Integrated Information Theory and Isomorphic Feed-Forward Philosophical Zombies

A mathematical analysis shows that Integrated Information Theory (IIT), a leading theory of consciousness, relies on a measure called Φ that can differ between two physically isomorphic systems—systems identical in size, function, and causal structure—solely due to a permutation of the binary labels representing internal functional states. This means a system with Φ > 0 (deemed conscious) and an isomorphic system with Φ = 0 (a philosophical zombie) can be mathematically identical except for arbitrary labeling. The finding challenges IIT's assumption that feedback is necessary for consciousness and suggests any quantitative theory of consciousness should be invariant under such isomorphisms to avoid epistemological problems.

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Abstract

Any theory amenable to scientific inquiry must have testable consequences. This minimal criterion is uniquely challenging for the study of consciousness, as we do not know if it is possible to confirm via observation from the outside whether or not a physical system knows what it feels like to have an inside - a challenge referred to as the "hard problem" of consciousness. To arrive at a theory of consciousness, the hard problem has motivated the development of phenomenological approaches that adopt assumptions of what properties consciousness has based on first-hand experience and, from these, derive the physical processes that give rise to these properties. A leading theory adopting this approach is Integrated Information Theory (IIT), which assumes our subjective experience is a "unified whole", subsequently yielding a requirement for physical feedback as a necessary condition for consciousness. Here, we develop a mathematical framework to assess the validity of this assumption by testing it in the context of isomorphic physical systems with and without feedback. The isomorphism allows us to isolate changes in $\Phi$ without affecting the size or functionality of the original system. Indeed, we show that the only mathematical difference between a "conscious" system with $\Phi>0$ and an isomorphic "philosophical zombies" with $\Phi=0$ is a permutation of the binary labels used to internally represent functional states. This implies $\Phi$ is sensitive to functionally arbitrary aspects of a particular labeling scheme, with no clear justification in terms of phenomenological differences. In light of this, we argue any quantitative theory of consciousness, including IIT, should be invariant under isomorphisms if it is to avoid the existence of isomorphic philosophical zombies and the epistemological problems they pose.