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Full Idea
I define nought as the Number which belongs to the concept 'not identical with itself'. ...I choose this definition as it can be proved on purely logical grounds.
Gist of Idea
Nought is the number belonging to the concept 'not identical with itself'
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §74)
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.87
A Reaction
An important part of Frege's logicist programme, along with his use of Hume's Principle (Idea 8649). He needed a prior definition of 'Number' (in §68). Clever, but intuitively a rather weird idea of zero. It is more of an example than a definition.
Related Idea
Idea 8649 Two numbers are equal if all of their units correspond to one another [Hume]
| 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] |