 As with the Generalized Second Law, one of the most fascinating aspects of Hawking radiation from a foundational point of view is the multiplicity and multifariousness of the derivations known for it. They also differ radically among themselves with regard to the mathematical rigor of the framework they adopt and the mathematical character of the structures they assume, and almost all are valid in different regimes than the others, using different types of physical systems and different approximations and idealizations, basing their arguments on different physical principles, with varying degrees of physical perspecuity and intuitiveness. In consequence, these different derivations seem to suggest different physical interpretations of Hawking radiation itself, both for its origin and for its character (Brout et al. 1995). It is thus not even clear, at a foundational level, what the physical content of the prediction of Hawking radiation is. Indeed, as in the case of the Generalized Second Law, some of the derivations of Hawking radiation make assumptions that seem to contradict some of the assumptions of other derivations—but if A implies B and not-A implies B, then B must be a tautology. Since this is an unappealing attitude to take towards Hawking radiation, some other way must be found to reconcile the contrary derivations. Again, standard consilience cannot be invoked here, for the same reasons as discussed at the end of  section 5.4.1  for different proofs of the Generalized Second Law. 