Function and Concept explained

"Function and Concept" (German: "Funktion und Begriff", "Function and Concept") is a lecture delivered by Gottlob Frege in 1891.^[1] The lecture involves a clarification of his earlier distinction between concepts and objects. It was first published as an article in 1962.^[2]

Overview

In general, a concept is a function whose value is always a truth value (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-values (147). First level concepts have the value of true or false depending on whether the object falls under the concept. So, the concept

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

(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

, the concept expressed by the sentence:

\forallx\forallyf(x,y) → \forallz(f(x,z) → 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:

x²=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

External links

Notes and References

Gottlob Frege. Function und Begriff. Vortrag gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medicin und Naturwissenschaft (Function and Concept. An Address to the Jenaische Gesellschaft für Medizin und Naturwissenschaft on 9 January 1891). Verlag Hermann Pohle, Jena, 1891.
G. Patzig (ed.), Funktion, Begriff, Bedeutung, Göttingen: Vandenhoeck & Ruprecht, 1962.