Function and Concept

Short description: Work by Gottlob Frege

"Function and Concept" (German: "Funktion und Begriff") is a lecture delivered by Gottlob Frege in Jena at a meeting of the Jenaische Gesellschaft für Medicin und Naturwissenschaft on 9 January 1891, and published the same year as an article.[1] The lecture involves a clarification of his earlier distinction between concepts and objects. It

The original article was reprinted in 1962.[2]

## Contents

* 1 Overview
* 2 Translations
* 3 References
* 4 External links

## 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∀yf(x,y)->∀z(f(x,z)->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:

x2=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

1. ↑ Gottlob Frege. 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.
2. ↑ G. Patzig (ed.), Funktion, Begriff, Bedeutung, Göttingen: Vandenhoeck & Ruprecht, 1962.

## External links

* "Logical Constants"
* "Chronological Catalog of Frege's Work"
* List of English translations

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