Full Idea
Cantor took the ordinal numbers to be primary: in his generalization of the cardinals and ordinals into the transfinite, it is the ordinals that he calls 'numbers'.
Gist of Idea
Cantor took the ordinal numbers to be primary
Source
report of George Cantor (works [1880]) by William W. Tait - Frege versus Cantor and Dedekind VI
Book Reference
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.49
A Reaction
[Tait says Dedekind also favours the ordinals] It is unclear how the matter might be settled. Humans cannot give the cardinality of large groups without counting up through the ordinals. A cardinal gets its meaning from its place in the ordinals?