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Metalanguages
In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quotation marks, or writing on a separate line. The structure of sentences and phrases in a metalanguage can be described by a metasyntax. For example, to say that the word "noun" can be used as a noun in a sentence, one could write ''"noun" is a ''. Types of metalanguage There are a variety of recognized types of metalanguage, including ''embedded'', ''ordered'', and ''nested'' (or ''hierarchical'') metalanguages. Embedded An ''embedded metalanguage'' is a language formally, naturally and firmly fixed in an object language. This idea is found in Douglas Hofstadter's book, ''Gödel, Escher, Bach'', in a discussion of the relationship between formal languages and number theory: "... it is in the nature of any formalization of number theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metasyntax
A metasyntax is a syntax used to define the syntax of a programming language or formal language. It describes the allowable structure and composition of phrases and sentences of a metalanguage, which is used to describe either a natural language or a computer programming language.Sellink, Alex, and Chris Verhoef.Development, assessment, and reengineering of language descriptions" Software Maintenance and Reengineering, 2000. Proceedings of the Fourth European. IEEE, 2000. Some of the widely used formal metalanguages for computer languages are Backus–Naur form (BNF), extended Backus–Naur form (EBNF), Wirth syntax notation (WSN), and augmented Backus–Naur form (ABNF). Metalanguages have their own metasyntax each composed of terminal symbols, nonterminal symbols, and ''metasymbols''. A terminal symbol, such as a word or a token, is a stand-alone structure in a language being defined. A nonterminal symbol represents a syntactic category, which defines one or more valid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Proof
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is generally effective, but there may be no method by which we can reliably find proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof. The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mental Content
The mental world is an Ontology, ontological category in metaphysics, populated by nonmaterial mental objects, without physical Extension (metaphysics), extension (though possibly with mental extension as in a visual field, or possibly not, as in an olfactory field) contrasted with the physical world of space and time populated with physical objects, or Plato's world of Platonic ideal, ideals populated, in part, with mathematical objects.Metaphysics, Richard Clyde Taylor, Richard Taylor, ''Foundations of Philosophy'' series''History of Western Philosophy'', Bertrand Russell Properties The mental world may be populated with, or framed with, intentions, sensory fields, and corresponding objects. The mental world is usually considered to be Subjectivity, subjective and not Objectivity (science), objective. In psychologism, mathematical objects are mental objects. Relation to physical world Descartes argued for a mental world as separate from the physical world.''Meditations'', R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conduit Metaphor
In linguistics, the conduit metaphor is a dominant class of figurative expressions invoked when linguists discuss communication itself (metalanguage). It operates whenever people speak or write as if they "insert" their mental contents (feelings, meanings, thoughts, concepts, etc.) into "containers" (words, phrases, sentences, etc.) whose contents are then "extracted" by listeners and readers. Thus, in this model, language is viewed as a "conduit" conveying mental content between people. The conduit metaphor was first defined and described by linguist Michael J. Reddy in 1979. Reddy's proposal of this conceptual metaphor refocused debate within and outside the linguistic community on the importance of metaphorical language. Fellow linguist George Lakoff stated: "The contemporary theory that metaphor is primarily conceptual, conventional, and part of the ordinary system of thought and language can be traced to Michael Reddy's now classic essay... With a single, thoroughly analyzed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word
A word is a basic element of language that carries semantics, meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consensus among linguistics, linguists on its definition and numerous attempts to find specific criteria of the concept remain controversial. Different standards have been proposed, depending on the theoretical background and descriptive context; these do not converge on a single definition. Some specific definitions of the term "word" are employed to convey its different meanings at different levels of description, for example based on phonology, phonological, grammar, grammatical or orthography, orthographic basis. Others suggest that the concept is simply a convention used in everyday situations. The concept of "word" is distinguished from that of a morpheme, which is the smallest unit of language that has a meaning, even if it cannot stand on its own. Words a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valuation (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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Ritzer
George Ritzer (born October 14, 1940) is an American sociologist, professor, and author who has mainly studied globalization, metatheory, patterns of consumption, and modern/postmodern social theory. His concept of McDonaldization draws upon Max Weber's idea of rationalization through the lens of the fast food industry. He coined the term in a 1983 article for ''The Journal of American Culture,'' developing the concept in ''The McDonaldization of Society'' (1993), which is among the best selling monographs in the history of American sociology. Ritzer has written many general sociology books, including ''Introduction to Sociology'' (2012) and ''Essentials to Sociology'' (2014), and modern/postmodern social theory textbooks. Many of his works have been translated into over 20 languages, with over a dozen translations of ''The McDonaldization of Society'' alone''.'' Ritzer is currently a Distinguished Professor Emeritus at the University of Maryland, College Park. Biography ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metatheory
A metatheory or meta-theory is a theory on a subject matter that is a theory in itself. Analyses or descriptions of an existing theory would be considered meta-theories. For mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. Meta-theoretical investigations are part of the philosophy of science. The topic of metascience is an attempt to use scientific knowledge to improve the practice of science itself. The study of metatheory became widespread during the 20th century after its application to various topics, including scientific linguistics and its concept of metalanguage. Examples of metatheories Metascience Metascience is the use of scientific method to study science itself. Metascience is an attempt to increase the quality of scientific research while reducing wasted activity; it uses research methods to study how research is done or can be improved. It has been described as "''research on research''", "''the sci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth
Truth or verity is the Property (philosophy), 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 statement, 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 correspon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metatheorem
In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metatheory but not the object theory. A formal system is determined by a formal language and a deductive system (axioms and rules of inference). The formal system can be used to prove particular sentences of the formal language with that system. Metatheorems, however, are proved externally to the system in question, in its metatheory. Common metatheories used in logic are set theory (especially in model theory) and primitive recursive arithmetic (especially in proof theory). Rather than demonstrating particular sentences to be provable, metatheorems may show that each of a broad class of sentences can be proved, or show that certain sentences cannot be proved. Examples Examples of metatheorems include: * The deduction theorem for first-order log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statement (logic)
In logic and semantics, the term statement is variously understood to mean either: #a meaningful sentence (linguistics)#By_function_or_speech_act, declarative sentence that is Truth, true or false (logic), false, or #a proposition. Which is the ''Denotation, assertion'' that is made by (i.e., the Meaning (linguistics), meaning of) a true or false declarative sentence. "A statement is defined as that which is ''expressible'' by a ''sentence'', and is either true or false... A statement is a more abstract entity than even a sentence type. It is not identical with the sentence used to express it... [That is,] different sentences can be used to express the same statement." In the latter case, a (declarative) sentence is just one way of expressing an underlying statement. A statement is what a sentence means, it is the notion or idea that a sentence expresses, i.e., what it represents. For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
