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Contradictory
In traditional logic, a contradiction occurs when a proposition conflicts 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 ens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradox
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 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 the identificatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Explosion
In classical logic, intuitionistic logic and similar logical systems, the principle of explosion (, 'from falsehood, anything ollows; or ), or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a contradiction. That is, once a contradiction has been asserted, any proposition (including their negations) can be inferred from it; this is known as deductive explosion. The proof of this principle was first given by 12th-century French philosopher William of Soissons. Priest, Graham. 2011. "What's so bad about contradictions?" In ''The Law of Non-Contradicton'', edited by Priest, Beal, and Armour-Garb. Oxford: Clarendon Press. p. 25. Due to the principle of explosion, the existence of a contradiction ( inconsistency) in a formal axiomatic system is disastrous; since any statement can be proven, it trivializes the concepts of truth and falsity. Around the turn of the 20th century, the discovery of contradictions such as Russell's par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Noncontradiction
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "''p is the case''" and "''p is not the case''" are mutually exclusive. Formally this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case" holds. One reason to have this law is the principle of explosion, which states that anything follows from a contradiction. The law is employed in a ''reductio ad absurdum'' proof. To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say "contradictory propositions cannot both be true 'at the same time and in the same sense'". It is one of the so called three laws of thought, along with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Socrates
Socrates (; ; –399 BC) was a Greek philosopher from Athens who is credited as the founder of Western philosophy and among the first moral philosophers of the ethical tradition of thought. An enigmatic figure, Socrates authored no texts and is known mainly through the posthumous accounts of classical writers, particularly his students Plato and Xenophon. These accounts are written as dialogues, in which Socrates and his interlocutors examine a subject in the style of question and answer; they gave rise to the Socratic dialogue literary genre. Contradictory accounts of Socrates make a reconstruction of his philosophy nearly impossible, a situation known as the Socratic problem. Socrates was a polarizing figure in Athenian society. In 399 BC, he was accused of impiety and corrupting the youth. After a trial that lasted a day, he was sentenced to death. He spent his last day in prison, refusing offers to help him escape. Plato's dialogues are among the most co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal 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 usu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fact
A fact is a datum about one or more aspects of a circumstance, which, if accepted as true and proven true, allows a logical conclusion to be reached on a true–false evaluation. Standard reference works are often used to check facts. Scientific facts are verified by repeatable careful observation or measurement by experiments or other means. For example, "This sentence contains words." accurately describes a linguistic fact, and "The sun is a star" accurately describes an astronomical fact. Further, "Abraham Lincoln was the 16th President of the United States" and "Abraham Lincoln was assassinated" both accurately describe historical facts. Generally speaking, facts are independent of belief and of knowledge and opinion. Facts are different from theories, values, and objects. Etymology and usage The word ''fact'' derives from the Latin ''factum''. It was first used in English with the same meaning: "a thing done or performed"a meaning now obsolete."Fact" (1a). Oxf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disingenuous
Deception or falsehood is an act or statement that misleads, hides the truth, or promotes a belief, concept, or idea that is not true. It is often done for personal gain or advantage. Deception can involve dissimulation, propaganda and sleight of hand as well as distraction, camouflage or concealment. There is also self-deception, as in bad faith. It can also be called, with varying subjective implications, beguilement, deceit, bluff, mystification, ruse, or subterfuge. Deception is a major relational transgression that often leads to feelings of betrayal and distrust between relational partners. Deception violates relational rules and is considered to be a negative violation of expectations. Most people expect friends, relational partners, and even strangers to be truthful most of the time. If people expected most conversations to be untruthful, talking and communicating with others would require distraction and misdirection to acquire reliable information. A significant amount ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Maynard Hutchins
Robert Maynard Hutchins (January 17, 1899 – May 14, 1977) was an American educational philosopher. He was president (1929–1945) and chancellor (1945–1951) of the University of Chicago, and earlier dean of Yale Law School (1927–1929). His first wife was the novelist Maude Hutchins. Although his father and grandfather were both Presbyterian ministers, Hutchins became one of the most influential members of the school of secular perennialism. A graduate of Yale College and the law school of Yale University, Hutchins joined the law faculty and soon was named dean. While dean, he gained notice for Yale's development of the philosophy of Legal Realism. Hutchins was thirty years old when he became Chicago's president in 1929, and implemented wide-ranging and sometimes controversial reforms of the university, including the elimination of varsity football. He supported interdisciplinary programs, including during World War II, establishing the Metallurgical Laboratory. Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Of Opposition, Set Diagrams
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides. It is the only regular polygon whose internal angle, central angle, and external angle are all equal (90°), and whose diagonals are all equal in length. A square with vertices ''ABCD'' would be denoted . Characterizations A convex quadrilateral is a square if and only if it is any one of the following: * A rectangle with two adjacent equal sides * A rhombus with a right vertex angle * A rhombus with all angles equal * A parallelogram with one right vertex angle and two adjacent equal sides * A quadrilateral with four equal sides and four right angles * A quadrilateral where the diagonals are equal, and are the perpendicular bisectors of each other (i.e., a rhombus with equal diagonals) * A convex quadrilateral with success ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopædia Britannica
The (Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various times through the centuries. The encyclopaedia is maintained by about 100 full-time editors and more than 4,000 contributors. The 2010 version of the 15th edition, which spans 32 volumes and 32,640 pages, was the last printed edition. Since 2016, it has been published exclusively as an online encyclopaedia. Printed for 244 years, the ''Britannica'' was the longest running in-print encyclopaedia in the English language. It was first published between 1768 and 1771 in the Scottish capital of Edinburgh, as three volumes. The encyclopaedia grew in size: the second edition was 10 volumes, and by its fourth edition (1801–1810) it had expanded to 20 volumes. Its rising stature as a scholarly work helped recruit eminent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chicago
(''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name = United States , subdivision_type1 = State , subdivision_type2 = Counties , subdivision_name1 = Illinois , subdivision_name2 = Cook and DuPage , established_title = Settled , established_date = , established_title2 = Incorporated (city) , established_date2 = , founder = Jean Baptiste Point du Sable , government_type = Mayor–council , governing_body = Chicago City Council , leader_title = Mayor , leader_name = Lori Lightfoot ( D) , leader_title1 = City Clerk , leader_name1 = Anna Valencia ( D) , unit_pref = Imperial , area_footnotes = , area_total ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False (logic)
In logic, false or untrue is the state of possessing negative truth value or a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth. Usual notations of the false are 0 (especially in Boolean logic and computer science), O (in prefix notation, O''pq''), and the up tack symbol \bot. Another approach is used for several formal theories (e.g., intuitionistic propositional calculus), where a propositional constant (i.e. a nullary connective), \bot, is introduced, the truth value of which being always false in the sense above. It can be treated as an absurd proposition, and is often called absurdity. In classical logic and Boolean logic In Boolean logic, each variable denotes a truth value which can be either true (1), or false (0). In a classical propositional calculus, each proposition will be assigned a truth value of either true or false. Some systems of c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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