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Topic: Epimenides paradox

	Epimenides paradox - Wikipedia, the free encyclopedia
		Paradoxical versions of the Epimenides problem are closely related to a class of more difficult logical problems, including the liar paradox, Russell's paradox, and the Burali-Forti paradox, all of which have self-reference in common with Epimenides.
		(The Epimenides paradox is usually classified as a variation on the liar paradox, and sometimes the two are not distinguished.) The study of self-reference led to important developments in logic and mathematics in the twentieth century.
		Epimenides was a philosopher and religious prophet who, against the general sentiment of Crete, proposed that Zeus was immortal.
	en.wikipedia.org /wiki/Epimenides_paradox (1138 words)

	Wikipedia: Paradox
		A paradox is an apparently true statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition.
		Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured on the roof, and disassembled in the basement.
		Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.
	www.factbook.org /wikipedia/en/p/pa/paradox.html (1443 words)

	Liar paradox - Wikipedia, the free encyclopedia
		"Epimenides paradox" is often considered an equivalent or interchangeable term for "liar paradox" and it is also the kind of supposed "liar paradox" that is best known to the general public.
		This response to the paradox is, in effect, to reject one of our common beliefs about truth and falsity: the claim that every statement has to be one or the other.
		And in the self-referential spirit of the Liar Paradox, the phrase "it is true that..." is equivalent to "this whole statement is true and...".
	en.wikipedia.org /wiki/Liar_paradox (1495 words)

	Paradox - Wikipedia
		The identification of a paradox based on seemingly simple and reasonable concepts has often lead to siginificant advances in science, philosophy and mathematics.
		Epimenides paradox: a Cretan says "all Cretans are liars".
		Simpson's paradox: data sets support opposite hypothesis when taken together than when taken separately.
	nostalgia.wikipedia.org /wiki/Paradox (164 words)

	SOAS: The Brunei Gallery: Exhibitions: Paradoxes: An exhibition exploring contradiction
		A paradox is an apparently true statement that appears to lead to a contradiction or to a situation that defies intuition.
		Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, exposing the limitations of assumed language and reason.
		Paradoxes are an illustration of the nature of reality evincing that whilst we live in a time when things appear increasingly explainable, logical, and rational - therein lay flaws and anomalies.
	www.soas.ac.uk /gallery/paradoxes/home.html (327 words)

	Are all Cretan Liars as Epimenides the Exorcist says?
		Epimenides, numbered by some among the seven wise men, was revered throughout Greece as one whom a heavenlier genius animated and inspired.
		Epimenides complied with the prayer of the Athenians he arrived at Athens, and completed the necessary expiation in a manner somewhat simple for so notable an exorcist.
		Interestingly, St. Paul makes reference to this paradox, in a way that shows he knew of it but did not understand it: He says of Cretans that "they are all liars, as one of their own has said." But the context (Titus 1:12-14) suggests that he took it seriously as a denunciation of Cretans.
	www.mlahanas.de /Greeks/CretanLiars.htm (1208 words)

	Liar paradox: Encyclopedia topic (Site not responding. Last check: 2007-10-21)
		Epimenides (Epimenides: epimenides of knossos (crete) was a semi-mythical 6th century bc greek prophetseer...
		The latter sentence is not a paradox, of course, because it is only our ignorance, not our deeply held beliefs about truth, that leave us unable to assign truth values to the clauses.
		This is the essence of the liar paradox.
	www.absoluteastronomy.com /reference/liar_paradox (2080 words)

	liar (Site not responding. Last check: 2007-10-21)
		This paper applies both classical (Boolean) and quantum logic to analysis of the Liar paradox which is taken as a typical example of a self-referential negation in the perception space of an undivided observer.
		The paradoxes are 'I, a Cretan, say that all Cretans are liars' (Epimenides), 'who shaves the barber who shaves everyone who does not shave himself?' (Russell) and 'the first natural number that cannot be named in less than fourteen words' (a thirteen word definition allegedly due to Berry).
		E may escape the paradox by becoming an element of the meta-set NC, however, the operation is either infinitely repeated or E adopts the truth-value [0] = NL for good.
	cogprints.org /1210/02/liarfin3.html (5394 words)

	[No title]
		The paradox is that the Axiom of Doubt must allow for the possibility that this dominant view may be correct.
		We could attempt to eliminate the paradox by saying that the Axiom of Doubt applies to all beliefs except one, namely itself, but in my opinion this is a petty move and severely undermines the force of the axiom.
		The Axiom of Doubt (explicitly paradoxical version) While the truth is something that we can collectively make progress towards, I must allow that the beliefs I currently hold, including this axiom, may be false and that others' beliefs may be true.
	home.vtown.com.au /~jmcnicol/NvT/30/30.9.txt (1245 words)

	Little Bummer - February 2003 (Site not responding. Last check: 2007-10-21)
		Some students have the misconception that paradoxes are manifestations of contradictions, but a paradox may or may not be a contradictory statement.
		Epimenides states, "All Cretans are liars.", so each and every Cretan is a liar, including himself.
		I have convinced myself that the Epimenides Paradox founds on the definitions of logic and that there is no contradiction in the statement regardless of what other people may think.
	www.jarwey.net /index.php?m=200302 (917 words)

	imagination required: My home page (Site not responding. Last check: 2007-10-21)
		The Cretan Paradox is attributed to the Cretan poet Epimenides.
		Epimenides the Cretan says "All Cretans are liars." This statement, because it was uttered by a Cretan, is true if and only if it is false.
		The Epimenides statement was clearly an attempt, however flawed, to exhibit a logical antinomy.
	www.20six.co.uk /quanyie/weblogEntries/send.htm?entryId=15h1hq0ets3gy (566 words)

	epimenides
		Epimenides was a Greek philosopher and prophet who lived around 6 th century BC on the island Knossos (now known as Crete).
		This is probably where the origin of the famous Epimenides' paradox lies: the lie being that the Cretans lied that Zeus was dead or/and mortal.
		Epimenides' skin was preserved and kept at the court of Sparta and for a long time it was considered to bring good luck to the warriors.
	www.mathsisgoodforyou.com /people/Epiminides.htm (289 words)

	Paradoxes!
		His most famous paradox was the set paradox developed in 1901.It is If S is a member of itself, then by definition it must not be a member of itself.
		The paradox was of significance to Frege's logical work since, in effect, it showed that the axioms Frege was using to formalize his logic were inconsistent.
		These four responses to the paradox, in turn, have helped logicians develop an explicit awareness of the nature of formal systems and of the kinds of metalogical results which are today commonly associated with them.
	www.andrews.edu /~calkins/math/biograph/199900/topparad.htm (849 words)

	Liar paradox - Wikipedia
		The liar paradox, attributed to the Greek philosopher Eubulides of Miletus who lived in the fourth century B.C., is the statement
		As opposed to the Epimenides paradox, this is a true paradox: assuming that the statement is true, then it must be false; assuming it is false, then it must be true.
		The proof of Gödels Incompleteness Theorem essentially consists of a formally correct formulation of a variation of this paradox in the context of a sufficiently strong axiomatic system.
	nostalgia.wikipedia.org /wiki/Liar_paradox (151 words)

	Emptybottle.org: Pointing
		Of course, if the statement is true, then Epimenides is a liar, and thus the statement is false.
		The same paradox is manifest if you say "I am lying" or "This statement is false".
		It would be possible, of course, to build a group of 3 or 4 or more sentences, each of which in isolation is perfectly acceptable, but which as a group leads us into botheration again.
	www.emptybottle.org /glass/2002/06/pointing.php (547 words)

	Epimenides Paradox: Was Paul "Inspired"? (Islamic Attack on Paul's Inspiration)
		If it is not a paradox, one may argue that Paul's calling it "true" was a subtle bit of mockery with tremendous foresight regarding later developments in logic.
		We may feel intuitively that the argument is paradoxical; yet, from a formal logic point of view, it does not really have the look of a paradox.
		If sophisticated analysis determines after all that this statement by Epimenides is not paradoxical, and thus has a truth value, the only consistent supposition we can make is that it is false.
	www.freerepublic.com /focus/f-religion/1283048/posts (2502 words)

	Trexle - Paradoxes (Site not responding. Last check: 2007-10-21)
		The Berry Paradox and Godel's Incompleteness Theorem - Transcript of a lecture by Gregory Chaitin on how the Berry Paradox ("the smallest number that needs at least n words to specify it, where n is large") illuminates Godel's Incompleteness Theorem.
		Paradoxes and Dilemmas - Common paradoxes and dilemmas, particularly of the social type: the Voting Paradox, Prisoner's Dilemma, Newcomb's Paradox, Unexpected Hanging, Execution Paradox, and the Self-Amendment Paradox.
		Paradox or Fallacy - A discussion on paradox, with the goal being to determine what is paradox and what is fallacy.
	www.trexle.com /Directory/Top/Society/Philosophy/Philosophy_of_Logic/Paradoxes (274 words)

	Talk:Stephenson:Neal:Quicksilver:688:Theologians? Sorcerers? (Neal Stephenson) - Metaweb (Site not responding. Last check: 2007-10-21)
		This is, of course, a Biblical reference to Epimenides' Paradox.
		The Greek philosopher Epimenides relates in the 6th century BC that "All Cretans are liars...
		It should not be confused with the Liar paradox, which is in fact paradoxical.
	www.metaweb.com /wiki/wiki.phtml?title=Talk:Stephenson:Neal:Quicksilver:688:Theologians?_Sorcerers?_(Neal_Stephenson) (487 words)

	Epimenides (Site not responding. Last check: 2007-10-21)
		Epimenides was also said to have prophesied at Sparta on military matters.
		Pausanias reports that when Epimenides died, his skin was found to be covered with tattooed writing.
		The earliest unmistakable reference to the Epimenides paradox as it is known today is an article by Bertrand Russell on the theory of types dating to 1908.
	pda.molinu.com /wiki/en/ep/Epimenides.htm (496 words)

	Some paradoxes (Site not responding. Last check: 2007-10-21)
		In this paradox, Epimenides, the Cretan, says, "All Cretans are liars." If he is telling the truth he is lying; and if he is lying, he is telling the truth.
		The paradox is simply a proof that no village can contain a man who shaves all and only those men in it who do not shave themselves.
		The paradox arises from a disguised breach of the arithmetical prohibition on division by zero, occurring at (5): since a = b, dividing both sides by (a - b) is dividing by zero, which renders the equation meaningless.
	www.wordsmith.demon.co.uk /paradoxes (3977 words)

	Paradox
		Epimenides from Crete became famous for the liars paradox, for saying that all cretans are liars (well, his wording could be more strict but you know what he meant).
		We have what is called a latch, something that within binary circutry can be used as memory to save a binary digit (well, to use it as memory you must have an extra input to tell it what it should remember).
		That a paradox is self-referencing, that it is talking about itself is something that has been known, I do not know for how long.
	web.comhem.se /~u42145233/pdox.htm (684 words)

	Epimenides' Paradox: Was Paul Inspired?
		Epimenides was a Cretan who said: "All Cretans are liars".
		One of the interesting things is that Paul quote the Epimenides' Paradox, specifying that the speaker himself was a Cretan.
		People have been trying to show that it is no longer a paradox when fuzzy logic is brought into the scene.
	www.islamic-awareness.org /Bible/Text/paul.html (338 words)

	Amazon.co.uk: Paradox: Books (Site not responding. Last check: 2007-10-21)
		Paradox may be a little heavy on martial-arts action for some tastes, but the roller-coaster plot is full of unexpected twists, revelations, biotechnological oddities, changes of course and unlikely alliances.
		However, it could be said that Paradox lacks some of the characterisation that served his first novel so well.
		Sometimes, it seems as though Paradox could easily become dated by being too informed by twentieth century science, and may have already been superseded by events The Big Crunch would seem to be vital, but recent research on supernova tends to suggest that there's some force in space continually expanding the universe, contrary to gravity.
	www.amazon.co.uk /exec/obidos/ASIN/0593045734 (1655 words)

	Muhammad & Islam :: Jesus & Christianity
		Eubulides, the Megarian sixth century B.C. Greek philosopher, and successor to Euclid, invented the paradox of the liar.
		Epimenides cannot be telling the truth, but he may be lying: the truth may be that some Cretans, including Epimenides, are liars, but not all.
		Epimenides Paradox -- from MathWorld A version of the liar's paradox, attributed to the philosopher Epimenides in the sixth century BC.
	muhammad-jesus.blogspot.com (1416 words)

	Apologetics Press - Epimenides' Paradox: A Logical Discrepancy In Titus 1:12?
		However, when Paul spoke to Titus concerning his mission on the island of Crete, some critics have suggested that the apostle committed a logical fallacy by quoting the Cretan poet Epimenides: “One of them, a prophet of their own, said, ‘Cretans are always liars, evil beasts, lazy gluttons.’ This testimony is true” (Titus 1:12-13a).
		This is a form of the logical paradox commonly known as Epimenides’ Paradox: “A Cretan said, ‘All Cretans are liars.’ ” If, as Paul affirms, this statement is true, then the statement is false because a Cretan, who is a liar, made it.
		Epimenides had made a hyperbolic statement regarding the conduct of the people of Crete, and Paul was agreeing with him in order to point out to Titus the difficulty facing the Cretan elders.
	www.apologeticspress.org /articles/620 (498 words)

	ipedia.com: Liar paradox Article (Site not responding. Last check: 2007-10-21)
		The liar paradox, attributed to the Greek philosopher Eubulides of Miletus who lived in the fourth century B.C, is the paradoxical statement I am lying now.
		The liar paradox, attributed to the Greek philosopher Eubulides of Miletus who lived in the fourth century B.C, is the paradoxical statement
		As opposed to the Epimenides paradox, this statement is indeed paradoxical: assuming that the statement is true, then it must be false; assuming it is false, then it is not false.
	www.ipedia.com /liar_paradox.html (764 words)

	Paradoxes in general (Site not responding. Last check: 2007-10-21)
		Paradoxes are as old as the known history of the western philosophy.
		One of the most famous paradoxes of ancient times is Epimenides' paradox of the Cretan who utters: "All Cretans are liars!".
		And in addition there are other paradoxes such as: Sorite's paradox; the analysis paradox; zenon's paradoxes and pragmatic paradoxes.
	www.algonet.se /~jen-tale/para_gen.html (1043 words)

	Intractable Problems Issue 12
		Consider the Epimenides paradox, which states: “This statement is false.” Actually, Epimenides, who was a Cretan, really said that “All Cretans are liars!” However, because ethnic and cultural bias is frowned upon today we try to use the more general form that does not single out one specific group of people.
		More importantly, the Russell paradox showed that all of mathematics cannot be built on the unshakable foundation of logic, there is a crack in the foundation.
		Well, the Berry paradox was used by computer scientist Gregory Chaitin [1] to prove that every computer, every formal system, and every human production is limited; there are always sequences too complex to be generated, outcomes too complex to be predicted, and events too dense to be compressed.
	www.kisekaeworld.com /Intractable/issue12.html (550 words)

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