Paradox of the Day
Liar's Paradox
Epimenides (attributed) / Eubulides c. 600 BCE / c. 350 BCE
'This sentence is false.' If it is true, then it is false. If it is false, then it is true.
Why it's paradoxical
The simplest self-referential paradox. It cannot be consistently assigned a truth value under classical logic. Godel used a mathematical version to prove his Incompleteness Theorems, showing that any sufficiently powerful formal system contains true statements it cannot prove.