Science requires faith.
I realise that statement will upset people, but those are the facts. The comic above, from the excellent xkcd, presents the issue particularly well. To do science at all, we must at the very least have faith in our rationality and the ability of our brains to discover truth. Faith in the regularity of the universe helps, too.
Philosopher Alvin Plantinga published a book last year entitled Where the Conflict Really Lies: Science, Religion, and Naturalism, which was reviewed by Thomas Nagel in the New York Review of Books. The excerpt below comes from that review:
[Plantinga] holds, first, that the theistic conception of the relation between God, the natural world, and ourselves makes it reasonable for us to regard our perceptual and rational faculties as reliable. It is therefore reasonable to believe that the scientific theories they allow us to create do describe reality. He holds, second, that the naturalistic conception of the world, and of ourselves as products of unguided Darwinian evolution, makes it unreasonable for us to believe that our cognitive faculties are reliable, and therefore unreasonable to believe any theories they may lead us to form, including the theory of evolution. In other words, belief in naturalism combined with belief in evolution is self-defeating. However, Plantinga thinks we can reasonably believe that we are the products of evolution provided that we also believe, contrary to naturalism, that the process was in some way guided by God.
Put another way, if we believe that evolutionary pressures select purely for reproductive fitness and survival, why would we believe that our mental faculties have been evolutionarily selected to reliably discern truth?