Saul Aaron Kripke (; born November 13, 1940) is an _{2}O. 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 20th century. It introduces the concept of names as rigid designators, true in every possible world, as contrasted with descriptions. It also contains Kripke's causal theory of reference, disputing the Descriptivist theory of names, descriptivist theory found in Gottlob Frege's concept of Sense and reference, sense and Bertrand Russell's theory of descriptions.
Kripke also gave an original reading of Ludwig Wittgenstein, known as "Kripkenstein", in his ''Wittgenstein on Rules and Private Language''. The book contains his rule-following argument, a paradox for skepticism about Meaning (philosophy of language), meaning.

modal logic
Modal logic is a collection of formal systems originally developed and still widely used to represent statements about Linguistic modality, necessity and possibility. The basic Unary operation, unary (1-place) modal operators are most often interpr ...

. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke. Kripke introduced the now-standard _{1} ⊆ ''L''_{2} are normal modal logics that correspond to the same class of frames, but ''L''_{1} does not prove all theorems of ''L''_{2}. Then ''L''_{1} is Kripke incomplete. For example, the schema $\backslash Box(A\backslash equiv\backslash Box\; A)\backslash to\backslash Box\; A$ 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 (logic), tautology $\backslash Box\; A\backslash to\backslash Box\backslash Box\; A$.

_{i}'' for each ''i'' ∈ ''I''. The definition of a satisfaction relation is modified as follows:
: $w\backslash Vdash\backslash Box\_i\; A$ if and only if $\backslash forall\; u\backslash ,(w\backslash ;R\_i\backslash ;u\backslash Rightarrow\; u\backslash Vdash\; A).$

_{i}'' ⊆ ''W'' for each modality. Satisfaction is defined as:
: $w\backslash Vdash\backslash Box\_i\; A$ if and only if $\backslash forall\; u\backslash in\; D\_i\backslash ,(w\backslash ;R\backslash ;u\backslash Rightarrow\; u\backslash Vdash\; A).$
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.

_{w}'' is a
(classical) ''L''-structure for each node ''w'' ∈ ''W'', and the following compatibility conditions hold whenever ''u'' ≤ ''v'':
* the domain of ''M_{u}'' is included in the domain of ''M_{v}'',
* realizations of function symbols in ''M_{u}'' and ''M_{v}'' agree on elements of ''M_{u}'',
* for each ''n''-ary predicate ''P'' and elements ''a''_{1},...,''a_{n}'' ∈ ''M_{u}'': if ''P''(''a''_{1},...,''a_{n}'') holds in ''M_{u}'', then it holds in ''M_{v}''.
Given an evaluation ''e'' of variables by elements of ''M_{w}'', we define the satisfaction relation $w\backslash Vdash\; A[e]$:
* $w\backslash Vdash\; P(t\_1,\backslash dots,t\_n)[e]$ if and only if $P(t\_1[e],\backslash dots,t\_n[e])$ holds in ''M_{w}'',
* $w\backslash Vdash(A\backslash land\; B)[e]$ if and only if $w\backslash Vdash\; A[e]$ and $w\backslash Vdash\; B[e]$,
* $w\backslash Vdash(A\backslash lor\; B)[e]$ if and only if $w\backslash Vdash\; A[e]$ or $w\backslash Vdash\; B[e]$,
* $w\backslash Vdash(A\backslash to\; B)[e]$ if and only if for all $u\backslash ge\; w$, $u\backslash Vdash\; A[e]$ implies $u\backslash Vdash\; B[e]$,
* not $w\backslash Vdash\backslash bot[e]$,
* $w\backslash Vdash(\backslash exists\; x\backslash ,A)[e]$ if and only if there exists an $a\backslash in\; M\_w$ such that $w\backslash Vdash\; A[e(x\backslash to\; a)]$,
* $w\backslash Vdash(\backslash forall\; x\backslash ,A)[e]$ if and only if for every $u\backslash ge\; w$ and every $a\backslash in\; M\_u$, $u\backslash Vdash\; A[e(x\backslash to\; a)]$.
Here ''e''(''x''→''a'') is the evaluation which gives ''x'' the value ''a'', and otherwise agrees with ''e''.

_{2}O" and other identity claims where two names refer to the same object.
Finally, Kripke gave an argument against physicalism, 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 fiber, 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.) 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 were in many respects a continuation of ''Naming and Necessity'', and deal with the subjects of fictional names and perceptual error. In 2013 Oxford University Press published the lectures as a book, also titled ''Reference and Existence''.
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. 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.

CUNY Graduate Center Philosophy Department faculty page

The Saul Kripke Center, at the CUNY Graduate Center

Saul Kripke's archive on the CUNY Philosophy Commons

Second Annual Saul Kripke Lecture by John Burgess on the Necessity of Origin at the CUNY Graduate Center, November 13th, 2012

*

"Saul Kripke, Genius Logician"

a short, non-technical interview by Andreas Saugstad, February 25, 2001.

with a video of his speech "The First Person", January 25–26, 2006

Video of his talk "From Church's Thesis to the First Order Algorithm Theorem,"

June 13, 2006.

Podcast of his talk "Unrestricted Exportation and Some Morals for the Philosophy of Language,"

May 21, 2008.

* [http://www.nysun.com/article/26585 Celebrating CUNY's Genius Philosopher], by Gary Shapiro, January 27, 2006, in The New York Sun.

information from 'Wisdom Supreme' website

Roundtable on Kripke's critique of mind-body identity with Scott Soames as the main presenter

May 26, 2010. {{DEFAULTSORT:Kripke, Saul 1940 births 20th-century American non-fiction writers 20th-century American philosophers 20th-century essayists 21st-century American non-fiction writers 21st-century American philosophers 21st-century essayists American logicians American male non-fiction writers American metaphysics writers American people of Lithuanian-Jewish descent Analytic philosophers Corresponding Fellows of the British Academy Epistemologists Harvard University alumni Historians of philosophy Jewish American academics Jewish American writers Jewish philosophers Jews and Judaism in Omaha, Nebraska Lecturers Living people Mathematicians from New York (state) Members of the European Academy of Sciences and Arts Members of the Norwegian Academy of Science and Letters Metaphysicians Modal logicians Omaha Central High School alumni Ontologists People from Bay Shore, New York Philosophers from Nebraska Philosophers from New York (state) Philosophers of history Philosophers of Judaism Philosophers of language Philosophers of logic Philosophers of mathematics Philosophers of mind Princeton University faculty Rolf Schock Prize laureates Set theorists Writers from Omaha, Nebraska 20th-century American male writers 21st-century American male writers 21st-century American Jews

American philosopher
American(s) may refer to:
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** Americans, citizens and nationals of the United States of America
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and logician
Logic (from Greek: grc, λογική, label=none, lit=possessed of reason
Reason is the capacity of consciously making sense of things, applying logic
Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=n ...

in the analytic tradition. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York
The Graduate School and University Center of the City University of New York (The Graduate Center) is a public research institution and post-graduate university in New York City. It is the principal doctoral-granting institution of the City Univ ...

and emeritus professor at Princeton University
Princeton University is a private
Private or privates may refer to:
Music
* "In Private
"In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly two ...

. Since the 1960s, Kripke has been a central figure in a number of fields related to mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal syst ...

, modal logic
Modal logic is a collection of formal systems originally developed and still widely used to represent statements about Linguistic modality, necessity and possibility. The basic Unary operation, unary (1-place) modal operators are most often interpr ...

, philosophy of language
In analytic philosophy
Analytic philosophy is a branch and tradition of philosophy
Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, E ...

, philosophy of mathematics
The philosophy of mathematics is the branch
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, metaphysics
Metaphysics is the branch of philosophy
Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and ...

, epistemology
Epistemology (; ) is the concerned with . Epistemologists study the nature, origin, and scope of knowledge, epistemic , the of , and various related issues. Epistemology is considered a major subfield of philosophy, along with other major ...

, and recursion theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since ex ...

. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts.
Kripke has made influential and original contributions to logic
Logic is an interdisciplinary field which studies truth and reasoning
Reason is the capacity of consciously making sense of things, applying logic
Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit ...

, especially modal logic
Modal logic is a collection of formal systems originally developed and still widely used to represent statements about Linguistic modality, necessity and possibility. The basic Unary operation, unary (1-place) modal operators are most often interpr ...

. His principal contribution is a semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference
Reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another o ...

for modal logic involving possible world
A possible world is a complete and consistent way the world is or could have been. They are widely used as a formal device in logic
Logic is an interdisciplinary field which studies truth and reasoning
Reason is the capacity of consciously ...

s, now called Kripke semantics
Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joya ...

. He received the 2001 Schock Prize
The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm
Stockholm is the Capital city, capital of Sweden. It has the most populous urba ...

in Logic and Philosophy.
Kripke is also partly responsible for the revival of metaphysics
Metaphysics is the branch of philosophy
Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and ...

after the decline of logical positivism, claiming Metaphysical necessity, necessity is a metaphysical notion distinct from the Epistemology, epistemic notion of ''a priori and a posteriori, a priori'', and that there are Logical truth, necessary truths that are known ''Empirical evidence, a posteriori'', such as that water is HLife and career

Saul Kripke is the oldest of three children born to Dorothy K. Kripke and Rabbi Myer S. Kripke. 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 Kripke, Madeline and Netta, attended Dundee Grade School and Omaha Central High School. Kripke was labeled a Child prodigy, prodigy, teaching himself Biblical Hebrew, 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. He wrote his first completeness theorem inmodal logic
Modal logic is a collection of formal systems originally developed and still widely used to represent statements about Linguistic modality, necessity and possibility. The basic Unary operation, unary (1-place) modal operators are most often interpr ...

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."
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
Princeton University is a private
Private or privates may refer to:
Music
* "In Private
"In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly two ...

. 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. He won the Rolf Schock Prizes, Schock Prize in Logic and Philosophy in 2001.
Kripke was married to philosopher Margaret Gilbert. He is the second cousin once removed of television writer, director, and producer Eric Kripke.
Work

Kripke's contributions to philosophy include: #Kripke semantics
Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joya ...

for modal logic, modal and related logics, published in several essays beginning in his teens.
# His 1970 Princeton lectures ''Naming and Necessity'' (published in 1972 and 1980), which significantly restructured philosophy of language
In analytic philosophy
Analytic philosophy is a branch and tradition of philosophy
Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, E ...

.
# His interpretation of Wittgenstein.
# His theory of truth.
He has also contributed to recursion theory (see admissible ordinal and Kripke–Platek set theory).
Modal logic

Two of Kripke's earlier works, "A Completeness Theorem in Modal Logic" (1959) and "Semantical Considerations on Modal Logic" (1963), the former written when he was a teenager, were onKripke semantics
Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joya ...

(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 $\backslash langle\; W,R\backslash rangle$, 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 (Transitive relation, transitivity, reflexivity, etc.), the corresponding frame is described, by extension, as being transitive, reflexive, etc.
A Kripke model is a triple $\backslash langle\; W,R,\backslash Vdash\backslash rangle$, where $\backslash langle\; W,R\backslash rangle$ is a Kripke frame, and Turnstile (symbol), $\backslash Vdash$ is a relation between nodes of ''W'' and modal formulas, such that:
* $w\backslash Vdash\backslash neg\; A$ if and only if $w\backslash nVdash\; A$,
* $w\backslash Vdash\; A\backslash to\; B$ if and only if $w\backslash nVdash\; A$ or $w\backslash Vdash\; B$,
* $w\backslash Vdash\backslash Box\; A$ if and only if $\backslash forall\; u\backslash ,(w\backslash ;\; R\backslash ;\; u$ implies $u\backslash Vdash\; A)$.
We read $w\backslash Vdash\; A$ as "''w'' satisfies ''A''", "''A'' is satisfied in ''w''", or "''w'' forces ''A''". The relation $\backslash Vdash$ is called the ''satisfaction relation'', ''evaluation'', or ''Forcing (mathematics), forcing relation''. The satisfaction relation is uniquely determined by its value on propositional variables.
A formula ''A'' is valid in:
* a model $\backslash langle\; W,R,\backslash Vdash\backslash rangle$, if $w\backslash Vdash\; A$ for all ''w'' ∈ ''W'',
* a frame $\backslash langle\; W,R\backslash rangle$, if it is valid in $\backslash langle\; W,R,\backslash Vdash\backslash rangle$ for all possible choices of $\backslash Vdash$,
* 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 : $\backslash Box\; A\backslash to\; A$. T is valid in any reflexive relation, reflexive frame $\backslash langle\; W,R\backslash rangle$: if $w\backslash Vdash\; \backslash Box\; A$, then $w\backslash Vdash\; A$ 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: $u\backslash Vdash\; p$ if and only if ''w'' ''R'' ''u''. Then $w\backslash Vdash\; \backslash Box\; p$, thus $w\backslash Vdash\; p$ by T, which means ''w'' ''R'' ''w'' using the definition of $\backslash Vdash$. 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 ''L''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 $\backslash langle\; W,R,\backslash Vdash\backslash rangle$, where ''W'' is the set of all ''L''-''MCS'', and the relations ''R'' and $\backslash Vdash$ are as follows: : $X\backslash ;R\backslash ;Y$ if and only if for every formula $A$, if $\backslash Box\; A\backslash in\; X$ then $A\backslash in\; Y$, : $X\backslash Vdash\; A$ if and only if $A\backslash in\; X$. 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 compactness theorem, 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 (Robert Goldblatt, Goldblatt, 1991), but the combined logic S4.1 (in fact, even K4.1) is canonical. In general, it is decision problem, 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 logic, 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 $\backslash $ as the set of its necessity operators consists of a non-empty set ''W'' equipped with binary relations ''RCarlson models

A simplified semantics, discovered by Tim Carlson, is often used for polymodal provability logics. A Carlson model is a structure $\backslash langle\; W,R,\backslash \_,\backslash Vdash\backslash rangle$ with a single accessibility relation ''R'', and subsets ''DIntuitionistic 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 $\backslash langle\; W,\backslash le,\backslash Vdash\backslash rangle$, where $\backslash langle\; W,\backslash le\backslash rangle$ is a partially ordered set, partially ordered Kripke frame, and $\backslash Vdash$ satisfies the following conditions: * if ''p'' is a propositional variable, $w\backslash le\; u$, and $w\backslash Vdash\; p$, then $u\backslash Vdash\; p$ (''persistency'' condition), * $w\backslash Vdash\; A\backslash land\; B$ if and only if $w\backslash Vdash\; A$ and $w\backslash Vdash\; B$, * $w\backslash Vdash\; A\backslash lor\; B$ if and only if $w\backslash Vdash\; A$ or $w\backslash Vdash\; B$, * $w\backslash Vdash\; A\backslash to\; B$ if and only if for all $u\backslash ge\; w$, $u\backslash Vdash\; A$ implies $u\backslash Vdash\; B$, * not $w\backslash Vdash\backslash bot$. 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 logic, first-order language. A Kripke model of ''L'' is a triple $\backslash langle\; W,\backslash le,\backslash \_\backslash rangle$, where $\backslash langle\; W,\backslash le\backslash rangle$ is an intuitionistic Kripke frame, ''M''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 Gottlob Frege, Frege, Bertrand Russell, Russell, Ludwig Wittgenstein, 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 Descriptivist theory of names, 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 names, 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 designation, rigid designators: that is, a proper name refers to the named object in every possible worlds, 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 1968 United States presidential election, United States presidential election of 1968" could refer to Richard Nixon, Nixon, Humphrey, or others in different possible worlds. Kripke also raised the prospect of ''A Posteriori Necessity, a posteriori necessities'' — facts that are necessarily true, though they can be known only through empirical investigation. Examples include "Hesperus is Phosphorus (morning star), Phosphorus", "Cicero is Cicero, Tully", "Water is H"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, 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" (1988) 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 Coreference, 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.Wittgenstein

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.Truth

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." Nevertheless, it has been shown by Proof sketch for Gödel's first incompleteness theorem, 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 undefinability theorem, Tarski's theorem that truth cannot be consistently defined. It has thus been claimed 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 Consistency proof, acceptable proving methods used inmathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal syst ...

.
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.
Saul Kripke Center

The Saul Kripke Center at theGraduate Center of the City University of New York
The Graduate School and University Center of the City University of New York (The Graduate Center) is a public research institution and post-graduate university in New York City. It is the principal doctoral-granting institution of the City Univ ...

is dedicated to preserving and promoting Kripke's work. Its director is Romina Padro. The Saul Kripke Center 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. 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."
Awards and recognitions

*Fulbright Scholar (1962–1963) *Society of Fellows, Harvard University (1963–1966). *Doctor of Humane Letters, honorary degree, University of Nebraska, 1977. *Fellow, American Academy of Arts and Sciences (1978–). *Corresponding Fellow, British Academy (1985–). *Howard Behrman Award,Princeton University
Princeton University is a private
Private or privates may refer to:
Music
* "In Private
"In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly two ...

, 1988.
*Fellow, Academia Scientiarum et Artium Europaea (1993–).
*Doctor of Humane Letters, honorary degree, Johns Hopkins University, 1997.
*Doctor of Humane Letters, honorary degree, University of Haifa, Israel, 1998.
*Fellow, Norwegian Academy of Sciences (2000–).
*Schock Prize
The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm
Stockholm is the Capital city, capital of Sweden. It has the most populous urba ...

in Logic and Philosophy, Swedish Academy of Sciences, 2001.
*Doctor of Humane Letters, honorary degree, University of Pennsylvania, 2005.
*Fellow, American Philosophical Society (2005–).
Works

* ''Naming and Necessity''. Cambridge, Mass.: Harvard University Press, 1972. * ''Wittgenstein on Rules and Private Language, Wittgenstein on Rules and Private Language: an Elementary Exposition''. Cambridge, Mass.: Harvard University Press, 1982. . * ''Philosophical Troubles. Collected Papers Vol. 1''. New York: Oxford University Press, 2011. * ''Reference and Existence – The John Locke Lectures''. New York: Oxford University Press, 2013.See also

* American philosophy * List of American philosophers * Barry Kripke (a character on ''The Big Bang Theory'' who is believed to be named after Saul)References

Further reading

* Arif Ahmed (2007), ''Saul Kripke''. New York, NY; London: Continuum. . * Alan Berger (editor) (2011) "Saul Kripke." . * Taylor Branch (1977), "New Frontiers in American Philosophy: Saul Kripke". ''The New York Times Magazine''. * John Burgess (2013), "Saul Kripke: Puzzles and Mysteries." . * G. W. Fitch (2005), ''Saul Kripke''. . * Christopher Hughes (2004), ''Kripke : Names, Necessity, and Identity''. . * Martin Kusch (2006), ''A Sceptical Guide to Meaning and Rules. Defending Kripke's Wittgenstein''. Acumben: Publishing Limited. * Colin McGinn (1984), ''Wittgenstein on Meaning''. . * Christopher Norris (2007), ''Fiction, Philosophy and Literary Theory: Will the Real Saul Kripke Please Stand Up?'' London: Continuum * Consuelo Preti (2002), ''On Kripke''. Wadsworth. . * Nathan Salmon (1981), ''Reference and Essence''. . * Scott Soames (2002), ''Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity''. .External links

CUNY Graduate Center Philosophy Department faculty page

The Saul Kripke Center, at the CUNY Graduate Center

Saul Kripke's archive on the CUNY Philosophy Commons

Second Annual Saul Kripke Lecture by John Burgess on the Necessity of Origin at the CUNY Graduate Center, November 13th, 2012

*

"Saul Kripke, Genius Logician"

a short, non-technical interview by Andreas Saugstad, February 25, 2001.

with a video of his speech "The First Person", January 25–26, 2006

Video of his talk "From Church's Thesis to the First Order Algorithm Theorem,"

June 13, 2006.

Podcast of his talk "Unrestricted Exportation and Some Morals for the Philosophy of Language,"

May 21, 2008.

* [http://www.nysun.com/article/26585 Celebrating CUNY's Genius Philosopher], by Gary Shapiro, January 27, 2006, in The New York Sun.

information from 'Wisdom Supreme' website

Roundtable on Kripke's critique of mind-body identity with Scott Soames as the main presenter

May 26, 2010. {{DEFAULTSORT:Kripke, Saul 1940 births 20th-century American non-fiction writers 20th-century American philosophers 20th-century essayists 21st-century American non-fiction writers 21st-century American philosophers 21st-century essayists American logicians American male non-fiction writers American metaphysics writers American people of Lithuanian-Jewish descent Analytic philosophers Corresponding Fellows of the British Academy Epistemologists Harvard University alumni Historians of philosophy Jewish American academics Jewish American writers Jewish philosophers Jews and Judaism in Omaha, Nebraska Lecturers Living people Mathematicians from New York (state) Members of the European Academy of Sciences and Arts Members of the Norwegian Academy of Science and Letters Metaphysicians Modal logicians Omaha Central High School alumni Ontologists People from Bay Shore, New York Philosophers from Nebraska Philosophers from New York (state) Philosophers of history Philosophers of Judaism Philosophers of language Philosophers of logic Philosophers of mathematics Philosophers of mind Princeton University faculty Rolf Schock Prize laureates Set theorists Writers from Omaha, Nebraska 20th-century American male writers 21st-century American male writers 21st-century American Jews