The discussion on whether the subjective character of consciousness can be explained in physical and functional terms occupies a central place in modern philosophy of mind. Some of the most well-known competing positions in this discussion either defend or reject such explainability; however, the possibility that the central problem is unsolvable due to the constraints of complex systems hasn’t received much attention. This article illustrates a rudimentary complex system, gives an outline of the main characteristics of such systems, and, based on this, introduces a preliminary argument that tries to establish the undecidability of the question of whether the subjective character of consciousness, or, more precisely, qualia, can be given a physical and functional explanation.