the.com/liar paradox

means A statement like 'this sentence is false' that cannot be consistently labeled true or false, because each label flips into its opposite.

from Traced to the ancient Greek thinker Eubulides of Miletus, who posed versions of self-referential puzzles like this; it's often tangled up with the 'Epimenides paradox,' where a Cretan declares 'all Cretans are liars' — though that version is really more of a cousin than the strict logical paradox. The core trick is self-reference: the sentence takes itself as its own subject, so any verdict you hand down gets swallowed back into the claim.