User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-5029411-20130811125215/@comment-5150073-20140621081403

That's actually natural if we define I(2)[a] without context and referring to psi. But we want I(2) to be the diagonalizer of $$\psi_{I(2)}$$ function, and "I(2)[a] = a" won't work properly.