> what is the label "non-physical" actually describing
In this case, it would be describing the consciousness phenomenon -- which we can't get at using normal, scientific, physical observations of the world.
If X exists, we all know it exists and can talk about it, but we have no way to observe it (in fact, all our observations are restricted to being through it) - then I'd venture we're on an edge of reality itself. In my opinion, a non-physical hypothesis here is allowable if it has more explanatory power than the alternative.
> which we can't get at using normal, scientific, physical observations of the world
Why? This would make it unusual compared to every other process in biology and everything we actually do know about consciousness. We know that most of the faculties we subjectively attribute to the conscious experience are rooted in physical biology (reasoning, instinct, emotion, memory etc), so I am not sure what the possibility of a non-physical component adds to the model.
In this case, it would be describing the consciousness phenomenon -- which we can't get at using normal, scientific, physical observations of the world.
If X exists, we all know it exists and can talk about it, but we have no way to observe it (in fact, all our observations are restricted to being through it) - then I'd venture we're on an edge of reality itself. In my opinion, a non-physical hypothesis here is allowable if it has more explanatory power than the alternative.