(Second Part of “Causality Explained”)
Axiomatic Systems Are Fragile:
Frege was one of the founders of mathematical logic and analytic philosophy. Frege wrote the Grundgesetze der Arithmetik [Basic Laws of Arithmetic], in three volumes. He published the first volume in 1894 (paying for it himself). Just before the second volume was going to press, in 1903, a young Bertrand Russell informed Frege of a dangerous contradiction, Russell’s paradox (a variant of the Cretan Liar Paradox). Frege was thrown in total confusion: a remedy he tried to apply reduced the number of objects his system could be applied to, to just ONE. Oops.
Frege was no dummy: he invented quantifiers (Second Order Logic, crucial to all of mathematics). It is just that logic can be pitiless.