After making important contributions to logic and the foundations of mathematics, the Austrian philosopher Ludwig Wittgenstein (1889-1951) moved away from formalism to an investigation of the logic of informal language.

Ludwig Wittgenstein was born in Vienna on April 26, 1889, the last of eight children in a wealthy and highly cultured family. He was educated at home, particularly in music, which both parents pursued, and raised as a Catholic. At the age of 14, having shown a talent for mechanics, Ludwig was sent to a school in Linz that emphasized mathematics and physical sciences. Three years later he entered the Hochschule in Berlin to pursue a course in mechanical engineering. Becoming dissatisfied, Wittgenstein moved to England, where he did experimental work in aeronautics and eventually registered as a research student in engineering at the University of Manchester.

In 1912 Wittgenstein read Bertrand Russell's Principles of Mathematics and became fascinated with the question...