The classical Board-Hall model is re-examined and shown to imply that, contrary to the model＇s intention and widely-held interpretation, multiphase thermal detonations are not physically possible. A new key physical concept is introduced, and the results show the existence of supercritical detonations, even in lean (melt content) premixtures, in agreement with recent experimental evidence. This opens the way for a rational approach to predicting the energetics of such explosions, and indicates the kind of constitutive laws needed for this purpose.