"Function and Concept" (German: "Funktion und Begriff", "Function and Concept") is a

lecture A lecture (from Latin ''lēctūra'' “reading” ) is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical infor ...

delivered by

Gottlob 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 ph ...

in 1891. The lecture involves a clarification of his earlier distinction between concepts and objects. It was first published as an article in 1962.G. Patzig (ed.), ''Funktion, Begriff, Bedeutung'', Göttingen: Vandenhoeck & Ruprecht, 1962.

Overview

In general, a concept is a

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

whose value is always a

truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...

(139). A relation is a two place function whose value is always a truth value (146). Frege draws an important distinction between concepts on the basis of their level. Frege tells us that a first-level concept is a one-place function that correlates objects with

truth-value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some progra ...

s (147). First level concepts have the value of true or false depending on whether the object falls under the concept. So, the concept

F

has the value the True with the argument the object named by 'Jamie' if and only if Jamie falls under the concept

F

(or is in the extension of F). Second order concepts correlate concepts and relations with truth values. So, if we take the relation of identity to be the argument

f

, the concept expressed by the sentence:

\forall x \forall y f(x, y) \rightarrow \forall z (f (x, z) \rightarrow y=z)

correlates the relation of identity with the True. The conceptual range (''Begriffsumfang'' in Frege 1891, p. 16) follows the truth value of the function:

x^2 = 1

and

(x + 1)^2 = 2(x + 1)

have the same conceptual range.

Translations

* "On Function and Concept" in Michael Beaney, ed., ''The Frege Reader'', Blackwell, 1997, pp. 130–148

References

External links

"Logical Constants"

1891 essays Philosophy essays Philosophy of language Works by Gottlob Frege Logic literature philo-stub {{philo-essay-stub