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The Totality Axiom and the principles on which it is based identify physical structure with conscious experience. Additional implications from these assumptions are listed in the following rules of consciousness. All of them echo ideas that have long been present in this field.

Assumed Rules of Consciousness

Physical structure completely determines conscious experience.
This is problematic. I claimed that there are nonstructural aspects of consciousness, for example, the experience of green. One might assume that these are independent to some degree (or completely) of structural constraints. The simplest assumptions is that they are not, that identical physical structures are the same conscious experience. Saying more about this easily leads to a never never land of metaphysics that investigates the `structure' of nonstructural aspects of consciousness.
Identical structures are identical experiences. Your perfect clone, in an exact duplicate of your environment, would have the same experience you do.
This follows from the first rule.
Just as structural organization can exist at multiple levels (molecules, cells, neural networks, etc.) so can conscious experience.
Our stream of consciousness seems to exist at a high structural level. Most of the hierarchy of structure within the brain is not part of our conscious awareness. The Totality Axiom implies conscious experience exists at all levels of physical structure.
Lower level structures affect higher level consciousness only to the degree they affect structure at the higher level.
This is the simplest possible assumption and will become an empirical question when we are able to replace parts of the brain with nonbiological prosthetics that exactly duplicate the function of the part being replaced.⁹
Isomorphic structures have (are) the same experience at the level of the isomorphism. Perfect duplication of the functioning of your neural circuits, even with different technology such as electronics, combined with a perfect simulation of your environment, would duplicate your conscious experience.
This follows from the previous rule and the second rule.
Changes in physical structure are isomorphic to changes in conscious experience.
This follows from the assumption that the totality of physical structure is conscious experience.
The depth and richness of conscious experience associated with a physical structure is limited by the level of abstraction and self reflection in the structure.
This is based on mathematics and empirical evidence. The ordinal numbers¹⁰ definable within a mathematical system determine what structures can be defined within that system. The ordinal numbers form a hierarchy involving ever more complex abstraction and self reflection.¹¹ The human mind seems to be capable of rich and deep experience because, in part, of the high level of abstraction and self reflection that it is capable of. We will expand on this in subsequent sections.

These rules and the Totality Axiom clarify the connection between physical structure and conscious experience. They imply that mathematics, as the study of all possible structures, is the study of all possible conscious experience. Before exploring some implications we need a little mathematics.

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Next: The Mathematics of Self Up: implyh Previous: Consciousness and Structure

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