Bertrand Russell formulated the liar paradox in terms of set theory. He discovered this form of the paradox, known as Russell's paradox, in 1901. First, he conceived of a set that included other sets. An example of this is the set of all sets. By definition, all sets, including this set, are members of the set of all sets. He then conceived of the set of all sets that do not include themselves. He pondered if this set included itself, and realized that it does if it does not, and it does not if it does.