The biggest issue, however, is that we don't have a rigorous, precise and most of all consistent, definition of any sort of "naturalism", methodological, intrinsic, qualified or otherwise.
There are at least three definitions I'm aware of. (I've applied entirely ad hoc, arbitrary labels.)
- Nonteleological Naturalism: the universe is fundamentally not intelligent, sentient or conscious.
- Internal Naturalism: all scientific explanations should reference causes "inside" the universe.
- Epistemic Naturalism: science can only establish empirically falsifiable explanations by trying and failing to falsify them.
Nonteleological Naturalism is fuzzy; we don't understand teleology very well. Furthermore, if we provisionally define "teleology" as "the sort of thing that human beings do (whatever that might happen to be)" it's fairly obvious that teleology is operative within the physical universe. It is both unjustified and unnecessary to assume the universe is fundamentally nonteleological; we can instead draw conclusions about fundamental teleology or nonteleology from empirical evidence.
Internal Naturalism is in one sense incoherent: one definition of "universe" is "everything that exists"; if a god exists, it is by definition part of the universe or the universe itself.
Adding a qualifier and talking about just the "physical" universe doesn't help much: what precisely does one mean by "physical" in this context? Furthermore, even if we could adequately define "physical", an interventionist god would by definition have to have to leave some sort of physical "fingerprint", which would then be by definition within the domain of science (and from which we might draw conclusions about the "part" of God outside the "physical" universe.)
This leaves us (assuming there are no alternative definitions) with Epistemic Naturalism: science can deal only with falsifiable theories (note that a statement that is confirmable is also falsifiable).
This definition has the added advantage that there seem to be statements — even seemingly prosaic statements — that seem semantically propositional (i.e. truth-apt, could be true or false) that talk about existence, and that are not falsifiable: statements about "the matrix", the assertion that not the real Mona Lisa but a perfect replica hangs in The Louvre, etc. The existence of unfalsifiable ontological propositions injects "philosophical life" into the discussion: we have real, constructable, apparently comprehensible sentences about the world that at least seem to have truth value, and which science seems to exclude a priori from consideration.