Paradox of the Day
Liar's Paradox
'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.