Work · Analytic Philosophy
Principia Mathematica
Mathematics derived from logic – the proposition from which 1+1=2 follows comes only at *54.43, on page 379 of the first volume.
Introduction
Russell and Whitehead worked on the book for about a decade; its three volumes appeared in 1910, 1912 and 1913, and the authors had to contribute to the printing costs. The aim was logicism: to derive mathematics from a small number of logical axioms and definitions. To avoid the paradox Russell had found in Frege’s system, the book uses a theory of types, which arranges entities and classes in levels, supplemented by the disputed axiom of reducibility. A planned fourth volume on geometry was never written. Its notation, adapted from Peano, shaped modern logic, and Gödel formulated his incompleteness theorems of 1931 for “Principia Mathematica and related systems”.
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Connections
Builds on
- Begriffsschrift1879 · Gottlob Frege
- The Foundations of Arithmetic1884 · Gottlob Frege
Taken up in
- Tractatus Logico-Philosophicus1921 · Ludwig Wittgenstein
- The Logical Structure of the World1928 · Rudolf Carnap
- A Modern Introduction to Logic1930 · Susan Stebbing
Answered in
- Foundations of the General Theory of Sets I1916 · Stanisław Leśniewski
- On Formally Undecidable Propositions of Principia Mathematica and Related Systems I1931 · Kurt Gödel
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