Principia Mathematica

The Principia Mathematica (often abbreviated PM) is a three-volume work on the <a href="/facts/Foundations_of_mathematics/yjpbbUkt">foundations of mathematics</a> written by the mathematician–philosophers <a href="/facts/Alfred_North_Whitehead/7KuylmP3">Alfred North Whitehead</a> and <a href="/facts/Bertrand_Russell/SRpwNX2U">Bertrand Russell</a> and published in 1910, 1912, and 1913. In 1925–1927, it appeared in a second edition with an important Introduction to the Second Edition, an Appendix A that replaced ✱9 with a new Appendix B and Appendix C. PM was conceived as a sequel to Russell's 1903 <a href="/facts/The_Principles_of_Mathematics/Vd3bSkkt">The Principles of Mathematics</a>, but as PM states, this became an unworkable suggestion for practical and philosophical reasons: "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, according to its introduction, had three aims: (1) to analyze to the greatest possible extent the ideas and methods of mathematical logic and to minimize the number of <a href="/facts/Primitive_notion/PrQue1HG">primitive notions</a>, <a href="/facts/Axiom/mLjP14Mc">axioms</a>, and <a href="/facts/Inference_rule/QV5NklQ9">inference rules</a>; (2) to precisely express mathematical propositions in <a href="/facts/Mathematical_logic/SaI7Y3wN">symbolic logic</a> using the most convenient notation that precise expression allows; (3) to solve the paradoxes that plagued logic and <a href="/facts/Set_theory/1ptfsvUP">set theory</a> at the turn of the 20th century, like <a href="/facts/Russell%2527s_paradox/XupqWGYt">Russell's paradox</a>.
This third aim motivated the adoption of the theory of <a href="/facts/System_of_types/xj0xzVqI">types</a> in PM. The theory of types adopts grammatical restrictions on formulas that rule out the unrestricted comprehension of classes, properties, and functions. The effect of this is that formulas such as would allow the comprehension of objects like the Russell set turn out to be ill-formed: they violate the grammatical restrictions of the system of PM.
PM sparked interest in symbolic logic and advanced the subject, popularizing it and demonstrating its power. The <a href="/facts/Modern_Library/HY0x3k13">Modern Library</a> placed PM 23rd in their list of the top 100 English-language nonfiction books of the twentieth century.

Principia Mathematica open-in-new

Principia Mathematica