Saul Aaron Kripke is an American philosopher and logician. He is a professor
emeritusEmeritus is a post-positive adjective that is used to designate a retired professor, bishop, or other professional or as a title. The female equivalent emerita is also sometimes used.-History:...
at
PrincetonPrinceton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
and teaches as a Distinguished Professor of Philosophy at the
CUNY Graduate CenterThe Graduate Center of the City University of New York brings together graduate education, advanced research, and public programming to midtown Manhattan hosting 4,600 students, 33 doctoral programs, 7 master's programs, and 30 research centers and institutes...
. Since the 1960s Kripke has been a central figure in a number of fields related to
mathematical logicMathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
,
philosophy of languagePhilosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language...
,
philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
,
metaphysicsMetaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
,
epistemology, and
set theorySet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
. Much of his work remains unpublished or exists only as tape-recordings and privately circulated manuscripts. Kripke was the recipient of the 2001
Schock PrizeThe Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock . The prizes were first awarded in Stockholm, Sweden, in 1993 and have been awarded every two years since...
in Logic and Philosophy. A recent poll conducted among philosophers ranked Kripke among the top ten most important philosophers of the past 200 years.
Kripke has made influential and original contributions to logic, especially
modal logicModal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
, since he was a teenager. Unusually for a professional philosopher, his only degree is an
undergraduateA bachelor's degree is usually an academic degree awarded for an undergraduate course or major that generally lasts for three or four years, but can range anywhere from two to six years depending on the region of the world...
degree from
HarvardHarvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, in mathematics. His work has profoundly influenced
analytic philosophyAnalytic philosophy is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century...
, with his principal contribution being a
metaphysicalMetaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
description of
modality-Humanities:* In law: the basis of legal argumentation in United States constitutional law* In theology: Modality : the organization and structure of the church, as distinct from sodality or parachurch organizations...
, involving
possible worldIn philosophy and logic, the concept of a possible world is used to express modal claims. The concept of possible worlds is common in contemporary philosophical discourse and has also been disputed.- Possibility, necessity, and contingency :...
s as described in a system now called
Kripke semanticsKripke semantics is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems...
. Another of his most important contributions is his argument that there are necessary a posteriori truths, such as "Water is H
2O." He has also contributed an original reading of
WittgensteinLudwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
, referred to as "
KripkensteinWittgenstein on Rules and Private Language by philosopher of language Saul Kripke was first published in 1982. The book contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of us ever...
." His most famous work is
Naming and NecessityNaming and Necessity is a book by the philosopher Saul Kripke that was first published in 1980 and deals with the debates of proper nouns in the philosophy of language. The book is based on a transcript of three lectures given at Princeton University in 1970...
(1980).
Biography
Saul Kripke is the oldest of three children born to
Dorothy K. KripkeDorothy K. Kripke was an author of Jewish educational books.-Biography:...
and
RabbiIn Judaism, a rabbi is a teacher of Torah. This title derives from the Hebrew word רבי , meaning "My Master" , which is the way a student would address a master of Torah...
Myer Kripke. His father was the leader of Beth El Synagogue, the only Conservative congregation in
OmahaOmaha may refer to:*Omaha , a Native American tribe that currently resides in the northeastern part of the U.S. state of Nebraska-Places:United States* Omaha, Nebraska* Omaha, Arkansas* Omaha, Georgia* Omaha, Illinois* Omaha, Texas...
,
NebraskaNebraska is a state on the Great Plains of the Midwestern United States. The state's capital is Lincoln and its largest city is Omaha, on the Missouri River....
, while his mother wrote educational Jewish books for children. Saul and his two sisters, Madeline and Netta, attended Dundee Grade School and
Omaha Central High SchoolOmaha Central High School, originally known as Omaha High School, was founded in 1859.The current building, located in Downtown Omaha, Nebraska, was designed by John Latenser, Sr. and built between 1900 and 1912...
. Kripke was labelled a
prodigyA child prodigy is someone who, at an early age, masters one or more skills far beyond his or her level of maturity. One criterion for classifying prodigies is: a prodigy is a child, typically younger than 18 years old, who is performing at the level of a highly trained adult in a very demanding...
, having taught himself Ancient Hebrew by the age of six, read the complete works of Shakespeare by nine, and mastered the works of Descartes and complex mathematical problems before graduating elementary school. He wrote his first completeness theorem in
modal logicModal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
at the age of 17, and had it published a year later. After graduating from high school in 1958, Kripke attended
Harvard UniversityHarvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
and graduated summa cum laude obtaining a bachelor's degree in mathematics. During his sophomore year at Harvard, Kripke taught a graduate-level logic course at nearby MIT. Upon graduation (1962) he received a Fulbright Fellowship, and in 1963 was appointed to the Society of Fellows.
After teaching briefly at Harvard, he moved to
Rockefeller UniversityThe Rockefeller University is a private university offering postgraduate and postdoctoral education. It has a strong concentration in the biological sciences. It is also known for producing numerous Nobel laureates...
in New York City in 1967, and then received a full-time position at
Princeton UniversityPrinceton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1977. In 1988 he received the university's Behrman Award for distinguished achievement in the humanities. In 2002 Kripke began teaching at the
CUNY Graduate CenterThe Graduate Center of the City University of New York brings together graduate education, advanced research, and public programming to midtown Manhattan hosting 4,600 students, 33 doctoral programs, 7 master's programs, and 30 research centers and institutes...
in midtown Manhattan, and was appointed a distinguished professor of philosophy there in 2003. He was married to philosopher
Margaret GilbertMargaret Gilbert is a philosopher best known for her work in the philosophy of social science, and, more specifically, for her founding contributions to the analytic philosophy of social phenomena...
.
He has received honorary degrees from the University of Nebraska, Omaha (1977),
Johns Hopkins UniversityThe Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
(1997),
University of HaifaThe University of Haifa is a university in Haifa, Israel.The University of Haifa was founded in 1963 by Haifa mayor Abba Hushi, to operate under the academic auspices of the Hebrew University of Jerusalem....
, Israel (1998), and the
University of PennsylvaniaThe University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
(2005). He is a member of the
American Philosophical SocietyThe American Philosophical Society, founded in 1743, and located in Philadelphia, Pa., is an eminent scholarly organization of international reputation, that promotes useful knowledge in the sciences and humanities through excellence in scholarly research, professional meetings, publications,...
, an elected Fellow of the
American Academy of Arts and SciencesThe American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
and a Corresponding Fellow of the
British AcademyThe British Academy is the United Kingdom's national body for the humanities and the social sciences. Its purpose is to inspire, recognise and support excellence in the humanities and social sciences, throughout the UK and internationally, and to champion their role and value.It receives an annual...
. He won the Schock Prize in Logic and Philosophy in 2001.
Work
Kripke's contributions to philosophy include:
- Kripke semantics
Kripke semantics is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems...
for modal and related logicsModal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
, published in several essays beginning while he was still in his teens.
- His 1970 Princeton lectures Naming and Necessity
Naming and Necessity is a book by the philosopher Saul Kripke that was first published in 1980 and deals with the debates of proper nouns in the philosophy of language. The book is based on a transcript of three lectures given at Princeton University in 1970...
(published in 1972 and 1980), that significantly restructured philosophy of languagePhilosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language...
.
- His interpretation of Wittgenstein.
- His theory of truth
Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...
.
He has also contributed to set-theory (see
admissible ordinalIn set theory, an ordinal number α is an admissible ordinal if Lα is an admissible set ; in other words, α is admissible when α is a limit ordinal and Lα⊧Σ0-collection....
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 while he was still a teenager, were on the subject of
modal logicModal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke for his contributions to modal logic. Kripke introduced the now-standard
Kripke semanticsKripke semantics is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems...
(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 prior to Kripke.
A
Kripke frame or
modal frame is a pair
, where
W is a
non-empty set, and
R is a
binary relationIn mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = . More generally, a binary relation between two sets A and B is a subset of...
on
W. Elements
of
W are called
nodes or
worlds, and
R is known as the
accessibility relationIn modal logic, an accessibility relation is a binary relation, written as R\,\! between possible worlds.-Description of terms:A statement in logic refers to a sentence that can be true or false...
. Depending on the properties of the accessibility relation (
transitivityIn mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c....
, 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 
.
We read
as “
w satisfies
A”, “
A is satisfied in
w”, or
“
w forces
A”. The relation
is called the
satisfaction relation,
evaluation, or
forcingIn the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory...
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 wrt
C if
L ⊇ Thm(
C).
Semantics is useful for investigating a logic (i.e. a derivation system) only if the semantical
entailmentIn logic, entailment is a relation between a set of sentences and a sentence. Let Γ be a set of one or more sentences; let S1 be the conjunction of the elements of Γ, and let S2 be a sentence: then, Γ entails S2 if and only if S1 and not-S2 are logically inconsistent...
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 logicIn logic, a normal modal logic is a set L of modal formulas such that L contains:* All propositional tautologies;* All instances of the Kripke schema: \Box\toand it is closed under:...
(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
reflexiveIn mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation ~ on S where x~x holds true for every x in S. For example, ~ could be "is equal to".-Related terms:...
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-
tautologyIn logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...
.
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 algebraIn mathematical logic, the Lindenbaum–Tarski algebra of a logical theory T consists of the equivalence classes of sentences of the theory...
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 lemmaZorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory that states:Suppose a partially ordered set P has the property that every chain has an upper bound in P...
, 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
compactIn mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model...
.
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
undecidableIn computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters. For example, the problem "given two numbers x and y, does x evenly divide y?" is a decision problem...
whether a given axiom is
canonical. We know a nice sufficient condition: H.
Sahlqvist identified a broad class of formulas (now called
Sahlqvist formulaIn modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every Sahlqvist formula is canonical, and corresponds to a first-order definable class of Kripke frames....
s) such that
- a Sahlqvist formula is canonical,
- the class of frames corresponding to a Sahlqvist formula is first-order
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
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 propertyIn logic, we say a logic L has the finite model property if there is a class of models M of L such that any non-theorem of L is falsified by some finite model in M...
(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 
A simplified semantics, discovered by Tim Carlson, is often used for
polymodal
provability logicProvability logic is a modal logic, in which the box operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic....
s. 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," has become especially useful in the analysis of hyperfiction.
Intuitionistic logic
Kripke semantics for the
intuitionistic logicIntuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well-formed statements are assumed to be either true or false, even if we do not have a proof of either...
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 orderedIn mathematics, especially order theory, a partially ordered set formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the...
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-orderFirst-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
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(
x→
a) is the evaluation which gives
x the
value
a, and otherwise agrees with
e.
Naming and Necessity
Kripke's three lectures constitute an attack on descriptivist theories of proper names. Kripke attributes variants of descriptivist theories to
FregeFriedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
,
RussellBertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
,
Ludwig WittgensteinLudwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
and
John SearleJohn Rogers Searle is an American philosopher and currently the Slusser Professor of Philosophy at the University of California, Berkeley.-Biography:...
, 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
descriptivismDescriptivist theory of names is a view of the nature of the meaning and reference of proper names generally attributed to Gottlob Frege and Bertrand Russell...
implausible as a theory of how names get their references determined (e.g., surely
AristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
could have died at age two and so not satisfied any of the descriptions we associate with his name, and yet it would seem wrong to deny that he was 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: A proper name refers to the named object in every
possible worldPossible Worlds may refer to:* Possible worlds, a concept in philosophy* Possible Worlds , by John Mighton** Possible Worlds , by Robert Lepage, based on the Mighton play* Possible Worlds , by Peter Porter...
in which the object exists, while most descriptions designate different objects in different possible worlds. For example, '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'The United States presidential election of 1968 was the 46th quadrennial United States presidential election. Coming four years after Democrat Lyndon B. Johnson won in a historic landslide, it saw Johnson forced out of the race and Republican Richard Nixon elected...
could refer to
NixonRichard Milhous Nixon was the 37th President of the United States, serving from 1969 to 1974. The only president to resign the office, Nixon had previously served as a US representative and senator from California and as the 36th Vice President of the United States from 1953 to 1961 under...
, Humphrey, or others in different possible worlds.
Kripke also raised the prospect of
a posterioriApart from the album, some additional remixes were released exclusively through the iTunes Store. They are:*"Eppur si muove" – 6:39*"Dreaming of Andromeda" Apart from the album, some additional remixes were released exclusively through the iTunes Store. They are:*"Eppur si muove" (Tocadisco...
necessities-Humanities:* In law: the basis of legal argumentation in United States constitutional law* In theology: Modality : the organization and structure of the church, as distinct from sodality or parachurch organizations...
— facts that are necessarily true, though they can be known only through empirical investigation. Examples include “
HesperusIn Greek mythology, Hesperus is the Evening Star, the planet Venus in the evening. He is the son of the dawn goddess Eos and is the brother of Eosphorus , the Morning Star. Hesperus' Roman equivalent is Vesper...
is
PhosphorusPhosphorus , a name meaning "Light-Bringer", is the Morning Star, the planet Venus in its morning appearance. Φαοσφόρος and Φαεσφόρος are forms of the same name in some Greek dialects....
”, “
CiceroMarcus Tullius Cicero , was a Roman philosopher, statesman, lawyer, political theorist, and Roman constitutionalist. He came from a wealthy municipal family of the equestrian order, and is widely considered one of Rome's greatest orators and prose stylists.He introduced the Romans to the chief...
is
TullyTully is a surname of Irish origin. The surname itself and its variants include; Tally, MacTully, Tilly and Flood, all of which can derive from several different unrelated Irish families such as; Ó Maoltuile, Taithligh, Mac Maoltuile, Ó Taithligh, and Mac an Tuile...
”, “Water is H
2O” and other identity claims where two names refer to the same object.
Finally, Kripke gave an argument against
identity materialismPhysicalism is a philosophical position holding that everything which exists is no more extensive than its physical properties; that is, that there are no kinds of things other than physical things...
in the
philosophy of mindPhilosophy of mind is a branch of philosophy that studies the nature of the mind, mental events, mental functions, mental properties, consciousness and their relationship to the physical body, particularly the brain. The mind-body problem, i.e...
, the view that every
mental factMental facts include such things as perceptions, feelings, and judgments. Mental facts are ultimately caused by physical facts, in that mental facts depend on physical and biological functions which are required for consciousness. The physical and biological processes which are necessary for...
is identical with some physical fact. Kripke argued that the only way to defend this identity is as an
a posteriori necessary identity, but that such an identity — e.g., pain is C-fibers firing — could not be necessary, given the possibility of pain that has nothing to do with C-fibers firing. Similar arguments have been proposed by
David ChalmersDavid John Chalmers is an Australian philosopher specializing in the area of philosophy of mind and philosophy of language, whose recent work concerns verbal disputes. He is Professor of Philosophy and Director of the Centre for Consciousness at the Australian National University...
.
Kripke delivered the
John Locke lecturesThe John Locke Lectures are a series of annual lectures in philosophy given at the University of Oxford. They are one of the world's most prestigious academic lecture series, comparable to the Gifford Lectures given in Scottish universities...
in philosophy at
OxfordThe city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...
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 have never been published and the transcript is officially available only in a reading copy in the university philosophy library, which cannot be copied or cited without Kripke's permission.
In a 1995 paper, philosopher
Quentin SmithQuentin Persifor Smith is an American contemporary philosopher, scholar and professor of philosophy at Western Michigan University in Kalamazoo, Michigan. He has worked in the philosophy of time, philosophy of language, philosophy of physics and philosophy of religion...
argued that key concepts in Kripke's new theory of reference had originated from the work of
Ruth Barcan MarcusRuth Barcan Marcus is the American philosopher and logician after whom the Barcan formula is named. She is a pioneering figure in the quantification of modal logic and the theory of direct reference...
more than a decade earlier. Smith identified six significant ideas to the New Theory that he claimed Marcus had developed: (1) The idea that proper names are direct references, which don't consist of contained definitions. (2) While one can single out a single thing by a description, this description is not equivalent with 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 designatorIn modal logic and the philosophy of language, a term is said to be a rigid designator when it designates the same thing in all possible worlds in which that thing exists and does not designate anything else in those possible worlds in which that thing does not exist...
, though the actual name of the concept was coined by Kripke.(6) The idea of a posteriori identity. Smith proceeded to argue that Kripke failed to understand Marcus' theory at the time, yet 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.
A Puzzle about Belief
Kripke’s main propositions in
Naming and Necessity concerning proper names 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.
In the article “A Puzzle about Belief” Kripke seems to oppose even this possibility. His argument can be reconstructed in the following way: 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 the following: “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 in which he lives, so he 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 prove.
Wittgenstein
First published in 1982, Saul Kripke's
Wittgenstein on Rules and Private Language contends that the central argument of the
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). Kripke argues 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. Whilst most commentators accept that the
Philosophical Investigations contains the rule-following paradox as Kripke presents it, few have concurred with Kripke when he attributes a skeptical solution to Wittgenstein. It should be noted that Kripke himself expresses doubts in
Wittgenstein on Rules and Private Language as to whether Wittgenstein would endorse his interpretation of the
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" (p. 5). The portmanteau "
KripkensteinWittgenstein on Rules and Private Language by philosopher of language Saul Kripke was first published in 1982. The book contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of us ever...
" has been coined as a jesting nickname for Kripke's reading of the
Philosophical Investigations.
The real significance of "
KripkensteinWittgenstein on Rules and Private Language by philosopher of language Saul Kripke was first published in 1982. The book contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of us ever...
" was to put forward a clear statement of a new kind of skepticism, dubbed "meaning skepticism", which is 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 HackerPeter Michael Stephan Hacker is a British philosopher.His principal expertise is in the philosophy of mind andphilosophy of language...
, who argue that his meaning skepticism is a pseudo-problem that stems from a confused, selective reading of Wittgenstein. Kripke's position has, however recently been defended against these and other attacks by the Cambridge philosopher
Martin KuschMartin Kusch is Professor of philosophy at the University of Vienna. Until 2009, Kusch was Professor of Philosophy and Sociology of science at the Department of History and Philosophy of Science at Cambridge University...
(2006), and Wittgenstein scholar David G. Stern considers the book to be "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
truthTruth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...
predicate, which was deemed impossible by
Alfred TarskiAlfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
, a pioneer in the area of 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 which 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."
Religious views
Kripke is an observant Jew.
Discussing how his religious views influenced his philosophical views (in an interview with Andreas Saugstad) he stated: "I don't have the prejudices many have today, I don't believe in a
naturalistNaturalism commonly refers to the philosophical viewpoint that the natural universe and its natural laws and forces operate in the universe, and that nothing exists beyond the natural universe or, if it does, it does not affect the natural universe that we know...
world view. I don't base my thinking on prejudices or a world view and do not believe in
materialismIn philosophy, the theory of materialism holds that the only thing that exists is matter; that all things are composed of material and all phenomena are the result of material interactions. In other words, matter is the only substance...
."
Awards and recognitions
- Fulbright Scholar (1962–1963)
- Society of Fellows, Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
(1963–1966).
- Doctor of Humane Letters, honorary degree, University of Nebraska, 1977.
- Fellow, American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
(1978–).
- Corresponding Fellow, British Academy
The British Academy is the United Kingdom's national body for the humanities and the social sciences. Its purpose is to inspire, recognise and support excellence in the humanities and social sciences, throughout the UK and internationally, and to champion their role and value.It receives an annual...
(1985–).
- Howard Behrman Award, Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, 1988.
- Fellow, Academia Scientiarum et Artium Europaea (1993–).
- Doctor of Humane Letters, honorary degree, Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
, 1997.
- Doctor of Humane Letters, honorary degree, University of Haifa
The University of Haifa is a university in Haifa, Israel.The University of Haifa was founded in 1963 by Haifa mayor Abba Hushi, to operate under the academic auspices of the Hebrew University of Jerusalem....
, 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 . The prizes were first awarded in Stockholm, Sweden, in 1993 and have been awarded every two years since...
in Logic and Philosophy, Swedish Academy of Sciences, 2001.
- Doctor of Humane Letters, honorary degree, University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
, 2005.
- Fellow, American Philosophical Society
The American Philosophical Society, founded in 1743, and located in Philadelphia, Pa., is an eminent scholarly organization of international reputation, that promotes useful knowledge in the sciences and humanities through excellence in scholarly research, professional meetings, publications,...
(2005–).
Books
- 1980. Naming and Necessity
Naming and Necessity is a book by the philosopher Saul Kripke that was first published in 1980 and deals with the debates of proper nouns in the philosophy of language. The book is based on a transcript of three lectures given at Princeton University in 1970...
. Cambridge, Mass.: Harvard University Press. ISBN 0-674-59845-8 and reprints 1972.
- 1982. Wittgenstein on Rules and Private Language: an Elementary Exposition. Cambridge, Mass.: Harvard University Press. ISBN 0-674-95401-7. Sets out his interpretation of Wittgenstein aka Kripkenstein
Wittgenstein on Rules and Private Language by philosopher of language Saul Kripke was first published in 1982. The book contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of us ever...
.
- Collected Papers, Vol. I. New York: Oxford University Press, 2011.
Abstracts and articles
- 1959. "A Completeness Theorem in Modal Logic", Journal of Symbolic Logic 24(1):1–14.
- 1959. "Distinguished Constituents" (abstract), The Journal of Symbolic Logic, 24(4):323.
- 1959. "Semantical Analysis of Modal Logic" (abstract), The Journal of Symbolic Logic, 24(4):323-324.
- 1959. "The Problem of Entailment" (abstract), The Journal of Symbolic Logic, 24(4):324.
- 1962. "‘Flexible’ Predicates of Formal Number Theory," Proceedings of the American Mathematical Society, 13(4):647-650.
- 1962. "The Undecidability of Monadic Modal Quantification Theory", Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 8:113–116
- 1963. "Semantical Considerations on Modal Logic", Acta Philosophica Fennica 16:83–94
- 1963. "Semantical Analysis of Modal Logic I: Normal Modal Propositional Calculi", Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9:67–96
- 1964. "Transfinite Recursions on Admissible Ordinals, I" (abstract), The Journal of Symbolic Logic, Vol. 29, No. 3, p. 162.
- 1964. "Transfinite Recursions on Admissible Ordinals, II" (abstract), The Journal of Symbolic Logic, Vol. 29, No. 3, p. 162.
- 1964. "Admissible Ordinals and the Analytic Hierarchy" (abstract), The Journal of Symbolic Logic, Vol. 29, No. 3, p. 162.
- 1965. "Semantical Analysis of Intuitionistic Logic I", In Formal Systems and Recursive Functions, edited by M. Dummett and J. N. Crossley. Amsterdam: North-Holland Publishing Co.
- 1965. "Semantical Analysis of Modal Logic II: Non-Normal Modal Propositional Calculi", In The Theory of Models, edited by J. W. Addison, L. Henkin and A. Tarski. Amsterdam: North-Holland Publishing Co.
- 1967. Research Announcement: "Deduction-preserving ‘Recursive Isomorphisms’ between Theories" (with Marian Boykan Pour-El), Bulletin of the American Mathematical Society, 73:145-148.
- 1967. "An Extension of a Theorem of Gaifman-Hales-Solovay," Fundamenta Mathematicae, Vol. 61, pp. 29–32.
- 1967. "Transfinite Recursion, Constructible Sets, and Analogues of Cardinals," Summaries of Talks Prepared in Connection with the Summer Institute on Axiomatic Set Theory, American Mathematical Society, U.C.L.A., pp. IV-0-1 - IV-0-12.
- 1967. "On the Application of Boolean-Valued Models to Solutions of Problems in Boolean Algebra," in Summaries of Talks Prepared in Connection with the Summer Institute on Axiomatic Set Theory, American Mathematical Society, U.C.L.A. (1967), pp. IV-T-1 through IV-T-7.
- 1967. "Deduction-preserving ‘Recursive Isomorphisms’ between Theories" (with Marian Boykan Pour-El), Fundamenta Mathematicae 61:141-163.
- 1971. "Identity and Necessity", In Identity and Individuation, edited by M. K. Munitz. New York: New York University Press.
- 1972 (1980). "Naming and Necessity", In Semantics of Natural Language, edited by D. Davidson and G. Harman. Dordrecht; Boston: Reidel. Sets out the causal theory of reference
A causal theory of reference is a theory of how terms acquire specific referents. Such theories have been used to describe many referring terms, particularly logical terms, proper names, and natural kind terms...
.
- 1975. "Outline of a Theory of Truth", Journal of Philosophy 72:690–716. Sets his theory of truth (against Alfred Tarski), where an object language can contain its own truth predicate.
- 1976. "Is There a Problem about Substitutional Quantification?", In Truth and Meaning: Essays in Semantics, edited by Gareth Evans and John McDowell. Oxford: Oxford University Press.
- 1976. "A Theory of Truth I. Preliminary Report," abstract, Journal of Symbolic Logic, Vol. 41, No. 2, pp. 556.
- 1976. "A Theory of Truth II. Preliminary Report," abstract, Journal of Symbolic Logic, Vol. 41, No. 2, pp. 556–557.
- 1977. "Speaker's Reference and Semantic Reference", Midwest Studies in Philosophy 2:255–276.
- 1979. "A Puzzle about Belief", In Meaning and Use, edited by A. Margalit. Dordrecht and Boston: Reidel.
- 1982. "Nonstandard Models of Peano Arithmetic" (with S. Kochen), in Logic and Algorithmics: International Symposium Held in Honor of Ernst Specker, H. Lauchli (ed.), University of Geneva: 277-295.
- 1986. “A Problem in the Theory of Reference: the Linguistic Division of Labor and the Social Character of Naming,” Philosophy and Culture (Proceedings of the XVIIth World Congress of Philosophy), Montreal, Editions Montmorency: 241-247.
- 1992. “Summary: Individual Concepts: Their Logic, Philosophy, and Some of Their Uses.” Proceedings and Addresses of the American Philosophical Association 66: 70-73
- 2005. "Russell's Notion of Scope", Mind 114:1005–1037
- 2008. "Frege’s Theory of Sense and Reference: Some Exegetical Notes,” Theoria 74:181-218
- 2009. "Presupposition and Anaphora: Remarks on the formulation of the projection problem," Linguistic Inquiry 40(3):367-386.
- 2009. "The Collapse of the Hilbert Program," (Abstract) Bulletin of Symbolic Logic 15(2):229-231.
- (Forthcoming). "The First Person," Collected Papers Vol. I, Oxford University Press. The videos "The First Person" and "Questions and Answers" in which the paper is based are available here.
- (Forthcoming). "Two Paradoxes of Knowledge," Collected Papers Vol. I, Oxford University Press.
- (Forthcoming). "Nozick on Knowledge," Collected Papers Vol. I, Oxford University Press.
- (Forthcoming). "A Puzzle about Time and Thought," Collected Papers Vol. I, Oxford University Press.
- (Forthcoming). "Vacuous Names and Fictional Entities," Collected Papers Vol. I, Oxford University Press.
- (Forthcoming). "Unrestricted Exportation and Some Morals for the Philosophy of Language," Collected Papers Vol. I, Oxford University Press. Podcast of the talk available here.
- (Forthcoming). “Another Approach: The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem,” in Computability: Gödel, Turing, Church, and beyond, Copeland, B. J., Posy, C., and Shagrir, O. (eds), Cambridge, Mass., MIT Press.
Unpublished manuscripts and lectures
- 1963. “History and Idealism: the Theory of R. G. Collingwood”.
- 1973. John Locke Lectures: "Reference and Existence". (Transcript available in the Philosophy Library, Oxford University)
- 1975. "Three Lectures on Truth". Princeton University. Discussed here.
- 197-. “On The Completeness and Decidability of Intuitionistic Propositional Logic”.
- 1978. "Time and Identity". Seminar given at Princeton University, 1978. Several versions of this material have circulated. Some of its ideas are discussed by Ted Sider in his book Four-Dimensionalism: An Ontology of Persistence and Time
- 19- "Non-Standard Models and Godel's Theorem: A Model-Theoretic Proof of Godel's Theorem". Summary by Hilary Putnam
Hilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...
.
- 1984. "Lessons on Functionalism and Automata". (Delivered at the International Wittgenstein Symposium, 1984. Transcribed by Roderick Chisholm
Roderick M. Chisholm was an American philosopher known for his work on epistemology, metaphysics, free will, and the philosophy of perception. He received his Ph.D. at Harvard University under Clarence Irving Lewis and Donald C. Williams, and taught at Brown University...
.
- 198-. “A Proof of Gamma.”
- 198-. “A Note on Zabludowski’s Critique of Goodman’s Theory of Projection”.
- 1986. “Rigid Designation and the Contingent A Priori: The Meter Stick Revisited” (Notre Dame, 1986).
- 1988/89. "Seminars on Truth". Three-semester seminar at Princeton in 1988-89, only the first two semesters have been transcribed by Jim Cain. See here.
- 19- "Semantical Analysis of Intuitionistic Logic II. Undecidability of the Monadic Fragment" (Undated manuscript).
- 19- "Semantical Analysis of Intuitionistic Logic III" (Undated manuscript).
- 1989. "No Fool's Red? Some Considerations on the Primary/Secondary Quality Distinction"(includes comments by David Velleman). University of Michigan, 1989.
- 1992. Whitehead Lectures: "Logicism, Wittgenstein, and De Re Beliefs about Natural Numbers". Delivered at Harvard University, 1992.
- 1992. "Individual Concepts: Their Logic, Philosophy, and Some of Their Uses". Transcribed by Stephen Webb.
- 1996.“The Ordered Pair: A Philosophical Paradigm Revisited”.
- 1996. "Elementary Recursion Theory and its Applications to Formal Systems." Transcribed by Mario Gomez Torrente and John Barker. Index available here.
- 1999. "The Road to Gödel". (Read at Haifa University, Israel, 1999. Several transcripts exist.
- 2006. "From Church's Thesis to the First Order Algorithm Theorem," Tel Aviv University, June 13, 2006. Video available here and abstract available here.
- 2007. "Roundtable on Externalism" (Hilary Putnam
Hilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...
, Tyler BurgeTyler Burge is a Professor of Philosophy at UCLA. He has made contributions to several areas of philosophy, including the philosophy of mind, epistemology, and the history of philosophy. In the history of philosophy, he has published articles on the philosophy of Gottlob Frege...
, Saul Kripke, and Michael DevittMichael Devitt is an Australian philosopher currently teaching at the City University of New York in New York City. His primary interests include philosophy of language, philosophy of mind, metaphysics and epistemology...
). University College Dublin, Ireland. Podcast available here.
- 2007. "The Collapse of the Hilbert Program". Indiana University, Presidential Lecture. Video available here.
- 2008. “Mathematical Incompleteness Results in Peano Arithmetic, a Revisionist View of the Early History”.
Interviews and articles
- "New Frontiers in American Philosophy" by Taylor Branch, New York Times Magazine, August 14, 1977.
- "Saul Kripke, Genius Logician." Interview by Andreas Saugstad, February 25, 2001.
- "Celebrating CUNY's Genius Philosopher" by Gary Shapiro, The New York Sun, January 27, 2006.
- "Philosopher, 65, Lectures Not About 'What Am I?' but 'What Is I?'" by Charles McGrath, The New York Times
The New York Times is an American daily newspaper founded and continuously published in New York City since 1851. The New York Times has won 106 Pulitzer Prizes, the most of any news organization...
, January 28, 2006.
- "The Best Five Books on the Philosophy of Language" by Scott Soames, October 15, 2010.
Further reading
- Taylor Branch (1977), "New Frontiers in American Philosophy: Saul Kripke". New York Times Magazine.
- Nathan Salmon (1981), Reference and Essence. ISBN 1591022150 ISBN 978-1591022152.
- Consuelo Preti (2002), On Kripke. Wadsworth. ISBN 0-534-58366-0.
- Scott Soames (2002), Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity. ISBN 0-19-514529-1.
- Christopher Hughes (2004), Kripke : Names, Necessity, and Identity. ISBN 0-19-824107-0.
- G.W. Fitch (2005), Saul Kripke. ISBN 0-7735-2885-7.
- Martin Kusch (2006), A sceptical Guide to Meaning and Rules. Defending Kripke's Wittgenstein. Acumben: Publishing Limited.
- Arif Ahmed (2007), Saul Kripke. New York, NY; London: Continuum. ISBN 0-8264-9262-2.
- Christopher Norris (2007), Fiction, Philosophy and Literary Theory: Will the Real Saul Kripke Please Stand Up? London: Continuum
External links
- CUNY Graduate Center Philosophy Department faculty page
- The Saul Kripke Center, at the CUNY Graduate Center
- Saul Kripke, Genius Logician A short, non-technical interview by Andreas Saugstad, February 25, 2001.
- The conference in honor of Kripke's sixty-fifth birthday 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.
- London Review of Books article by Jerry Fodor discussing Kripke's work
- Celebrating CUNY's Genius Philosopher, by Gary Shapiro, January 27, 2006, in The New York Sun.
- information from 'Philosophy Professor' website
- A New York Times article about his 65th birthday
- Roundtable on Kripke's critique of mind-body identity with Scott Soames as the main presenter May 26, 2010.