Inspired by some ideas from Shahn Majid and Michael Heller, I've just written a new paper, 'The Duality of the Universe'. Using the concepts of mathematical category theory, and the mathematical concept of a dual, it proposes that the physical universe is an instance of a mathematical structure which possesses a dual structure, and that this dual structure is the collection of all possible knowledge of the physical universe. In turn, the physical universe is then the dual space of the latter. Contrary to the proposals of Majid and Heller, it is postulated that the dual space of the physical universe possesses a distinct structure to that of the physical universe. In particular:
Epistemology is the dual of metaphysics.
It is proposed that knowledge consists of various types of mathematical representation, and this proposition incorporates the representational theory of the mind (RTM), an approach to the mind-brain relationship which falls under the umbrella of functionalism. The latter holds that the mind possesses a structure which cannot be identified with the structure of the brain. In other words, functionalism holds that the structure of the mind is non-isomorphic to the structure of the brain.
Supervenience holds that any change in the higher level properties, states and processes of a composite system, must correspond to a change in the lower level properties, states and processes. All functionalist accounts accept that the mind supervenes on the brain, but they reject the idea that the higher-level structure can be defined in terms of the lower-level structure. One can accept that the mind is essentially subjective, but one can still hold that it possesses a structure, a distinct structure from the structure of the brain. The structure may well be a non-spatial structure, which cannot be reduced to any of the structures which characterise the brain, but it is, nevertheless, the structure of subjective experience. Intentional mental states are not observable by means of the sense organs, are directly accessible only to their owners, and do not occupy space, yet they nevertheless possess a structure which functionalism and the RTM sets out to capture. The proposal made in this paper entails that this structure is part of the dual structure of the physical universe.