# 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.