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Logical Paradoxes
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found set theory on t ... [...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] |
Abstraction
Abstraction is a process where general rules and concepts are derived from the use and classifying of specific examples, literal (reality, real or Abstract and concrete, concrete) signifiers, first principles, or other methods. "An abstraction" is the outcome of this process — a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''.Suzanne K. Langer (1953), ''Feeling and Form: A Theory of Art Developed from Philosophy in a New Key'', p. 90: "Sculpture, Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through sensory system, touch and sight." Conceptual abstractions may be made by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosopher
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy. However, they are considered separate academic disciplines in the modern sense of the term. Influential traditions in the history of philosophy include Western philosophy, Western, Islamic philosophy, Arabic–Persian, Indian philosophy, Indian, and Chinese philosophy. Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the Spirituality, spiritual problem of how to reach Enlightenment in Buddhism, enlighten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Language
Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed language, signed forms, and may also be conveyed through writing system, writing. Human language is characterized by its cultural and historical diversity, with significant variations observed between cultures and across time. Human languages possess the properties of Productivity (linguistics), productivity and Displacement (linguistics), displacement, which enable the creation of an infinite number of sentences, and the ability to refer to objects, events, and ideas that are not immediately present in the discourse. The use of human language relies on social convention and is acquired through learning. Estimates of the number of human languages in the world vary between and . Precise estimates depend on an arbitrary distinction (dichotomy) established between languages and dialects. Natural languages are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Half-truth
A half-truth is a deceptive statement that includes some element of truth. The statement might be partly true, the statement may be totally true, but only part of the whole truth, or it may use some deceptive element, such as improper punctuation, or double meaning, especially if the intent is to deceive, evade, blame or misrepresent the truth. Purpose The purpose and or consequence of a half-truth is to make something that is really only a belief appear to be knowledge, or a truthful statement to represent the whole truth or possibly lead to a false conclusion. The order in which the true and false information is presented in a "half-truth" can make a difference in ultimate believability. Barchetti and colleagues show that when two unrelated statements are put together with syntax that suggests causality, the statement is believed if the premise is true (even if the conclusion is unrelated or false). Conversely, if the false statement is placed in the premise, the combined st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Regress
Infinite regress is a philosophical concept to describe a series of entities. Each entity in the series depends on its predecessor, following a recursive principle. For example, the epistemic regress is a series of beliefs in which the justification of each belief depends on the justification of the belief that comes before it. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it must demonstrate not just that the theory in question entails an infinite regress but also that this regress is ''vicious''. There are different ways in which a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of ''metaphysical impossibility''. Other forms occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. Traditionally, it was of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Reasoning
Circular reasoning (, "circle in proving"; also known as circular logic) is a fallacy, logical fallacy in which the reasoner begins with what they are trying to end with. Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion. As a consequence, the argument becomes a matter of faith and fails to persuade those who do not already accept it. Other ways to express this are that there is no reason to accept the premises unless one already believes the conclusion, or that the premises provide no independent ground or evidence for the conclusion. Circular reasoning is closely related to begging the question, and in modern usage the two generally refer to the same thing. Circular reasoning is often of the form: "A is true because B is true; B is true because A is true." Circularity can be difficult to detect if it involves a longer chain of propositions. An example of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function (mathematics), function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references can occur. A process that exhibits recursion is ''recursive''. Video feedback displays recursive images, as does an infinity mirror. Formal definitions In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: * A simple ''base case'' (or cases) — a terminating scenario that does not use recursion to produce an answer * A ''recursive step'' — a set of rules that reduce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liars Paradox
A liar is a person who tells lies. Liar may also refer to: People with the name * The Liar, an American video artist and member of Angelspit Arts, entertainment, and media Films * ''The Liar'' (1961 film), West German film directed by Ladislao Vajda * ''The Liar'' (1981 film), Finnish film directed by Mika Kaurismäki * ''The Liars'' (film), 1996 French film * ''Liar'' (1997 film) (UK title for ''Deceiver'') Literature * ''Liar'' (novel), a 2009 novel by Justine Larbalestier * "Liar!" (short story), a 1941 short story by Isaac Asimov * ''The Liar'' (Corneille play), a 1644 play by Pierre Corneille * ''The Liar'' (novel), a 1991 novel by Stephen Fry * "The Liar" (novella), a 2016 short story by John P. Murphy * "The Liar" (short story), a short story by Henry James Music Albums * ''Liar'' (Harisu album), 2002 * ''Liar'' (The Jesus Lizard album), 1992 * '' L.I.A.R.'', a 2016 album by Keri Hilson * '' Liar/Dead Is the New Alive'', a 2006 EP by Emilie Autumn * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contradiction
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect." In modern formal logic and type theory, the term is mainly used instead for a ''single'' proposition, often denoted by the falsum symbol \bot; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to "contain" a contradiction. History By creation of a paradox, Plato's '' Euthydemus'' dialogue demonstrates the need for the notion of ''contradiction''. In the ensuing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barber
A barber is a person whose occupation is mainly to cut, dress, groom, style and shave hair or beards. A barber's place of work is known as a barbershop or the barber's. Barbershops have been noted places of social interaction and public discourse since at least classical antiquity. In some instances, barbershops were also public forums. They were the locations of open debates, voicing public concerns, and engaging citizens in discussions about contemporary issues. In previous times, barbers (known as barber surgeons) also performed surgery and dentistry. With the development of safety razors and the decreasing prevalence of beards in English-speaking world, Anglophonic cultures, most barbers now specialize in cutting men's scalp hair as opposed to facial hair. Names In modern times, the term "barber" is used both as a professional title and to refer to hairdressers who specialize in men's hair. Historically, all hairdressers were considered barbers. In the 20th century, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barber Paradox
The barber paradox is a puzzle derived from Russell's paradox. It was used by Bertrand Russell as an illustration of the paradox, though he attributes it to an unnamed person who suggested it to him.Russell, Bertrand (1919). "The Philosophy of Logical Atomism", reprinted in ''The Collected Papers of Bertrand Russell, 1914-19'', Vol 8, p. 228 The puzzle shows that an apparently plausible scenario is logically impossible. Specifically, it describes a barber who is defined such that he both shaves himself and does not shave himself, which implies that no such barber exists. Paradox The barber is the "one who shaves all those, and those only, who do not shave themselves". The question is, does the barber shave himself? Any answer to this question results in a contradiction: # The barber cannot shave himself, as he only shaves those who do ''not'' shave themselves. Thus, if he shaves himself he ceases to be the barber specified. # Conversely, if the barber does not shave himself ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
