This paper has a threefold purpose: first, to show why, contrary to widespread opinion, science and religion are in fact incompatible approaches to the investigation of reality, both in the methodology and worldviews they respectively entail. Second, to show why the noma thesis, according to which there should not be conflict between science and religion, is in fact untenable, and third, to show why the typical retort addressed to science supporters and critics of religious faith, according to which «belief» in science is just another kind of «faith» or even science itself is just another «religion», is unfounded.