Russell's Paradox
Consider the set of all sets that do not contain themselves. Does that set contain itself? Either answer is wrong.
1901 (discovered), 1902 (letter to Frege), 1903 (published)19 min read
British analytic philosophy and mathematical logic
Bertrand Russell
1872 – 1970
British philosopher, logician and public intellectual. In 1901 he found the contradiction that bears his name while examining Cantor's diagonal argument, and in 1902 reported it to Frege in a letter that demolished the foundations of Frege's life's work. His theory of types (1908) and Principia Mathematica (1910-13, with A. N. Whitehead) were attempts to rebuild mathematics on paradox-free ground.
6 entries
The Tristram Shandy Paradox
A man writes his autobiography but keeps falling behind. If he had infinite time, would he ever catch up?
1759 (novel), 1903 (paradox formulated)8 min read
Berry's Paradox
"The smallest number that cannot be described in fewer than twelve words." That description is eleven words long.
1906 (published by Russell, crediting Berry); communicated c. 190419 min read
The Grelling-Nelson Paradox
Is the word "heterological" heterological? Either answer generates a contradiction.
19087 min read
The Barber Paradox
The barber shaves every man in town who does not shave himself, and no one else. So who shaves the barber?
1918 (Russell's lectures); the story circulated earlier11 min read
Gödel's Incompleteness Theorems
In any system of arithmetic strong enough to be useful, there are true statements it can never prove. Including this one.
193125 min read