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