In mathematical logic, a second-order predicate is a predicate that takes a first-order predicate as an argument. Compare higher-order predicate.
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. Sometimes a concept can itself be the subject of a proposition, such as in "There are no Albanian philosophers". In this case, we are not saying anything of any Albanian philosophers, but of the concept "is an Albanian philosopher" that it is not satisfied. Thus the predicate "is not satisfied" attributes something to the concept "is an Albanian philosopher", and is thus a second-level predicate.
This idea is the basis of Frege's theory of number.
Famous quotes containing the word predicate:
“The only thing that one really knows about human nature is that it changes. Change is the one quality we can predicate of it. The systems that fail are those that rely on the permanency of human nature, and not on its growth and development. The error of Louis XIV was that he thought human nature would always be the same. The result of his error was the French Revolution. It was an admirable result.”
—Oscar Wilde (1854–1900)