Here is one objection by Roderick Fitts
So the upshot, the epiphenomenalist would have us believe that his position is true, or is genuine knowledge, but conscious understanding has nothing to do with with why he holds this position. So conscious knowledge of Epiphenomenalism plays no role in why one may believe in the theory, therefore he has no claim to actual knowledge. Which seems self-refuting.
The epiphenomenalist claims, as knowledge, that brain events produce mental events, and that the latter are causally inefficacious–presumably, this also includes beliefs. In effect, he’s claiming that he’s previously witnessed the evidence and logically established that his viewpoint is true (i.e. that he believes he has knowledge). While at the same time, his position as an epiphenomenalist implies that his beliefs and observations have nothing to do with the fact that he’s now advocating that position, as such advocacy would be the exclusive result of brain events (recall that only physical processes are causally effective, on his view). By his own theory, he’s being made to believe and produce epiphenomenalist “word sounds” by brain activity, which make his claim to knowledge meaningless.
http://www.philosophyinaction.com/blog/?p=2809
http://www.philosophyinaction.com/blog/?p=2809
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