Lowder summarizes his debate with Frank Turek  "what best explains reality: naturalism or theism?" He defines his terms: “naturalism” "the physical exists and, if the mental exists, the physical explains why the mental exists. If naturalism is true, then there are no purely mental beings which can exist apart from a physical body and so there is no God or any person or being much like God." He defines supernaturalism: "...the mental exists and, if the physical exists, the mental explains why anything physical exists. If supernaturalism is true, then there is no purely physical matter which can exist without some sort of ultimate mental creator."
He has three contentions but I will only deal today with matters pertaining to the definitions, I will deal with the contentions in days to come. Lowder defines Naturalism as "the view that the physical exists and, if the mental exists, the physical explains why the mental exists. If naturalism is true, then there are no purely mental beings which can exist apart from a physical body and so there is no God or any person or being much like God." Then Supernaturalism is just the reverse, if it exists then mental explains physical.
This asserts that God is a being one among many, ("...no purely mental beings"). The theological trajectory developed by Tillich, John Macquarrie, (and others) voiced at Vatican II, indicates God is not a being but being itself. Moreover we have a problem in understanding what "mental" is when divorced from the physical process involving brain. I guess I don't mind your definition in principle but it is kind a metaphysical constrict to assert that we can see into the black box deeply enough to know that God's mental process well enough to critique it. I just assume that is part of what is meant by "God transcends our understanding."
If I were to say the physical is only a form of energy and matter is not the primary state or the primordial state of energy, you would probably say I am being too literal about the physical. It's not matter per se that makes something physical, such that energy is a from of the physical. I assume you might say something like that? I say we don't know all forms of energy. We don't know all that is involved in reality. Thus since the mental is a form of energy how do you know all physical doesn't reduce to the mental? Why make this sharp distinction between physical physical ?