Single Idea 9191

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

Full Idea

It can be argued that the notion of ordinal numbers is more fundamental than that of cardinals. To count objects, we must count them in sequence. ..The theory of ordinals forms the substratum of Cantor's theory of cardinals.

Gist of Idea

Ordinals seem more basic than cardinals, since we count objects in sequence

Source

Michael Dummett (The Philosophy of Mathematics [1998], 5)

Book Reference

'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.156


A Reaction

Depends what you mean by 'fundamental'. I would take cardinality to be psychologically prior ('that is a lot of sheep'). You can't order people by height without first acquiring some people with differing heights. I vote for cardinals.