One of the most interesting papers in the Alter and Walter collection is Martine Nida-Rümelin's "Grasping Phenomenal Properties", which gives a new argument against the materialist thesis that phenomenal properties are physical properties. Nida-Rümelin's argument uses the two-dimensional apparatus at various points in an auxiliary role, but she argues that her argument requires weaker and less controversial assumptions than my two-dimensional argument. Here I'll look into this a bit. (It might be worth looking at these two papers first, if you're not familiar with the issues.)
Nida-Rümelin's argument runs roughly as follows.
(1) A person who grasps a property via two distinct concepts is in a position to rationally judge that those concepts are necessarily coextensive.
(2) Phenomenal properties are grasped via phenomenal concepts.
(3) Any physical property can be grasped via a physical concept, by someone with relevant physical background knowledge.
(4) No amount of physical background knowledge puts one in a position to rationally judge that a phenomenal concept and a physical concept are necessarily coextensive.
(5) No phenomenal property is a physical property.