Full Idea
The higher types are needed for intensional phenomena, cases where the same class is picked out by distinct propositional functions.
Gist of Idea
Higher types are needed to distinguished intensional phenomena which are coextensive
Source
Bernard Linsky (Russell's Metaphysical Logic [1999], 6.4)
Book Reference
Linsky,Bernard: 'Russell's Metaphysical Logic' [CSLI 1999], p.101
A Reaction
I take it that in this way 'x is renate' can be distinguished from 'x is cordate', a task nowadays performed by possible worlds.