1. Russell's Paradox - Wikipedia, The Free Encyclopedia From Wikipedia, the free encyclopedia. Jump to navigation, search. Part of the foundations of mathematics, Russell s paradox (also known as Russell s http://en.wikipedia.org/wiki/Russell's_paradox

Russell's paradox From Wikipedia, the free encyclopedia Jump to: navigation search Part of the foundations of mathematics Russell's paradox (also known as Russell's antinomy ), discovered by Bertrand Russell in , showed that the naive set theory of Frege leads to a contradiction. It might be assumed that, for any formal criterion, a set exists whose members are those objects (and only those objects) that satisfy the criterion; but this assumption is disproved by a set containing exactly the sets that are not members of themselves. If such a set qualifies as a member of itself, it would contradict its own definition as a set containing sets that are not members of themselves . On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition. This contradiction is Russell's paradox. In 1908, two ways of avoiding the paradox were proposed, Russell's type theory and Ernst Zermelo 's axiomatic set theory , the first consciously constructed axiomatic set theory . Zermelo's axioms went well beyond Frege's axioms of extensionality and unlimited set abstraction , and evolved into the now-canonical ZFC set theory.

2. Upto11.net - Wikipedia Article For We could not find this article in our database. If you feel that you ve reached this page in error please let us know about it. http://www.upto11.net/generic_wiki.php?q=russell's_paradox

3. Puzzles/Set Theory Puzzles/Russell's Paradox - Wikibooks, Collection Of Open-con From Wikibooks, the opencontent textbooks collection. Puzzles Set theory puzzles. Jump to navigation, search. Puzzles Set theory Puzzles A strange http://en.wikibooks.org/wiki/Puzzles/Set_theory_puzzles/Russell's_Paradox

Puzzles/Set theory puzzles/Russell's Paradox From Wikibooks, the open-content textbooks collection Puzzles Set theory puzzles Jump to: navigation search Puzzles Set theory Puzzles Does the set of all sets that do not contain themselves exist? hint Retrieved from " http://en.wikibooks.org/wiki/Puzzles/Set_theory_puzzles/Russell%27s_Paradox Subject Puzzles Views Module Discussion Edit this page History Personal tools Log in / create account Navigation Main Page Help Cookbook Wikijunior ... Donations Community Bulletin Board Community portal Reading room Help cleanup ... Contact us Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 00:08, 24 May 2007. All text is available under the terms of the GNU Free Documentation License (see for details). Wikibooks® is a registered trademark of the Wikimedia Foundation, Inc. About Wikibooks

4. Russell's Paradox - Interaction-Design.org: A Site About HCI, Usability, UI Desi URL http//www.interactiondesign.org/dictionary/russell s_paradox.html. Advertise here.. © Site Copyright/IP Policy Privacy Changelog http://www.interaction-design.org/dictionary/russell's_paradox.html

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Web Kids.Net.Au Web Sites Encyclopedia Dictionary Thesaurus Search Web Kids.Net.Au Encyclopedia Sponsors Encyclopedia Article Content Warning function.include ]: failed to open stream: No such file or directory in /home/kidsnetau/kidsnetau2006/encyclopedia/wiki/tero-dump/wikipedia/index.php on line Warning function.include /home/kidsnetau/kidsnetau2006/encyclopedia/wiki/tero-dump/wikipedia/index.php on line All Wikipedia text is available under the terms of the GNU Free Documentation License Link to Kids.Net.Au About Us Submit a question, comment or suggestion K ... u - kids safe portal for children, parents, schools and teachers.

8. Russell's Paradox - Biocrawler Russell s_paradox. Wikipedia (http//en.wikipedia.org/wiki/Main_Page) Russell s_paradox (http//en.wikipedia.org/wiki/Russell s_paradox) version history http://www.biocrawler.com/encyclopedia/Russell's_paradox

Inline videos See also: Category: Articles with embedded Videos. Russell's paradox From Biocrawler Russell's paradox (also known as Russell's antinomy ) is a paradox discovered by Bertrand Russell in which shows that the naive set theory of Cantor and Frege is contradictory. Consider the set M to be "The set of all sets that do not contain themselves as members". Formally: A is an element of M if and only if A is not an element of A In Cantor's system, M is a well-defined set . Does M contain itself? If it does, it is not a member of M according to the definition. On the other hand, if we assume that M does not contain itself, then it has to be a member of M , again according to the very definition of M . Therefore, the statements " M is a member of M " and " M is not a member of M " both lead to contradictions (but see Independence from Excluded Middle below). In Frege's system, M corresponds to the concept does not fall under its defining concept . Frege's system also leads to a contradiction: that there is a class defined by this concept, which falls under its defining concept just in case it does not. Note: This article uses specialized mathematical symbols Table of contents showTocToggle("show","hide")

9. X = All Groups That Do Not Include Itself [Archive] - TheologyOnline Forums Greywolf. February 5th, 2007, 0620 PM. Are you thinking of Russell s Paradox? http//en.wikipedia.org/wiki/Russell s_paradox http://www.theologyonline.com/forums/archive/index.php/t-35396.html

TheologyOnline Forums Politics, Religion, And The Rest . . . and The Rest PDA View Full Version : X = all groups that do not include itself OlDove February 5th, 2007, 05:14 PM X = all groups that do not include itself. whats the fancy word for that? does "X" belong in group X? what would be the opposite to this? Greywolf February 5th, 2007, 05:20 PM Are you thinking of Russell's Paradox? http://en.wikipedia.org/wiki/Russell's_paradox OlDove February 5th, 2007, 05:24 PM Are you thinking of Russell's Paradox? http://en.wikipedia.org/wiki/Russell's_paradox yep, thank you.

10. Concepts As Sets http//en.wikipedia.org/wiki/Russell s_paradox Speculative reason will be misapplied beyond the limits of possible experience while considering such topics http://www.mathkb.com/Uwe/Forum.aspx/math-logic/3607/Concepts-as-sets

Home Contact Us FAQ Link to Us ... Discussion Groups Mathematics General Topics Research Operations Research Statistics ... Recreational Math Math Software Maple Mathematica MATLAB Scilab ... December 2006 Tip: Looking for answers? Try searching our database. Concepts as sets Thread view: Tree View List View (postings sorted by date) Single Message View Enable EMail Alerts Start New Thread Thread rating: uweWriteArtHdr('','','',1) J P - 26 Dec 2006 08:49 GMT The naive set theory says that there is no "Universal" set or a "set of everything" as this set leads to paradoxes. Considering that in natural language a concept is a set then the creation of universal sets or sets of everything in the form of absolute concepts (truth, good, God, etc.) leads to paradoxes. OTOH all of the arguments that take place using natural language can be reduced to three types: 1. Attempts to find the common ground or the intersection of the properties included in our individual definitions of concepts; 2.Attempts to find the differences or the relative complements in our individual definitions of the concepts' 3 Attempts to find, to create a union of all the properties included in

11. Russell's Paradox (logic) - Philosophy Dictionary And Research Guide Wikipedia and Wikis. Russell s paradox Wikipedia http//en.wikipedia. org/wiki/Russell s_paradox. Other. Stanford Encyclopedia of Philosophy entry http://www.123exp-beliefs.com/t/00804075899/

The Language of Philosophy - Dictionary and Research Guide Provided by Search: Add to Favorites Russell's paradox Russell's paradox (also known as Russell's antinomy) is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Frege is contradictory. Wikipedia and Wikis Russell's paradox - Wikipedia http://en.wikipedia.org/wiki/Russell's_paradox Other Stanford Encyclopedia of Philosophy entry http://plato.stanford.edu/entries/russell-paradox/ Russell's Paradox http://www.cut-the-knot.org/selfreference/russell. ... Keywords and Synonyms Russell's paradox, List of all lists which do not contain themselves, Russell set, Russel's paradox, Paradosso di Russell, Russell paradox, Russell's antinomy, List of lists which do not include themselves, List of all lists which do not include themselves, List of lists not listed anywhere, List of all lists that do not contain themselves, List of every Wikipedia list that does not contain itself, List of lists that do not contain themselves, List of all Wikipedia lists that do not contain themselves, Bertrand Russell Paradox More topics about: Russell's paradox Edit this page Add new links, rate and edit existing links, or make suggestions. - Staff

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13. SetTheory - PineWiki But you can get into trouble if you try to build sets that are too big Russell s_paradox constructs the set S = { x x x }, and asks if S is an element http://pine.cs.yale.edu/pinewiki/SetTheory

PineWiki Search: Login SetTheory FrontPage FindPage ... SetTheory Immutable Page Comments Info Attachments More Actions: Raw Text Print View Render as Docbook Delete Cache Check Spelling Like Pages Local Site Map Rename Page Copy Page Delete Page My Pages Subscribe User Remove Spam Revert to this revision Package Pages Sync Pages Load Save Set theory is the dominant foundation for mathematics. The idea is that everything else in mathematics—numbers, functions, etc.—can be written in terms of sets, so that if you have a consistent description of how sets behave, then you have a consistent description of how everything built on top of them behaves. If predicate logic is the machine code of mathematics, set theory would be assembly language. Set theory is defined by a collection of axioms, which describe the behavior of its only predicate symbol, ∈, a mutated version of the Greek letter epsilon. The interpretation of x∈y is that x is a member of (also called an element of) y. There is also the symbol ∉ (is not an element of), where x ∉ y is defined to mean ¬(x∈y); and ∋ (contains), where y ∋ x is the same as x ∈ y. Any set contains zero or more elements, and has no other properties other than what elements it contains. Formally, this means that if two sets contain the same elements, they're the same set. To make this explicit, we have the Axiom of Extensionality ∀x ∀y (x = y ⇔ ∀z (z ∈ x ⇔ z ∈ y)).

14. Logical Paradoxes By Robert L. Baber Wikipedia, The Free Encyclopedia, Russell s paradox , http//en2.wikipedia. org/wiki/Russell s_paradox. See also Alfred North Whitehead, Bertrand Russell, http://baber.servehttp.com/Professional/MiscWritings/LogicalParadoxes.html

Logical paradoxes: Fundamental difficulties in mathematics or just ordinary word problems? (Draft) by Robert L. Baber, Bob@RLBaber.de 2004 January 18, modified 2004 May 8 Abstract: The Liar's Paradox: Consider the sentence This sentence is false. [1] and the question whether this sentence is true or false. The noun phrase "This sentence" is interpreted to refer to the above sentence as a whole. [ Wikipedia, Liar paradox Mathematically, sentence [1] above can be viewed (modeled) as a Boolean expression (an expression that evaluates to "true" or to "false"). The phrase "This sentence" can be viewed as a Boolean variable which we will call s below. Sentence [1] above can be interpreted to mean that the Boolean value of s is equal to the Boolean constant "false": s = false [2] The mathematical expression [2] is a translation of sentence [1] into the language of mathematics. The statement of the problem restricts the value of the variable s to be the Boolean value of sentence [1], i.e. to be the value of the expression [2] above, leading to the requirement (condition on the value of s) that s = (s = false) [3] Often this result is viewed as a fundamental problem or paradox, but it need not be so viewed. Many equations in mathematics have no solution, e.g. x=x+4 in the numbers, sin(x)=2, etc. Mathematics abounds with examples of problems that have no solution, one solution, or two or more solutions (e.g. x

15. Russell's Paradox And The Excluded-Middle Reasoning Text - Physics Forums Librar http//en.wikipedia.org/wiki/Russell s_paradox Settheoretic_responses_to_the_Russell_Paradox edited for typos. Lama. 07.10.04, 0418 http://www.physicsforums.com/archive/index.php/t-30569.html

Physics Help and Math Help - Physics Forums Physics General Physics Archives ... PDA View Full Version : Russell's Paradox and the Excluded-Middle reasoning Lama By tautology x = x means: x is itself, otherwise we cannot talk about x. Now we can ask if a teotology is also recursive, for example: x = x = x = ... If we do not get any new information by this recursion, then x = x is enough, which is like a one_step_recursion. So, Russel's paradox is like if by teotology we ask if x is not_x or x = not_x , which is a meaningless question trough an exluded-middle point of view. Because our one_step_recursion cannot be done, we have no product of tautology and we can conclude that the whole idea of Russel's paradox simply does not hold in an excluded-middle logical reasoning. By the way, in Russell's paradox x is not the set, but the word "contain". So I hope that you agree with me that the question: Is "contain" = "do_not_contain", is meaningless through an excluded-middle reasoning. The set of ALL_sets_that_contain_themselves

16. UNIVERSE {{{ 01110101011011100110 10010111011001100101 Don t things like Russel s paradox (http//en.wikipedia.org/wiki/Russell s_paradox), which effectively means that mathematics cannot be logically derived http://www.urbanhonking.com/universe/archives/2006/07/011000100110100.html

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17. Curry's Paradox - IIDB Russell s_paradox? To quote the Wiki page It might be assumed that, for any formal criterion, a set exists whose members are those objects (and only those http://iidb.infidels.org/vbb/showthread.php?t=238977

18. Minesweeper: Does A Container Contain Itself? When I googled, I got this page http//en.wikipedia.org/wiki/Russell s_paradox. Posted by Selvamuthukumar at 617 PM http://selvamuthukumar.blogspot.com/2007/06/does-container-contain-itself.html

skip to main skip to sidebar Minesweeper Thursday, June 28, 2007 Does a container contain itself? Two days before Rams asked a question "A container can contain many things in it. Does a container contain itself?" Say, thickness of the container is n units. Let make the container thickness to n/2 by cutting the inner part of the container. In this case we can say half of the container is inside the container. That is, container contains half of itself. We can repeat the same, and say the container contains (1/2)+(1/4) part of it. In general the container can contain 1/2 + 1/4 + 1/8 + 1/16 + .. part of itself. When the container contains itself thickness of the container reaches zero and the container is no more. This is how I thought when he asked this question. But I know for sure that he would have some theory or proof to answer this question. When I googled, I got this page http://en.wikipedia.org/wiki/Russell's_paradox Posted by Selvamuthukumar at 6:17 PM comments: Post a Comment Newer Post Older Post Home Subscribe to: Post Comments (Atom) Blog Archive February November Venbaa August ... Hard life !!!

19. ColabWiki: Data Property Properties are therefore subject to the Russell s_Paradox/GrellingNelson paradox. It differs from the logical concept of class by not having any concept of http://colab.cim3.net/cgi-bin/wiki.pl?Data_Property

20. Hacker News | Russell's Paradox.http://en.wikipedia.org/wiki/Russell's_paradox 1 point by mercurio 37 minutes ago link parent. Russell s paradox. http//en.wikipedia.org/wiki/Russell s_paradox. http://news.ycombinator.com/item?id=133751

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