"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]
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 {\displaystyle F} has the value the True with the argument the object named by 'Jamie' if and only if Jamie falls under the concept F {\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 f {\displaystyle f} , the concept expressed by the sentence:
∀ x ∀ y f ( x , y ) → ∀ z ( f ( x , z ) → y = z ) {\displaystyle \forall x\forall yf(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 {\displaystyle x^{2}=1} and ( x + 1 ) 2 = 2 ( x + 1 ) {\displaystyle (x+1)^{2}=2(x+1)} have the same conceptual range.
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