In his The Road to Reality, Roger Penrose espouses three distinct realities - the physical, mental and mathematical.
The physical and mental are basically good old dualism, although he is an atheist and the mental aspect is accordingly shorn of angels dancing on pinheads. The mathematical is in essence Plato's realm of ideals.
Although my own ideas differ in much detail from his, this eternal triptych or whatever it is called appeals to me. However I remain unconvinced that the worlds of Plato and of experience are necessarily distinct. It might be that every quale of experience is attached to some ideal, and that every ideal has a quale attached to it, such that quale and idea are merely aspects of a single entity. It seem to me that information theory, especially in its philosophical aspect of semantics, must have a strong role to play in resolving this question. But I need to better understand the reasons for considering these worlds distinct.
Dualism has been flogged to death in philosophical circles, but has this kind of triple-ism received significant attention?