Single Idea 14116

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic]

Full Idea

It used to be common to define numbers by means of 1, with 2 being 1+1 and so on. But this method was only applicable to finite numbers, made a tiresome different between 1 and the other numbers, and left + unexplained.

Gist of Idea

Numbers were once defined on the basis of 1, but neglected infinities and +

Source

Bertrand Russell (The Principles of Mathematics [1903], §109)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.112


A Reaction

Am I alone in hankering after the old approach? The idea of a 'unit' is what connected numbers to the patterns of the world. Russell's approach invites unneeded platonism. + is just 'and', and infinities are fictional extrapolations. Sounds fine to me.