Russell

Russell inaugurated analytic philosophy new-style. His initial concern was with rationality. He took its display in science to be best and the clearest. He therefore had two initial aims: to render philosophy scientific and to prove that science is certain (since tradition equates reason with provability). This led him to efforts to improve logic. He argued that whereas every class is a subclass of itself, no class is a member of itself. He wanted to prove this. So he defined “normal” a class is normal if it is not a member of itself: x ε N ↔ ~(x ε x) and tried to prove that all classes are normal: N = V. This made him wonder: is the normal class itself normal? As we saw, the answer is, yes-and-no; which is absurd. Now absurdities were never problematic as everybody always pronounced them false. Russell’s paradox, like any paradox (or antinomy or puzzle), is demonstrably true and false. A language that contains a paradox has all its statements proven. Russell managed to block paradoxes but he allowed contradictions as well-formed. This was the birth of the first fully formal language.