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Definite Description
In formal semantics and philosophy of language, a definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is ''proper'' if X applies to a unique individual or object. For example: " the first person in space" and " the 42nd President of the United States of America", are proper. The definite descriptions "the person in space" and "the Senator from Ohio" are ''improper'' because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from some Country" are ''improper'' because X applies to nothing. Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content. Russell's analysis As France is currently a republic, it has no king. Bertrand Russell pointed out that this raises a puzzle about the truth value of the sentence "The present King of France is bald." The sen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Semantics (natural Language)
Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse-engineering the semantic components of natural languages' grammars. Overview Formal semantics studies the denotations of natural language expressions. High-level concerns include compositionality, reference, and the nature of meaning. Key topic areas include scope, modality, binding, tense, and aspect. Semantics is distinct from pragmatics, which encompasses aspects of meaning which arise from interaction and communicative intent. Formal semantics is an interdisciplinary field, often viewed as a subfield of both linguistics and ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 metaphysical elements. 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 K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the development of modern logic in the ''Begriffsschrift'' and work in the foundations of mathematics. His book the ''Foundations of Arithmetic'' is the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syncategorematic
In logic and linguistics, an expression is syncategorematic if it lacks a denotation but can nonetheless affect the denotation of a larger expression which contains it. Syncategorematic expressions are contrasted with categorematic expressions, which have their own denotations. For example, consider the following rules for interpreting the plus sign. The first rule is syncategorematic since it gives an interpretation for expressions containing the plus sign but does not give an interpretation for the plus sign itself. On the other hand, the second rule does give an interpretation for the plus sign itself, so it is categorematic. # ''Syncategorematic'': For any numeral symbols "n" and "m", the expression "n + m" denotes the sum of the numbers denoted by "n" and "m". # ''Categorematic'': The plus sign "+" denotes the operation of addition. Syncategorematicity was a topic of research in medieval philosophy since syncategorematic expressions cannot stand for any of Aristotle's categ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Application
In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. In this sense, function application can be thought of as the opposite of function abstraction. Representation Function application is usually depicted by juxtaposing the variable representing the function with its argument encompassed in parentheses. For example, the following expression represents the application of the function ''ƒ'' to its argument ''x''. :f(x) In some instances, a different notation is used where the parentheses aren't required, and function application can be expressed just by juxtaposition. For example, the following expression can be considered the same as the previous one: :f\; x The latter notation is especially useful in combination with the currying isomorphism. Given a function f : (X \times Y) \to Z, its application is represented as f(x, y) by the former notation and f\;(x,y) (or f \; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (mathematical Logic)
In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicate which applies to the individual constants a and b. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation used to interpret them. While first-order logic only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates. Predicates in different systems * In propositional logic, atomic formulas are sometimes regarded as zero-place predicates In a sense, these are nullar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q'', there could be other scenarios where ''P'' is true and ''Q'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Property
Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, redefine, rent, mortgage, pawn, sell, exchange, transfer, give away or destroy it, or to exclude others from doing these things, as well as to perhaps abandon it; whereas regardless of the nature of the property, the owner thereof has the right to properly use it under the granted property rights. In economics and political economy, there are three broad forms of property: private property, public property, and collective property (also called cooperative property). Property that jointly belongs to more than one party may be possessed or controlled thereby in very similar or very distinct ways, whether simply or complexly, whether equally or unequally. However, there is an expectation that each party's will (rather discretion) with rega ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambda Calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing § lambda terms and performing § reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Quantifier
In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases. For example, the generalized quantifier ''every boy'' denotes the set of sets of which every boy is a member: \ This treatment of quantifiers has been essential in achieving a compositional semantics for sentences containing quantifiers. Type theory A version of type theory is often used to make the semantics of different kinds of expressions explicit. The standard construction defines the set of types recursively as follows: #''e'' and ''t'' are types. #If ''a'' and ''b'' are both types, then so is \langle a,b\rangle #Nothing is a type, except what can be constructed on the basis of lines 1 and 2 above. Given this definition, we have the simple types ''e'' and ''t'', but also a countable infinity of complex types, some of which include: \langle e,t\rangle;\qquad \langle t,t\rangle;\qquad \langle\langle e,t\rangle, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Neale
Stephen Roy Albert Neale (born 9 January 1958) is a British philosopher and specialist in the philosophy of language who has written extensively about meaning, information, interpretation, and communication, and more generally about issues at the intersection of philosophy and linguistics. Neale is a Distinguished Professor of Philosophy and Linguistics and holder of the John H. Kornblith Family Chair in the Philosophy of Science and Values at the Graduate Center, City University of New York (CUNY). Education and career Neale completed his BA in linguistics at University College London working with linguist Deirdre Wilson. He completed his PhD in Philosophy at Stanford University with philosopher John Perry as his dissertation advisor. Prior to joining the CUNY faculty, Neale held positions at Princeton University, University of California, Berkeley, and Rutgers University. Neale's doctoral students include Pierre Baumann (University of Puerto Rico), Herman Cappelen ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Excluded Middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradiction, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law (or principle) of the excluded third, in Latin ''principium tertii exclusi''. Another Latin designation for this law is ''tertium non datur'': "no third ossibilityis given". It is a tautology. The principle should not be confused with the semantical principle of bivalence, which states that every proposition is either true or false. The principle of bivalence always implies the law of excluded middle, while the converse is not always true. A commonly cited counterexample uses statements unprovable now, but provable in the future ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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