Principia Mathematica

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 and one cannot speak of the "set of all sets" and similar constructs, which lead to paradoxes.