Function and Concept

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 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:

∀ x ∀ y f ( x , y ) → ∀ z ( f ( x , z ) → y = z )

correlates the relation of identity with the True.

The conceptual range (Begriffsumfang) follows the truth value of the function:

Works cited