Here's the Wikipedia definition: "Methodological naturalism (MN) is the operational ground rule that, within natural science enquiry, one can only use natural explanations - i.e. one's explanations must not make reference to the existence of supernatural forces and entities. Note that methodological naturalism does not hold that such entities or forces do not exist, but merely that one cannot use them within a scientific explanation. Methodological naturalism is often considered to be an implied working rule of all scientific research and logically entails neither philisophical naturalism nor atheism, though some would argue that it implies such a connection."
I suppose we are going to need some clarifications of the terms "natural"and "supernatural."
The point about Lewontin's quote has to do with my question as to whether this is supposed to be an absolute principle or not, and whether the prinicple defines science or not. Some initial commitment to methodological naturalism seems to me to make perfect sense as part of science commitment to something like Ockham's Razor. But some people MN is an absolute and that it is definitive of science. Lewontin is an example, and plenty of people have argued that ID is a pseudoscience merely from its apparent supernaturalist commitments. I have a problem with that. Apart from that, I would just note that Dembski's The Design Revolution was written to answer a lot of the standard objections to ID. I'm not an ID expert and am a poor person to defend them on a lot of issues. Maybe others can do better.
On the other hand we do have, in ordinary life, situations where we have to decide whether there was design or not, and shouldn't we be using those principles in the investigation of nature. If I am playing cards, and one person gets 3 royal flushes in a row, I probably should have gone home a long time ago, because now I'm going to have to go home in my underwear. Even if the acceptance of design requires something on the order of the supernatural, I believe that there is some point at which enough is enough.
I remember one time I read a paper by old housemate and atheist philosopher Keith Parsons. It involved a strong commitment to methodological naturalism in the case of miracles. I told him, "This seems to imply that if I were God I couldn't persuade you no matter how many miracles I performed." And he said "No. If the stars the Virgo cluster were to spell out the words "Turn or Burn: This Means You Parsons," I'd turn. But I've read others who say they would not turn!
If by the "fact" of evolution you mean the gradual emergence of species, that's hard to doubt, I'll grant. Lots of scientists have thought that there is design in the universe, though they have often been shy about making it part of science. Can this conviction be made scientific?