Bertrand Russell - Mathematical Logic (.pdf) - monkeyfied

The Philosophical Importance of Mathematical Logic

by Bertrand Russell

Bio of Bertrand Russell:
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these in any profound sense. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain.

Introductory:
IN SPEAKING OF "Mathematical logic", I use this word in a very broad sense. By it I understand the works of Cantor on transfinite numbers as well as the logical work of Frege and Peano. Weierstrass and his successors have "arithmetised" mathematics; that is to say, they have reduced the whole of analysis to the study of integer numbers. The accomplishment of this reduction indicated the completion of a very important stage, at the end of which the spirit of dissection might well be allowed a short rest.