5. No statement ascribing a mental predicate can be derived from any set of purely physical descriptions.
Finally, there is (5). What reason is there for thinking that is true? Well, we can compare it with a number of similar principles to get the general idea. In moral philosophy, there is a principle sometimes called Hume's law that says it is not possible to derive a normative judgement from a descriptive judgement. A normative judgement is a judgement about what is good or bad, right or wrong, and a descriptive judgement is basically anything else. Another way this is stated is that you cannot deduce an "ought" from an "is": you can't derive what ought to be the case solely on the basis of what is the case. This principle is almost universally acknowledged. And it is merely part of a more general pattern. For example, you can't derive a statement describing distances from any set of statements that don't describe distances. You can not derive a statement about colors from any set of non-color statements. You can't derive geometrical statements from non-geometrical ones. And generally, if you have an inference in which the conclusion talks about one thing and the premises talk about something else, the inference is invalid. In the same way, it is a conceptual truth that you cannot derive a mental description from a physical description. After all, just consider some physical concepts, such as spatial/geometrical properties, mass, force, and electric charge. Is it plausible that there is any way that these concepts could be used to explain what it feels like to be in pain? Say whatever you like about masses, positions, and forces of particles, you will not have ascribed any mental states to anything.
Descartes argued that he could clearly and distinctly conceive of any physical state existing without any conscious experiences accompanying it, so it follows that conscious experiences cannot be derived solely on the basis of the existence of any given physical state. And it looks as if he is right. We can forgo the Cartesian lingo about clear and distinct conceptions and say that for any physical description, that description could have been true even if there were no such thing as consciousness. Another way to put this is the following: for any physical property P, it is an open question whether a thing that has P is conscious. It makes sense to ask, "Granted that it has the feature P, but can it really think/feel/etc.?" and it's a significant question, so it follows that saying a thing has P is different from saying it is conscious, so having P can't be the same thing as thinking/feeling/etc. Of course, it might turn out that everything that has P is conscious, but that would be an additional piece of information beyond the fact that everything that has P has P.
But from this it follows that physical descriptions do not explain why there is consciousness, since they don't say anything about consciousness. They talk about a different subject matter.
Now it might be tried to challenge the sharp mental/physical dichotomy that has been drawn, to claim that mental and physical are not two mutually exclusive categories corresponding to completely different subject matters but that mental things can also simultaneously be physical. This view flies in the face of common sense (as well as the above argument), and I don't find it very comprehensible. But moreover, it won't help matters any because I could just as well have substituted "non-mental" for "physical" everywhere in the statement of the five theses and their defense. That is, we can simply restate (3) as, properties of atoms are all non-mental, and (5) as, non-mental properties cannot entail mental properties, and the problem is back in full force without having to assume that "physical" = "non-mental".
LOL (more than once)