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.