Second-order predicate

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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]


  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.