She's arguing, as I understand it, that science cannot be ontologically complete, that it always coexists with other kinds of truth:
There is always ‘room left’ for alternative ontologies in cognitive-intellectual space, a realm that is neither cramped nor finite but, on the contrary, appears – both historically and for humans individually – exceedingly and perhaps infinitely elastic. ... For many people … accepting, applying, and/or producing scientific knowledge and being religiously observant are no more in conflict than would be, for any of us, both playing the violin and practising law.Interesting, maybe, as a bare assertion; more for the particular argument. Let's say, on the one hand, that we accept a scientific view of religion. It's a pattern of human behavior created by the interaction of our biological brains and our social environment; the potential for it was favored by its usefulness to our savannah ancestors and its actual existence by its usefulness for some social-political purpose today. Group cohesion then, the ploys of the Jesuits now, something like that.
The problem with this isn't that it isn't true; it is true, within some limits. The problem is that it explains too much. Every human belief system is the product of our Darwinianly-evolved brains and our social environment. You can fully explain religion, in principle, by a combination of genetic predisposition and practical advantage, but you can just as fully explain science, or anything else that people do. After all, we're natural beings in the natural world; everything we do has a natural explanation. The most you can say in this framework is that science has displaced religion from many areas of life because of its greater utility; but by the same token you have to concede that religion has held on in other areas thanks to its greater utility. A purely naturalistic account of human beliefs has no place for them being true or false. People adopt them all for the same kind of reasons.
(Sraffa to Wittgenstein: "If the rules of language can be constructed only by observation, there can never be any nonsense said. This identifies the cause and the meaning of a word. The language of birds, as well as the language of metaphysicians can be interpreted consistently in this way. It is only a matter of finding the occasion on which they say a thing, just as one finds the occasion on which they sneeze.")
On the other hand, almost anyone who cares about science prefers to believe it corresponds to some external truth about the world. One can't object to this (Thomas Nagel, in this review, accuses Smith of objecting, but I suspect he's got her wrong), but it's not consistent with science being ontologically complete. A scientific account of scientific beliefs can offer various reasons for why people happen to hold them, but it has nothing to say about whether they are true. You may believe, if you like, that Betelgeuse would be 630 light years from the Earth whether anyone had measured the distance or not; but in a naturalistic account of why people do believe that, it all comes down to the measurements; independent of those the "objective" distance has no effect on anyone.
Put it another way: science offers heuristics for sorting beliefs into relatively confirmed and relatively falsified piles; but it doesn't, and can't, tell you why should prefer to hold the beliefs in the confirmed pile. Oh, say the new atheists, because they're more useful. But right there they've conceded that if someone finds some social or psychological advantage in being religious, that's as justified as anyone's belief in science. To get along with your neighbors, to be free of angst about The Point of It All: aren't those useful too?
Galileo is a hero of science and of civilization for eppur si muove. But what's he saying? With respect to the heavens, he's asserting that the demands of reality take precedence over what we think is right. But with respect to the earth, it's just the opposite: He's insisting on the priority of abstract right over concrete reality. After all, if he applied the same unromantic empiricism to his life as he did to his astronomy, he'd take one look at the instruments and conclude that practical experimentation revealed that the Earth goes around the Sun. (As did Brecht's Galileo.) A belief that's liable to get you tortured to death is pretty clearly less practically useful than a belief that leaves you torture-free. Galileo's insistence that one should believe in science, come what may, is entirely unscientific, and -- Brecht struggled with this -- so much the better for Galileo.
The thing about the contradiction between the scientific method and belief in science is that it can be resolved either way. Nagel thinks that Smith is trying to apply the naturalistic, constructivist view of human beliefs "all the way down". Me, I prefer to think she's showing that's exactly what you cannot do.