Brown does not offer a very penetrating analysis of the question, in my opinion. He does not define what he means by "science", and following that failure mostly flounders around in generalities. If he does actually answer his own question, it is not clear to me what the answer is. His main point seems to be that the rise of scientific knowledge and the fall of religious belief are not as closely correlated in reality as campaigning atheists would have us believe.
Instead of defining science, Brown begins with an in-from-left-field announcement of something totally non-obvious, thus:
Obviously the two [i.e. science and atheism] are closely linked, in as much as science assumes the falsity or at least irrelevance of supernaturalism.This statement is a category mistake. Science, when properly defined, is the study of nature in order to search for general principles which can describe observed behaviour and predict future behaviour. Science studies the natural world in order to be able to describe patterns.
Being the study of the natural world, science can by definition make no assumptions or statements about either the falsity or irrelevance of the supernatural. It is not within its remit. Looking at nature to discover what is beyond nature is a self-contradiction. Asking science to make such statements is like asking a tennis umpire to declare a player off-side, or asking a soccer referee to send the goalkeeper off for LBW. (For non-British readers, off-side is a soccer rule, and LBW comes from the world of cricket!). It is out of scope. "False" or "irrelevant" are rulings that can only be made for something "in scope". Brown appears to be talking about "scientism" (the unprovable philosophical assumption that every question is potentially satisfiable by science), not true science.
It's important also to recognise that science is descriptive, not prescriptive. When science codifies its predictions and calls them a "law", this needs to be understood with care. The word "law" has misled many people. To predict, using Newton's "laws" of gravity, at what time the sun will rise tomorrow is quite different to explaining why the motions predicted will take place. The law tells us what we expect to see - but not why we see that thing. To say that a force of gravity is at work that obeys an inverse-square law is one thing; but to account for that force and why it is inverse-square instead of something totally different is something else. Science can note that an inverse-square law appears to consistently be at work (description); but to account for that law (prescription) is something very different.
This leads to the search for a "theory of everything". Perhaps the inverse-square law, and every other law, are natural consequences of some other working within nature. But even if they were - then that other working within nature would also need accounting for. Either then you have an infinite chain of causes, or at some point you have to allow the supernatural: that nature is ultimately caused by something beyond nature. Ultimately, nature itself needs accounting for. Searching within nature to account for nature is absurd. In other words, making science the arbiter of supernaturalism is absurd. Richard Dawkins argues that we cannot attribute the cosmos to an intelligent being, because then we would have to account for that intelligent being. But this argument only works if the intelligent being is itself within nature, and not outside it. And the Christian claim which Dawkins hopes to refute is precisely the latter: thus, Dawkins' argument is irrelevant. Dawkins has not faced up to the regress in his own position - if physical forces are sufficient to account for all we find in nature, what accounts for those physical forces themselves? Other physical forces? Or are they just suspended over nothing, having no origin and needing no explanation? This is ultimately a philosophical question, not a scientific one. Science cannot decide it, nor is it meant to.
The fact is that science itself needs accounting for, and cannot account for itself. Why should everything work together in an orderly way? Why should we be able to reduce our observations to rationally understandable principles and then generate descriptions from them? Whence this comprehensibility and orderliness?
If science needs accounting for, then the question ought to be, "does atheism count for science better or worse than theism does?". This is the question that Brown ought to ask, but skips over because he appears to have been led by such as Dawkins to confuse science with a particular (and erroneous) brand of philosophy. Theism accounts for science very well by stating that nature is orderly and understandable to human minds because it is itself created and ordered by a divine mind who fashioned it and us for each other. We were made to live in the world and to harness it. The belief that God is orderly in his being and ways and that he made us to enjoy his creation generates the expectation that nature will be orderly and possible for us to investigate and harness for our use. That is precisely why modern science was born out of the soil of Christian Europe - people expected that studying the works of their Creator would be a fruitful enterprise, not a random and frustrating one. They did not believe that order came from chaos, and so they studied the Creation expecting to find order that could be described in orderly ways: exactly what happened.
How, though, does atheism account for science and for nature itself? It does not, and cannot. Ruling out the possibility of a mind being behind the cosmos, atheism leaves scientific "laws" hanging in mid-air: they just exist, whether we like it or not and we cannot tell you why. For an atheist, the scientific enterprise is essentially a huge irrational faith-leap: he has no reason for believing that nature should be coherent or comprehensible, but he investigates it with that expectation anyway. It's just pot luck, a fortuitous hand dealt to us! (But who set up the pot, and who was the controller dealing the hand?) The compatibility between his mind and the objects being studied by his mind is just a big happy fluke. Ultimately atheism is not supported by science; rather, it removes its foundations.
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