According to the integrated information theory of consciousness (IIT), consciousness is a fundamental observer-independent property of physical systems, and the measure Φ (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 Φ consistent with the axioms of IIT, and there should not be cases of Φ being ill-defined. This article presents three ways in which Φ, in its current formulation, fails to meet these standards, and discusses how this problem might be addressed
