Here is a philosophical viewpoint that has been put forth by Roger Penrose about what exactly composes reality. In this philosophical viewpoint, Reality is only understood by the Mind when it has obtained an objective understanding of (1) the intricacies involved in the Platonic Mathematical World, (2) how the Platonic Mathematical World represents the Physical World that we live in, and (3) how the Physical World we live in gives rise to the Mind that has the ability to comprehend both the Platonic and the Physical Worlds.
Update 6/15/2012 - This blog author’s clarification and interpretation of the matter:
There is the Logical Set of Numerical and Geometrical Relations (the Platonic Realm of Forms and Functions), which is independent of Nature (the units of quantities that obey various symmetry and conservation laws), which is independent of Mind (the conscious experience of nature and the level of understanding of numerical and geometric logic).
However, there are backwards dependencies, the mind is dependent on both nature and the Logical Set of Numerical and Geometric Relations.
Nature is dependent on the Logical Set of Numerical and Geometrical Relations that govern it.
It would be impossible for the mind to use logic to prove otherwise, as using logic would thereby demonstrate the dependence on logic. It also would be impossible for the mind to demonstrate that it can be independent of nature as well, since it is dependent (in my view consciousness is a function of sensory feedback loops and computing cycles).
Update 12/26/10 - The opening theme song to The Twilight Zone outlines this philosophy of 3 World Reality as well. "3 World Reality - a place where the Mind's Eye, the dimension of Inner Knowledge (The Mental World), and the Mind's Ear, the study of Outer Knowledge (Nature) meet, and where the mind charts a course through the Logos of the Unknown (Platonic Realm of Abstract Forms and Ideas)..."