Full Idea
It is possible to hold that phenomenal properties (qualia) are irreducible, while holding intentional properties, including propositional attitudes, to be reducible (functionally, or biologically).
Gist of Idea
Maybe intentionality is reducible, but qualia aren't
Source
Jaegwon Kim (Mind in a Physical World [1998], §1 p.017)
Book Reference
Kim,Jaegwon: 'Mind in the Physical World' [MIT 2000], p.17
A Reaction
This is the position which Kim has settled for, but I find it baffling. If the universe is full of irreducibles that is one thing, but if everything in the universe is reducible except for one tiny item, that is implausible.