I love this topic, and hope I can contribute fruitfully to the discussion without bringing any more confusion. Draper’s definitions are somewhat helpful, but he asserts that MdN favors the PhNists. I disagree with Draper on this point. I think MdN is part of a robust Christian theology when one recognizes the demarcation and limitations of scientific research. MdN is the appropriate scientifically experimental approach for the physical and biomedical sciences but not the social sciences.
I think there is a lot of conflation when it comes to understanding and discussing the differences between methodological (MdN) and philosophical naturalism (PhN). I’m actually editing my article on this topic that will be in an upcoming edition of The Canadian-American Theological Review. It seems @Ronald_Cram is making some very important distinctions. But I know @swamidass makes the appropriate distinctions as well.
One of the critical distinctions is that science has real physical/metaphysical boundaries as to what it can detect or attempt to detect/measure. Someone who is committed to PhN might possibly deny this in theory and think that, theoretically, one day we will be able to explain mechanisms of all of life’s events. One committed to MdN will acknowledge the boundaries of science but may remain skeptical as to when those boundaries have been reached.
Another distinction that needs to be made is that a scientist who is committed to MdN in their scientific work but who is not a PhNist can rationally, logically, reasonably, and justifiably reach conclusions that suggest God has been, and indeed still is, at work in the Universe. His work can be indicated by, just not proven or shown through, scientific evidences. Science cannot prove God’s existence or work. (But paradoxically science works because of God’s established order in nature.)
A rational scientist (or person) should never be limited to consider only the scientifically verifiable as an individual making arguments to the best explanation. Many things are rational without being particularly scientific.