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Quine's Paradox
Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine. It is related to the liar paradox as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals (i.e. it does not explicitly refer to itself). The paradox can be expressed as follows: :"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation. If the paradox is not clear, consider each part of the above description of the paradox incrementally: :it = ''yields falsehood when preceded by its quotation'' :its quotation = ''"yields falsehood when preceded by its quotation"'' :it preceded by its quotation = ''"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.'' With these tools, the description of the paradox may now be reconsidered; it can be seen to assert the following: :The statement "''yields falsehood when precede ... [...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 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quotation Marks
Quotation marks are punctuation marks used in pairs in various writing systems to identify direct speech, a quotation, or a phrase. The pair consists of an opening quotation mark and a closing quotation mark, which may or may not be the same glyph. Quotation marks have a variety of forms in different languages and in different media. History The single quotation mark is traced to Ancient Greek practice, adopted and adapted by monastic copyists. Isidore of Seville, in his seventh century encyclopedia, , described their use of the Greek ''diplé'' (a chevron): The double quotation mark derives from a marginal notation used in fifteenth-century manuscript annotations to indicate a passage of particular importance (not necessarily a quotation); the notation was placed in the outside margin of the page and was repeated alongside each line of the passage. In his edition of the works of Aristotle, which appeared in 1483 or 1484, the Milanese Renaissance humanist Francesco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yablo's Paradox
Stephen Yablo (; born 1957) is a Canadian-born American philosopher. He is the Emeritus David W. Skinner Professor of Philosophy at the Massachusetts Institute of Technology (MIT) and taught previously at the University of Michigan, Ann Arbor. He specializes in the philosophy of logic, philosophy of mind, metaphysics, philosophy of language, and philosophy of mathematics. Life and career He was born in Toronto, on 30 September 1957, to a Polish father Saul Yablo and Romanian-Canadian mother Gloria Yablo (née Herman), both Jewish. He is married to fellow MIT philosopher Sally Haslanger. His Ph.D. is from University of California, Berkeley, where he worked with Donald Davidson and George Myro. In 2012, he was elected a Fellow of the American Academy of Arts and Sciences. Philosophical work Yablo has published a number of influential papers in philosophy of mind, philosophy of language, and metaphysics, and gave the John Locke Lectures at Oxford in 2012, which formed the basis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-reference
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields. In natural or formal languages, self-reference occurs when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philosophy, self-reference also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun "I" in English. Self-reference is studied and has applications in mathematics, philosophy, computer programming, second-order cybernetics, and linguistics, as well as in humor. Self-referential statements are sometimes paradoxical, and can also be considered recursive. In logic, mathematics and computing In classical philosophy, paradoxes were created b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russell Paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. According to the unrestricted comprehension principle, for any sufficiently well-defined property, there is the set of all and only the objects that have that property. Let ''R'' be the set of all sets that are not members of themselves. (This set is sometimes called "the Russell set".) If ''R'' is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell's paradox. In symbols: : Let R = \. Then R \in R \iff R \not \in R. Russell also showed that a version of the paradox co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Source Code
In computing, source code, or simply code or source, is a plain text computer program written in a programming language. A programmer writes the human readable source code to control the behavior of a computer. Since a computer, at base, only understands machine code, source code must be Translator (computing), translated before a computer can Execution (computing), execute it. The translation process can be implemented three ways. Source code can be converted into machine code by a compiler or an assembler (computing), assembler. The resulting executable is machine code ready for the computer. Alternatively, source code can be executed without conversion via an interpreter (computing), interpreter. An interpreter loads the source code into memory. It simultaneously translates and executes each statement (computer science), statement. A method that combines compilation and interpretation is to first produce bytecode. Bytecode is an intermediate representation of source code tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quine (computing)
A quine is a computer program that takes no input and produces a copy of its own source code as its only output. The standard terms for these programs in the computability theory and computer science literature are "self-replicating programs", "self-reproducing programs", and "self-copying programs". A quine is a Fixed point (mathematics), fixed point of an execution environment, when that environment is viewed as a Function (mathematics), function transforming programs into their outputs. Quines are possible in any Turing completeness, Turing-complete programming language, as a direct consequence of Kleene's recursion theorem. For amusement, programmers sometimes attempt to develop the shortest possible quine in any given programming language. Name The name "quine" was coined by Douglas Hofstadter, in his popular 1979 science book ''Gödel, Escher, Bach'', in honor of philosopher Willard Van Orman Quine (1908–2000), who made an extensive study of indirect self-reference, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Paradoxes
This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their own article in this encyclopedia. These paradoxes may be due to fallacious reasoning (falsidical), or an unintuitive solution (Veridical paradox, veridical). The term ''paradox'' is often used to describe a counter-intuitive result. However, some of these paradoxes qualify to fit into the mainstream viewpoint of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called ''antinomy,'' point out genuine problems in our understanding of the ideas of truth and Definite description, description. Logic * : The supposition that, "if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved" leads to paradoxical conseq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grelling Paradox
Grelling is a surname. Notable people with the surname include: *Kurt Grelling (1886–1942), German logician and philosopher *Richard Grelling Richard Grelling (11 June 1853 − 14 January 1929) was a German lawyer, writer and pacifist who wrote the international best selling book ''J'Accuse'' in World War I, publicly criticizing the actions of Germany for waging a war of aggression in Eu ... (1853−1929), German lawyer, writer, and pacifist {{Short pages monitor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel's Incompleteness Theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistency, consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of Mathematical proof, proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency. Employing a Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indirect Self-reference
Indirect self-reference describes an object referring to itself indirectly. For example, the "this sentence is false." contains a direct self-reference, in which the phrase "this sentence" refers directly to the sentence as a whole. An indirectly self-referential sentence would replace the phrase "this sentence" with an expression that effectively still referred to the sentence, but did not use the pronoun "this." If the quine of a phrase is defined to be the quotation of the phrase followed by the phrase itself, then the quine of: is a sentence fragment would be: "is a sentence fragment" is a sentence fragment which, incidentally, is a true statement. Now consider the sentence: "when quined, makes quite a statement" when quined, makes quite a statement The quotation here, plus the phrase "when quined," indirectly refers to the entire sentence. The importance of this fact is that the remainder of the sentence, the phrase "makes quite a statement," can now make a statement abou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
