Second-order predicate

In mathematical logic, a second-order predicate is a predicate that takes a first-order predicate as an argument.[1] 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.[2] 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.[3]

References

Yaqub, Aladdin M. (2013), An Introduction to Logical Theory, Broadview Press, p. 288, ISBN 9781551119939.
Oppy, Graham (2007), Ontological Arguments and Belief in God, Cambridge University Press, p. 145, ISBN 9780521039000.
Kremer, Michael (1985), "Frege's theory of number and the distinction between function and object", Philosophical Studies, 47 (3): 313–323, doi:10.1007/BF00355206, MR 0788101.

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[1] Yaqub, Aladdin M. (2013), An Introduction to Logical Theory, Broadview Press, p. 288, ISBN 9781551119939.

[2] Oppy, Graham (2007), Ontological Arguments and Belief in God, Cambridge University Press, p. 145, ISBN 9780521039000.

[3] Kremer, Michael (1985), "Frege's theory of number and the distinction between function and object", Philosophical Studies, 47 (3): 313–323, doi:10.1007/BF00355206, MR 0788101.