Function and Concept

"Function and Concept" (German: "Funktion und Begriff", "Function and Concept") is a lecture delivered by Gottlob Frege in 1891.Gottlob Frege. [https://archive.org/details/functionundbegr00freggoog Function und Begriff. Vortrag gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medicin und Naturwissenschaft] (Function and Concept. An Address to the Jenaische Gesellschaft für Medizin und Naturwissenschaft on 9 January 1891). Verlag Hermann Pohle, Jena, 1891. The lecture involves a clarification of his earlier distinction between concepts and objects. It was first published as an article in 1962.G. Patzig (ed.), Funktion, Begriff, Bedeutung, Göttingen: Vandenhoeck & Ruprecht, 1962.

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:

$\forall x \forall y f(x, y) \rightarrow \forall z (f (x, z) \rightarrow y=z)$

correlates the relation of identity with the True.

The conceptual range (Begriffsumfang in Frege 1891, p. 16) follows the truth value of the function:

$x^2 = 1$ and $(x + 1)^2 = 2(x + 1)$ have the same conceptual range.

Translations

"On Function and Concept" in Michael Beaney, ed., The Frege Reader, Blackwell, 1997, pp. 130–148

References

External links

[http://plato.stanford.edu/entries/logical-constants/ "Logical Constants"]
[http://plato.stanford.edu/entries/frege/catalog.html "Chronological Catalog of Frege's Work"]
[http://www.ocf.berkeley.edu/~brianwc/frege/fenglish.html List of English translations]

Category:1891 essays

Category:Philosophy essays

Category:Philosophy of language

Category:Works by Gottlob Frege

Category:Logic literature