The danger that Eliezer warns against is absolutely real. So what's special about math? In the case of math, I think that there is something special, and that is that it's really, really hard to make a bogus argument in math and pass it by somebody who's paying attention. In the case of experimental science, the experiment is deliberately constructed to take the result out of the hands of the experimenter. At least it should be. The experimenter only controls certain variables.

So why is there ever a danger? The problem seems to arise with the mode of argument that involves "the preponderance of evidence". That kind of argument is totally exposed to cherry-picking, allowing the cherry-picker to create whatever preponderance he wants. It is, unfortunately, maybe the most common argument that you'll find in the world.