Principia Mathematica

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.

PM, as it is often abbreviated, is an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic. One of the main inspirations and motivations for PM was Frege's earlier work on logic, which had led to paradoxes discovered by Russell. These were avoided in PM by building an elaborate system of types: a set of elements is of a different type than is each of its elements (a set is not an element; one element is not the set) and one cannot speak of the "set of all sets" and similar constructs, which would lead to paradoxes (see Russell's paradox).

PM is not to be confused with Russell's 1903 Principles of Mathematics. PM states: "The present work was originally intended by us to be comprised in a second volume of Principles of Mathematics... 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."

PM is widely considered by specialists in the subject to be one of the most important and seminal works in mathematical logic and philosophy since Aristotle's Organon. The Modern Library placed it 23rd in a list of the top 100 English-language nonfiction books of the twentieth century.