second-order predicate

{{Short description|Aspect of mathematical logic}}

In mathematical logic, a second-order predicate is a predicate that takes a first-order predicate as an argument.{{citation|title= An Introduction to Logical Theory|first=Aladdin M.|last=Yaqub|publisher=Broadview Press|year=2013|isbn=9781551119939|page=288|url=https://books.google.com/books?id=93Z1-MdIkVcC&pg=PA288}}. 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.{{citation|title=Ontological Arguments and Belief in God|first=Graham|last=Oppy|publisher=Cambridge University Press|year=2007|isbn=9780521039000|page=145|url=https://books.google.com/books?id=qg0spmMuC98C&pg=PA145}}. Sometimes a concept can itself be the subject of a proposition, such as in "There are no Bosnian philosophers". In this case, we are not saying anything of any Bosnian philosophers, but of the concept "is a Bosnian philosopher" that it is not satisfied. 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.{{citation

| last = Kremer | first = Michael

| doi = 10.1007/BF00355206

| issue = 3

| journal = Philosophical Studies

| mr = 788101

| pages = 313–323

| title = Frege's theory of number and the distinction between function and object

| volume = 47

| year = 1985}}.