The Liar Paradox
"This sentence is false." Decide whether you are looking at something true or something false, and see how far you get.
c. 600 BCE (the Epimenides line); c. 350 BCE (Eubulides' paradox)26 min read
Polish logic; later Berkeley
Alfred Tarski
1901 – 1983
Logician and mathematician, born in Warsaw, from 1942 at Berkeley. He gave the modern semantic definition of truth and proved the undefinability of truth within a formal system. His first major result, with Banach in 1924, was the paradoxical decomposition of the ball — work he began as a doctoral student of Leśniewski.
4 entries
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 Banach–Tarski Paradox
Cut a solid ball into five pieces, move them around, and you have two balls the same size as the first. Nothing was stretched.
192423 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