Paradox

RUSSELL’S SET 319Georg Cantor was persuading more and more mathematiciansthat his transfinite arithmetic solved Zeno’s paradoxes.Giuseppe Peano had axiomitized arithmetic. All of thisshowed that an effective cadre of mathematicians did takecontradictions seriously. There were far fewer unsolvablecontradictions than implied by Hegel. By 1899, Russell feltthe number of contradictions had dwindled to one: “Thenumber of finite numbers is infinite. Every number is finite.These two statements seem indubitable, though the firstcontradicts the second, and the second contradicts Cantor.”(Russell 1994, 123) But even this paradox seemed to disappearwhen Russell became persuaded that mathematics was notreally the science of quantity. Once mathematics was picturedmore abstractly, as a study of symbol manipulation, allcontradictions appeared to evaporate. Mathematics lookedincreasingly like a body of secure tautologies.THE SECOND ANALYTIC PHILOSOPHERRussell’s empty catch made him ripe for defection. Hiscolleague at Cambridge University, G. E. Moore, was developingan analytic alternative to Hegelianism. Moore attackedidealism with a combination of conceptual analysis andappeals to common sense. Nowadays, many philosophy studentsregard Moore’s writings as a pedantic defender of thestatus quo. But at the beginning of the twentieth century,Moore’s writings were electrically dissident. Idealism was inmagisterial hegemony in Europe and the Untied States.Moore countered with a charismatic naiveté.Moore admitted that he could not pinpoint the misstepsof many idealist arguments. He just knew that they were