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Full Idea
In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not.
Gist of Idea
A concept is a function mapping objects onto truth-values, if they fall under the concept
Source
report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5
Book Ref
'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.147
A Reaction
As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts.
| 13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
| 10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
| 9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
| 9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
| 13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
| 9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
| 18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
| 18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
| 18165 | My Basic Law V is a law of pure logic [Frege] |