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Topic: Barber paradox

Related Topics

Paradox

Liar paradox

Mathematical class

Berry paradox

Zenos paradoxes

Principia Mathematica

Bertrand Russell

The Barber of Seville

Monty Hall problem

Haircut

Allegany County, New York

Facial hair

Bowl cut

List of lawsuits relating to haircuts

Barbershop

	Russell's paradox - Wikipedia, the free encyclopedia
		There are some versions of this paradox which are closer to real-life situations and may be easier to understand for non-logicians: for example, the Barber paradox supposes a barber who shaves everyone who does not shave himself, and no one else.
		The Barber paradox, in addition to leading to a tidier set theory, has been used twice more with great success: Kurt Gödel proved his incompleteness theorem by formalizing the paradox, and Turing proved the undecidability of the Halting problem (and with that the Entscheidungsproblem) by using the same trick.
		Thus, it may be tempting to think that the paradox is avoidable by avoiding the law of excluded middle, as with Intuitionistic logic.
	en.wikipedia.org /wiki/Russells_paradox (1512 words)

	Barber paradox - Wikipedia, the free encyclopedia
		The Barber paradox is a puzzle attributed to Bertrand Russell.
		Smullyan argues that the paradox is akin to the statement "I know a man who is both five feet tall and six feet tall," in effect claiming that the "paradox" is merely a contradiction, not a true paradox at all, as the two axioms above are mutually exclusive.
		A paradox is supposed to arise from plausible and apparently consistent statements; Smullyan suggests that the "rule" the barber is supposed to be following is too absurd to seem plausible.
	en.wikipedia.org /wiki/Barber_paradox (415 words)

	Barber paradox: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-13)
		A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition, such as "this...
		The raven paradox is a paradox proposed by the german logician carl gustav hempel in the 1940s to illustrate a problem where inductive logic violates...
		The omnipotence paradox is a philosophical paradox that arises when philosophers attempt to reconcile omnipotence with the existence of logic in debating...
	www.absoluteastronomy.com /encyclopedia/b/ba/barber_paradox.htm (1144 words)

	Paradox (Site not responding. Last check: 2007-10-13)
		Of the paradoxes we have to draw on, only the barber paradox can be considered to be veridical, for it is generally conceded that there is no flaw in the paradoxical argument, either in the premises or in the reasoning.
		But it is now generally recognized that the story that gives rise to the paradox (there is a village in which there is a barber who cuts the hair of all and only those villagers who do not cut their own hair) is incoherent, that it is impossible for there to be such a village.
		There are thus two principal options in providing a resolution for a type I paradox: (i) we may dispel the illusion that the argument is air-tight by isolating and diagnosing a flaw or fallacy in the argument; or (ii) we may explain away the appearance of falsity in the conclusion.
	www.wordtrade.com /philosophy/contemporary/paradox.htm (5816 words)

	PARADOX (Site not responding. Last check: 2007-10-13)
		If the barber is assumed to be in one set, he appears in the other.
		This situation occurs because the barber both appears in the set and is used to define the set.
		Paradoxes appear not only in logic but also in interpersonal communication, e.g., double-bind, in social organization and might be the stimulus for morphogenesis.
	pespmc1.vub.ac.be /ASC/PARADOX.html (481 words)

	Russell’s paradox
		A paradox uncovered by Bertrand Russell in 1901, which forced a reformulation of set theory.
		One version of Russell's paradox, known as the barber paradox, considers a town with a male barber who, every day, shaves every man who doesn't shave himself, and no one else.
		Russell's paradox underlies the proof of Gödel's incompleteness theorem as well as Alan Turing's proof of the undecidability of the halting problem.
	www.daviddarling.info /encyclopedia/R/Russells_paradox.html (341 words)

	Paradox - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-13)
		A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition, such as "This statement is false".
		Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context (or language) to lose their paradox quality.
		Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement.
	www.phatnav.com /wiki/index.php?title=Paradox (1984 words)

	Peter Suber, Paradox of Self-Amendment, Section 1
		Paradoxes are disturbing because we have difficulty denying them status as meaningful statements subject to the normal rules about contradiction and truth, and we are rarely willing to amend our logical rules merely to accommodate a string of words that twists them up.
		Russell's paradox is of the Barber-type, not the Liar-type.
		Lawyers under a deadline are normally unaware of the centuries of prior thought on the paradoxes, and in any case might find it irrelevant to the "condensation" of the paradox in their particular case and to the inherited rules under which they must devise a solution.
	www.earlham.edu /~peters/writing/psa/sec01.htm (7901 words)

	Peter Suber, "Paradox of Self-Amendment in Constitutional Law"
		The paradox of the Barber is that of a shaved man who shaves all and only those in his own town who do not shave themselves.
		The paradox of omnipotence seems to be of the "Barber-type", for it seems to prove that omnipotence cannot exist as naively conceived.
		Insofar as the paradox depends on an inconsistency between premises and conclusion, it may be defined away by adopting a definition of inconsistency that does not cover most instances of self-amendment.
	www.earlham.edu /~peters/writing/psaessay.htm (9915 words)

	Paradoxes (Site not responding. Last check: 2007-10-13)
		The paradoxes in intuitive set theory are actually antinomies and are the result of the use of the unrestricted principle of comprehension/abstraction (defining a set A= {x : P(x)} where no restriction is placed on P(x).
		That paradoxes should arise in what intuitively appears to be a simple and correct theory illustrates the pitfalls of informal thought.
		Paradox of the race course: it is impossible for a runner to traverse a race course.
	cs.wwc.edu /~aabyan/CII/Paradox.html (767 words)

	ipedia.com: Russell's paradox Article (Site not responding. Last check: 2007-10-13)
		There are some versions of this paradox which are closer to real-life situations and may be easier to understand for non-logicians: For example, the Barber paradox which considers a barber who shaves everyone who does not shave himself, and no one else.
		After this paradox was described, set theory had to be reformulated axiomatically as axiomatic set theory in a way that avoided this and other related problems.
		In context of the Barber example, the latter requirement would ensure the consideration instead, for instance, of a barber who shaves everyone who does not shave himself, as well as the barber himself; perhaps along with a town sheriff who may arrest all those who cannot arrest themselves, with exception of the sheriff.
	www.ipedia.com /russell_s_paradox.html (1040 words)

	Set Theory and Paradoxes (Site not responding. Last check: 2007-10-13)
		Yet if the barber does shave himself, then he is shaved by the barber, but according to the statement the barber only shaves those who do not shave themselves, so he does not shave himself.
		Grelling's paradox and Russell's paradox are usually considered to be of distinct types, although the distinction is subtle and contested.
		In contrast, Russell's paradox is not a paradox of semantics but one of set theory, and the appropriate resolution is Russell's own "theory of types".
	www.geocities.com /mathfair2002/school/logi/logi0.htm (3337 words)

	Zeno's Paradoxes--"True Implies False"
		Yet it is the nature of paradoxes that they mask such logical errors with clever wordings.
		The assumption is the premise (1) is false.
		Thus, the paradox requires as true that which it is trying to prove false.
	www.allthatcounts.com /misc/zenlogic.htm (421 words)

	TheBarber.html
		A paradox is a statement or group of statements that lead to a logical self-contradiction.
		If the barber shaves himself then he is a man on the island who shaves himself hence he, the barber, does not shave himself.
		If the barber does not shave himself then he is a man on the island who does not shave himself hence he, the barber, shaves him(self).
	www.umsl.edu /~siegel/SetTheoryandTopology/TheBarber.html (243 words)

	Aristotle and the Paradoxes of Logic
		A paradox however is only due to a striking violation of at least one of Aristotle's laws of logic.
		The barber is not aware that his claim violates both the laws of noncontradiction and identity.
		One has to consider such paradoxes as a warning that an element m is neither the member of a set S nor of the complementary set S'.
	www.homestead.com /nilog/files/aristotle_and_the_paradoxes_of_l.htm (1985 words)

	LINGUIST List 3.750: The Barber Paradox (Site not responding. Last check: 2007-10-13)
		In a certain village there is a man, so the paradox runs, who is a barber; this barber shaves all and only those men in the village who do not shave themselves.
		This paradox as studied in Mathematics is a result of an inherent problem with defining a set as {xx possesses certain properties} where x is an individual in the universe of entities under study (and "" means "such that").
		The paradox is that S can neither be a member of itself nor not be a member of itself.
	www.ling.ed.ac.uk /linguist/issues/3/3-750.html (799 words)

	Paradox
		Paradoxes are interesting bit of logic, literally meaning "a self-contradiction".
		The Barber paradox is a paradox that relates to mathematical logic and
		I think that the point of the paradox is that barber can't shave and not shave himself at the same time.
	www.trap17.com /forums/page-1-t9464-s0.html (818 words)

	Re: Russell's paradox re-stated as a tautology
		One involves a barber, and another a set (the > proof that the class of barbers is disjoint from the class of sets is > left to the reader with too much time on his hands).
		It quite utterly fails to meet the requirement of showing that the Barber paradox is a pseudo-paradox as opposed to a paradox.
		In the Russell-paradox case, R is epsilon; in the Barber of Seville case, R is "shaves".
	www.usenet.com /newsgroups/sci.logic/msg05470.html (1029 words)

	Mathematical mysteries: The Barber's Paradox
		This is the Barber's Paradox, discovered by mathematician, philosopher and conscientious objector Bertrand Russell, at the begining of the twentieth century.
		The paradox raises the frightening prospect that the whole of mathematics is based on shaky foundations, and that no proof can be trusted.
		In the Barber's Paradox, the condition is "shaves himself", but the set of all men who shave themselves can't be constructed, even though the condition seems straightforward enough - because we can't decide whether the barber should be in or out of the set.
	plus.maths.org /issue20/xfile (971 words)

	Barber paradox: Encyclopedia topic (Site not responding. Last check: 2007-10-13)
		This paradox is attributed to Bertrand Russell (Bertrand Russell: English philosopher and mathematician who collaborated with Whitehead (1872-1970)), a British logician (logician: A person skilled at symbolic logic) who in 1901 constructed Russell's paradox (Russell's paradox: russells paradox (also known as russells antinomy) is a paradox discovered by...
		As shown in the "impossible situation" analysis above, if the given definition of this barber can be used in a logical analysis, then one is led to the contradiction that the barber both does shave himself and does not shave himself.
		The actual contradiction in the Barber paradox, following Prior's analysis, is in the implicit assertion that the flawed definition of the barber can be used in a logical analysis.
	www.absoluteastronomy.com /reference/barber_paradox (382 words)

	Some paradoxes (Site not responding. Last check: 2007-10-13)
		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)

	Gödel and the 'paradoxes' Metalogic A3/4 - abelard
		Whether or not the purported barber shaves himself is a matter of empiric fact, it is not a ‘matter of logic’.
		Russell’s ‘paradox’ is founded on the error of not distinguishing the formation of a new item, that is the forming of the catalogue, from the original items to be catalogued.
		In just the ‘same’ manner as in the barber ‘paradox’, where in reality the barber either does or does not ‘shave himself ’, in the real world Epimenides’s Cretan jokester is either ‘a liar’ or he is not.
	www.abelard.org /metalogic/metalogicA3.htm (8471 words)

	LINGUIST List 3.741: he Barber Paradox (Site not responding. Last check: 2007-10-13)
		But the Spanish Barber's paradox, because it claims to be a paradox, whatever its exact wording, rules that out: male and clean-shaven they must be, and using tweezers, smouldering walnut shells, and other untonsorial artifices on themselves is out too.
		The first time I read the Barber paradox, I remember saying to myself immediately "this is stupid, it would have me believe that the barber is not himself".
		The barber of barbers must belong to a new caste, the catalog of catalogs that do not list themselves hide on a different floor.
	www.ling.ed.ac.uk /linguist/issues/3/3-741.html (2003 words)

	Amazon.com: Paradoxes: Their Roots, Range, and Resolution: Books: Nicholas Rescher (Site not responding. Last check: 2007-10-13)
		A paradox (from the Greek word meaning “contrary to expectation”) is a statement that seems self-contradictory but may be true.
		Exploring the distinction between truth and plausibility, the author presents a standardized, straightforward approach for deciphering paradoxes — one that can be applied to all their forms, whether clever wordplay or more complex issues.
		His point here is that paradoxes become resoluble if we break them out into propositions, each of which is under consideration as a _candidate_ for truth, but which we can decide to reject if we like.
	www.amazon.com /exec/obidos/tg/detail/-/0812694376?v=glance (1657 words)

	Barber's paradox
		The barber is not included in "the men"(third person) as referred in the last sentence.
		A little known fact: There were actually TWO barbers in Seville (and the next nearest barber is a hundred mile train ride away in Quadalquivir).
		Since, there are only TWO barbers in town, and it was mentioned that he has a terrible haircut.
	www.physicsforums.com /showthread.php?t=89952 (1224 words)

	Testing Your Skepticism Quotient
		Hence, if our barber shaves himself, then he doesn't and if he does not shave himself, then he does.
		A paradox of this genre essentially destroyed approximately ten years work by Bertrand Russell and A.N. Whitehead.
		When the paradox was revealed to Russell by Frege, he was devastated by the revelation.
	www.skeptic.ca /testing_your_skepticism_quotient.htm (1199 words)

	The Barber Paradox (Site not responding. Last check: 2007-10-13)
		Consider all of the men in a small town as members of a set.
		Obviously, we can further divide the set of men in this town into two further sets, those who shave themselves, and those who are shaved by the barber.
		The barber cannot shave himself, because he has said he shaves only those men who do not shave themselves.
	www.geocities.com /CapitolHill/Lobby/3022/barber.html (113 words)

	53. The Barber (Site not responding. Last check: 2007-10-13)
		Russell's famous Barber Paradox was very important to the subject of set theory.
		There is a barber in the town of Seville who shaves all and only those men who do not shave themselves.
		Russell's solution to this paradox is simply to deny that sets can be members of themselves.
	people.uncw.edu /stanleym/bewitch/53.html (346 words)

	[No title]
		The Spanish barber paradox has always seemed vacuous to me. The argument makes sense if, and only if, you subscribe to the hidden assumption that the barber is not himself.
		This is how I have explained this paradox (and the heterological paradox, and the halting problem, and in fact all diagonalization arguments) to students: You have a square matrix M, all of whose cells contain either a 1 or a 0.
		As presented in J. Guy's posting, the 'paradox' is reduced to: For every individual x in the Spanish town, Either x shaves x Or Pablo (the barber) shaves x And hence the 'paradox' is not a paradox.
	www.umich.edu /~archive/linguistics/linguist.list/volume.3/no.701-750 (13208 words)

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