Function and Concept

"Function and Concept" (German: Über Funktion und Begriff, "On Function and Concept") is an article by Gottlob Frege, published in 1891. The article involves a clarification of his earlier distinction between concepts and objects.

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 ${\displaystyle F}$ has the value the True with the argument the object named by 'Jamie' if and only if Jamie falls under the concept ${\displaystyle F}$ (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 ${\displaystyle f}$, the concept expressed by the sentence:

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