The great figures of the Scientific Revolution -- Galileo, Kepler, Newton -- were crystal clear on why science could be a rational enterprise: scientists were reading Nature, "the book of God"... and God being the supremely rational mind, naturally the book had a rational design, one that, with effort, our more limited minds could follow.
The major part of the history of the philosophy of science since the 18th-century has been the hunt to find some other, any other, basis for science's rationality. Once Hume destroyed the purely empiricist case for science, the search had an air of desperation to it. Instrumentalism, verificationism, falsificationism: all were attempts to patch up the whole Hume had noted.
All these attempts have failed.