Full Idea
We know a great deal about a class without enumerating its members …so definition by extension is not necessary to knowledge about a class ..but enumeration of infinite classes is impossible for finite beings, so definition must be by intension.
Gist of Idea
We can enumerate finite classes, but an intensional definition is needed for infinite classes
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], II)
Book Reference
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.13
A Reaction
Presumably mathematical induction (which keeps apply the rule to extend the class) will count as an intension here.