Recent analytical philosophy is premissed on the assumption of naturalism. This is the assumption, in its contemporary version, that whatever there is in the world, there is nothing which the natural sciences fail to encompass; there is nothing non-natural, nothing preternatural, nothing supernatural.
The assumption is not sharply defined. For example, there are differences over the demarcation of the natural sciences, and differences over what it is for those sciences to encompass an area. It may be required that every entity in the area is recognized by natural scientists or merely that it is definable by some operation on such entities. Again, it may be required that every property ascribed to those entities is reducible to scientific properties or only that it is supervenient on them.
But, however it is construed, the prevailing analytical view is that the assumption of naturalism is sound. This consensus has dictated a problem for philosophy, and an accompanying research programme. The problem is to determine how far a commitment to naturalism undermines our received view of things, our working image of the world. The programme is to develop, where necessary, a naturalistic replacement for that view.
(Philip Pettit, Richard Sylvan, and Jean Norman, "Preface," in Metaphysics and Morality: Essays in Honour of J. J. C. Smart, ed. Philip Pettit, Richard Sylvan, and Jean Norman [Oxford: Basil Blackwell, 1987], vii-viii, at vii)
Note from KBJ: As these paragraphs make clear, naturalism is not itself part of science. It is a philosophical doctrine about science. Science itself says nothing about whether there is a supernatural world, or, if there is, what that world is like. Science, in short, has nothing to say about whether God exists. Science conjoined with naturalism (we can call this "scientism") does, however, imply that there is no god. Keep this in mind the next time someone says, or implies, that science rules out the possibility of God. No; scientism rules out the possibility of God.