Function and Concept

"On Function and Concept" (Über Funktion und Begriff) 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 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 $$ F$$ correlated 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) follows the truth value of the function:


 * x2 = 1 and (x + 1)2 = 2(x + 1) have the same conceptual range.