Parsons dismisses substance dualism's empirical arguments as small in number and moves on to the philosophical arguments. What he leaves out, however, is the fact that what they lose in quantity they make up for in quality. He mentions Mines to blow off his arguments but doesn't actually quote him:
qualia, intentionality, privileged access, non physicality, and free will] therefore provides evidence that there is a God who created them.
This is not quite the way Mines sells the argument but it is the basis of the so called "hard problem." David Chalmers calls it that because no one has a clue how to solve it, The problem is basically that we don't know what consciousness is.We all know we have it none one seriously tries to argue that we are not conscious, But we can't definite it because can't explain what what causes it, The reductionist want to lose the phenomena and pretend it doesn't exist. Parsons treats this like the weak little old philosophical argument but I think is also empirical. We live empirical evidence that consciousnesses is basic. Parsons asserts that NDE is the only argument but I don't even make reference to it.
But Parsons rejects consciousnesses as an argument for God, he asserts that if consciousness is not reducible we could still be property duelists and not believe in God. "This seems a bit hasty[evoking God via irreconcilability of mind] and abrupt to me. Even if we conceded that the accepted terms of neuroscience—electrical and chemical happenings in neurons—cannot explain consciousness, could we not adopt a property rather than a substance dualism as a more parsimonious option?" that is following the example of Chalmers who is an atheist. First my point is not argue for God here, I think we could it makes a good argument, I do use it. I think there is a more important argument to be made: that irreducibility is important for all people, Theist or other wise,Secondly, while property dualism is compatible with either atheism or belief in God,Neither position is mandated by property dualism. Of course my God arguments are about warrant not proof. Irreducibility mind could still be a good reason to believe in God without mandating belief.
Mines seems to be misquoting Nagel,however,in saying that "Nagel argues that they present an insurmountable conceptual challenge to naturalism." He is an atheist he does not argue against Naturalism. Yet Parsons rejects Negals's argumemt, he has no real logical. Instead he evokes one of Denett's branding arguments labeling the Bat argument as 'an intuition pump." This is very misleading because it dismisses the argument as something less than it is. He's trying to pretend it's only rhetorical and emotive but in reality it is also logical. If in fact experiential knowledge is closed to us except through experience then it's only logical that we not regard facts as full knowledge without the experiential dimension. But Dennett is merely losing the phenomena one tactic of a certain kind of reductionism. (For a full take down of Dennett's work Consciousness Explained see Doxa) 
Parsons goes on and admits that there is a basis to the idea that first person perspective gives a dimension that "Dorothy when she steps from the sepia of Kansas into the technicolor of Oz. Her experience is different in a way that she could not have explained, even if she were thoroughly versed in the physiology of color vision, to the Dorothy that sees only the gray shades of Kansas."  Sort of makes Quoting Denmett unnecessary.
Parsons major objection to the hard problem (at least Nagel's Bat) is the idea that first person experience could be physically or nationalistically caused:
There is nothing in the qualitative content of my consciousness that informs me that such experience could not have been physically produced. Maybe I cannot intuitively see why brain processes would cause qualia (Chalmers’ “hard” problem), but it does not follow that a brain cannot do it. So, the relevant question is not whether there are some items of knowledge that can only be had via first-person consciousness. The important question is whether first person experience can be physically caused. Why not? Nor is there any reason to think that we could not know, in detail, how it was caused. That is what neuroscience does. If neuroscience can explain how my brain produces first-person experience, then such experience is subsumable under a naturalistic ontology.Again he has reduced consciousness to brain function. Here he says if neuroscience can explain how the brain produces first person, (that is brain function). If we understood how first person experience is produced that would not necessarily tell us what consciousness is, it would tell part of how consciousness is produced but not necessarily what it is or what it means. Moreover, there are more God arguments to be derived from consciousnesses than just one stemming from cause and effect.
Parsons wants to defeat consciousnesses as a God argument, but there are more versions of that than just knowing the brain functions that produce consciousness. (see my existential version of the argument, see also my TS argument where mind is a crucial part of the argumemt.