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<p><b>New page</b></p><div>"On '''Function and Concept'''" ({{lang-de|Über Funktion und Begriff}}) is an article by [[Gottlob Frege]], published in 1891. The article involves a clarification of his earlier distinction between concepts and objects.<br />
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In general, a concept is a [[function (mathematics)|function]] whose value is always a [[truth value]] (139). A relation is a two place function whose value is always a truth value (146).<br />
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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-value]]s (147). First level concepts have the value of true or false depending on whether the object falls under the concept. So, the concept <math> F</math> has the value the True with the argument the object named by 'Jamie' if and only if Jamie falls under the concept <math> F </math> (or is in the extension of F).<br />
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Second order concepts correlate concepts and relations with truth values. So, if we take the relation of identity to be the argument <math> f </math>, the concept expressed by the sentence:<br />
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<math> \forall x \forall y f(x, y) \rightarrow \forall z (f (x, z) \rightarrow y=z ) </math><br />
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correlates the relation of identity with the True.<br />
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The [[conceptual range]] (Begriffsumfang) follows the truth value of the function:<br />
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* x2 = 1 and (x + 1)2 = 2(x + 1) have the same conceptual range.<br />
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==Works cited==<br />
In English: "On Function and Concept" in '''The Frege Reader''', ed. Michael Beaney 1997, pp.&nbsp;130–148<br />
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==External links==<br />
*[http://plato.stanford.edu/entries/logical-constants/ Logical constants]<br />
*[http://plato.stanford.edu/entries/frege/catalog.html Frege's writings]<br />
*[http://www.ocf.berkeley.edu/~brianwc/frege/fenglish.html English versions]<br />
*[http://www.humnet.ucla.edu/humnet/phil/Lectures/LangWork/Parsons1980.pdf Terence D. Parsons: Frege's Hierarchies, 1981]<br />
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{{DEFAULTSORT:Function And Concept}}<br />
[[Category:1891 works]]<br />
[[Category:Philosophy essays]]<br />
[[Category:Philosophy of language]]<br />
[[Category:Works by Gottlob Frege]]<br />
[[Category:Logic literature]]</div>en>Linas