The Principles of Mathematics

Russell's first full argument that mathematics is logic, and the book in which he published the paradox that brought down Frege's system.

He wrote it between 1900 and 1902, and it was published in 1903. The case is made in prose rather than symbols: the whole of pure mathematics follows from a small number of logical premises. Appendix B states the contradiction of the class of all classes that are not members of themselves. That is Russell's paradox, and the same appendix sketches the theory of types he and Whitehead would later build out in Principia Mathematica. This is the second edition. George Allen & Unwin issued it in 1937 with a new introduction, in which Russell reconsiders the argument after thirty-five years and says how much of it he no longer holds. The copy here is the seventh impression.

Russell (1872-1970) wrote it before the Principia, before the Nobel and before the political work. He had lately read Peano and was rebuilding the subject from its premises. It is filed in this wing as the foundational end of a shelf that runs on into cipher manuals: the formal machinery that mathematical cryptography, and computing after it, was assembled from.