1.2.3.4 Russell's Paradox



Unfortunately, it became evident that the Principia
( although a monumental work )
was flawed.

Some logical paradoxes had been found which caused great problems
. One of these is as follows

- sets, that contain themselves

sets that do not contain themselves


Any set either belogns to or to



Let A be to set of all sets that do not contain themselves


Does A

Does A

Both cases lead to a contradiction
Thus it is impossible to define "belongin to " in this context
As this was one of Russells axioms, there is a serious problem here
One must redefine the meaning of