Editing Second-order predicate (section)

{{Short description|Aspect of mathematical logic}}
In [[mathematical logic]], a '''second-order predicate''' is a [[predicate (logic)|predicate]] that takes a [[first-order predicate]] as an argument.<ref>{{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}}.</ref> Compare [[higher-order predicate]].

The idea of second order predication was introduced by the [[Germany|German]] mathematician and philosopher [[Gottlob Frege|Frege]]. It is based on his idea that a predicate such as "is a philosopher" designates a [[concept and object|concept, rather than an object]].<ref>{{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}}.</ref> Sometimes a concept can itself be the subject of a proposition, such as in "There are no [[Bosnia and Herzegovina|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 [[satisfiability|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]].<ref>{{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}}.</ref>