The Phi measure of integrated information is not well-defined for general physical systems

Summary

If consciousness can be measured, its formula must be precise and universally applicable. A foundational theory in q-bio.NC posits consciousness is a fundamental system property quantifiable by a measure called Phi. However, a recent analysis reveals that Phi, in its current mathematical form, isn't consistently well-defined or uniquely formulated across all physical systems. This theoretical work identifies three specific ways its current definition falls short, offering crucial insights for refining the measure and strengthening the theory's mathematical foundations.

Abstract

According to the Integrated Information Theory of Consciousness, consciousness is a fundamental observer-independent property of physical systems, and the measure Phi of integrated information is identical to the quantity or level of consciousness. For this to be plausible, there should be no alternative formulae for Phi consistent with the axioms of IIT, and there should not be cases of Phi being ill-defined. This article presents three ways in which Phi, in its current formulation, fails to meet these standards, and discusses how this problem might be addressed.

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