How burdens of proof are allocated in science has an important bearing on how new knowledge develops. Usually, the burden is on new theories to prove their worth relative to a default, baseline of knowledge that is considered established and secure. However, in the case of classical vs. quantum social science matters are not that simple because the long-standing classical default has itself already failed to pass crucial tests, which has spurred the search for quantum solutions instead. Part I of this paper, therefore, tries to ‘re-balance’ the burdens of proof with Quantum Mind and Social Science’ critics, by highlighting two significant limits to date of classical thinking about the mind and society: the philosophical problem of finding a place for consciousness in the universe, and the scientific problem of explaining the Kahneman–Tversky anomalies in psychology. Acknowledging these outstanding problems does not equalize the burdens of proof, but it does mean that as we head into the more substantive discussion in Part II there is no secure default position. Just burdens of proof all around.