罗素悖论是罗素于1901年提出来的。罗素称一个集x是正常的,如果x不是x的元素,即x■x;否则称x是异常的。令X是一切正常集所构成的集,若X∈X,则X是正常的,故X■X;若X■X,则由X的构成法则,可得X∈X。这就导致了循环,构成了罗素悖论。1918年,罗素又提出了一个罗素悖论的“通俗版”,即“理发师悖论”。其内容是这样 Russell’s paradox was raised in 1901 by Russell. Russell said a set of x is normal, if x is not an element of x, that is, x ■ x; otherwise, x is abnormal. Let X be a set of all normal sets. If X ∈ X, then X is normal, so X ■ X; if X ■ X, the law of X is given by X ∈ X. This led to a cycle that constituted Russell’s paradox. In 1918, Russell again put forward a “popular version” of Russell’s paradox, “barber paradox.” Its content is like this