On the Non-uniqueness Problem in Integrated Information Theory

Abstract

Integrated Information Theory is currently the leading mathematical theory of consciousness. The core of the theory relies on the calculation of a scalar mathematical measure of consciousness, {Phi}, which is deduced from the phenomenological axioms of the theory. Here, we show that despite its widespread use, {Phi} is not a well-defined mathematical concept in the sense that the value it specifies is neither unique nor specific. This problem, occasionally referred to as "undetermined qualia", is the result of degeneracies in the optimization routine used to calculate {Phi}, which leads to ambiguities in determining the consciousness of systems under study. As demonstration, we first apply the mathematical definition of {Phi} to a simple AND+OR logic gate system and show 83 non-unique {Phi} values result, spanning a substantial portion of the range of possibilities. We then introduce a Python package called PyPhi-Spectrum which, unlike currently available packages, delivers the entire spectrum of possible {Phi} values for a given system. We apply this to a variety of examples of recently published calculations of {Phi} and show how virtually all {Phi} values from the sampled literature are chosen arbitrarily from a set of non-unique possibilities, the full range of which often includes both conscious and unconscious predictions. Lastly, we review proposed solutions to this degeneracy problem, and find none to provide a satisfactory solution, either because they fail to specify a unique {Phi} value or yield {Phi} = 0 for systems that are clearly integrated. We conclude with a discussion of requirements moving forward for scientifically valid theories of consciousness that avoid these degeneracy issues.