1. Paradox - Wikipedia, The Free Encyclopedia A paradox can be an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition; or it can be, http://en.wikipedia.org/wiki/Paradox

Paradox From Wikipedia, the free encyclopedia Jump to: navigation search For other uses, see Paradox (disambiguation) Look up paradox in Wiktionary , the free dictionary. A paradox can be an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition ; or it can be, seemingly opposite, an apparent contradiction that actually expresses a non-dual truth (cf. Koan ). Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The word paradox is often used interchangeably with contradiction . Often, mistakenly, it is used to describe situations that are ironic The recognition of ambiguities equivocations , and unstated assumptions underlying known paradoxes has led to significant advances in science philosophy and mathematics . But many paradoxes, such as Curry's paradox , do not yet have universally accepted resolutions. Sometimes the term paradox is used for situations that are merely surprising. The

2. Mark's Paradox Page paradoxes are as old as humankind. The ancient Greeks studied them intensely which eventually helped lead to the discovery of irrational numbers, http://www.geocities.com/CapitolHill/Lobby/3022/

These are old fond paradoxes to make fools laugh i' the alehouse. - Othello, Act 1, Scene 1 Paradoxes are as old as humankind. The ancient Greeks studied them intensely which eventually helped lead to the discovery of irrational numbers, and paradoxes are mentioned in the Bible: "It was one of their own prophets who said 'Cretans were never anything but liars, dangerous animals, all greed and laziness;' and that is a true statement." (Titus 1:12-13) Even today, we are surrounded by paradoxes such as Blackwood's "the more terrible the prospect of thermonuclear war becomes the less likely it is to happen," or the Moebius Strip - a topological paradox. For this article, we define a paradox as a statement or sentiment that is seemingly contradictory or opposed to common sense and yet is perhaps true in fact. Another way of thinking of a paradox is a statement that is actually self-contradictory and hence false even though its true character is not immediately apparent. One of the oldest paradoxes is the one cited by the Apostle Paul in his letter to Titus (see above.) The Liar Paradox is interesting because it cannot be true because it would make the speaker a liar and therefore what he says is false. Neither can it be true because that would imply that Cretans are truth-tellers, and consequently what the speaker says would be true. (For classic

3. Paradox - Definitions From Dictionary.com One exhibiting inexplicable or contradictory aspects The silence of midnight, to speak truly, though apparently a paradox, rung in my ears (Mary Shelley) http://dictionary.reference.com/browse/paradox

SafeAddOnload(_init_luna); SafeAddOnload(show_sp); var pid = 450249; var nid = 450291; var mid = 679788; var word = 'paradox'; SafeAddOnload(init_near); Premium Content Register Log In Help ... The Web Advertisement 12 results for: paradox Browse Nearby Entries Paradiso paradoctor paradontosis ... parados paradox paradoxal Paradoxer paradoxes paradoxical ... Share This par·a·dox ˈp¦r əˌdɒks Pronunciation Key Show Spelled Pronunciation par uh -doks Pronunciation Key Show IPA Pronunciation –noun a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth. a self-contradictory and false proposition. any person, thing, or situation exhibiting an apparently contradictory nature. an opinion or statement contrary to commonly accepted opinion. [Origin: < L paradoxum < Gk par¡doxon, n. use of neut. of par¡doxos unbelievable, lit., beyond belief. See para- orthodox —Related forms par·a·dox·i·cal, par·a·dox·al, adjective par·a·dox·i·cal·ly, adverb par·a·dox·i·cal·ness, par·a·dox·i·cal·i·ty, noun par·a·dox·ol·o·gy

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HOME GAMES Paradox Titles Crusader Kings ... Lost Empire: Immortals A 4X space strategy game with thousands of stars to explore and colonize. Europa Universalis: Rome Experience one of the most defining periods in world history brought to life by this epic title. MOST SOLD GAMES EU3: Napoleon's Ambition Hearts of Iron 2 DD Armageddon Lost Empire Immortals Hearts of Iron 2 Doomsday ... Europa Universalis II LATEST NEWS NEWS ARCHIVE Official website for Europa Universalis Rome New Supreme Ruler 2020 Developer Briefing Paradox Interactive releases new in-game trailer ... Intelligence Coup Spies Supreme Ruler 2020 Screenshots PARADOX MEMBERS SOCIETY DISCUSSION FORUM Meet great people, learn more about our games and get inside tips from dedicated gamers. forum.paradoxplaza.com NEWSLETTER Sign up for the Paradox newsletter, and get all the news directly form Paradox Interactive. Sign up! SUPPORT USA / North America Click here Europe Click here Rest of the World Click here Privacy Legal Notice

7. Russell's Paradox (Stanford Encyclopedia Of Philosophy) Russell s paradox is the most famous of the logical or settheoretical paradoxes. The paradox arises within naive set theory by considering the set of all http://plato.stanford.edu/entries/russell-paradox/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Russell's Paradox First published Fri Dec 8, 1995; substantive revision Thu May 1, 2003 Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox. Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves " R ." If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics. History of the paradox Significance of the paradox Bibliography Other Internet Resources ... Related Entries History of the paradox Russell appears to have discovered his paradox in the late spring of 1901

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10. Paradox - Definition From The Merriam-Webster Online Dictionary Definition of paradox from the MerriamWebster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games. http://www.merriam-webster.com/dictionary/paradox

Home Visit Our Sites Unabridged Dictionary Learner's Dictionary ... Contact Us Also Visit: Unabridged Encyclopedia Britannica Visual ESL: Learner's for Kids: Spell It! Word Central Dictionary Thesaurus Spanish/English Medical Search "paradox" in: Thesaurus Spanish/English Medical Dictionary Open Dictionary Browse words next to: paradox Browse the Dictionary: A B C D ... Z paradox One entry found. paradox Main Entry: Pronunciation: däks, Function: noun Etymology: Latin paradoxum, from Greek paradoxon, from neuter of paradoxos contrary to expectation, from para- dokein decent Date:  a tenet contrary to received opinion 2 a  a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true b  a self-contradictory statement that at first seems true c  an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises  one (as a person, situation, or action) having seemingly contradictory qualities or phases Learn more about "paradox" and related topics at Britannica.com Pronunciation Symbols Products Premium Services ... Advertising Info

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13. Some Paradoxes - An Anthology Eubulides, the Megarian sixth century B.C. Greek philosopher, and successor to Euclid, invented the paradox of the liar. In this paradox, Epimenides, http://www.paradoxes.co.uk/

Some paradoxes - an anthology Maintained by Geoff Wilkins - email paradoxes@geoffwilkins.net 2,951,364 hits between October 2006 and February 2008 Click the W links for related Wikipedia articles God is not all-powerful as he cannot build a wall he cannot jump Contents hide Catch-22 A paradoxical notice Some proofs: Happiness or a ham sandwich? Proof that either Tweedledum or Tweedledee exists Proof that Tweedledoo exists Proofs that Santa Claus exists ... Proof that I am Dracula Liars and truthtellers: Epimenides the Cretan The liar paradox Hanging or beheading Knights and knaves ... Quine's paradox -' Yields a falsehood when appended to its quotation' Infinity: Hilbert's hotel paradox Infinite income-tax Olbers' paradox - why is the night sky dark? The unexpected hanging ... Berry's paradox - the least integer not nameable in fewer than nineteen syllables Two of Zeno's paradoxes Achilles and the tortoise Paradox of the arrow The ship of Theseus Protagoras's pupil ... Sorites paradox (paradox of the heap) Escher: Drawing hands Belvedere Waterfall Mobius band ... Curry's paradox Arithmetic and algebraic paradoxes: Proving that 2 = 1 Proving that 3 + 2 = 0 Proving that n = n + 1 Bibliography Catch-22 There was only one catch and that was Catch-22, which specified that concern for one's own safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to.

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15. Olbers's Paradox This is much less than needed to produce Olbers s paradox. The fact that the Universe has a finite age is the principal explanation of Olbers s paradox. http://zebu.uoregon.edu/~imamura/123/lecture-5/olbers.html

Olbers's Paradox for a similar picture for galaxies There is a simple, seemingly trivial question one can ask Why is the night sky dark? This question was originally posed many years ago by a series of people (Kepler, Halley ===> Jean de Cheseaux ===> Heinrich Olbers [1823]). The answer to this seemingly simple question is not trivial and tells us profound things about the Universe. Assumptions: the Universe is finite in size the stars fill the Universe uniformly each star has a luminosity L the inverse square law holds, i.e., the flux of energy from a star (energy flow per second per unit area) is given by f = L / (4 pi D ). Here L is the intrinsic luminosity of the star and D is its distance from us. Consider a shell of stars of thickness T and radius R. How much light do we receive from this shell of stars? Well, the flux of energy from one star is f = L / ( 4 pi R By insepction of the figure, if there are n stars per unit volume of the shell, then the total number of stars per shell is N = n x volume = n x 4 pi R x T The total amount of flux we receive from the shell is then F = f x N = L x n x T ===> a pretty simple and interesting result.

16. Paradox -- From Wolfram MathWorld 5) uses the term pseudoparadox to describe an apparent paradox for which, however, there is no underlying actual contradiction. http://mathworld.wolfram.com/Paradox.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Paradoxes Paradox A statement which appears self-contradictory or contrary to expectations, also known as an antinomy . Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent paradox for which, however, there is no underlying actual contradiction. Bertrand Russell classified known logical paradoxes into seven categories. Ball and Coxeter (1987) give several examples of geometrical paradoxes. SEE ALSO: Allais Paradox Aristotle's Wheel Paradox Arrow's Paradox Banach-Tarski Paradox ... Zeno's Paradoxes REFERENCES: Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 84-86, 1987. Bunch, B. Mathematical Fallacies and Paradoxes. New York: Dover, 1982. Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, 1958. Church, A. "Paradoxes, Logical." In The Dictionary of Philosophy, rev. enl. ed. (Ed. D. D Runes). New York: Rowman and Littlefield, p. 224, 1984. Curry, H. B.

17. Welcome To Paradox paradox Your plastic Pal Who’s fun to be with. Mister X. PROGRAMS. Alphas Gumby 2.0 A1 Comic Book Viewer 1.0 - A2C BETAS Gumby 1.0 - 50C http://gumby.misplacedmac.com/

Paradox Mister X PROGRAMS Alphas Gumby 2.0 - A1 Comic Book Viewer 1.0 - A2C BETAS Gumby 1.0 - 50C Comic Book Viewer - B1 DOCUMENTATION GUMBY manual 1.1 manual 1.5 COMIC BOOK VIEWER None (at the moment) SUPPORT GUMBY: Help Forums (temp down) BLOG SPECIAL THANKS TO: Sir lurch CASE Anubis ADSON JOHN DRAKE TONY THE MIDGET Happy Birthday Norm Monday August 19th, 2007 ALPHA VERSION UPDATE: Over the last 5 days, I've been helping a friend restore his site which was hacked. The alpha release will therefore happen next week-end. Well it's been a long road and it looks like the Alpha version of Gumby 2.0 will be available this coming week-end Since this will be an alpha, it will be incomplete and probably buggy. But it will give you the chance to test the modules and see if it works to your satisfaction. Of course, your feedback is essential and you can report any bugs, issues or problems you might encounter so I can fix them :D Sunday July 8th, 2007 PROGRESS REPORT Our crack staff of 60's looking non-existant engineers have been hard at work studying and coding some of the new features you have requested. So far work has been done on: Now the Xbox DL burning module is a big step for Gumbyy. I sort of have to do it because Toast won't burn Xbox360 DL discss properly. It's up to you, the users, to decide if this will be an xbox360-only feature or if I should make the disc burning more 'generic' and burn any kind of discs.

18. The Python Paradox Hence what, for lack of a better name, I ll call the Python paradox if a company chooses to write its software in a comparatively esoteric language, http://www.paulgraham.com/pypar.html

August 2004 In a recent talk I said something that upset a lot of people: that you could get smarter programmers to work on a Python project than you could to work on a Java project. I didn't mean by this that Java programmers are dumb. I meant that Python programmers are smart. It's a lot of work to learn a new programming language. And people don't learn Python because it will get them a job; they learn it because they genuinely like to program and aren't satisfied with the languages they already know. Which makes them exactly the kind of programmers companies should want to hire. Hence what, for lack of a better name, I'll call the Python paradox: if a company chooses to write its software in a comparatively esoteric language, they'll be able to hire better programmers, because they'll attract only those who cared enough to learn it. And for programmers the paradox is even more pronounced: the language to learn, if you want to get a good job, is a language that people don't learn merely to get a job. Only a few companies have been smart enough to realize this so far. But there is a kind of selection going on here too: they're exactly the companies programmers would most like to work for. Google, for example. When they advertise Java programming jobs, they also want Python experience.

19. Rhetorical Figures In Sound: Paradox paradox Figure that employs an apparent contradiction which, nonetheless, evokes some measure of truth; a statement which seems at one level to be http://www.americanrhetoric.com/figures/paradox.htm

P aradox Figure that employs an apparent contradiction which, nonetheless, evokes some measure of truth; a statement which seems at one level to be nonsensical because it moves against a normalcy. At another level, however, the figure conjures a new way of seeing or understanding, a novel meaning. Example: "I don't hustle with people who are dishonest." Woody Harrelson (from the movie White Men Can't Jump Further Examples Michael Collins They let us out of jail just so we could do our best to be put inside again , Harry. Don't you see a certain paradox in that? Hmm? Harry Boland Michael Collins : "Paradox a contradiction: Where an immovable force meets an immovable object kind of thing. Harry Boland : Zzzzzzz. Michael Collins : Hey.... delivered by Liam Neeson and Aidan Quinn (from the movie Michael Collins "Mr. Chairman, Mr. President, my fellow Democrats, my fellow Americans: I proudly and humbly accept your nomination." Hubert Humphrey

20. Time Travel Paradoxes A paradox of time travel arises in relation to this story. The narrator does indeed set himself up by his bootstraps his present and future selves all http://www.friesian.com/paradox.htm

Time Travel Paradoxes Robert Heinlein's 1941 story "By His Bootstraps" begins with the narrator writing in a philosophy thesis that time travel is impossible because time, in Immanuel Kant's terms, is only empirically real and does not exist independently among things in themselves. The narrator is then suddenly surprised to find two different versions of himself arriving from the future, with conflicting warnings and promises about what he can do. Traveling to the future, he meets an older man who repeats the promises, but whom he ends up distrusting. After some confusion, back in the present, he obtains some supplies and returns to the future to a period significantly earlier than when he would met the older man, intending to contest the future with him. Eventually, however, it turns out that he himself is the older man and his future is in fact, pace Immanuel Kant, secured. A paradox of time travel arises in relation to this story. The narrator does indeed set himself up "by his bootstraps" his present and future selves all interact with each other to produce the events. The paradoxical nature of this comes down to the case of a notebook that was provided to the narrator by the older man in the future. It contained a vocabulary of the language that was spoken by people in the future. The narrator learns the language and, as the book wears out over the years, copies it over into a notebook he had fetched from the present. This notebook, as it happens, is the very one he, as the older man, then provides to his other self. He is therefore the same person who both learns the knowledge from the notebook and put the knowledge into the notebook in the first place. The vocabulary as a certain list of items arranged in a certain way was thus complied by

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