Mathematical Logic
The formalization of reasoning using mathematical methods. From Frege's predicate calculus through Russell's logicism to Godel's incompleteness. The foundation of analytic philosophy and computer science.
Sub-topics
Gottlob Frege (1848-1925). Father of analytic philosophy and modern logic. Begriffsschrift (1879) invented predicate logic with quantifiers. Sense (Sinn) vs reference (Bedeutung). Failed logicist program undermined by Russell's Paradox.
Bertrand Russell (1872-1970). Principia Mathematica (with Whitehead) attempted to derive all mathematics from logic. Theory of descriptions, logical atomism. Nobel Prize in Literature. Pacifist, activist, popularizer of philosophy.
Ludwig Wittgenstein, Tractatus Logico-Philosophicus (1921). The world is the totality of facts, not things. Language pictures reality. 'Whereof one cannot speak, thereof one must be silent.' Believed he had solved all problems of philosophy.