In
mathematical logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...
, a second-order predicate is a
predicate
Predicate or predication may refer to:
* Predicate (grammar), in linguistics
* Predication (philosophy)
* several closely related uses in mathematics and formal logic:
**Predicate (mathematical logic)
**Propositional function
**Finitary relation, o ...
that takes a
first-order predicate In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s).. Compare second-order predicate and higher-order predicate.
This is not to be confused with a one-place predicate o ...
as an argument. Compare
higher-order predicate.
The idea of second order predication was introduced by the
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
mathematician and philosopher
Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philo ...
. It is based on his idea that a predicate such as "is a philosopher" designates a
concept, rather than an object. 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
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
.
[.]
References
Predicate logic
Concepts in logic
{{Logic-stub