Difference between revisions of "Russell's Paradox"

Revision as of 22:51, February 28, 2015

IT PROVES THE EXISTANCE OF GOD.

ONLY THE CHRISTIAN GOD, MIND YOU.

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-[[Bertrand Russell]]'s Paradox revealed a flaw in 1901 in early or naive [[set theory]].  (It is likely others saw this flaw before [[Bertrand Russell]].) It is a form of the [[liar's paradox]] expressed in the terms of [[set theory]].
+IT PROVES THE EXISTANCE OF GOD.
-The defect is as follows.  Let S be the set of all sets that do not contain  themselves as members.  In other words, set T is an element of S if, and only if, T is not an element of T:
-: <math>S=\{T\mid T\not\in T\}.</math>
-Here is the flaw.  Is Set S a member of itself?  If S is a member of itself, then it cannot be a member of itself by the very definition of S.  But if S is not a member of itself, then it must be a member of itself, again by its very definition.  Hence there is a fundamental logical contradiction in this type of set, and in any theory that allows it. In formal terms,
-:<math> S\in S \iff S\not\in S.</math>
-Russel's paradox and others like it can be avoided only at the expense of giving up the idea that any criteria can be used to construct sets. For example in [[Zermelo-Fraenkel]] set theory the construction <math>S=\{T\mid T\not\in T\}</math> would not qualify as [[well-founded]]. Some formulations of set theory would allow such a construction but then S would be a [[proper class]] rather than a set.
-==External Links==
-:[http://plato.stanford.edu/entries/russell-paradox/ Russell's Paradox at Stanford Encyclopedia of Philosophy]
-[[Category:Set Theory]]
+ONLY THE CHRISTIAN GOD, MIND YOU.

Difference between revisions of "Russell's Paradox"

Revision as of 22:51, February 28, 2015

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