Classical astrology didn't even include Uranus and Neptune.
Pluto is the only planet discovered by an American. If it had been discovered by a Mayan or an Aztec or an African, I doubt that we'd be having this conversation right now.
At one time the asteroid Ceres was considered a planet, but when dozens (now thousands) of similar "main belt" asteroids were found, it was demoted.
Clearly, one way, the current way, to define planets is by roster. I'm just glad that Clyde Tombaugh didn't live to see this day.