I wouldn’t classify myself as a naturalist, because I do think that the supernatural realm is possible even though I don’t see any evidence of it. Though, I suppose if we proved the supernatural existed then it would be totally compatible with naturalism; we’d just start calling it “natural”.
Anyways, I think Sean Carroll does an excellent job making a 10-minute case for naturalism. I don’t think he is claiming, with certainty, that nothing else exists or that science is the only method by which we can obtain any sort of knowledge, but rather making the claim that naturalism does the best job of explaining our world. Watch the video and let me know what you think.