On the basis of the distinction between phenomenal and psychological consciousness, I propose a formal framework where we can express and analyze a strong form of Chalmers’ zombie argument. By employing such formal framework, I make clear the kind of problem that this argument poses to anyone who is willing to (i) construct a theory of phenomenal consciousness and (ii) maintain the reductive explainability of phenomenal consciousness by physics. I then extend such formal framework so as to provide a theory of consciousness in axiomatized form. The explanation of phenomenal consciousness provided by this theory is by no means inconsistent with a physicalist perspective. In fact, once the theory is supplemented with a minimal physicalist assumption, we can prove the reductive explainability of phenomenal consciousness by physics and, as a consequence, the logical impossibility of zombie worlds. I then conclude that Chalmers’ intuition, according to which phenomenal consciousness is beyond the scope of any physical theory, is not tenable. Finally, I hint at a possible source of such erroneous perception, that is, not realizing that the hard problem of consciousness is not a problem of scientific explanation but, rather, a philosophical problem of conceptual explication.