Changes

732 bytes added , 01:03, January 6, 2007

no edit summary

[[Bertrand Russell]]'s Paradox reveals a flaw in the early or naive set theory. (It is doubtful Bertrand Russell was the first to see this basic flaw.)

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.

Aschlafly

Anthony, Irenaeus, Siteadmin, apieditor, Bureaucrats, Check users, nsAm_Govt_101RO, nsAm_Govt_101RW, nsAm_Govt_101_ta, nsJudgesRO, nsJudgesRW, nsJudges_talkRO, nsJudges_talkRW, nsTeam2RO, nsTeam2RW, nsTeam2_talkRO, nsTeam2_talkRW, oversight, Administrators

126,357

edits

Changes

Russell's Paradox (view source)

Revision as of 01:03, January 6, 2007