Russell paradox and Principia Mathematica
Paradoja de Russell y Principia Mathematica
- Date
- 1901 · confidence high
- Place
- Cambridge, England
- Credited to
- Bertrand Russell; Principia Mathematica with Alfred North Whitehead (1910-1913)
- People
- 👤 Alfred North Whitehead1861–1947👤 Bertrand Russell1872–1970👤 Ernst Zermelo1871–1953
- Field
- Knowledge & symbols
What was discovered
The set of all sets that do not contain themselves leads to contradiction, which ruined naive set theory and Frege's system. The type theory of the Principia attempted to rebuild mathematics from logic.
Zermelo independently discovered the paradox around 1900 without publishing it.
What it led to
- Zermelo-Fraenkel axiomatics
- type theory and typed programming languages
- Gödel's theorems (which refute full logicism)
Built on
- Cantor's set theory
- Frege's Begriffsschrift
- Burali-Forti paradox