Saul Aaron Kripke (/sɔːl ˈkrɪpki/; born November 13, 1940) is an American philosopher and logician. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Since the 1960s, Kripke has been a central figure in a number of fields related to mathematical logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and set theory. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts. Kripke was the recipient of the 2001 Schock Prize in Logic and Philosophy.
Kripke has made influential and original contributions to logic, especially modal logic. His work has profoundly influenced analytic philosophy; his principal contribution is a semantics for modal logic involving possible worlds, now called Kripke semantics. Another of his most important contributions is his argument that necessity is a "metaphysical" notion that should be separated from the epistemic notion of a priori, and that there are necessary truths that are a posteriori truths, such as that water is H2O. He has also contributed an original reading of Wittgenstein, referred to as "Kripkenstein." A 1970 Princeton lecture series, published in book form in 1980 as Naming and Necessity, is considered one of the most important philosophical works of the twentieth century.
|Born||November 13, 1940|
|Education||Harvard University (B.A., 1962)|
|Awards||Rolf Schock Prizes in Logic and Philosophy (2001)|
CUNY Graduate Center
|Logic (particularly modal)|
Philosophy of language
Philosophy of mind
History of analytic philosophy
|Kripke–Platek set theory|
Work on theory of reference (causal theory of reference, causal-historical theory of reference, direct reference theory, criticism of the Frege–Russell view)
Rigid vs. flaccid designator
A posteriori necessity
The possibility of analytic a posteriori judgments
Semantic theory of truth (Kripke's theory)
Non-analytic, a posteriori necessary truths
Contingent a priori
Rule-following paradox (Kripkenstein)
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 and Netta, attended Dundee Grade School and Omaha Central High School. Kripke was labeled a prodigy, teaching himself Ancient Hebrew by the age of six, reading Shakespeare's complete works by nine, and mastering the works of Descartes and complex mathematical problems before finishing elementary school. He wrote his first completeness theorem in modal logic at 17, and had it published a year later. After graduating from high school in 1958, Kripke attended Harvard University and graduated summa cum laude in 1962 with a bachelor's degree in mathematics. During his sophomore year at Harvard, he taught a graduate-level logic course at nearby MIT. Upon graduation he received a Fulbright Fellowship, and in 1963 was appointed to the Society of Fellows. Kripke later said, "I wish I could have skipped college. I got to know some interesting people but I can't say I learned anything. I probably would have learned it all anyway just reading on my own."
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. 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 Schock Prize in Logic and Philosophy in 2001.
Kripke's contributions to philosophy include:
Two of Kripke's earlier works, A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic, the former written when he was a teenager, were on modal logic. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke. Kripke introduced the now-standard Kripke semantics (also known as relational semantics or frame semantics) for modal logics. Kripke semantics is a formal semantics for non-classical logic systems. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The discovery of Kripke semantics was a breakthrough in the making of non-classical logics, because the model theory of such logics was absent before Kripke.
A Kripke frame or modal frame is a pair , where W is a non-empty set, and R is a binary relation on W. Elements of W are called nodes or worlds, and R is known as the accessibility relation. Depending on the properties of the accessibility relation (transitivity, reflexivity, etc.), the corresponding frame is described, by extension, as being transitive, reflexive, etc.
We read as "w satisfies A", "A is satisfied in w", or "w forces A". The relation is called the satisfaction relation, evaluation, or forcing relation. The satisfaction relation is uniquely determined by its value on propositional variables.
A formula A is valid in:
We define Thm(C) to be the set of all formulas that are valid in C. Conversely, if X is a set of formulas, let Mod(X) be the class of all frames which validate every formula from X.
A modal logic (i.e., a set of formulas) L is sound with respect to a class of frames C, if L ⊆ Thm(C). L is complete with respect to C if L ⊇ Thm(C).
Semantics is useful for investigating a logic (i.e., a derivation system) only if the semantical entailment relation reflects its syntactical counterpart, the consequence relation (derivability). It is vital to know which modal logics are sound and complete with respect to a class of Kripke frames, and for them, to determine which class it is.
For any class C of Kripke frames, Thm(C) is a normal modal logic (in particular, theorems of the minimal normal modal logic, K, are valid in every Kripke model). However, the converse does not hold generally. There are Kripke incomplete normal modal logics, which is unproblematic, because most of the modal systems studied are complete of classes of frames described by simple conditions.
A normal modal logic L corresponds to a class of frames C, if C = Mod(L). In other words, C is the largest class of frames such that L is sound wrt C. It follows that L is Kripke complete if and only if it is complete of its corresponding class.
Consider the schema T : . T is valid in any reflexive frame : if , then since w R w. On the other hand, a frame which validates T has to be reflexive: fix w ∈ W, and define satisfaction of a propositional variable p as follows: if and only if w R u. Then , thus by T, which means w R w using the definition of . T corresponds to the class of reflexive Kripke frames.
It is often much easier to characterize the corresponding class of L than to prove its completeness, thus correspondence serves as a guide to completeness proofs. Correspondence is also used to show incompleteness of modal logics: suppose L1 ⊆ L2 are normal modal logics that correspond to the same class of frames, but L1 does not prove all theorems of L2. Then L1 is Kripke incomplete. For example, the schema generates an incomplete logic, as it corresponds to the same class of frames as GL (viz. transitive and converse well-founded frames), but does not prove the GL-tautology .
For any normal modal logic L, a Kripke model (called the canonical model) can be constructed, which validates precisely the theorems of L, by an adaptation of the standard technique of using maximal consistent sets as models. Canonical Kripke models play a role similar to the Lindenbaum–Tarski algebra construction in algebraic semantics.
A set of formulas is L-consistent if no contradiction can be derived from them using the axioms of L, and modus ponens. A maximal L-consistent set (an L-MCS for short) is an L-consistent set which has no proper L-consistent superset.
The canonical model of L is a Kripke model , where W is the set of all L-MCS, and the relations R and are as follows:
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
A union of canonical sets of formulas is itself canonical. It follows from the preceding discussion that any logic axiomatized by a canonical set of formulas is Kripke complete, and compact.
The axioms T, 4, D, B, 5, H, G (and thus any combination of them) are canonical. GL and Grz are not canonical, because they are not compact. The axiom M by itself is not canonical (Goldblatt, 1991), but the combined logic S4.1 (in fact, even K4.1) is canonical.
This is a powerful criterion: for example, all axioms listed above as canonical are (equivalent to) Sahlqvist formulas. A logic has the finite model property (FMP) if it is complete with respect to a class of finite frames. An application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable, provided it is decidable whether a given finite frame is a model of L. In particular, every finitely axiomatizable logic with FMP is decidable.
There are various methods for establishing FMP for a given logic. Refinements and extensions of the canonical model construction often work, using tools such as filtration or unravelling. As another possibility, completeness proofs based on cut-free sequent calculi usually produce finite models directly.
Most of the modal systems used in practice (including all listed above) have FMP.
In some cases, we can use FMP to prove Kripke completeness of a logic: every normal modal logic is complete wrt a class of modal algebras, and a finite modal algebra can be transformed into a Kripke frame. As an example, Robert Bull proved using this method that every normal extension of S4.3 has FMP, and is Kripke complete.
Kripke semantics has a straightforward generalization to logics with more than one modality. A Kripke frame for a language with as the set of its necessity operators consists of a non-empty set W equipped with binary relations Ri for each i ∈ I. The definition of a satisfaction relation is modified as follows:
A simplified semantics, discovered by Tim Carlson, is often used for polymodal provability logics. A Carlson model is a structure with a single accessibility relation R, and subsets Di ⊆ W for each modality. Satisfaction is defined as:
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.
Kripke semantics for intuitionistic logic follows the same principles as the semantics of modal logic, but uses a different definition of satisfaction.
An intuitionistic Kripke model is a triple , where is a partially ordered Kripke frame, and satisfies the following conditions:
Intuitionistic logic is sound and complete with respect to its Kripke semantics, and it has the Finite Model Property.
Intuitionistic first-order logic
Let L be a first-order language. A Kripke model of L is a triple , where is an intuitionistic Kripke frame, Mw is a (classical) L-structure for each node w ∈ W, and the following compatibility conditions hold whenever u ≤ v:
Given an evaluation e of variables by elements of Mw, we define the satisfaction relation :
Here e(x→a) is the evaluation which gives x the value a, and otherwise agrees with e.
The three lectures that form Naming and Necessity constitute an attack on descriptivist theory of names. Kripke attributes variants of descriptivist theories to Frege, Russell, Wittgenstein and John Searle, among others. According to descriptivist theories, proper names either are synonymous with descriptions, or have their reference determined by virtue of the name's being associated with a description or cluster of descriptions that an object uniquely satisfies. Kripke rejects both these kinds of descriptivism. He gives several examples purporting to render descriptivism implausible as a theory of how names get their references determined (e.g., surely Aristotle could have died at age two and so not satisfied any of the descriptions we associate with his name, but it would seem wrong to deny that he was still Aristotle).
As an alternative, Kripke outlined a causal theory of reference, according to which a name refers to an object by virtue of a causal connection with the object as mediated through communities of speakers. He points out that proper names, in contrast to most descriptions, are rigid designators: that is, a proper name refers to the named object in every possible world in which the object exists, while most descriptions designate different objects in different possible worlds. For example, "Richard Nixon" refers to the same person in every possible world in which Nixon exists, while "the person who won the United States presidential election of 1968" could refer to Nixon, Humphrey, or others in different possible worlds.
Kripke also raised the prospect of a posteriori necessities — facts that are necessarily true, though they can be known only through empirical investigation. Examples include "Hesperus is Phosphorus", "Cicero is Tully", "Water is H2O" and other identity claims where two names refer to the same object.
Finally, Kripke gave an argument against identity materialism in the philosophy of mind, the view that every mental particular is identical with some physical particular. Kripke argued that the only way to defend this identity is as an a posteriori necessary identity, but that such an identity — e.g., that pain is C-fibers firing — could not be necessary, given the (clearly conceivable) possibility that pain could be separate from the firing of C-fibers, or the firing of C-fibers be separate from pain. (Similar arguments have since been made by David Chalmers.) In any event, the psychophysical identity theorist, according to Kripke, incurs a dialectical obligation to explain the apparent logical possibility of these circumstances, since according to such theorists they should be impossible.
Kripke delivered the John Locke Lectures in philosophy at Oxford in 1973. Titled Reference and Existence, they are in many respects a continuation of Naming and Necessity, and deal with the subjects of fictional names and perceptual error. They were recently published by Oxford University Press.
In a 1995 paper, philosopher Quentin Smith argued that key concepts in Kripke's new theory of reference originated in the work of Ruth Barcan Marcus more than a decade earlier. 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.
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" Kripke seems to oppose even this possibility. His argument can be reconstructed as follows: The idea that two names referring to the same object may have different semantic properties is supposed to explain that coreferring names behave differently in propositions about beliefs (as in Lois Lane's case). But the same phenomenon occurs even with coreferring names that obviously have the same semantic properties: Kripke invites us to imagine a French, monolingual boy, Pierre, who believes that "Londres est joli" ("London is beautiful"). Pierre moves to London without realizing that London = Londres. He then learns English the same way a child would learn the language, that is, not by translating words from French to English. Pierre learns the name "London" from the unattractive part of the city where he lives, and so comes to believe that London is not beautiful. If Kripke's account is correct, Pierre now believes both that Londres is joli and that London is not beautiful. This cannot be explained by coreferring names having different semantic properties. According to Kripke, this demonstrates that attributing additional semantic properties to names does not explain what it is intended to.
First published in 1982, Kripke's Wittgenstein on Rules and Private Language contends that the central argument of Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date", and that Wittgenstein does not reject the argument that leads to the rule-following paradox, but accepts it and offers a "skeptical solution" to ameliorate the paradox's destructive effects.
Most commentators accept that Philosophical Investigations contains the rule-following paradox as Kripke presents it, but few have agreed with his attributing a skeptical solution to Wittgenstein. Kripke himself expresses doubts in Wittgenstein on Rules and Private Language as to whether Wittgenstein would endorse his interpretation of Philosophical Investigations. He says that the work should not be read as an attempt to give an accurate statement of Wittgenstein's views, but rather as an account of Wittgenstein's argument "as it struck Kripke, as it presented a problem for him".
The portmanteau "Kripkenstein" has been coined for Kripke's interpretation of Philosophical Investigations. Kripkenstein's main significance was a clear statement of a new kind of skepticism, dubbed "meaning skepticism": the idea that for an isolated individual there is no fact in virtue of which he/she means one thing rather than another by the use of a word. Kripke's "skeptical solution" to meaning skepticism is to ground meaning in the behavior of a community.
Kripke's book generated a large secondary literature, divided between those who find his skeptical problem interesting and perceptive, and others, such as Gordon Baker and Peter Hacker, who argue that his meaning skepticism is a pseudo-problem that stems from a confused, selective reading of Wittgenstein. Kripke's position has been defended against these and other attacks by the Cambridge philosopher Martin Kusch, and Wittgenstein scholar David G. Stern considers Kripke's book "the most influential and widely discussed" work on Wittgenstein since the 1980s.
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 Gödel that self-reference cannot be avoided naively, since propositions about seemingly unrelated objects (such as integers) can have an informal self-referential meaning, and this idea – manifested by the diagonal lemma – is the basis for Tarski's theorem that truth cannot be consistently defined. It has thus been claimed that Kripke's suggestion does lead to contradiction: while its truth predicate is only partial, it does give truth value (true/false) to propositions such as the one built in Tarski's proof, and is therefore inconsistent. There is still a debate about whether Tarski's proof can be implemented to every variation of such a partial truth system, but none has been shown to be consistent by acceptable proving methods used in mathematical logic.
Kripke's proposal is also problematic in the sense that while the language contains a "truth" predicate of itself (at least a partial one), some of its sentences – such as the liar sentence ("this sentence is false") – have an undefined truth value, but the language does not contain its own "undefined" predicate. In fact it cannot, as that would create a new version of the liar paradox, called the strengthened liar paradox ("this sentence is false or undefined"). Thus while the liar sentence is undefined in the language, the language cannot express that it is undefined.
Kripke is an observant Jew. On how his religious views influenced his philosophical views, he has said: "I don't have the prejudices many have today. I don't believe in a naturalist worldview. I don't base my thinking on prejudices or a worldview and do not believe in materialism."
The Saul Kripke Center at the Graduate Center of the City University of New York is dedicated to preserving and promoting Kripke's work. Its director is Gary Ostertag. The SKC holds events related to Kripke's work and is creating a digital archive of previously unpublished recordings of Kripke's lectures, lecture notes, and correspondence dating back to the 1950s. 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."
A posteriori necessity is a thesis in metaphysics and the philosophy of language, that some statements of which we must acquire knowledge a posteriori are also necessarily true. It challenges previously widespread belief that only a priori knowledge can be necessary. It draws on a number of philosophical concepts such as necessity, the causal theory of reference, rigidity, and the a priori a posteriori distinction.
It was first introduced by philosopher Saul Kripke in his 1970 series of lectures at Princeton University. The transcript of these lectures was then compiled and assembled into his seminal book, Naming and Necessity.Causal theory of reference
A causal theory of reference is a theory of how terms acquire specific referents based on evidence. Such theories have been used to describe many referring terms, particularly logical terms, proper names, and natural kind terms. In the case of names, for example, a causal theory of reference typically involves the following claims:
a name's referent is fixed by an original act of naming (also called a "dubbing" or, by Saul Kripke, an "initial baptism"), whereupon the name becomes a rigid designator of that object.
later uses of the name succeed in referring to the referent by being linked to that original act via a causal chain.Weaker versions of the position (perhaps not properly called "causal theories"), claim merely that, in many cases, events in the causal history of a speaker's use of the term, including when the term was first acquired, must be considered to correctly assign references to the speaker's words.
Causal theories of names became popular during the 1970s, under the influence of work by Saul Kripke and Keith Donnellan. Kripke and Hilary Putnam also defended an analogous causal account of natural kind terms.Descriptivist theory of names
In the philosophy of language, the descriptivist theory of proper names (also descriptivist theory of reference) is the view that the meaning or semantic content of a proper name is identical to the descriptions associated with it by speakers, while their referents are determined to be the objects that satisfy these descriptions. Bertrand Russell and Gottlob Frege have both been associated with the descriptivist theory, which is sometimes called the Frege–Russell view.In the 1970s, this theory came under attack from causal theorists such as Saul Kripke, Hilary Putnam and others. However, it has seen something of a revival in recent years, especially under the form of what are called two-dimensional semantic theories. This latter trend is exemplified by the theories of David Chalmers, among others.Direct reference theory
A direct reference theory (also called referentialism or referential realism) is a theory of language that claims that the meaning of a word or expression lies in what it points out in the world. The object denoted by a word is called its referent. Criticisms of this position are often associated with Ludwig Wittgenstein.In the 19th century, mathematician and philosopher Gottlob Frege argued against it, and contrasted it with mediated reference theory. In 1953, with his Philosophical Investigations, Wittgenstein argued against referentialism, famously saying that "the meaning of a word is its use." Direct reference theory is a position typically associated with logical positivism and analytical philosophy. Logical positivist philosophers in particular have significantly devoted their efforts in countering positions of the like of Wittgenstein's, and they aim at creating a "perfectly descriptive language" purified from ambiguities and confusions.Index of philosophy of language articles
This is an index of articles in philosophy of language
Alfred Jules Ayer
Alphabet of human thought
Applicative Universal Grammar
Archie J. Bahm
Association for Logic, Language and Information
Bob Hale (philosopher)
Carl Gustav Hempel
Causal theory of reference
César Chesneau Dumarsais
Cheung Kam Ching
Concept and object
Contrast theory of meaning
David Kellogg Lewis
De dicto and de re
Descriptivist theory of names
Direct reference theory
Direction of fit
Donald Davidson (philosopher)
Ethics and Language
European Summer School in Logic, Language and Information
F. H. Bradley
Failure to refer
Form of life (philosophy)
Function and Concept
G. E. M. Anscombe
Gareth Evans (philosopher)
Gordon Park Baker
Ideal speech situation
Indeterminacy of translation
Inferential role semantics
Internalism and externalism
J. L. Austin
James F. Conant
Jonathan Bennett (philosopher)
Journal of Logic, Language and Information
Language and thought
Language of thought
Language, Truth, and Logic
Linguistics and Philosophy
List of philosophers of language
Meaning (philosophy of language)
Mediated reference theory
Metaphor in philosophy
Modularity of mind
Mumbo Jumbo (phrase)
Naming and Necessity
Ordinary language philosophy
P. F. Strawson
Philosophical interpretation of classical physics
Philosophy and literature
Philosophy of language
Principle of charity
Principle of compositionality
Private language argument
Proper name (philosophy)
Redundancy theory of truth
Rhetoric of social intervention model
Richard von Mises
Robert Maximilian de Gaynesford
Round square copula
S. Morris Engel
Sense and reference
Sense and Sensibilia (Austin)
The Naturalization of Intentionality
Theory of descriptions
Two Dogmas of Empiricism
Willard Van Orman Quine
William C. Dowling
Wittgenstein on Rules and Private Language
Word and Object
Kripke is a surname. Notable people with the surname include:
Dorothy K. Kripke (1912–2000), American author of Jewish educational books, and the mother of Saul Kripke
Eric Kripke (born 1974), American television writer, director, and producer
Margaret L. Kripke, professor of immunology
Myer S. Kripke (1914–2014), American rabbi based in Omaha, Nebraska, and the husband of Dorothy K. Kripke
Saul Kripke (born 1940), American philosopher and logicianFictional characters:
Barry Kripke, a character in the sitcom The Big Bang TheoryKripke–Platek set theory
The Kripke–Platek axioms of set theory (KP), pronounced , are a system of axiomatic set theory developed by Saul Kripke and Richard Platek.
KP is considerably weaker than Zermelo–Fraenkel set theory (ZFC), and can be thought of as roughly the predicative part of ZFC. The consistency strength of KP with an axiom of infinity is given by the Bachmann–Howard ordinal. Unlike ZFC, KP does not include the power set axiom, and KP includes only limited forms of the axiom of separation and axiom of replacement from ZFC. These restrictions on the axioms of KP lead to close connections between KP, generalized recursion theory, and the theory of admissible ordinals.List of philosophers of language
This is a list of philosophers of language.
G. E. M. Anscombe
Saint Thomas Aquinas, OP
J. L. Austin
Alfred Jules Ayer
Archie J. Bahm
F. H. Bradley
Cardinal Thomas Cajetan, OP
Cheung Kam Ching
James F. Conant
William C. Dowling
César Chesneau Dumarsais
S. Morris Engel
Robert Maximilian de Gaynesford
Wilhelm von Humboldt
Carrie Ichikawa Jenkins
David Kellogg Lewis
Ruth Barcan Marcus
John Stuart Mill
Charles W. Morris
William of Ockham
Jesús Padilla Gálvez
Charles Sanders Peirce
Willard Van Orman Quine
Bertrand Russell's views on philosophy
John of St. Thomas, OP (John Poinsot)
P. F. Strawson
Kenneth Allen Taylor
Georg Henrik von Wright
Edward N. Zalta
Dean ZimmermanLogical possibility
Logically possible refers to a proposition which can be the logical consequence of another, based on the axioms of a given system of logic. The logical possibility of a proposition will depend on the system of logic being considered, rather than on the violation of any single rule. Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions. Other logical systems have more than two truth-values instead of a binary of such values. However, when talking about logical possibility it is often assumed that the system in question is classical propositional logic. Similarly, the criterion for logical possibility is often based on whether or not a proposition is contradictory and as such is often thought of as the broadest type of possibility.
Logical possibility should be distinguished from other sorts of subjunctive possibilities. But the relationship between modalities (if there is any) is the subject of debate and may depend on how one views logic, as well as the relationship between logic and metaphysics. For example, many philosophers following Saul Kripke have held that discovered identities such as "Hesperus = Phosphorus" are metaphysically necessary because they pick out the same object in all possible worlds where the terms have a referent. However, it is nonetheless logically possible for “Hesperus = Phosphorus” to be false, since denying it doesn't violate a logical rule such as consistency. Other philosophers are of the view that logical possibility is broader than metaphysical possibility, so that anything which is metaphysically possible is also logically possible.Martian scientist
A Martian scientist or Martian researcher is a hypothetical Martian frequently used in thought experiments as an outside observer of conditions on Earth. The most common variety is the Martian anthropologist, but Martians researching subjects such as philosophy, linguistics and biology have also been invoked.
The following extract from an essay by Richard Dawkins is more or less typical.
A Martian taxonomist who didn't know that all human races happily interbreed with one another, and didn't know that most of the underlying genetic variance in our species is shared by all races might be tempted by our regional differences in skin colour, facial features, hair, body size and proportions to split us into more than one species.In American structuralist linguistics, the Martian approach is recommended for language description:
The descriptive analyst must be guided by certain very fixed principles if he is to be objective in describing accurately any language or part of any language. It would be excellent if he could adopt a completely man-from-Mars attitude toward any language he analyzes and describes.The hypothetical Martian anthropologist is described in the writings of Noam Chomsky as one who, upon studying the world's languages, would conclude that they are all dialects of a single language embodying a "universal grammar" reflecting a hardwired, genetically determined linguistic module inherent in the human brain.
In philosophy, especially philosophy of language and philosophy of mind, the Martian is often invoked as an example of an intelligent being with a cognitive apparatus that differs from that of humans, e.g. the following example given by Saul Kripke:
I will not here argue that simplicity is relative, or that it is hard to define, or that a Martian might find the quus function simpler than the plus function.In a common rhetorical turn, invoking the Martian scientist forces the reader to observe an obvious state of affairs that is ordinarily overlooked:
If a Martian graced our planet, it would be struck by one remarkable similarity among Earth's living creatures and a key difference.(NB: The similarity Chomsky et al. mean is the universal hereditary language of DNA, while the difference is the lack of a universal language of communication.)Mediated reference theory
A mediated reference theory (also indirect reference theory) is any semantic theory that posits that words refer to something in the external world, but insists that there is more to the meaning of a name than simply the object to which it refers. It thus stands opposed to the theory of direct reference. Gottlob Frege is a well-known advocate of mediated reference theories. Similar theories were widely held in the middle of the twentieth century by philosophers such as Peter Strawson and John Searle.
Mediated reference theories are contrasted with theories of direct reference.
Saul Kripke, a proponent of direct reference theory, in his Naming and Necessity dubbed mediated reference theory the Frege–Russell view and criticized it. Subsequent scholarship refuted the claim that Bertrand Russell's views on reference theory were the same as Frege's, since Russell was also a proponent of direct reference theory.Naming and Necessity
Naming and Necessity is a 1980 book with the transcript of three lectures, given by the philosopher Saul Kripke, at Princeton University in 1970, in which he dealt with the debates of proper names in the philosophy of language. The transcript was brought out originally in 1972 in Semantics of Natural Language, edited by Donald Davidson and Gilbert Harman. Among analytic philosophers, Naming and Necessity is widely considered one of the most important philosophical works of the twentieth century.Non-rigid designator
In the philosophy of language and modal logic, a term is said to be a non-rigid designator (or flaccid designator) or connotative term if it does not extensionally designate (denote, refer to) the same object in all possible worlds. This is in contrast to a rigid designator, which does designate the same object in all possible worlds in which that object exists, and does not designate anything else in those worlds in which that object does not exist. The term was coined by Saul Kripke in his 1970 lecture series at Princeton University, later published as the book Naming and Necessity.Property dualism
Property dualism describes a category of positions in the philosophy of mind which hold that, although the world is composed of just one kind of substance—the physical kind—there exist two distinct kinds of properties: physical properties and mental properties. In other words, it is the view that non-physical, mental properties (such as beliefs, desires and emotions) inhere in or supervene upon certain physical substances (namely brains). As a doctrine, 'property dualism' is epistemic, as distinct from ontic.
Substance dualism, on the other hand, is the view that there exist in the universe two fundamentally different kinds of substance: physical (matter) and non-physical (mind or consciousness), and subsequently also two kinds of properties which adhere in those respective substances. Substance dualism is thus more susceptible to the mind-body problem. Both substance and property dualism are opposed to reductive physicalism. As a doctrine, 'substance dualism' is ontic, as distinct from epistemic.Scientific essentialism
Scientific essentialism, a view espoused by Saul Kripke and Hilary Putnam, maintains that there exist essential properties that objects possess (or instantiate) necessarily. In other words, having such and such essential properties is a necessary condition for membership in a given natural kind. For example, tigers are tigers in virtue of possessing a particular set of genetic properties, but identifying (or appearance-based) properties are nonessential properties. If a tiger lost a leg, or didn't possess stripes, we would still call it a tiger. They are not necessary for being a member of the class of tigers.
It is important, however, that the set of essential properties of an object not be used to identify or be identified with that object because they are not necessary and sufficient, but only necessary. Having such and such a genetic code does not suffice for being a tiger. We wouldn't call a piece of tiger tail a tiger, even though a piece of tiger tail contains the genetic information essential to being a tiger.
Other advocates of scientific essentialism include Brian Ellis, Caroline Lierse, John Bigelow, and Alexander Bird.Scott Soames
Scott Soames (; born August 11, 1946) is an American philosopher. He is a professor of philosophy at the University of Southern California. He specializes in the philosophy of language and the history of analytic philosophy. He is well known for defending and expanding on the program in the philosophy of language started by Saul Kripke as well as being a major critic of two-dimensionalist theories of meaning.The Ashtray (Or the Man Who Denied Reality)
The Ashtray (Or the Man Who Denied Reality) is a book by Errol Morris in which he criticizes the philosophy of Thomas Kuhn. In the book, Morris argues that Kuhn was a relativist and a philosophical idealist, contrasting his interpretation of Kuhn's views with his own epistemology, drawing on Hilary Putnam and Saul Kripke, which he describes as "investigative realism", based on the belief that there is an objective reality whilst rejecting naïve realism. Morris accepts that investigation of truth involves considerable effort, with no guarantee of reaching the absolute truth, and that knowledge can be attained "through reason, through observation, through investigation, through thought, through science".In a piece for the Los Angeles Review of Books, Philip Kitcher compared Morris' critique to Samuel Johnson's appeal to the stone regarding George Berkeley's belief in subjective idealism, stating that "Morris has no interest in considering what Kuhn might have had in mind", and rejecting his characterisation of Kuhn as a relativist and an irrealist.Theory of descriptions
The theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's theory of descriptions (commonly abbreviated as RTD). In short, Russell argued that the syntactic form of descriptions (phrases that took the form of "The aardvark" and "An aardvark") is misleading, as it does not correlate their logical and/or semantic architecture. While descriptions may seem fairly uncontroversial phrases, Russell argued that providing a satisfactory analysis of the linguistic and logical properties of a description is vital to clarity in important philosophical debates, particularly in semantic arguments, epistemology and metaphysics.
Since the first development of the theory in Russell's 1905 paper "On Denoting", RTD has been hugely influential and well-received within the philosophy of language. However, it has not been without its critics. In particular, the philosophers P. F. Strawson and Keith Donnellan have given notable, well known criticisms of the theory. Most recently, RTD has been defended by various philosophers and even developed in promising ways to bring it into harmony with generative grammar in Noam Chomsky's sense, particularly by Stephen Neale. Such developments have themselves been criticised, and debate continues.
Russell viewed his theory of descriptions as a kind of analysis that is now called logical analysis or propositional analysis (not to be confused with propositional calculus).Wittgenstein on Rules and Private Language
Wittgenstein on Rules and Private Language is a 1982 book by philosopher of language Saul Kripke, in which the author contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date" (p. 60). He argues that Wittgenstein does not reject the argument that leads to the rule-following paradox, but accepts it and offers a "skeptical solution" to alleviate the paradox's destructive effects.
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