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In my view, the gut instinct which dumb people are more likely to rely on is sometimes right, while the analytical approach that smart folks have a habit of taking at times leads to mistakes. For example, the General Social Survey asked 901 Americans, "One of the bad effects of science is that it breaks down people's ideas of right and wrong."
The graph above shows that the percent agreeing with this statement tends to decline with increasing IQ, but I would argue that the statement is correct. Now, in terms of logic, science does not undermine morality: facts do not imply values. But the question is asking about cause and effect, not logic, and I think it is clear that science often works like an acid on established value systems.
The values of traditional religion, for example, do not have the status among the Western elites that they used to have, and this is due in part to the advance of science. I don't like to include cultural anthropology and sociology as sciences, but they share the epistemology of the hard sciences, and anyone who has taken even an introductory course in one of these subjects learns that values and norms are arbitrary. They are nothing more than social convention, and could easily be something else. These ideas come from the observed fact that cultures vary a lot.
Now, of course, you can argue that there is more to values than mere convention, but science will never argue that they are God-given, or that they have some transcendent, Platonic status. Science reduces values to a human level.
It looks like unintelligent people intuit this, while that understanding is drowned out in smarter folks as they deliberate over the question. Perhaps many smart people fail to appreciate the irrational nature of humans. Science doesn't corrode traditional ideas of right and wrong through logic: it does so through a psychological, irrational process.
For example, let's assume for a moment that heterosexual monogamy is right. Science has taught us that polygyny has been common among humans and is found among closely related species like gorillas. This knowledge might convince a person that monogamy is not right--it is just one way to organize human sexuality.
Logically, this makes no sense since the observed fact of polygyny does not imply that monogamy is either right, wrong, or neutral. Science doesn't deal in right or wrong, but it has an impact on our definitions of morality nevertheless. Smart people might not see this because they have these models of rational humans which are incorrect.
(It would be nice to see answers for people smarter than those shown in the graph. The people who are disagreeing with the statement in large numbers really aren't that smart, so it could be that they, by their answer, are simply saying that science is good because that's the respectable thing to say. And yeah, I might have just thrown out my earlier ideas. Get used to it: I do that all the time. I still like the idea of smart people using an incorrect model of rational humans, though.)