Full Idea
The truth of "a=b" doesn't require much of 'a' and 'b' other than that there is a single thing to which they both refer. They needn't be interdefinable, or have supervenient properties. In this sense, identity is a very weak relation.
Gist of Idea
Identity is a very weak relation, which doesn't require interdefinability, or shared properties
Source
John Perry (Knowledge, Possibility and Consciousness [2001], §1.2)
Book Reference
Perry,John: 'Knowledge, Possibility and Consciousness' [MIT 2001], p.6
A Reaction
Interesting. This is seeing the epistemological aspects of identity. Ontologically, identity must invoke Leibniz's Law, and is the ultimately powerful 'relation'. A given student, and the cause of a crop circle, may APPEAR to be quite different.