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Use–mention Distinction
The USE–MENTION DISTINCTION is a foundational concept of analytic philosophy , according to which it is necessary to make a distinction between using a word (or phrase) and mentioning it, and many philosophical works have been "vitiated by a failure to distinguish use and mention". The distinction is disputed by non-analytic philosophers. The distinction between use and mention can be illustrated for the word cheese: * Use: Cheese is derived from milk. * Mention: 'Cheese' is derived from the Old English word ċēse.The first sentence is a statement about the substance called "cheese"; it _uses_ the word 'cheese' to refer to that substance. The second is a statement about the word 'cheese' as a signifier ; it _mentions_ the word without _using_ it to refer to anything other than itself
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Douglas Hofstadter
DOUGLAS RICHARD HOFSTADTER (born February 15, 1945) is an American professor of cognitive science whose research focuses on the sense of "I" (sense of self in relation to the external world), consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics. Hofstadter's book _Gödel, Escher, Bach: An Eternal Golden Braid _, first published in 1979, won both the Pulitzer Prize for general non-fiction and a National Book Award (at that time called The American Book Award) for Science. His 2007 book _ I Am a Strange Loop _ won the Los Angeles Times Book Prize for Science and Technology
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Foundational
FOUNDATIONALISM concerns philosophical theories of knowledge resting upon justified belief , or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises. Its main rival is coherentism , whereby a body of knowledge, not requiring a secure foundation, can be established by the interlocking strength of its components, like a puzzle solved without prior certainty that each small region was solved correctly. Identifying the alternatives as either circular reasoning or infinite regress , and thus exhibiting the regress problem , Aristotle
Aristotle
made foundationalism his own clear choice, positing basic beliefs underpinning others. Descartes , the most famed foundationalist, discovered a foundation in the fact of his own existence and in the "clear and distinct" ideas of reason, whereas Locke found a foundation in experience
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Formal Language
In mathematics , computer science , and linguistics , a FORMAL LANGUAGE is a set of strings of symbols together with a set of rules that are specific to it. The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed. The strings formed from this alphabet are called words, and the words that belong to a particular formal language are sometimes called _well-formed words_ or _well-formed formulas _. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar , also called its formation rule . The field of FORMAL LANGUAGE THEORY studies primarily the purely syntactical aspects of such languages—that is, their internal structural patterns. Formal language
Formal language
theory sprang out of linguistics, as a way of understanding the syntactic regularities of natural languages
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Diagonal Lemma
In mathematical logic , the DIAGONAL LEMMA or FIXED POINT THEOREM establishes the existence of self-referential sentences in certain formal theories of the natural numbers —specifically those theories that are strong enough to represent all computable functions . The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel\'s incompleteness theorems and Tarski\'s undefinability theorem . CONTENTS * 1 Background * 2 Statement of the lemma * 3 Proof * 4 History * 5 See also * 6 Notes * 7 References BACKGROUNDLet N be the set of natural numbers . A theory T REPRESENTS the computable function f : N→N if there exists a "graph" predicate Γf(x,y) in the language of T such that for each X in N, T proves (∀y)
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Gödel's Incompleteness Theorem
GöDEL\'S INCOMPLETENESS THEOREMS are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic . These results, published by Kurt Gödel
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 consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm ) is capable of proving all truths about the arithmetic of the natural numbers . For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system
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International Standard Book Number
The INTERNATIONAL STANDARD BOOK NUMBER (ISBN) is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation (except reprintings) of a book. For example, an e-book , a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, and 10 digits long if assigned before 2007. The method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit STANDARD BOOK NUMBERING (SBN) created in 1966. The 10-digit ISBN format was developed by the International Organization for Standardization (ISO) and was published in 1970 as international standard ISO 2108 (the SBN code can be converted to a ten digit ISBN by prefixing it with a zero)
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Paradox
A PARADOX is a statement that, despite apparently sound reasoning from true premises, leads to a self-contradictory or a logically unacceptable conclusion. A paradox involves contradictory yet interrelated elements that exist simultaneously and persist over time. Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking . Some paradoxes have revealed errors in definitions 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 identification of sets with properties or predicates were flawed. Others, such as Curry\'s paradox , are not yet resolved
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Quine's Paradox
QUINE\'S PARADOX is a paradox concerning truth values , attributed to Willard Van Orman Quine
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
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George Boolos
GEORGE STEPHEN BOOLOS (September 4, 1940 – May 27, 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts
Massachusetts
Institute of Technology . CONTENTS * 1 Life * 2 Work * 3 Publications * 3.1 Books * 3.2 Articles * 4 See also * 5 Notes * 6 References * 7 External links LIFEBoolos graduated from Princeton University
Princeton University
in 1961 with an A.B. in mathematics . Oxford University
Oxford University
awarded him the B.Phil. in 1963. In 1966, he obtained the first Ph.D.
Ph.D.
in philosophy ever awarded by the Massachusetts
Massachusetts
Institute of Technology , under the direction of Hilary Putnam . After teaching three years at Columbia University
Columbia University
, he returned to MIT
MIT
in 1969, where he spent the rest of his career until his death from cancer
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Pointer (computer Programming)
In computer science , a POINTER is a programming language object, whose value refers to (or "POINTS to") another value stored elsewhere in the computer memory using its memory address . A pointer references a location in memory, and obtaining the value stored at that location is known as dereferencing the pointer. As an analogy, a page number in a book's index could be considered a pointer to the corresponding page; dereferencing such a pointer would be done by flipping to the page with the given page number and reading the text found on the indexed page. Pointers to data significantly improve performance for repetitive operations such as traversing strings , lookup tables , control tables and tree structures. In particular, it is often much cheaper in time and space to copy and dereference pointers than it is to copy and access the data to which the pointers point
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Stanford Encyclopedia Of Philosophy
The _STANFORD ENCYCLOPEDIA OF PHILOSOPHY_ (_SEP_) combines an online encyclopedia of philosophy with peer reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University . Each entry is written and maintained by an expert in the field, including professors from many academic institutions worldwide. Authors contributing to the encyclopedia give Stanford University the permission to publish the articles, but retain the copyright to those articles. CONTENTS * 1 Approach and history * 2 See also * 3 References * 4 External links APPROACH AND HISTORYAs of January 2017, the _SEP_ has 1,554 published entries
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Peter Simons (academic)
PETER M. SIMONS, FBA (born 23 March 1950) is a retired professor of philosophy at Trinity College Dublin
Trinity College Dublin
. CONTENTS * 1 Biography * 2 Awards * 3 Publications * 4 External links BIOGRAPHYSimons studied at the University of Manchester
University of Manchester
, and has held teaching posts at the University of Bolton , the University of Salzburg , where he is Honorary Professor
Professor
of Philosophy, and the University of Leeds
University of Leeds
. He has been President of the European Society for Analytic Philosophy
Philosophy
and is current director of the Franz Brentano Foundation
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Encyclopedia Of Philosophy
The ENCYCLOPEDIA OF PHILOSOPHY is one of the major English encyclopedias of philosophy . The first edition of the encyclopedia was in eight volumes, edited by Paul Edwards , and published in 1967 by Macmillan ; it was reprinted in four volumes in 1972. A "Supplement" volume, edited by Donald M. Borchert , was added to the reprinted first edition in 1996, containing articles on developments in philosophy since 1967, covering new subjects and scholarship updates or new articles on those written about in the first edition. A second edition, also edited by Borchert, was published in ten volumes in 2006 by Thomson Gale
Thomson Gale
. Volumes 1–9 contain alphabetically ordered articles . Volume 10 consists of: * Appendix (pp. 1–48), containing updates and additions to the articles in the preceding volumes; * Thematic outline of content (pp. 49–66); * Bibliographies (pp. 67–177); * Index (pp
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Special
SPECIAL or SPECIALS may refer to: CONTENTS * 1 Music * 2 Film and television * 3 Other uses * 4 See also MUSIC * _Special_ (album) , a 1992 album by Vesta Williams * "Special" (Garbage song) , 1998 * "Special" (Mew song) , 2005 * "Special" (Stephen Lynch song) , 2000 * The Specials , a British band * "Special", a song by Violent Femmes on _The Blind Leading the Naked _ * "Special", a song on _ The Documentary _ album by GameFILM AND TELEVISION * Special (lighting) , a stage light that is used for a single, s
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Digital Object Identifier
In computing, a DIGITAL OBJECT IDENTIFIER or DOI is a persistent identifier or handle used to uniquely identify objects, standardized by the ISO . An implementation of the Handle System , DOIs are in wide use mainly to identify academic, professional, and government information, such as journal articles, research reports and data sets, and official publications though they also have been used to identify other types of information resources, such as commercial videos. A DOI aims to be "resolvable", usually to some form of access to the information object to which the DOI refers. This is achieved by binding the DOI to metadata about the object, such as a URL , indicating where the object can be found. Thus, by being actionable and interoperable, a DOI differs from identifiers such as ISBNs and ISRCs which aim only to uniquely identify their referents. The DOI system uses the indecs Content Model for representing metadata
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