Campbell needed to show that if parapsychological phenomena occur, then the central nervous system cannot be material. The most he has shown is that if these phenomena occur, then present-day science cannot explain them. For his argument to have any force he would have to show both that the phenomena could be not explained using presentday conceptions of the physical and that they could be explained under the hypothesis that humans are partly non-physical, or immaterial. Lacking a convincing argument for these two propositions, there is no reason to suppose that, even if they should be accepted as genuine, any of the phenomena under discussion could refute CSM. The likelihood of anyone producing arguments for these propositions appears to me to be remote. What could cause us to accept an unknown immaterial substance or property over an unknown physical one in explaining some phenomenon?
The parapsychological phenomena I have been discussing all, as I have said, fall into two classes: those phenomena in which the mind comes to be in some state by paranormal means, and those in which it causes something else to come to be in some state by paranormal means. Since I have shown that the existence of any or all of these phenomena is consistent with CSM, Campbell and those philosophers who agree with him are wrong in their belief that the existence of even a 'single example' of parapsychological phenomena would refute CSM.
I have not shown other possible kinds of parapsychological phenomena are compatible with CSM. However, until someone produces data to support a belief in the existence of another kind of phenomenon, and an argument to show its inconsistency with CSM, there is no reason to think that the results of parapsychological research are incompatible with CSM.