In recent controversies about Intelligent Design Creationism (IDC), the principle of methodological naturalism (MN) has played an important role. In this paper, an often neglected distinction is made between two different conceptions of MN, each with its respective rationale and with a different view on the proper role of MN in science. According to one popular conception, MN is a self-imposed or intrinsic limitation of science, which means that science is simply not equipped to deal with claims of the supernatural (...) (Intrinsic MN or IMN). Alternatively, we will defend MN as a provisory and empirically grounded attitude of scientists, which is justified in virtue of the consistent success of naturalistic explanations and the lack of success of supernatural explanations in the history of science (Provisory MN or PMN). Science does have a bearing on supernatural hypotheses, and its verdict is uniformly negative. We will discuss five arguments that have been proposed in support of IMN: the argument from the definition of science, the argument from lawful regularity, the science stopper argument, the argument from procedural necessity, and the testability argument. We conclude that IMN, because of its philosophical flaws, proves to be an ill-advised strategy to counter the claims of IDC. Evolutionary scientists are on firmer ground if they discard supernatural explanations on purely evidential grounds, instead of ruling them out by philosophical fiat. (shrink)