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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 tal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Truth
Truth or verity is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth, 2005 In everyday language, it is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences. True statements are usually held to be the opposite of false statements. The concept of truth is discussed and debated in various contexts, including philosophy, art, theology, law, and science. Most human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion, including journalism and everyday life. Some philosophers view the concept of truth as basic, and unable to be explained in any terms that are more easily understood than the concept of truth itself. Most commonly, truth is viewed as the correspondence of language or thought to a mind-independent world. This is called the correspondence theory of truth. Various theorie ... [...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" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, 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' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assignment (mathematical Logic)
In logic and model theory, a valuation can be: *In propositional logic, an assignment of truth values to propositional variables, with a corresponding assignment of truth values to all propositional formulas with those variables. *In first-order logic and higher-order logics, a structure, (the interpretation) and the corresponding assignment of a truth value to each sentence in the language for that structure (the valuation proper). The interpretation must be a homomorphism, while valuation is simply a function. Mathematical logic In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema. Valuations are also called truth assignments. In propositional logic, there are no quantifiers, and formulas are built from propositional variables using logical connectives. In this context, a valuation begins with an assignment of a truth value to each propositional variable. This assignment can be uniquely e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Sentence
In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. For example, "The dog ran" is atomic whereas "The dog ran and the cat hid" is molecular in natural language. From a logical analysis point of view, the truth of a sentence is determined by only two things: * the logical form of the sentence. * the truth of its underlying atomic sentences. That is to say, for example, that the truth of the sentence "John is Greek and John is happy" is a function of the meaning of " and", and the truth values of the atomic sentences "John is Greek" and "John is happy". However, the truth of an atomic sentence is not a matter that is within the scope of logic itself, but rather whatever art or science the content of the atomic sentence happens to be talking about. Logic has developed artificial languages, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constituent (linguistics)
In syntactic analysis, a constituent is a word or a group of words that function as a single unit within a hierarchical structure. The constituent structure of sentences is identified using ''tests for constituents''. These tests apply to a portion of a sentence, and the results provide evidence about the constituent structure of the sentence. Many constituents are phrases. A phrase is a sequence of one or more words (in some theories two or more) built around a head lexical item and working as a unit within a sentence. A word sequence is shown to be a phrase/constituent if it exhibits one or more of the behaviors discussed below. The analysis of constituent structure is associated mainly with phrase structure grammars, although dependency grammars also allow sentence structure to be broken down into constituent parts. Tests for constituents in English Tests for constituents are diagnostics used to identify sentence structure. There are numerous tests for constituents that are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first-order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. The most commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as duals; in classical logic: each can be defined in terms of the other using negation. They can also be used to define more complex quantifiers, as in the formula \neg \exists x P(x) which expresses that nothing has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective \lor can be used to join the two atomic formulas P and Q, rendering the complex formula P \lor Q . Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-schema
The T-schema ("truth schema", not to be confused with " Convention T") is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it as the "Equivalence Schema", a synonym introduced by Michael Dummett. The T-schema is often expressed in natural language, but it can be formalized in many-sorted predicate logic or modal logic; such a formalisation is called a "T-theory." T-theories form the basis of much fundamental work in philosophical logic, where they are applied in several important controversies in analytic philosophy. As expressed in semi-natural language (where 'S' is the name of the sentence abbreviated to S): 'S' is true if and only if S. Example: 'snow is white' is true if and only if snow is white. The inductive definition By using the schema one can give an inductive definition for the truth of compound sentences. Atomic sentences are assigned truth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Definition
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set ( Aczel 1977:740ff). Some examples of recursively definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs. For example, the factorial function is defined by the rules :\begin & 0! = 1. \\ & (n+1)! = (n+1) \cdot n!. \end This definition is valid for each natural number , because the recursion eventually reaches the base case of 0. The definition may also be thought of as giving a procedure for computing the value of the function , starting from and proceeding onwards with etc. The recursion theorem states that such a definition indeed defines a function that is unique. The proof uses mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth-conditional Semantics
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associated with Donald Davidson, and attempts to carry out for the semantics of natural language what Tarski's semantic theory of truth achieves for the semantics of logic. Truth-conditional theories of semantics attempt to define the meaning of a given proposition by explaining when the sentence is true. So, for example, because 'snow is white' is true if and only if snow is white, the meaning of 'snow is white' is snow is white. History The first truth-conditional semantics was developed by Donald Davidson in '' Truth and Meaning'' (1967). It applied Tarski's semantic theory of truth to a problem it was not intended to solve, that of giving the meaning of a sentence. Criticism Refutation from necessary truths Scott Soames has harshly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meaning (linguistics)
Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and reference. Sense is given by the ideas and concepts associated with an expression while reference is the object to which an expression points. Semantics contrasts with syntax, which studies the rules that dictate how to create grammatically correct sentences, and pragmatics, which investigates how people use language in communication. Lexical semantics is the branch of semantics that studies word meaning. It examines whether words have one or several meanings and in what lexical relations they stand to one another. Phrasal semantics studies the meaning of sentences by exploring the phenomenon of compositionality or how new meanings can be created by arranging words. Formal semantics (natural language), Formal semantics relies o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Davidson (philosopher)
Donald Herbert Davidson (March 6, 1917 – August 30, 2003) was an American philosopher. He served as Slusser Professor of Philosophy at the University of California, Berkeley, from 1981 to 2003 after having also held teaching appointments at Stanford University, Rockefeller University, Princeton University, and the University of Chicago. Davidson was known for his charismatic personality and difficult writing style, as well as the systematic nature of his philosophy. His work exerted considerable influence in many areas of philosophy from the 1960s onward, particularly in philosophy of mind, philosophy of language, and Action theory (philosophy), action theory. While Davidson was an analytic philosophy, analytic philosopher, with most of his influence lying in that tradition, his work has attracted attention in continental philosophy as well, particularly in literary theory and related areas. Early life and education Donald Herbert Davidson was born on March 6, 1917 in Springfield ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
