Throughout almost the entire history of science, it has be argued that important features of the human mind are beyond the reach of natural science. Today, many of these allegedly unsurpassable obstacles have been removed. It would be naïve to rule out that some of the problems that seem insurmountable to us, might be resolved in the future. This is true also for the so-called “puzzle of consciousness.” According to this position, neuroscience is unable, in principle, to provide an explanation for the emergence of consciousness. It will be demonstrated, however, that the arguments that seem to support this position are surprisingly weak. Still, a scientific explanation of consciousness seems hard to imagine, but it can be shown that our intuitions are subject to an ongoing change.