Principia Mathematica

Principia Mathematica, the monumental, three-volume work coauthored with Alfred North Whitehead and published in 1910–13, was the culmination of BR’s work on the foundations of mathematics. Conceived around 1901 as a replacement for the projected second volumes of BR’s Principles of Mathematics (1903) and of Whitehead’s Universal Algebra (1898), PM was intended to show how classical mathematics could be derived from purely logical principles. For a large swath of arithmetic this was done by actually producing the derivations. A fourth volume on geometry, to be written by Whitehead alone, was never finished. In 1925–27 BR, on his own, produced a second edition, adding a long introduction, three appendices and a list of definitions to the first volume and corrections to all three. (See B. Linsky, The Evolution of Principia Mathematica [Cambridge U. P., 2011].) In this edition, under the influence of Wittgenstein, he attempted to extensionalize the underlying intensional logic of the first edition.