 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 inconsistency of set theory would mean that no mathematical proof could be completely trustworthy. Only by eliminating Russell’s paradox could mathematics as a whole regain its consistency.