System, Subsystem, Hive: Boundary Problems in Computational Theories of Consciousness

Abstract

A computational theory of consciousness should include a quantitative measure of consciousness, or MoC, that (i) would reveal to what extent a given system is conscious, (ii) would make it possible to compare not only different systems, but also the same system at different times, and (iii) would be graded, because so is consciousness. However, unless its design is properly constrained, such an MoC gives rise to what we call the boundary problem: an MoC that labels a system as conscious will do so for some-perhaps most-of its subsystems, as well as for irrelevantly extended systems (e.g., the original system augmented with physical appendages that contribute nothing to the properties supposedly supporting consciousness), and for aggregates of individually conscious systems (e.g., groups of people). This problem suggests that the properties that are being measured are epiphenomenal to consciousness, or else it implies a bizarre proliferation of minds. We propose that a solution to the boundary problem can be found by identifying properties that are intrinsic or systemic: properties that clearly differentiate between systems whose existence is a matter of fact, as opposed to those whose existence is a matter of interpretation (in the eye of the beholder). We argue that if a putative MoC can be shown to be systemic, this ipso facto resolves any associated boundary issues. As test cases, we analyze two recent theories of consciousness in light of our definitions: the Integrated Information Theory and the Geometric Theory of consciousness.

Keywords: brain dynamics; consciousness; integrated information; intrinsic; open dynamical system; representational capacity; systemic properties; trajectory space.

Figure 1

Hot spot analysis (HsA). In HsA, an MoC is applied to different subsets of an array of measurements/elements in model. (A–D) A depiction of a normal brain (left) and a split brain (right) modeled as a set of elements and their connections. (A) For the normal brain the MoC gives a maximal value for a collection of elements spanning most of the brain. (B) In a split brain the same set of elements as in (A) gives a much lower, and non-maximal reading. (C) For the normal brain the maximal MoC reading in each hemisphere taken on its own is smaller than the maximal reading obtained from the whole brain network. (D) The opposite of (C) is true for the split brain: the maximal MoC readings are for two disparate networks each spanning most of a single hemisphere.