Finders keepers is half of an adage which dates back to the mid-1800s. Like many idioms and adages, the first half of the phrase is often quoted with the assumption that the listener knows the second half of the phrase. An adage is a common saying or phrase that shares advice or a universal truth.
Finders keepers is a statement one makes asserting the right of possession over an unclaimed object. The entire adage is finders keepers, losers weepers. This is an assertion that what is in one’s physical possession is owned by that person. Possession is rarely the sole requirement to establish legal ownership, though maritime law recognizes salvage claims after a ship has been lost for a certain amount of time. Today, finders keepers, losers weepers is most often used by children when finding a prized object, even if they know to whom the object originally belonged. Note that finders keepers, losers weepers is not spelled with any apostrophes.