a frame which validates T has to be reflexive: fix w ∈ W, and define satisfaction of a propositional variable p as follows: if and only if w R u. Then , thus by T, which means w R w using the definition of . T corresponds to the class of reflexive Kripke frames.

It is often much easier to characterize the corresponding class of L than to prove its completeness, thus correspondence serves as a guide to completeness proofs. Correspondence is also used to show incompleteness of modal logics: suppose L1 ⊆ L2 are normal modal logics that correspond to the same class of frames, but L1 does not prove all theorems of L2. Then L1 is Kripke incomplete. For example, the schema generates an incomplete logic, as it corresponds to the same class of frames as GL (viz. transitive and converse well-founded frames), but does not prove the GL-tautology .

Canonical models

For any normal modal logic L, a Kripke model (called the canonical model) can be constructed, which validates precisely the theorems of L, by an adaptation of the standard technique of using maximal consistent sets as models. Canonical Kripke models play a role similar to the Lindenbaum–Tarski algebra construction in algebraic semantics.

A set of formulas is L-consistent if no contradiction can be derived from them using the axioms of L, and modus ponens. A maximal L-consistent set (an L-MCS for short) is an L-consistent set which has no proper L-consistent superset.

The canonical model of L is a Kripke model , where W is the set of all L-MCS, and the relations R and are as follows:

if and only if for every formula , if then ,
if and only if .

The canonical model is a model of L, as every L-MCS contains all theorems of L. By Zorn's lemma, each L-consistent set is contained in an L-MCS, in particular every formula unprovable in L has a counterexample in the canonical model.

The main application of canonical models are completeness proofs. Properties of the canonical model of K immediately imply completeness of K with respect to the class of all Kripke frames. This argument does not work for arbitrary L, because there is no guarantee that the underlying frame of the canonical model satisfies the frame conditions of L.

We say that a formula or a set X of formulas is canonical with respect to a property P of Kripke frames, if

  • X is valid in every frame which satisfies P,
  • for any normal modal logic L which contains X, the underlying frame of the canonical model of L satisfies P.

A union of canonical sets of formulas is itself canonical. It follows from the preceding discussion that any logic axiomatized by a canonical set of formulas is Kripke complete, and compact.

The axioms T, 4, D, B, 5, H, G (and thus any combination of them) are canonical. GL and Grz are not canonical, because they are not compact. The axiom M by itself is not canonical (Goldblatt, 1991), but the combined logic S4.1 (in fact, even K4.1) is canonical.

In general, it is undecidable whether a given axiom is canonical. We know a nice sufficient condition: H. Sahlqvist identified a broad class of formulas (now called Sahlqvist formulas) such that:

  • a Sahlqvist formula is canonical,
  • the class of frames corresponding to a Sahlqvist formula is first-order definable,
  • there is an algorithm which computes the corresponding frame condition to a given Sahlqvist formula.

This is a powerful criterion: for example, all axioms listed above as canonical are (equivalent to) Sahlqvist formulas. A logic has the finite model property (FMP) if it is complete with respect to a class of finite frames. An application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable, provided it is decidable whether a given finite frame is a model of L. In particular, every finitely axiomatizable logic with FMP is decidable.

There are various methods for establishing FMP for a given logic. Refinements and extensions of the canonical model construction often work, using tools such as filtration or unravelling. As another possibility, completeness proofs based on cut-free sequent calculi usually produce finite models directly.

Most of the modal systems used in practice (including all listed above) have FMP.

In some cases, we can use FMP to prove Kripke completeness of a logic: every normal modal logic is complete wrt a class of modal algebras, and a finite modal algebra can be transformed into a Kripke frame. As an example, Robert Bull proved using this method that every normal extension of S4.3 has FMP, and is Kripke complete.

Kripke semantics has a straightforward generalization to logics with more than one modality. A Kripke frame for a language with as the set of its necessity operators consists of a non-empty set W equipped with binary relations Ri for each i ∈ I. The definition of a satisfaction relation is modified as follows:

if and only if

Carlson models

A simplified semantics, discovered by Tim Carlson, is often used for polymodal provability logics. A Carlson model is a structure with a single accessibility relation R, and subsets Di ⊆ W for each modality. Satisfaction is defined as:

if and only if

Carlson models are easier to visualize and to work with than usual polymodal Kripke models; there are, however, Kripke complete polymodal logics which are Carlson incomplete.

In Semantical Considerations on Modal Logic, published in 1963, Kripke responded to a difficulty with classical quantification theory. The motivation for the world-relative approach was to represent the possibility that objects in one world may fail to exist in another. If standard quantifier rules 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 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.

Kripke's possible worlds theory has been used by narratologists (beginning with Pavel and Dolezel) to understand "reader's manipulation of alternative plot developments, or the characters' planned or fantasized alternative action series." This application has become especially useful in the analysis of hyperfiction.[14]

Intuitionistic logic

Kripke semantics for intuitionistic logic follows the same principles as the semantics of modal logic, but uses a different definition of satisfaction.

An intuitionistic Kripke model is a triple , where is a partially ordered Kripke frame, and satisfies the following conditions:

  • if p is a propositional variable, , and , then (persistency condition),
  • if and only if and ,
  • if and only if or ,
  • if and only if for all , implies ,
  • not .

Intuitionistic logic is sound and complete with respect to its Kripke semantics, and it has the Finite Model Property.

Intuitionistic first-order logic

Let L be a first-order language. A Kripke model of L is a triple , where is an intuitionistic Kripke frame, Mw is a (classical) L-structure for each node w ∈ W, and the following compatibility conditions hold whenever u ≤ v:

  • the domain of Mu is included in the domain of Mv,
  • realizations of function symbols in Mu and Mv agree on elements of Mu,
  • for each n-ary predicate P and elements a1,...,an ∈ Mu: if P(a1,...,an) holds in Mu, then it holds in Mv.

Given an evaluation e of variables by elements of Mw, we define the satisfaction relation :

  • if and only if holds in Mw,
  • if and only if and ,
  • if and only if or ,
  • if and only if for all , implies ,
  • not ,
  • if and only if there exists an such that ,
  • if and only if for every and every , .

Here e(xa) is the evaluation which gives x the value a, and otherwise agrees with e.

Naming and Necessity

The three lectures that form Naming and Necessity constitute an attack on descriptivist theory of names. Kripke attributes variants of descriptivist theories to Frege, Russell, Wittgenstein and John Searle, among others. According to descriptivist theories, proper names either are synonymous with descriptions, or have their reference determined by virtue of the name's being associated with a description or cluster of descriptions that an object uniquely satisfies. Kripke rejects both these kinds of descriptivism. He gives several examples purporting to render descriptivism implausible as a theory of how names get their references determined (e.g., surely Aristotle could have died at age two and so not satisfied any of the descriptions we associate with his name, but it would seem wrong to deny that he was still Aristotle).

As an alternative, Kripke outlined 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. He points out that proper names, in contrast to most descriptions, are rigid designators: that is, a proper name refers to the named object in every possible world in which the object exists, while most descriptions designate different objects in different possible worlds. For example, "Richard Nixon" refers to the same person in every possible world in which Nixon exists, while "the person who won the United States presidential election of 1968" could refer to Nixon, Humphrey, or others in different possible worlds.

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", "Water is H2O" and other identity claims where two names refer to the same object.

Finally, Kripke gave an argument against identity materialism in the philosophy of mind, the view that every mental particular is identical with some physical particular. Kripke argued that the only way to defend this identity is as an a posteriori necessary identity, but that such an identity — e.g., that pain is C-fibers firing — could not be necessary, given the (clearly conceivable) possibility that pain could be separate from the firing of C-fibers, or the firing of C-fibers be separate from pain. (Similar arguments have since been made by David Chalmers.[15]) In any event, the psychophysical identity theorist, according to Kripke, incurs a dialectical obligation to explain the apparent logical possibility of these circumstances, since according to such theorists they should be impossible.

Kripke delivered the John Locke Lectures in philosophy at Oxford in 1973. Titled Reference and Existence, they are in many respects a continuation of Naming and Necessity, and deal with the subjects of fictional names and perceptual error. They were recently published by Oxford University Press.

In a 1995 paper, philosopher Quentin Smith argued that key concepts in Kripke's new theory of reference originated in the work of Ruth Barcan Marcus more than a decade earlier.[16] Smith identified six significant ideas in the New Theory that he claimed Marcus had developed: (1) that proper names are direct references that do not consist of contained definitions; (2) that while one can single out a single thing by a description, this description is not equivalent to a proper name of this thing; (3) the modal argument that proper names are directly referential, and not disguised descriptions; (4) a formal modal logic proof of the necessity of identity; (5) the concept of a rigid designator, though Kripke coined that term; and (6) a posteriori identity. Smith argued that Kripke failed to understand Marcus's theory at the time but later adopted many of its key conceptual themes in his New Theory of Reference.

Other scholars have subsequently offered detailed responses arguing that no plagiarism occurred.[17][18]

"A Puzzle about Belief"

Kripke's main propositions about proper names in Naming and Necessity are that the meaning of a name simply is the object it refers to and that a name's referent is determined by a causal link between some sort of "baptism" and the utterance of the name. Nevertheless, he acknowledges the possibility that propositions containing names may have some additional semantic properties,[19] properties that could explain why two names referring to the same person may give different truth values in propositions about beliefs. For example, Lois Lane believes that Superman can fly, although she does not believe that Clark Kent can fly. This can be accounted for if the names "Superman" and "Clark Kent", though referring to the same person, have distinct semantic properties.

But in his article "A Puzzle about Belief" Kripke seems to oppose even this possibility. His argument can be reconstructed as follows: The idea that two names referring to the same object may have different semantic properties is supposed to explain that coreferring names behave differently in propositions about beliefs (as in Lois Lane's case). But the same phenomenon occurs even with coreferring names that obviously have the same semantic properties: Kripke invites us to imagine a French, monolingual boy, Pierre, who believes that "Londres est joli" ("London is beautiful"). Pierre moves to London without realizing that London = Londres. He then learns English the same way a child would learn the language, that is, not by translating words from French to English. Pierre learns the name "London" from the unattractive part of the city where he lives, and so comes to believe that London is not beautiful. If Kripke's account is correct, Pierre now believes both that Londres is joli and that London is not beautiful. This cannot be explained by coreferring names having different semantic properties. According to Kripke, this demonstrates that attributing additional semantic properties to names does not explain what it is intended to.


First published in 1982, Kripke's Wittgenstein on Rules and Private Language contends that the central argument of Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date", and that Wittgenstein does not reject the argument that leads to the rule-following paradox, but accepts it and offers a "skeptical solution" to ameliorate the paradox's destructive effects.

Most commentators accept that Philosophical Investigations contains the rule-following paradox as Kripke presents it, but few have agreed with his attributing a skeptical solution to Wittgenstein. Kripke himself expresses doubts in Wittgenstein on Rules and Private Language as to whether Wittgenstein would endorse his interpretation of Philosophical Investigations. He says that the work should not be read as an attempt to give an accurate statement of Wittgenstein's views, but rather as an account of Wittgenstein's argument "as it struck Kripke, as it presented a problem for him".

The portmanteau "Kripkenstein" has been coined for Kripke's interpretation of Philosophical Investigations. Kripkenstein's main significance was a clear statement of a new kind of skepticism, dubbed "meaning skepticism": the idea that for an isolated individual there is no fact in virtue of which he/she means one thing rather than another by the use of a word. Kripke's "skeptical solution" to meaning skepticism is to ground meaning in the behavior of a community.

Kripke's book generated a large secondary literature, divided between those who find his skeptical problem interesting and perceptive, and others, such as Gordon Baker and Peter Hacker, who argue that his meaning skepticism is a pseudo-problem that stems from a confused, selective reading of Wittgenstein. Kripke's position has been defended against these and other attacks by the Cambridge philosopher Martin Kusch, and Wittgenstein scholar David G. Stern considers Kripke's book "the most influential and widely discussed" work on Wittgenstein since the 1980s.[20]


In his 1975 article "Outline of a Theory of Truth", Kripke showed that a language can consistently contain its own truth predicate, something deemed impossible by Alfred Tarski, a pioneer in formal theories of truth. The approach 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 that do not contain the truth predicate, and defining a truth predicate over just that segment: this action adds new sentences to the language, and truth is in turn defined for all of them. Unlike Tarski's approach, however, Kripke's 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."

Saul Kripke's Gödel lecture at UCSB
Saul Kripke gives a lecture about Gödel at the University of California, Santa Barbara.

Nevertheless, it has been shown by Gödel that self-reference cannot be avoided naively, since propositions about seemingly unrelated objects (such as integers) can have an informal self-referential meaning, and this idea – manifested by the diagonal lemma – is the basis for Tarski's theorem that truth cannot be consistently defined. It has thus been claimed[21] that Kripke's suggestion does lead to contradiction: while its truth predicate is only partial, it does give truth value (true/false) to propositions such as the one built in Tarski's proof, and is therefore inconsistent. There is still a debate about whether Tarski's proof can be implemented to every variation of such a partial truth system, but none has been shown to be consistent by acceptable proving methods used in mathematical logic.

Kripke's proposal is also problematic in the sense that while the language contains a "truth" predicate of itself (at least a partial one), some of its sentences – such as the liar sentence ("this sentence is false") – have an undefined truth value, but the language does not contain its own "undefined" predicate. In fact it cannot, as that would create a new version of the liar paradox, called the strengthened liar paradox ("this sentence is false or undefined"). Thus while the liar sentence is undefined in the language, the language cannot express that it is undefined.[22]

Religious views

Kripke is an observant Jew.[23] On how his religious views influenced his philosophical views, he has said: "I don't have the prejudices many have today. I don't believe in a naturalist worldview. I don't base my thinking on prejudices or a worldview and do not believe in materialism."[24]

Saul Kripke Center

The Saul Kripke Center at the Graduate Center of the City University of New York is dedicated to preserving and promoting Kripke's work. Its director is Gary Ostertag. The SKC holds events related to Kripke's work and is creating a digital archive of previously unpublished recordings of Kripke's lectures, lecture notes, and correspondence dating back to the 1950s.[25] In his favorable review of Kripke's Philosophical Troubles, the Stanford philosopher Mark Crimmins wrote, "That four of the most admired and discussed essays in 1970s philosophy are here is enough to make this first volume of Saul Kripke's collected articles a must-have... The reader's delight will grow as hints are dropped that there is a great deal more to come in this series being prepared by Kripke and an ace team of philosopher-editors at the Saul Kripke Center at The Graduate Center of the City University of New York."[26]

Awards and recognitions


  • Naming and Necessity. Cambridge, Mass.: Harvard University Press, 1972. ISBN 0-674-59845-8
  • Wittgenstein on Rules and Private Language: an Elementary Exposition. Cambridge, Mass.: Harvard University Press, 1982. ISBN 0-674-95401-7.
  • Philosophical Troubles. Collected Papers Vol. 1. New York: Oxford University Press, 2011. ISBN 9780199730155
  • Reference and Existence – The John Locke Lectures. New York: Oxford University Press, 2013. ISBN 9780199928385

See also


  1. ^ Cumming, Sam (30 May 2018). Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University – via Stanford Encyclopedia of Philosophy.
  2. ^ Palmquist, Stephen (December 1987). "A Priori Knowledge in Perspective: (II) Naming, Necessity and the Analytic A Posteriori". The Review of Metaphysics. 41 (2): 255–282.
  3. ^ Georg Northoff, Minding the Brain: A Guide to Philosophy and Neuroscience, Palgrave, p. 51.
  4. ^ Michael Giudice, Understanding the Nature of Law: A Case for Constructive Conceptual Explanation, Edward Elgar Publishing, 2015, p. 92.
  5. ^ Saul Kripke (1986). "Rigid Designation and the Contingent A Priori: The Meter Stick Revisited" (Notre Dame).
  6. ^ Jerry Fodor, "Water's water everywhere", London Review of Books, 21 October 2004
  7. ^ Kripke, Saul (2011). Philosophical Troubles: Collected Papers Volume 1. Oxford: Oxford University Press. pp. xii. ISBN 978-0-19-973015-5.
  8. ^ Charles McGrath (2006-01-28). "Philosopher, 65, Lectures Not About 'What Am I?' but 'What Is I?'". The New York Times. Retrieved 2008-01-23.
  9. ^ A Companion to Analytic Philosophy (Blackwell Companions to Philosophy), by A. P. Martinich (Editor), E. David Sosa (Editor), 38. Saul Kripke (1940–)
  10. ^ McGrath, Charles (January 28, 2006). "Philosopher, 65, Lectures Not About 'What Am I?' but 'What Is I?'". The New York Times.
  11. ^ "Saul Kripke - American logician and philosopher".
  12. ^
  13. ^
  14. ^ Fludernik, Monika. "Histories of Narrative Theory: From Structuralism to Present." A Companion to Narrative Theory. Ed. Phelan and Rabinowitz. Blackwell Publishing, MA:2005.
  15. ^ Chalmers, David. 1996. The Conscious Mind. Oxford University Press pp. 146–9.
  16. ^ Smith, Quentin (2 August 2001). "Marcus, Kripke, and the Origin of the New Theory of Reference". Synthese. 104 (2): 179–189. doi:10.1007/BF01063869. Archived from the original on 7 May 2006. Retrieved 2007-05-28.
  17. ^ Stephen Neale (9 February 2001). "No Plagiarism Here" (PDF). Times Literary Supplement. 104 (2): 12–13. doi:10.1007/BF01063869. Archived from the original (.PDF) on 14 July 2010. Retrieved 2009-11-13.
  18. ^ John Burgess, "Marcus, Kripke, and Names" Philosophical Studies, 84: 1, pp. 1–47.
  19. ^ Kripke, 1980, p. 20
  20. ^ Stern, David G. 2006. Wittgenstein's Philosophical Investigations: An Introduction. Cambridge University Press. p. 2
  21. ^ Keith Simmons, Universality and the Liar: An Essay on Truth and the Diagonal Argument, Cambridge University Press, Cambridge 1993
  22. ^ Bolander, Thomas (30 May 2018). Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University – via Stanford Encyclopedia of Philosophy.
  23. ^ "Kripke is Jewish, and he takes this seriously. He is not a nominal Jew and he is careful keeping the Sabbath, for instance he doesn't use public transportation on Saturdays." Andreas Saugstad, "Saul Kripke: Genius logician", 25 February 2001.
  24. ^ Andreas Saugstad, "Saul Kripke: Genius logician", 25 February 2001.
  25. ^ Saul Kripke Center website: Most of these recordings and lecture notes were created by Nathan Salmon while he was a student and, later, a colleague of Kripke's.
  26. ^ Crimmins, Mark (30 October 2013). "Review of Philosophical Troubles: Collected Papers, Volume 1" – via Notre Dame Philosophical Reviews.

Further reading

  • Arif Ahmed (2007), Saul Kripke. New York, NY; London: Continuum. ISBN 0-8264-9262-2.
  • Alan Berger (editor) (2011) "Saul Kripke." ISBN 978-0-521-85826-7.
  • Taylor Branch (1977), "New Frontiers in American Philosophy: Saul Kripke". The New York Times Magazine.
  • John Burgess (2013), "Saul Kripke: Puzzles and Mysteries." ISBN 978-0-7456-5284-9.
  • G. W. Fitch (2005), Saul Kripke. ISBN 0-7735-2885-7.
  • Christopher Hughes (2004), Kripke : Names, Necessity, and Identity. ISBN 0-19-824107-0.
  • Martin Kusch (2006), A Sceptical Guide to Meaning and Rules. Defending Kripke's Wittgenstein. Acumben: Publishing Limited.
  • Christopher Norris (2007), Fiction, Philosophy and Literary Theory: Will the Real Saul Kripke Please Stand Up? London: Continuum
  • Consuelo Preti (2002), On Kripke. Wadsworth. ISBN 0-534-58366-0.
  • Nathan Salmon (1981), Reference and Essence. ISBN 1-59102-215-0 ISBN 978-1591022152.
  • Scott Soames (2002), Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity. ISBN 0-19-514529-1.

External links

A posteriori necessity

A posteriori necessity is a thesis in metaphysics and the philosophy of language, that some statements of which we must acquire knowledge a posteriori are also necessarily true. It challenges previously widespread belief that only a priori knowledge can be necessary. It draws on a number of philosophical concepts such as necessity, the causal theory of reference, rigidity, and the a priori a posteriori distinction.

It was first introduced by philosopher Saul Kripke in his 1970 series of lectures at Princeton University. The transcript of these lectures was then compiled and assembled into his seminal book, Naming and Necessity.

Causal theory of reference

A causal theory of reference is a theory of how terms acquire specific referents based on evidence. Such theories have been used to describe many referring terms, particularly logical terms, proper names, and natural kind terms. In the case of names, for example, a causal theory of reference typically involves the following claims:

a name's referent is fixed by an original act of naming (also called a "dubbing" or, by Saul Kripke, an "initial baptism"), whereupon the name becomes a rigid designator of that object.

later uses of the name succeed in referring to the referent by being linked to that original act via a causal chain.Weaker versions of the position (perhaps not properly called "causal theories"), claim merely that, in many cases, events in the causal history of a speaker's use of the term, including when the term was first acquired, must be considered to correctly assign references to the speaker's words.

Causal theories of names became popular during the 1970s, under the influence of work by Saul Kripke and Keith Donnellan. Kripke and Hilary Putnam also defended an analogous causal account of natural kind terms.

Descriptivist theory of names

In the philosophy of language, the descriptivist theory of proper names (also descriptivist theory of reference) is the view that the meaning or semantic content of a proper name is identical to the descriptions associated with it by speakers, while their referents are determined to be the objects that satisfy these descriptions. Bertrand Russell and Gottlob Frege have both been associated with the descriptivist theory, which is sometimes called the Frege–Russell view.In the 1970s, this theory came under attack from causal theorists such as Saul Kripke, Hilary Putnam and others. However, it has seen something of a revival in recent years, especially under the form of what are called two-dimensional semantic theories. This latter trend is exemplified by the theories of David Chalmers, among others.

Direct reference theory

A direct reference theory (also called referentialism or referential realism) is a theory of language that claims that the meaning of a word or expression lies in what it points out in the world. The object denoted by a word is called its referent. Criticisms of this position are often associated with Ludwig Wittgenstein.In the 19th century, mathematician and philosopher Gottlob Frege argued against it, and contrasted it with mediated reference theory. In 1953, with his Philosophical Investigations, Wittgenstein argued against referentialism, famously saying that "the meaning of a word is its use." Direct reference theory is a position typically associated with logical positivism and analytical philosophy. Logical positivist philosophers in particular have significantly devoted their efforts in countering positions of the like of Wittgenstein's, and they aim at creating a "perfectly descriptive language" purified from ambiguities and confusions.

Index of philosophy of language articles

This is an index of articles in philosophy of language

A.P. Martinich


Adolph Stöhr

Alexis Kagame

Alfred Jules Ayer

Alphabet of human thought


Analytic-synthetic distinction


Andrea Bonomi

Applicative Universal Grammar

Archie J. Bahm

Arda Denkel


Artificial intelligence

Association for Logic, Language and Information

Avrum Stroll

Barry Loewer

Berlin Circle

Bertrand Russell

Bob Hale (philosopher)

Calculus ratiocinator

Carl Gustav Hempel

Ramsey sentence


Category mistake

Causal theory of reference

César Chesneau Dumarsais

Cheung Kam Ching

Circular definition

Claude Lévi-Strauss

Cognitive synonymy

Colloquial language

Computational humor


Concept and object

Conceptual metaphor

Context-sensitive grammar

Context principle


Contrast theory of meaning


Cooperative principle

Cora Diamond


Dagfinn Føllesdal

David Efird

David Kellogg Lewis

De dicto and de re



Descriptivist theory of names

Direct reference theory

Direction of fit

Discourse ethics

Disquotational principle

Donald Davidson (philosopher)

Donkey pronoun


Duns Scotus

Empty name

Engineered language

Enumerative definition


Ethics and Language

Eugen Rosenstock-Huessy

European Summer School in Logic, Language and Information


Extensional definition

F. H. Bradley

Family resemblance

Felicity conditions

Ferdinand Ebner

Failure to refer

Form of life (philosophy)

Franz Rosenzweig

Frege's Puzzle

Friedrich Waismann

Function and Concept

G. E. M. Anscombe

Gareth Evans (philosopher)

Genus–differentia definition

George Orwell

Gilbert Ryle

Gordon Park Baker

Gottlob Frege


Hans Kamp

Hector-Neri Castañeda

Henri Bergson

Ideal speech situation

Illocutionary act


Indeterminacy (philosophy)

Indeterminacy of translation


Indirect self-reference

Inferential role semantics

Ingeborg Bachmann


Intensional definition

Internalism and externalism

Interpretation (logic)

J. L. Austin

Jacques Bouveresse

James F. Conant

Jody Azzouni

John Etchemendy

John McDowell

Jonathan Bennett (philosopher)

Journal of Logic, Language and Information

Karl-Otto Apel

Katarzyna Jaszczolt

Keith Donnellan

Kent Bach

Kit Fine


Language and thought

Language of thought

Language, Truth, and Logic

Latitudinarianism (philosophy)

Lexical definition

Lexis (Aristotle)

Linguistic determinism

Linguistic relativity

Linguistic turn

Linguistics and Philosophy

List of philosophers of language

Logical atomism

Logical form

Logical positivism

Ludwig Wittgenstein

Marilyn Frye

Martian scientist

Max Black

Meaning (linguistics)

Meaning (non-linguistic)

Meaning (philosophy of language)

Meaning (semiotics)

Mediated reference theory

Meinong's jungle

Mental representation

Mental space


Metaphor in philosophy

Michael Devitt

Michael Dummett

Modal property


Modularity of mind

Moritz Schlick

Mumbo Jumbo (phrase)

Naming and Necessity

Nelson Goodman

New Foundations

Nino Cocchiarella

Noam Chomsky



Non-rigid designator


Norm (philosophy)

Object language

On Denoting

Ontological commitment

Operational definition

Ordinary language philosophy

Ostensive definition

Otto Neurath

P. F. Strawson

Paradigm-case argument


Paul Boghossian

Paul Grice

Performative contradiction

Performative text

Performative utterance

Persuasive definition

Peter Abelard

Peter Millican

Philosophical interpretation of classical physics

Philosophical Investigations

Philosophy and literature

Philosophy of language

Pirmin Stekeler-Weithofer

Plato's Problem

Port-Royal Grammar


Precising definition

Principle of charity

Principle of compositionality

Private language argument

Proper name (philosophy)




Radical translation

Rational reconstruction

Redundancy theory of truth


Relevance theory

Rhetoric of social intervention model

Richard von Mises

Rigid designator

Robert Brandom

Robert Maximilian de Gaynesford

Robert Stalnaker

Round square copula

Rudolf Carnap

S. Morris Engel

Saul Kripke

Scalar implicature

Scientific essentialism

Sebastian Shaumyan

Secondary reference


Semantic externalism

Semantic holism




Sense and reference

Sense and Sensibilia (Austin)



Singular term

Slingshot argument

Social semiotics

Speech act


Stanley Cavell

Statement (logic)

Stipulative definition


Supposition theory

Susan Stebbing




Symbol grounding


The Naturalization of Intentionality

Theoretical definition

Theory of descriptions

Þorsteinn Gylfason

Tractatus Logico-Philosophicus

Transparency (linguistic)

True name

Truth-conditional semantics

Truth-value link


Two Dogmas of Empiricism

Type physicalism

Universal grammar

Universal language

Universal pragmatics

Use–mention distinction


Verification theory


Vienna Circle

Virgil Aldrich

Walter Benjamin

Willard Van Orman Quine

William Alston

William C. Dowling

William Crathorn

Wittgenstein on Rules and Private Language

Word and Object

Word sense

Yehoshua Bar-Hillel

Zeno Vendler



Kripke is a surname. Notable people with the surname include:

Dorothy K. Kripke (1912–2000), American author of Jewish educational books, and the mother of Saul Kripke

Eric Kripke (born 1974), American television writer, director, and producer

Margaret L. Kripke, professor of immunology

Myer S. Kripke (1914–2014), American rabbi based in Omaha, Nebraska, and the husband of Dorothy K. Kripke

Saul Kripke (born 1940), American philosopher and logicianFictional characters:

Barry Kripke, a character in the sitcom The Big Bang Theory

Kripke–Platek set theory

The Kripke–Platek axioms of set theory (KP), pronounced , are a system of axiomatic set theory developed by Saul Kripke and Richard Platek.

KP is considerably weaker than Zermelo–Fraenkel set theory (ZFC), and can be thought of as roughly the predicative part of ZFC. The consistency strength of KP with an axiom of infinity is given by the Bachmann–Howard ordinal. Unlike ZFC, KP does not include the power set axiom, and KP includes only limited forms of the axiom of separation and axiom of replacement from ZFC. These restrictions on the axioms of KP lead to close connections between KP, generalized recursion theory, and the theory of admissible ordinals.

List of philosophers of language

This is a list of philosophers of language.

Virgil Aldrich

William Alston

G. E. M. Anscombe

Karl-Otto Apel

Saint Thomas Aquinas, OP


J. L. Austin

Alfred Jules Ayer

Joxe Azurmendi

Jody Azzouni

Kent Bach

Ingeborg Bachmann

Archie J. Bahm

Yehoshua Bar-Hillel

Walter Benjamin

Jonathan Bennett

Henri Bergson

Max Black

Paul Boghossian

Andrea Bonomi

Jacques Bouveresse

F. H. Bradley

Robert Brandom

Berit Brogaard

Cardinal Thomas Cajetan, OP

Herman Cappelen

Rudolf Carnap

Hector-Neri Castañeda

Stanley Cavell

David Chalmers

Cheung Kam Ching

Noam Chomsky

Alonzo Church

Nino Cocchiarella

James F. Conant

William Crathorn

Donald Davidson

Arda Denkel

Michael Devitt

Keith Donnellan

William C. Dowling

César Chesneau Dumarsais

Michael Dummett

David Efird

S. Morris Engel

John Etchemendy

Gareth Evans

Kit Fine

Dagfinn Føllesdal

Gottlob Frege

Marilyn Frye

Robert Maximilian de Gaynesford

Peter Geach

Alexander George

Allan Gibbard

Gongsun Long

Nelson Goodman

Paul Grice

Jeroen Groenendijk

Samuel Guttenplan

Þorsteinn Gylfason

Susan Haack

Jürgen Habermas

Peter Hacker

Ian Hacking

Axel Hägerström

Bob Hale

Oswald Hanfling

Gilbert Harman

John Hawthorne

Jaakko Hintikka

William Hirstein

Richard Hönigswald

Jennifer Hornsby

Paul Horwich

Wilhelm von Humboldt

Carrie Ichikawa Jenkins

David Kaplan

Jerrold Katz

Saul Kripke

Mark Lance

Stephen Laurence

Ernest Lepore

David Kellogg Lewis

John Locke

Béatrice Longuenesse

Paul Lorenzen

William Lycan

John McDowell

Colin McGinn

Merab Mamardashvili

Ruth Barcan Marcus

José Medina

Maurice Merleau-Ponty

John Stuart Mill

Ruth Millikan

Richard Montague

Charles W. Morris

Adam Morton

Stephen Neale

William of Ockham

Jesús Padilla Gálvez

Peter Pagin

L.A. Paul

Charles Sanders Peirce

Carlo Penco

John Perry

Gualtiero Piccinini

Steven Pinker


Hilary Putnam

Willard Van Orman Quine

Adolf Reinach

Denise Riley

Richard Rorty


Jay Rosenberg

Bertrand Russell's views on philosophy

Bertrand Russell

Gilbert Ryle

Robert Rynasiewicz

Mark Sainsbury

Nathan Salmon

Stephen Schiffer

Duns Scotus

John Searle

Susanna Siegel

Brian Skyrms

Quentin Smith

Scott Soames

David Sosa

Robert Stalnaker

Jason Stanley

John of St. Thomas, OP (John Poinsot)

Jaun Elia

Stephen Yablo

P. F. Strawson

Alfred Tarski

Kenneth Allen Taylor

Ernst Tugendhat

Michael Tye

Zeno Vendler

Vācaspati Miśra

Friedrich Waismann

Brian Weatherson

Michael Williams

Timothy Williamson

John Wisdom

Ludwig Wittgenstein

Crispin Wright

Georg Henrik von Wright

Edward N. Zalta

Eddy Zemach

Paul Ziff

Dean Zimmerman

Logical possibility

Logically possible refers to a proposition which can be the logical consequence of another, based on the axioms of a given system of logic. The logical possibility of a proposition will depend on the system of logic being considered, rather than on the violation of any single rule. Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions. Other logical systems have more than two truth-values instead of a binary of such values. However, when talking about logical possibility it is often assumed that the system in question is classical propositional logic. Similarly, the criterion for logical possibility is often based on whether or not a proposition is contradictory and as such is often thought of as the broadest type of possibility.

Logical possibility should be distinguished from other sorts of subjunctive possibilities. But the relationship between modalities (if there is any) is the subject of debate and may depend on how one views logic, as well as the relationship between logic and metaphysics. For example, many philosophers following Saul Kripke have held that discovered identities such as "Hesperus = Phosphorus" are metaphysically necessary because they pick out the same object in all possible worlds where the terms have a referent. However, it is nonetheless logically possible for “Hesperus = Phosphorus” to be false, since denying it doesn't violate a logical rule such as consistency. Other philosophers are of the view that logical possibility is broader than metaphysical possibility, so that anything which is metaphysically possible is also logically possible.

Martian scientist

A Martian scientist or Martian researcher is a hypothetical Martian frequently used in thought experiments as an outside observer of conditions on Earth. The most common variety is the Martian anthropologist, but Martians researching subjects such as philosophy, linguistics and biology have also been invoked.

The following extract from an essay by Richard Dawkins is more or less typical.

A Martian taxonomist who didn't know that all human races happily interbreed with one another, and didn't know that most of the underlying genetic variance in our species is shared by all races might be tempted by our regional differences in skin colour, facial features, hair, body size and proportions to split us into more than one species.In American structuralist linguistics, the Martian approach is recommended for language description:

The descriptive analyst must be guided by certain very fixed principles if he is to be objective in describing accurately any language or part of any language. It would be excellent if he could adopt a completely man-from-Mars attitude toward any language he analyzes and describes.The hypothetical Martian anthropologist is described in the writings of Noam Chomsky as one who, upon studying the world's languages, would conclude that they are all dialects of a single language embodying a "universal grammar" reflecting a hardwired, genetically determined linguistic module inherent in the human brain.

In philosophy, especially philosophy of language and philosophy of mind, the Martian is often invoked as an example of an intelligent being with a cognitive apparatus that differs from that of humans, e.g. the following example given by Saul Kripke:

I will not here argue that simplicity is relative, or that it is hard to define, or that a Martian might find the quus function simpler than the plus function.In a common rhetorical turn, invoking the Martian scientist forces the reader to observe an obvious state of affairs that is ordinarily overlooked:

If a Martian graced our planet, it would be struck by one remarkable similarity among Earth's living creatures and a key difference.(NB: The similarity Chomsky et al. mean is the universal hereditary language of DNA, while the difference is the lack of a universal language of communication.)

Mediated reference theory

A mediated reference theory (also indirect reference theory) is any semantic theory that posits that words refer to something in the external world, but insists that there is more to the meaning of a name than simply the object to which it refers. It thus stands opposed to the theory of direct reference. Gottlob Frege is a well-known advocate of mediated reference theories. Similar theories were widely held in the middle of the twentieth century by philosophers such as Peter Strawson and John Searle.

Mediated reference theories are contrasted with theories of direct reference.

Saul Kripke, a proponent of direct reference theory, in his Naming and Necessity dubbed mediated reference theory the Frege–Russell view and criticized it. Subsequent scholarship refuted the claim that Bertrand Russell's views on reference theory were the same as Frege's, since Russell was also a proponent of direct reference theory.

Naming and Necessity

Naming and Necessity is a 1980 book with the transcript of three lectures, given by the philosopher Saul Kripke, at Princeton University in 1970, in which he dealt with the debates of proper names in the philosophy of language. The transcript was brought out originally in 1972 in Semantics of Natural Language, edited by Donald Davidson and Gilbert Harman. Among analytic philosophers, Naming and Necessity is widely considered one of the most important philosophical works of the twentieth century.

Non-rigid designator

In the philosophy of language and modal logic, a term is said to be a non-rigid designator (or flaccid designator) or connotative term if it does not extensionally designate (denote, refer to) the same object in all possible worlds. This is in contrast to a rigid designator, which does designate the same object in all possible worlds in which that object exists, and does not designate anything else in those worlds in which that object does not exist. The term was coined by Saul Kripke in his 1970 lecture series at Princeton University, later published as the book Naming and Necessity.

Property dualism

Property dualism describes a category of positions in the philosophy of mind which hold that, although the world is composed of just one kind of substance—the physical kind—there exist two distinct kinds of properties: physical properties and mental properties. In other words, it is the view that non-physical, mental properties (such as beliefs, desires and emotions) inhere in or supervene upon certain physical substances (namely brains). As a doctrine, 'property dualism' is epistemic, as distinct from ontic.

Substance dualism, on the other hand, is the view that there exist in the universe two fundamentally different kinds of substance: physical (matter) and non-physical (mind or consciousness), and subsequently also two kinds of properties which adhere in those respective substances. Substance dualism is thus more susceptible to the mind-body problem. Both substance and property dualism are opposed to reductive physicalism. As a doctrine, 'substance dualism' is ontic, as distinct from epistemic.

Scientific essentialism

Scientific essentialism, a view espoused by Saul Kripke and Hilary Putnam, maintains that there exist essential properties that objects possess (or instantiate) necessarily. In other words, having such and such essential properties is a necessary condition for membership in a given natural kind. For example, tigers are tigers in virtue of possessing a particular set of genetic properties, but identifying (or appearance-based) properties are nonessential properties. If a tiger lost a leg, or didn't possess stripes, we would still call it a tiger. They are not necessary for being a member of the class of tigers.

It is important, however, that the set of essential properties of an object not be used to identify or be identified with that object because they are not necessary and sufficient, but only necessary. Having such and such a genetic code does not suffice for being a tiger. We wouldn't call a piece of tiger tail a tiger, even though a piece of tiger tail contains the genetic information essential to being a tiger.

Other advocates of scientific essentialism include Brian Ellis, Caroline Lierse, John Bigelow, and Alexander Bird.

Scott Soames

Scott Soames (; born August 11, 1946) is an American philosopher. He is a professor of philosophy at the University of Southern California. He specializes in the philosophy of language and the history of analytic philosophy. He is well known for defending and expanding on the program in the philosophy of language started by Saul Kripke as well as being a major critic of two-dimensionalist theories of meaning.

The Ashtray (Or the Man Who Denied Reality)

The Ashtray (Or the Man Who Denied Reality) is a book by Errol Morris in which he criticizes the philosophy of Thomas Kuhn. In the book, Morris argues that Kuhn was a relativist and a philosophical idealist, contrasting his interpretation of Kuhn's views with his own epistemology, drawing on Hilary Putnam and Saul Kripke, which he describes as "investigative realism", based on the belief that there is an objective reality whilst rejecting naïve realism. Morris accepts that investigation of truth involves considerable effort, with no guarantee of reaching the absolute truth, and that knowledge can be attained "through reason, through observation, through investigation, through thought, through science".In a piece for the Los Angeles Review of Books, Philip Kitcher compared Morris' critique to Samuel Johnson's appeal to the stone regarding George Berkeley's belief in subjective idealism, stating that "Morris has no interest in considering what Kuhn might have had in mind", and rejecting his characterisation of Kuhn as a relativist and an irrealist.

Theory of descriptions

The theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's theory of descriptions (commonly abbreviated as RTD). In short, Russell argued that the syntactic form of descriptions (phrases that took the form of "The aardvark" and "An aardvark") is misleading, as it does not correlate their logical and/or semantic architecture. While descriptions may seem fairly uncontroversial phrases, Russell argued that providing a satisfactory analysis of the linguistic and logical properties of a description is vital to clarity in important philosophical debates, particularly in semantic arguments, epistemology and metaphysics.

Since the first development of the theory in Russell's 1905 paper "On Denoting", RTD has been hugely influential and well-received within the philosophy of language. However, it has not been without its critics. In particular, the philosophers P. F. Strawson and Keith Donnellan have given notable, well known criticisms of the theory. Most recently, RTD has been defended by various philosophers and even developed in promising ways to bring it into harmony with generative grammar in Noam Chomsky's sense, particularly by Stephen Neale. Such developments have themselves been criticised, and debate continues.

Russell viewed his theory of descriptions as a kind of analysis that is now called logical analysis or propositional analysis (not to be confused with propositional calculus).

Wittgenstein on Rules and Private Language

Wittgenstein on Rules and Private Language is a 1982 book by philosopher of language Saul Kripke, in which the author contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date" (p. 60). He argues that Wittgenstein does not reject the argument that leads to the rule-following paradox, but accepts it and offers a "skeptical solution" to alleviate the paradox's destructive effects.

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