more from Richard Dedekind

Single Idea 9827

[catalogued under 18. Thought / E. Abstraction / 3. Abstracta by Ignoring]

Full Idea

If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind.

Gist of Idea

We derive the natural numbers, by neglecting everything of a system except distinctness and order


Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73)

Book Reference

Dedekind,Richard: 'Essays on the Theory of Numbers' [Dover 1963], p.68

A Reaction

[compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective.