The significance of Russell’s paradox can be seen once it is realized that, using classical logic, all sentences follow from a contradiction. For example, assuming both \(P\) and \({\sim}P,\) any arbitrary proposition, \(Q\), can be proved as follows: from \(P\) we obtain \(P \vee Q\) by the rule of Addition; then from \(P \vee Q\) and \({\sim}P\) we obtain \(Q\) by the rule of Disjunctive Syllogism. Because set theory underlies all branches of mathematics, many people began to worry that the in