more from Richard Dedekind

Single Idea 7524

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers]

Full Idea

Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number.

Gist of Idea

Order, not quantity, is central to defining numbers


report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4

Book Reference

Monk,Ray: 'Bertrand Russell: Spirit of Solitude' [Vintage 1997], p.116

A Reaction

Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661.

Related Ideas

Idea 646 When we count, are we adding, or naming numbers? [Aristotle]

Idea 8661 The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend]