A quick check of Bourget's site yielded two papers he's authored, one called Representationalism about Consciousness, and the second named Quantum Leaps in Philosophy of Mind. Given my demonstrated weakness for philosophy of mind, I'm certain I'll read both.
Nonetheless, it's the latter that really intrigues because it reminds me of UCLA psychiatrist Jeffrey Schwartz's September presentation at IF in Louisville. He believes that the mind supervenes on the brain - saying at one point during his presentation that "the brain puts out the call and the mind decides whether to listen" - and offered, in the form of brain scans, visual evidence in support of his view. He also suggested that quantum theory might be applied to explain that mind-brain relationship, a suggestion that drew a sharp objection from one physicist in attendance.
I'm frankly not qualified to say whether quantum mechanics might be applied in this way. But following Chalmer's link to Bourget's page reminded me that serious people believe there could be a fit and that wonderful discovery often requires a disregard for accepted boundaries. It's the willingness to be spectacularly wrong that can make so much right.