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Saul Kripke
Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was 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, modal logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and recursion theory. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts. Kripke made influential and original contributions to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now called Kripke semantics. He received the 2001 Schock Prize in Logic and Philosophy. Kripke was also partly responsible for the revival of metaphysics after the decline of logical positivism, claiming necessity i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Philosophy
Western philosophy encompasses the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" grc, φιλεῖν , "to love" and σοφία '' sophía'', "wisdom"). History Ancient The scope of ancient Western philosophy included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics). Pre-Socratics The pre-Socratic philosophers were interested in cosmology; the nature and origin of the universe, while rejecting mythical answers to such questions. They were specifically interested in the (the cause or first principle) of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kripke–Platek Set Theory
The Kripke–Platek set theory (KP), pronounced , is an axiomatic set theory developed by Saul Kripke and Richard Platek. The theory can be thought of as roughly the predicative part of ZFC and is considerably weaker than it. Axioms In its formulation, a Δ0 formula is one all of whose quantifiers are bounded. This means any quantification is the form \forall u \in v or \exist u \in v. (See the Lévy hierarchy.) * Axiom of extensionality: Two sets are the same if and only if they have the same elements. * Axiom of induction: φ(''a'') being a formula, if for all sets ''x'' the assumption that φ(''y'') holds for all elements ''y'' of ''x'' entails that φ(''x'') holds, then φ(''x'') holds for all sets ''x''. * Axiom of empty set: There exists a set with no members, called the empty set and denoted . * Axiom of pairing: If ''x'', ''y'' are sets, then so is , a set containing ''x'' and ''y'' as its only elements. * Axiom of union: For any set ''x'', there is a set ''y'' such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kripke's Theory Of Truth
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. Origin The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying Convention T for the sentences of a given language cannot be defined ''within'' that language. Tarski's theory of truth To formulate linguistic theories without semantic paradoxes such as the liar paradox, it is generally necessary to distinguish the language that one is talking abou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantic Theory Of Truth
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. Origin The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying Convention T for the sentences of a given language cannot be defined ''within'' that language. Tarski's theory of truth To formulate linguistic theories without semantic paradoxes such as the liar paradox, it is generally necessary to distinguish the language that one is talking a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic–synthetic Distinction
The analytic–synthetic distinction is a semantic distinction, used primarily in philosophy to distinguish between propositions (in particular, statements that are affirmative subject–predicate judgments) that are of two types: analytic propositions and synthetic propositions. Analytic propositions are true or not true solely by virtue of their meaning, whereas synthetic propositions' truth, if any, derives from how their meaning relates to the world. While the distinction was first proposed by Immanuel Kant, it was revised considerably over time, and different philosophers have used the terms in very different ways. Furthermore, some philosophers (starting with W.V.O. Quine) have questioned whether there is even a clear distinction to be made between propositions which are analytically true and propositions which are synthetically true. Debates regarding the nature and usefulness of the distinction continue to this day in contemporary philosophy of language. Kant Conceptual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Posteriori Necessity
''A posteriori'' necessity is a thesis in metaphysics and the philosophy of language, that some statements of which we must acquire knowledge a posteriori are also necessarily true. It challenges previously widespread belief that only ''a priori'' knowledge can be necessary. It draws on a number of philosophical concepts such as necessity, the causal theory of reference, rigidity, and the a priori a posteriori distinction. It was first introduced by philosopher Saul Kripke in his 1970 series of lectures at Princeton University. The transcript of these lectures was then compiled and assembled into his seminal book, ''Naming and Necessity''. Main argument for a posteriori necessity Here is an overview of the argument: :(P1) 'Hesperus' is a proper name that refers to the evening star. 'Phosphorus' is also a proper name and it refers to the morning star. But the evening star and the morning star are the same planetary body (Venus). So both names designate Venus. :(P2) If both ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flaccid 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''. Examples As an example, consider the phrase "The 43rd President of the United States of America": while the 43rd President of the United States is ''actually'' George W. Bush, things might have been different. Bush might have lost the election, meaning that the 43rd President might have been Al Gore or Ralph Nader instead. (''How remote'' these possible worlds are from the actual world is a disc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Designator
In modal logic and the philosophy of language, a term is said to be a rigid designator or absolute substantial term when it designates (picks out, denotes, refers to) the same thing in ''all possible worlds'' in which that thing exists. A designator is ''persistently rigid'' if it also designates nothing in all other possible worlds. A designator is ''obstinately rigid'' if it designates the same thing in every possible world, period, whether or not that thing exists in that world. Rigid designators are contrasted with ''connotative terms'', ''non-rigid'' or ''flaccid designators'', which may designate different things in different possible worlds. History The Scholastic philosophers in the Middle Ages developed a theory of properties of terms in which different classifications of concepts feature prominently. Concepts, and the terms that signify them, can be divided into absolute or connotative, according to the mode in which they signify. If they signify something absolutely, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kripke Structure
: ''This article describes Kripke structures as used in model checking. For a more general description, see Kripke semantics''. A Kripke structure is a variation of the transition system, originally proposed by Saul Kripke, used in model checking to represent the behavior of a system. It consists of a graph whose nodes represent the reachable states of the system and whose edges represent state transitions, together with a labelling function which maps each node to a set of properties that hold in the corresponding state. Temporal logics are traditionally interpreted in terms of Kripke structures. Formal definition Let be a set of ''atomic propositions'', i.e. boolean expressions over variables, constants and predicate symbols. Clarke et al. define a Kripke structure over as a 4-tuple consisting of * a finite set of states . * a set of initial states . * a transition relation such that is left-total, i.e., such that . * a labeling (or ''interpretation'') function . Since i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Admissible Ordinal
In set theory, an ordinal number ''α'' is an admissible ordinal if L''α'' is an admissible set (that is, a transitive model of Kripke–Platek set theory); in other words, ''α'' is admissible when ''α'' is a limit ordinal and L''α'' ⊧ Σ0-collection.. See in particulap. 265. The term was coined by Richard Platek in 1966. The first two admissible ordinals are ω and \omega_1^ (the least non-recursive ordinal, also called the Church–Kleene ordinal). Any regular uncountable cardinal is an admissible ordinal. By a theorem of Sacks, the countable admissible ordinals are exactly those constructed in a manner similar to the Church–Kleene ordinal, but for Turing machines with oracles. One sometimes writes \omega_\alpha^ for the \alpha-th ordinal that is either admissible or a limit of admissibles; an ordinal that is both is called ''recursively inaccessible''. There exists a theory of large ordinals in this manner that is highly parallel to that of (small) large c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frege–Russell View
A mediated reference theory (also indirect reference theory)Leszek Berezowski, ''Articles and Proper Names'', University of Wrocław, 2001, p. 67. 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 direct reference theory. 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. 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.Howard Wettstein, "Frege-Russell Semantics?", ''Dialectica'' 44(1/2), 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Reference Theory
A direct reference theory (also called referentialism or referential realism)Andrea Bianchi (2012) ''Two ways of being a (direct) referentialist'', in Joseph Almog, Paolo Leonardi, ''Having in Mind: The Philosophy of Keith Donnellan''p. 79/ref> 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.Severin Schroeder (2006), ''Wittgenstein''p. 30 "This view that the meaning of a word has to be explained in terms of what it stands for, its reference, I shall call referentialism." In the 19th century, mathematician and philosopher Gottlob Frege argued against it, and contrasted it with mediated reference theory.Emery J. Hyslop-Margison, Ayaz Naseem (2007), ''Scientism and Education: Empirical Research as Neo-Liberal Ideology''pp. 83–4/ref> In 1953, with his ''Philosophical Investigations'', Wittge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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