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Topic: Kurt Godel

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	Kurt Godel
		Kurt Godel (1906-1978), elected to Academy membership in 1955, was noted for his contributions to the foundations of logic and mathematics.
		In a celebrated paper published in 1931, Godel first put forward what came to be known simply as "Godel's Theorem": In certain formal systems, there exist propositions that cannot be proved or disproved using the axioms of that system.
		Godel's Theorem made a deep impact in the fields of mathematics and logic, and has been called the most significant mathematical truth of the 20th century.
	www.nas.edu /history/members/godel.html (157 words)

	kurt godel (Site not responding. Last check: 2007-11-04)
		Kurt Godel was a mathematician, logician, and mathematical philosopher who revolutionized mathematics by the creating what is known as the
		At the age of 18 Kurt entered the university in Vienna.
		It was in this dissertation that he presented the concept of the first-order predicate calculus(better known as Godel's completeness theorem).
	www.supernaturalminds.com /KurtGodel.html (403 words)

	Godel's Incompleteness Theorem
		Godel then points out that the following statement is a part of the system: a statement P which states "there is no proof of P".
		Godel's proof is designed to emphasize that the statement P is necessarily a part of the system, not something arbitrary that someone dreamed up.
		After showing the existence of that first "Godel" statement, Godel goes on to prove that there are an infinite number of Godel statements in the system, and that even if these were enumerated very carefully and added to the postulates of the system, more Godel statements would arise.
	www.myrkul.org /recent/godel.htm (1008 words)

	Kurt Godel (Site not responding. Last check: 2007-11-04)
		Mathematician-logician Kurt Godel (1906-1978) in 1931 proved that within a formal system questions exist that are neither provable nor disprovable on the basis of the axioms of that system.
		This is known as "Godel's Undecidability Theorem" or "Incompleteness Theorem".
		Godel's theorem has direct relevance for information theory and mathematical reasoning and is of great importance in complex systems.
	www.exploratorium.edu /complexity/lexicon/godel.html (85 words)

	Godel
		Kurt Gödel's father was Rudolf Gödel whose family were from Vienna.
		Kurt's mother, Marianne Handschuh, was from the Rhineland and the daughter of Gustav Handschuh who was also involved with textiles in Brünn.
		Although there is no evidence that he did have a weak heart, Kurt became convinced that he did, and concern for his health became an everyday worry for him.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Godel.html (2166 words)

	Kurt Godel (Site not responding. Last check: 2007-11-04)
		In 1931 the mathematician and logician Kurt Godel proved that within a formal system questions exist that are neither provable nor disprovable on the basis of the axioms that define the system.
		In establishing these theorems Godel showed that there are problems that cannot be solved by any set of rules or procedures; instead for these problems one must always extend the set of axioms.
		Alan Turing later provided a constructive interpretation of Godel's results by placing them on an algorithmic foundation: There are numbers and functions that cannot be computed by any logical machine.
	www.exploratorium.edu /complexity/CompLexicon/godel.html (195 words)

	Kurt Godel Papers
		The papers of Kurt Gödel (1906-1978), foremost mathematical logician of the twentieth century, were bequeathed by him to his wife Adele, who donated them to the Institute for Advanced Study in his memory prior to her death in 1981.
		Kurt Friedrich Gödel was born April 28, 1906, in Brünn, Moravia, and died January 14, 1978, in Princeton, New Jersey.
		The Papers of Kurt Gödel include documents spanning the years 1905-1980, with the bulk of the material falling between 1930 and 1970.
	libweb.princeton.edu /libraries/firestone/rbsc/aids/godel (3170 words)

	Nat' Academies Press, Biographical Memoirs V.56 (1987)
		Godel of- fered supplementary reasoning that adapted his treatment for the predicate calculus to the predicate calculus with equality, with "the domain {0, I, 2,...~" being replaced in his conclusions by "~0, I, 2,...) or a non-empty finite domain".
		KURT GODEL 143 the axioms that the range of the variables in them constitutes a countable collection, contradicting the theorem of Cantor by which the subsets of {0, I, 2,...} (which are among the sets for his theory) constitute an uncountable collection.
		Thus 1939b, commu- nicated by Godel on February 14, 1939, is put after 1939a, which is a set of notes by George W. Brown published in 1940 on lectures delivered by Godel in the fall term of 1938-39; and 1934 and 1946, only published in 1965, are in the right order.
	books.nap.edu /books/0309036933/html/134.html (4388 words)

	Bookslut \| Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein
		Kurt Godel, the greatest logician of our era and the heir to Aristotle, is best known for having proved the incompleteness of arithmetic.
		The rest of the book lays out Godel's early years and views, the mathematical and philosophical climate in which he was operating, a simplified version of the proof of Godel's theorem, and Godel's last, tragic years.
		She ably describes the tension between Godel's ideas and those of Wittgenstein, as well as those of the formalists (though her discussion of the latter is to some extent marred by the same problems which plague her discussion of the positivists).
	www.bookslut.com /nonfiction/2005_05_005364.php (805 words)

	KURT GODEL
		Kurt Gödel (1906-1978) was probably the most strikingly original and important logician of the twentieth century.
		He proved the incompleteness of axioms for arithmetic (his most famous result), as well as the relative consistency of the axiom of choice and continuum hypothesis with the other axioms of set theory.
		When his wife was incapacitated with illness, these factors combined to cause his death from self-starvation.
	www.usna.edu /Users/math/meh/godel.html (900 words)

	Amazon.co.uk: Kurt Godel: Collected Works: Publications 1938-1974 Vol 2: Books (Site not responding. Last check: 2007-11-04)
		Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis.
		Kurt Godel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis.
		Kurt Godel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy.
	www.amazon.co.uk /exec/obidos/ASIN/0195147219 (897 words)

	Kurt Gödel's Ontological Argument (Site not responding. Last check: 2007-11-04)
		Kurt Gödel is best known to mathematicians and the general public for his celebrated incompleteness theorems.
		Some of the pioneering work of Kurt Gödel showed that the modal logic of philosophers which was used to analyse the ontological argument for the existence of God was also very useful in proof theory and metamathematics.
		Kurt Gödel was born in what is now Brno in the Czech Republic in 1906.
	www.stats.uwaterloo.ca /~cgsmall/ontology.html (3107 words)

	Objectivism Without Platonism: Hao Wang on Kurt Godel
		Kurt Gödel is most famous for Gödel's Theorem, also known as the Incompleteness Theorem.
		However, his focus on projects, and on developing a worthy project for himself at a time when ambitious projects in philosophy were decidedly out of fashion, can make his thought somewhat scattered and unsystematic, although pregnant with possibilities.
		Unlike Godel, Wang is not especially interested in establishing or strengthening the philosophical foundations for his views.
	www.saint-andre.com /thoughts/wang-godel.html (6950 words)

	Omni: Life in Godel's universe: maps all the way - mathematician Kurt Godel (Site not responding. Last check: 2007-11-04)
		In 1931 Kurt Godel published a proof that claimed to reveal the kind of universe we inhabit.
		Godel himself believed that mathematical objects have as much reality as those we perceive with our senses.
		And the kind of universe that Godel's proof suggests is the one put forward by current cosmological modeling: an open-ended, infinite, eternal existence, requiring no beginning, in which our knowledge may become significant and extensive but never complete.
	www.findarticles.com /p/articles/mi_m1430/is_n7_v14/ai_12064291 (1231 words)

	Peter Suber, "Kurt Gödel in Blue Hill"
		For this HTML version I restore the footnotes, which I did not submit to the newspaper, and a sidebar, which the newspaper omitted perhaps for being too technical.
		Kurt Gödel and his wife Adele spent the summer of 1942 in Blue Hill, in the Blue Hill House at the top of the bay.
		The man who catalogued Gödel's papers after his death, John Dawson, believes that nothing of large mathematical importance is likely to be found in Gödel's untranscribed notebooks with the single possible exception of the reputed 1942 independence proof of the axiom of choice.
	www.earlham.edu /~peters/writing/godel.htm (2576 words)

	Amazon.com: Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries): Books: Rebecca Goldstein (Site not responding. Last check: 2007-11-04)
		Kurt Godel was 18 when he arrived in Vienna to begin his studies at the university.
		Godel was part of the Vienna Circle, so we get a lot of history about the Vienna Circle in general.
		She gives us Godel the passionate, the true believer in Platonic reality of mathematics, and shows us how this belief conditioned his response to 20th century thouught currents, and finally drove him to create his famous Incompleteness theorems.
	www.amazon.com /exec/obidos/tg/detail/-/0393051692?v=glance (2102 words)

	AllRefer.com - Kurt GOdel (Mathematics, Biography) - Encyclopedia
		Kurt GOdel[gO´dul] Pronunciation Key, 1906–78, American mathematician and logician, b.
		He came to the United States in 1940 and was naturalized in 1948.
		GOdel shared the 1951 Albert Einstein Award for achievement in the natural sciences with Julian Schwinger, Harvard mathematical physicist.
	reference.allrefer.com /encyclopedia/G/Godel-Ku.html (174 words)

	ipedia.com: Kurt Gödel Article (Site not responding. Last check: 2007-11-04)
		Kurt Gödel [gö:dl], was a mathematician whose biography lists quite a few nations, although he is usually associated with Austria.
		Kurt Gödel [gö:dl], (April 28, 1906 – January 14, 1978) was a mathematician whose biography lists quite a few nations, although he is usually associated with Austria.
		He was born in Brno in Austria-Hungary (which broke up after World War I), became Czechoslovak citizen at age 12, and Austrian citizen at age 23.
	www.ipedia.com /kurt_goedel_1.html (1679 words)

	Powell's Books - Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein (Site not responding. Last check: 2007-11-04)
		Kurt Godel is considered the twentieth century's greatest mathematician.
		From the famous Vienna Circle and sparring with Wittgenstein to Princeton's Institute for Advanced Study, where he was Einstein's constant companion, Godel was both a towering intellect and a deeply mysterious figure, whose strange habits and ever-increasing paranoia led to his sad death by self-starvation.
		Considered the 20th century's greatest mathematician, Kurt Godel is the subject of this lucid and accessible study, which explains the significance of his theorems and the remarkable vision behind them, while bringing this eccentric, tortured genius and his world to life.
	www.powells.com /cgi-bin/biblio?inkey=8-0393051692-0 (562 words)

	Kurt Godel Store
		Collegium Logicum: Annals of the Kurt Godel Society, Vol.
		Computational Logic and Proof Theory: 5th Kurt Godel Colloquium, Kgc'97, Vienna, Austria, August 25-29, 1997 Proceedings, Vol.
		Godel '96: Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Godel's Legacy, Vol.
	www.mathbook.com /godel-kurt.php (96 words)

	Amazon.com: Godel's Proof: Books (Site not responding. Last check: 2007-11-04)
		Godel's proof is not easy to follow, nor easy to grasp the full implications of its conclusions.
		Many mathematical texts, overviews, and historical summaries avoid directly discussing Godel's proof as these quotes indicate: "Godel's proof is even more abstruse than the beliefs it calls into question." "The details of Godel's proofs in his epoch-making paper are too difficult to follow without considerable mathematical training.
		In their short book (118 pages) Nagel and Newman present the basic structure of Godel's proof and the core of his conclusions in a way that is intelligible to the persistent layman.
	www.amazon.com /exec/obidos/tg/detail/-/0814758169?v=glance (2578 words)

	Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries) (Site not responding. Last check: 2007-11-04)
		Kurt Gödel is often held up as an intellectual revolutionary whose incompleteness theorem helped tear down the notion that there was anything certain about the universe.
		Philosophy professor, novelist, and MacArthur Fellow Rebecca Goldstein reinterprets the evidence and restores to Gödel's famous idea the meaning he claimed he intended: that there is a mathematical truth--an objective certainty--underlying everything and existing independently of human thought.
		Kurt Gödel is considered the greatest logician since Aristotle.
	www.mountainstatestech.com /mststore/item_00393051692P.html (476 words)

	Kurt Godel -- Encyclopædia Britannica
		More results on "Kurt Godel" when you join.
		This proof states that within any rigidly logical mathematical system there are propositions (or statements) that cannot be proved or disproved on the basis of the axioms within that system.
		German orchestra conductor Kurt Masur was noted for his comprehensive repertoire, which spanned the range of German Romanticism from the works of Ludwig van Beethoven to those of Gustav Mahler.
	www.britannica.com /eb/article-9037162 (548 words)

	Amazon.ca: Books: Reflections on Kurt Godel (Site not responding. Last check: 2007-11-04)
		Wang, professor of logic at Rockefeller University, was personally acquainted with Godel in his last years, and relies on recollected conversations as well as published and unpublished material in this first extended treatment of Godel's life and work.
		Known primarily as a mathematician/logician from his published work, Godel's extensive unpublished work, says Wang, contains "bold speculations on several perennial issues of universal concern." Those issues are only hinted at here, as most of the philosophical discussion concerns the philosophy of mathematics.
		I understand that Wang has been an important source in compiling information on Godel and bringing it to public attention over the years, but this is the first book of his I've read.
	www.amazon.ca /exec/obidos/ASIN/0262730871 (496 words)

	Kurt Godel (Site not responding. Last check: 2007-11-04)
		With this theorm, Godel had effectively demonstrated that soem mathematical propositions are undecidable.
		Godel's Theorem made a deep impression in the fields of mathematics and logic, and has been called the most significant mathematical truth of the 20th century.
		He studied physics in Vienna, and emigrated to the United States in 1939, where he took a position at Princeton's Institute for Advanced Study.
	www7.nationalacademies.org /archives/godel.html (187 words)

	TIME 100: Kurt Godel
		Kurt Godel at the Institute of Advanced Study
		He turned the lens of mathematics on itself and hit upon his famous "incompleteness theorem" —; driving a stake through the heart of formalism
		Kurt Gödel was born in 1906 in Brunn, then part of the Austro-Hungarian Empire and now part of the Czech Republic, to a father who owned a textile factory and had a fondness for logic and reason and a mother who believed in starting her son's education early.
	www.time.com /time/time100/scientist/profile/godel.html (449 words)

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