A Structural Theory of Consciousness

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As preparation for what follows, we note that we attempt to demonstrate that the phenomenal and the physical are dual aspects of one and the same underlying structure, hence the descriptor "Structural" in General Structural Theory (GST). The descriptor "General" serves to emphasize the generality of the theory, in the sense that certain terms, such as 'relation', are intentionally left unspecified in the face of uncertain empirical evidence (which presumably will become more certain in the near future). The GST aims to provide an answer to the hard problem of consciousness, which means explaining why conscious phenomena seem the way that they do and not otherwise. Further, the GST seeks to describe the exact relation between the phenomenal and the physical. We now proceed to present the GST.
The General Structural Theory (GST)
Notation
=> 'implies'. That is, a => b is equivalent to a implies b, or if a then b.
= 'equals'. This symbol denotes identity. If a => b and b => a, then a = b.
P, p These symbols denote propositions and are followed by numbers (i.e., are indexed). Thus, P1 denotes Proposition 1.
Definitions
Consciousness: A general term encompassing all forms of subjective experience. Elementary: Involving only the most simple and basic constituents.
Structure: The organization or topology of a matrix whose (i^{th}, j^{th}) entry quantifies the relation from the i^{th} elementary constituent (phenomenal or physical) to the j^{th} elementary constituent.
Propositions
P1. Consciousness, C, is a relation between elementary physical processes, P. That is, C = f(P), where f is a function.
P2. Relations between elementary conscious phenomena define a structure, S_{C}. Similarly, relations between elementary physical processes define a structure, S_{P}. That is, C => S_{C} and P => S_{P}.
Proof: Index the N elementary physical processes and construct an NxN matrix where the (i^{th}, j^{th}) entry quantifies the relation (such as similarity) from the i^{th} elementary physical process to the j^{th} elementary physical process. Use this matrix to construct the volumetric or manifold structure, S_{P}. Hence, P => S_{P}. A similar proof exists for C => S_{C}.
P3. The structure of elementary conscious phenomena is the same as the structure of elementary physical processes. That is, S_{C} = S_{P}.
P4. The structure of elementary conscious phenomena, or equivalently, the structure of elementary physical processes, uniquely determines the phenomenal aspects of conscious experience, C. That is, S_{C} => C, or equivalently, S_{P} => C.
Proof: If structure did not uniquely determine the phenomenal aspects of conscious experience, then multiple possible phenomenal solutions will exist for a given structure (i.e., inverted spectra), which is absurd.
Corollary: The relation between the phenomenal aspects of conscious experience and physical processes is not arbitrary, but is determined by necessity. That is, P => C since P => S_{P} = S_{C} = C.
Discussion
P1 answers the question, what is consciousness? We give consciousness the status of a fundamental property or law of nature, being identified as a relation between physical processes. The precise relation is left unspecified, and could be a similarity measure such as crosscorrelation or a causality measure indicating the degree to which physical processes causally effect each other. The choice of the relation is not arbitrary, but is constrained by the relations between conscious phenomena. For example, if the relations between conscious phenomena are symmetric, then a similarity measure would be a plausible candidate, whereas if some conscious phenomena are asymmetric, then a similarity measure could be ruled out and a causality measure would instead be used.
In order to more fully explain the basis of P2, it is worthwhile to begin with the following propositions, whose validity has been argued for elsewhere (and will not be repeated here):
p1: (Dis)similar physical processes give rise to (dis)similar phenomena.
p2: Relative magnitudes of (dis)similarity for the above physical processes and phenomena may be assigned.
Thus, p1 and p2 tell us that relative distances may be assigned between pairs of points existing in physical process space, and also in phenomena space. These points can be interpreted either as volumetric or manifold structures existing in very high dimensional spaces. P2 goes beyond p1 and p2 by generalizing the notion of 'relative distance' to include for the possibility of asymmetric relations, and also by telling us that the structure in physical process space is the same as the structure in phenomena space.
P3 is a restricted formulation of the Identity Thesis, which claims that every mental property is identical with some physical property.
P4 goes beyond P3 and, in fact, provides a solution to the hard problem of consciousness.
The GST is too general in its current form and needs to be refined in order to verify experimentally. We see two main competing refinements of the GST, depending on how 'relation' is quantitatively defined. Either it means similarity, (i.e., something like crosscorrelation, also known as 'functional connectivity'), or it means causal influence (i.e., something like the 'effective connectivities' calculated in Structural Equation Modeling). In following papers, we will consider empirical evidence stemming from fMRI research in the context of competing versions of the GST.
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