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Function and Concept

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"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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