# Principia Mathematica

book on the foundations of mathematics

The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1927, it appeared in a second edition with an important Introduction To the Second Edition, an Appendix A that replaced ✸9 and an all-new Appendix C.

## Quotes

• The present work was originally intended by us to be comprised in a second volume of The Principles of Mathematics. With that object in view, the writing of it was begun in 1900. But as we advanced, it became increasingly evident that the subject is a very much larger one than we had supposed; moreover on many fundamental questions which had been left obscure and doubtful in the former work, we have now arrived at what we believe to be satisfactory solutions. It therefore became necessary to make our book independent of The Principles of Mathematics.
• Preface, vol. I, p. iii
• We have found it necessary to give very full proofs, because otherwise it is scarcely possible to see what hypotheses are really required, or whether our results follow from our explicit premisses.
• Preface, vol.I, p. vi
• From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2.
• ✸54·43. In vol. I, part II, "Prolegomena to Cardinal Arithmetic", section A, "Unit Classes and Couples", ✸54, "Cardinal Couples", p. 362
• The above proposition [1 + 1 = 2] is occasionally useful.
• ✸110·643. In vol. II, part III, "Cardinal Arithmetic", section B, "Addition, Multiplication and Exponentiation", ✸110, "The arithmetical sum of two classes and of two cardinals", p. 83