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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. Types There are a variety of recognized metalanguages, 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 theory that its metalanguage is embedded within it." It occurs in natural, or informal, languages, as well—such as in English, where words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metasyntax
In logic and computer science, a metasyntax 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). These 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 phrasal or sentence structure consisted of an n-element subs ... [...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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...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 (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a 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 not in general effective, therefore there may be no method by which we can always find a 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 rule of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conduit Metaphor
In linguistics, the conduit metaphor is a dominant class of figurative expressions used when discussing 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, language is viewed as a "conduit" conveying mental content between people. Defined and described by linguist Michael J. Reddy, PhD, his proposal of this conceptual metaphor refocused debate within and outside the linguistic community on the importance of metaphorical language. Fellow linguist George Lakoff stated that "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 example, he allowed us to see, albeit in a restricted doma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word
A word is a basic element of language that carries an semantics, objective or pragmatics, practical 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 ... [...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 ext ... [...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 after writing ''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 Early life Ritzer was born in 1940 to a Jewish family in upper Manh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metatheory
A metatheory or meta-theory is a theory whose subject matter is theory itself, aiming to describe existing theory in a systematic way. In mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. Meta-theoretical investigations are part of the philosophy of science. A metatheory is not applied directly to practice, but may have applications to the practice of the field it studies. The emerging field of metascience seeks to use scientific knowledge to improve the practice of science itself. Examples of metatheories Metascience Metascience is the use of scientific methodology to study science itself. Metascience seeks to increase the quality of scientific research while reducing waste. It is also known as "''research on research''" and "''the science of science''", as it uses research methods to study how research is done and where improvements can be made. Metascience concerns itself with all fields of research and has been des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth
Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences. Truth is usually held to be the opposite of falsehood. The concept of truth is discussed and debated in various contexts, including philosophy, art, theology, and science. Most human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion; these include most of the sciences, law, 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 theo ... [...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 logic s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statement (logic)
In logic, the term statement is variously understood to mean either: #a meaningful declarative sentence that is true or false, or #a proposition. Which is the ''assertion'' that is made by (i.e., the meaning of) a true or false declarative sentence. In the latter case, a statement is distinct from a sentence in that a sentence is only one formulation of a statement, whereas there may be many other formulations expressing the same statement. Overview Philosopher of language, Peter Strawson advocated the use of the term "statement" in sense (b) in preference to proposition. Strawson used the term "Statement" to make the point that two declarative sentences can make the same statement if they say the same thing in different ways. Thus in the usage advocated by Strawson, "All men are mortal." and "Every man is mortal." are two different sentences that make the same statement. In either case a statement is viewed as a truth bearer. Examples of sentences that are (or make) tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory
A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and compr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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