A scientist involved in a research program based on theory T, can always perform a problem shift and claim that the theory T has not been falsified since uncontrolled factors Cn+1, Cn+2,… have acted. Bayesian inference is a statistical method that uses Bayes' theorem to update the probability for a theory being true as more evidence becomes available. If two alternative theories T1 and T2 do not appear to have a common interpretation of the experimental data, at least they could try to agree on how the phenomena appear to us in our conscious experiences. This Chapter discusses multiple inconsistencies in classical theories of consciousness that are based on the axioms of classical physics. The most entertaining one is provided by eliminative materialism according to which consciousness does not exist at all; hence we are hallucinating having experiences while in fact we have none.