{{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.<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 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.<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 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.<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>
==References== {{reflist}}
{{DEFAULTSORT:Second-Order Predicate}} Category:Predicate logic Category:Concepts in logic
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