Abstracts
The realm of the mental, and the mind-body problem, does not exhaust the realm of the non-physical. Non-mental non-physical entities include things such as gods, angels, and ghosts. As aforementioned, a demonstration beyond doubt of their existence(s) would place them in the realm of the physical, as far as physicalist/dualist metaphysics is concerned. Lacking such demonstrations, their existences and natures are widely debated, independently of the philosophy of mind.
Philosophers generally do agree, however, on the existence of certain other non-physical entities, namely abstract objects. These include concepts such as numbers, mathematical sets and functions, and philosohpical relations and properties. Such entities are not physical inasmuch as they exist outwith space and time. An abstract property such as redness has also has no location in space-time. Whilst older Cartesian dualists held the existence of non-physical minds, more limited forms of dualism propounded by 20th and 21st century philosophers (such as property dualism) hold merely the existence of non-physical properties.
Read more about this topic: Non-physical Entity