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Quantifier Shift
A quantifier shift is a logical fallacy in which the quantifiers of a statement are erroneously transposed during the rewriting process. The change in the logical nature of the statement may not be obvious when it is stated in a natural language like English. Definition The fallacious deduction is that: ''For every A, there is a B, such that C. Therefore, there is a B, such that for every A, C.'' :\forall x \,\exists y \,Rxy \vdash \exists y \,\forall x \,Rxy However, an inverse switching: :\exist y \,\forall x \,Rxy \vdash \forall x \,\exist y\, Rxy is logically valid. Examples 1. Every person has a woman that is their mother. Therefore, there is a woman that is the mother of every person. :\forall x \,\exists y \,(Px \to (Wy \land M(yx))) \vdash \exists y \,\forall x \,(Px \to (Wy \land M(yx))) It is fallacious to conclude that there is ''one woman'' who is the mother of ''all people''. However, if the major premise ("every person has a woman that is their mother ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Fallacy
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple ''mistake'' and a ''mathematical fallacy'' in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or deception in the presentation of the proof. For example, the reason why validity fails may be attributed to a division by zero that is hidden by algebraic notation. There is a certain quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifiers (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 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting. Example cases Logic In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Language
A natural language or ordinary language is a language that occurs naturally in a human community by a process of use, repetition, and change. It can take different forms, typically either a spoken language or a sign language. Natural languages are distinguished from constructed and formal languages such as those used to program computers or to study logic. Defining natural language Natural languages include ones that are associated with linguistic prescriptivism or language regulation. ( Nonstandard dialects can be viewed as a wild type in comparison with standard languages.) An official language with a regulating academy such as Standard French, overseen by the , is classified as a natural language (e.g. in the field of natural language processing), as its prescriptive aspects do not make it constructed enough to be a constructed language or controlled enough to be a controlled natural language. Natural language are different from: * artificial and constructed la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Language
English is a West Germanic language that developed in early medieval England and has since become a English as a lingua franca, global lingua franca. The namesake of the language is the Angles (tribe), Angles, one of the Germanic peoples that Anglo-Saxon settlement of Britain, migrated to Britain after its End of Roman rule in Britain, Roman occupiers left. English is the list of languages by total number of speakers, most spoken language in the world, primarily due to the global influences of the former British Empire (succeeded by the Commonwealth of Nations) and the United States. English is the list of languages by number of native speakers, third-most spoken native language, after Mandarin Chinese and Spanish language, Spanish; it is also the most widely learned second language in the world, with more second-language speakers than native speakers. English is either the official language or one of the official languages in list of countries and territories where English ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallacious Induction
A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument. All forms of human communication can contain fallacies. Because of their variety, fallacies are challenging to classify. They can be classified by their structure (formal fallacies) or content (informal fallacies). Informal fallacies, the larger group, may then be subdivided into categories such as improper presumption, faulty generalization, error in assigning causation, and relevance, among others. The use of fallacies is common when the speaker's goal of achieving common agreement is more important to them than utilizing sound reasoning. When fallacies are used, the premise should be recognized as not well-grounded, the conclusion as unproven (but not necessarily false), and the argument as unsound. Formal fallacies A formal fallacy is an error in the argument's form. All formal fallacies are types of . * Appeal to probability – taking something for granted because it wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Audi
Robert N. Audi (born November 1941) is an American philosopher whose major work has focused on epistemology, ethics (especially on ethical intuitionism), rationality and the theory of action. He is O'Brien Professor of Philosophy at the University of Notre Dame, and previously held a chair in the business school there. His 2005 book, ''The Good in the Right'', updates and strengthens Rossian intuitionism and develops the epistemology of ethics. He has also written important works of political philosophy, particularly on the relationship between church and state. He is a past president of the American Philosophical Association and the Society of Christian Philosophers. Audi's contributions to epistemology include his defense of '' fallibilistic foundationalism''. Audi has expanded his theory of justification to non-doxastic states, e.g. desires and intentions, by developing a ''comprehensive account of rationality''. A mental state is rational if it is "well-grounded" in a ''sourc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Cambridge Dictionary Of Philosophy
''The Cambridge Dictionary of Philosophy'' (1995; second edition 1999; third edition 2015) is a dictionary of philosophy published by Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ... and edited by the philosopher Robert Audi. There are 28 members on the Board of Editorial Advisors and 440 contributors. Publication history ''The Cambridge Dictionary of Philosophy'' was first published in 1995 by Cambridge University Press. A second edition followed in 1999, and a third edition in 2015. References Bibliography ;Books * External links More information at the Cambridge University Press website 1995 non-fiction books Books by Robert Audi Cambridge University Press books Dictionaries of philosophy Encyclopedias of philosophy English-language non ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barnes & Noble
Barnes & Noble Booksellers is an American bookseller with the largest number of retail outlets in the United States. The company operates approximately 600 retail stores across the United States. Barnes & Noble operates mainly through its Barnes & Noble Booksellers chain of bookstores. The company's headquarters are at 33 E. 17th Street on Union Square in New York City. After a series of mergers and bankruptcies in the American bookstore industry since the 1990s, Barnes & Noble is the United States' largest bookstore chain and the only national chain. Previously, Barnes & Noble operated the chain of small B. Dalton, B. Dalton Bookseller stores in malls until they announced the liquidation of the chain in 2010. The company was also one of the nation's largest manager of college textbook stores located on or near many college campuses when that division was spun off as a separate public company called Barnes & Noble Education in 2015. The company is known by its customers fo ... [...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] |
Antony Flew
Antony Garrard Newton Flew (; 11 February 1923 – 8 April 2010) was an English philosopher. Belonging to the analytic and evidentialist schools of thought, Flew worked on the philosophy of religion. During the course of his career he taught philosophy at the universities of Oxford, Aberdeen, Keele, and Reading in the United Kingdom, and at York University in Toronto, Canada. For much of his career Flew was an advocate of atheism, arguing that one should presuppose atheism until empirical evidence suggesting the existence of a God surfaces. He also criticised the idea of life after death, the free will defence to the problem of evil, and the meaningfulness of the concept of God. In 2003, he was one of the signatories of the Humanist Manifesto III. He also developed the No true Scotsman fallacy, and debated retrocausality with Michael Dummett. However, in 2004 he changed his position, and stated that he now believed in the existence of an intelligent designer of the u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
