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Full Idea
In Frege's system 'concept' and 'extension of a concept' are primitive notions; whereas 'zero' and 'successor' are defined.
Gist of Idea
For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Charles Chihara - A Structural Account of Mathematics 7.5
Book Ref
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.204
A Reaction
This is in contrast to the earlier Peano Postulates for arithmetic, which treat 'zero' and 'successor' as primitive. Interesting, given that Frege is famous for being a platonist.
| 9838 | Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett] |
| 9564 | For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Frege, by Chihara] |
| 10551 | If objects exist because they fall under a concept, 0 is the object under which no objects fall [Frege, by Dummett] |
| 8653 | Nought is the number belonging to the concept 'not identical with itself' [Frege] |
| 9837 | 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett] |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |