Single Idea 8653

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero]

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 Reference

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]