Russell's paradox
Russell's paradox: In 1902 Russell discovered a "vicious circle" (Russell's paradox) in Frege's "Grundgesetze der Arithmetik", derived from Frege's Basic Law V and he was determined not to repeat it in his 1903 "Principles of Mathematics". In two Appendices added at the last minute he devoted 28 pages to both a detailed analysis of Frege's theory contrasted against his own, and a fix for the paradox. But he was not optimistic about the outcome: