The Grandfather Paradox
Travel back in time and stop your own grandparents from ever meeting. Then who was it that went back?
1943 (Barjavel's novel), with antecedents from the 1920s18 min read
Nature
Logical contradiction
Accepting the premises and the reasoning forces you to accept both P and not-P. Something in the premises must go. These are the rarest and most consequential paradoxes.
A genuine contradiction derivable from apparently sound premises.
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Intermediate
Curious teenagers and general adult readers.
The Grelling-Nelson Paradox
Is the word "heterological" heterological? Either answer generates a contradiction.
19087 min read
Advanced
Undergraduate level in the relevant field.
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
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
The Sorites Paradox
One grain of sand is not a heap. Adding a single grain never turns a non-heap into a heap. So heaps do not exist.
c. 350 BCE20 min read
The Unexpected Hanging Paradox
A prisoner is told he will hang next week, on a day he cannot possibly predict. He proves it cannot happen. It happens.
1943 (in circulation), 1948 (first in print)21 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 Ross-Littlewood Paradox
You add ten balls and remove one, infinitely many times. At the end, the vase is empty. What happened to all the balls?
19887 min read