Integrated Information Theory (IIT) 3.0 is among the leading theories of consciousness in contemporary neuroscience. The core of the theory relies on the calculation of a scalar mathematical measure of consciousness, Φ, which is inspired by the phenomenological axioms of the theory. Here, we show that despite its widespread application, Φ is not a well-defined mathematical concept in the sense that the value it specifies is non-unique. To demonstrate this, we introduce an algorithm that calculates all possible Φ values for a given system in strict accordance with the mathematical definition from the theory. We show that, to date, all published Φ values under consideration are selected arbitrarily from a multitude of equally valid alternatives. Crucially, both [Formula: see text] and [Formula: see text] are often predicted simultaneously, rendering any interpretation of these systems as conscious or not, non-decidable in the current formulation of IIT.
Keywords: computational neuroscience; consciousness; integrated information theory (IIT); mathematical theories of consciousness; non-uniqueness.
© The Author(s) 2023. Published by Oxford University Press.