Full Idea
Armstrong says that if it can be proved a priori that a thing falls under a certain universal, then there is no such universal - and hence there is no universal of a thing being identical with itself.
Gist of Idea
A thing's self-identity can't be a universal, since we can know it a priori
Source
report of David M. Armstrong (A Theory of Universals [1978], II p.11) by Alex Oliver - The Metaphysics of Properties 11
Book Reference
-: 'Mind' [-], p.30
A Reaction
This is a distinctively Armstrongian view, based on his belief that universals must be instantiated, and must be discoverable a posteriori, as part of science. I'm baffled by self-identity, but I don't think this argument does the job.