Consciousness scientists have not reached consensus on two of the most central questions in their field: first, on whether consciousness overflows reportability; second, on the physical basis of consciousness. I review the scientific literature of the 19th century to provide evidence that disagreement on these questions has been a feature of the scientific study of consciousness for a long time. Based on this historical review, I hypothesize that a unifying explanation of disagreement on these questions, up to this day, is that scientific theories of consciousness are underdetermined by the evidence, namely, that they can be preserved “come what may” in front of (seemingly) disconfirming evidence. Consciousness scientists may have to find a way of solving the persistent underdetermination of theories of consciousness to make further progress.