Function and Concept

"On Function and Concept" (Über Funktion und Begriff) is an article by Gottlob Frege, published in 1891. The article is together with "On Concept and object" (1892) and "Sense and reference" (1892) one of his main writings on the distinction of intention and extension.

A concept is a function, which value is a truth value:

-1 and 1 follow the concept x2 = 1, but 0 and 2 do not.

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.

To understand the idea, it also is important to see the terms function and concept, as used by Frege, in the context of intensional sense and extensional reference.

Intention	Extension	Author
compréhension	extension	Port Royal


connotation	denotation	J.St. Mill


Sinn	Bedeutung	Frege


meaning	denotation	Russell


sense	reference	M. Black


Intension	Extension	Carnap, Stegmüller


meaning	reference	Quine

Herberger/Simon, Wissenschaftstheorie [1980], S. 243 [1]; M. Black = G. Frege, On sense and reference, in: P. Geach, M. Black (Eds.), Translations from the Philosophical Writings of Gottlob Frege, Blackwell Scientific Publications, Oxford, 1970, pp. 56--78.

The mentioned articles prepared Frege's: The Thought (Der Gedanke): A Logical Investigation. Beiträge zur Philosophie des deutschen Idealismus, I (1918), 58-77.

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