The idea of second order predication was introduced by the German mathematician and philosopher Frege.
It is based on his idea that a predicate such as "is a philosopher" designates a concept, rather than an object.
[2] Sometimes a concept can itself be the subject of a proposition, such as in "There are no Bosnian philosophers".
Thus the predicate "is not satisfied" attributes something to the concept "is a Bosnian philosopher", and is thus a second-level predicate.
This idea is the basis of Frege's theory of number.