I recently came across Stark's article at The Chronicle on Christianity, capitalism, and science (HT: Cliopatria). The argument manages to be both confused and confusing at the same time. In the first paragraph he seems to be trying to convey the problem of China, which did arise in Enlightenment circles here and there (the problem was why China, which was occasionally used by a handful of thinkers as a paradigmatic rational society, appeared not to be as advanced scientifically as Christian Europe); but he manages to make it sound as if it were a general problem pertaining to the 15th century, which is odd. And while shifting economic systems probably had a role somewhere in the mix, anything recognizable as (genuine) capitalism seems to have missed completely some of the major scientific advances of the early modern period. I suppose it depends on what you're willing to call 'capitalism'.
The more serious problem with the argument is that it seems to be mixing up genealogical and logical backgrounds, which need not be the same (or even consistent with each other). There is a strong argument that both Christianity and new economic awareness played a role in the genealogy of science as we know it. To name just one example, a number of early scientists saw themselves as doing something for Christianity and Christendom when they did their scientific work. But it isn't clear what this gets us. For instance, we could interpret this as meaning (1) that Christianity has some special aptness for incubating scientific development; (2) that the scientists were acting inconsistently; or (3) that the union of the two is little more than a coincidence. Even if we accept (1), it wouldn't follow that other things lack the same aptness. That something forms a genealogical background for a given historical/intellectual event tells us very little about how it is related to that event logically or in explanation. Stark gives us a largely genealogical argument that capitalism and Christianity played a role in the development of science, but tries to draw from this a conclusion about how the development of science is to be explained, as if he had shown that there was some deeper logical link between Christianity and scientific thought. Some of Stark's undeveloped claims are perhaps supposed to give this deeper explanatory link; but many of these are rather dubious. In fairness to Stark, he's clearly just putting up a summary of his forthcoming book, which (one would imagine) develops his claims at greater length, and perhaps in a more nuanced and argued way. But as it stands it's not a particularly great argument.