My attention was brought to this two millennia old paradox:
Horse can be black.
White horse cannot be black.
So white horse not horse.
See Wikipedia, When a white horse is not a horse for a discussion.
This paradox is of interest to me because I started to think that one of the reasons of collapse of the New Math reforms in the 1960s and 1970s was introduction of sets and not predicates; in my view, children appear to be more perceptive to the concept of unary predicate, or property. Properties are closely related to sets, but they are not sets. I was unaware that the universe of properties also has its share of paradoxes.