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

TL;DR

The paper critically examines the Phi measure of integrated information, revealing its limitations and ill-defined cases in general physical systems, challenging its validity as a measure of consciousness.

Contribution

It identifies specific issues with the current Phi formulation and discusses potential solutions to address these fundamental problems.

Findings

Phi is ill-defined for certain physical systems

Current Phi formulation fails to meet IIT axioms

Proposes directions to improve Phi's definition

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.