So trying to decide between approaches is at least partly tied to whether you think something is, say, really a biology problem, a computer science problem, or a mathematics problem.

This is an especially interesting problem, because it seems very difficult to rationally assess what kind of approach to an especially open problem is most likely to work. If we're looking at, for example, AI as a research problem, then what kind of evidence could we gather that would lead us to believe that one approach is likely to be more fruitful than another?

Gathering this evidence would seem to require that we know which features of intelligence are most important (so we can decide what details can be abstracted away in our approach and which details need to be modeled), but we really don't have access to that kind of information, and it's not clear what would give us access to it (this insight alone would constitute a large amount of progress on understanding intelligence).

This suggests important questions about the role of rationality in science. Namely, for all the talk of the "weapons-grade rationality" that Less Wrong offers, are such rationality techniques very useful for really hard scientific problems where we're ignorant of large chunks of the hypothesis space, and where accurately assessing the weight of the hypotheses we do know is highly nontrivial?

Edit: see comment below for why I think the last paragraph is wrong.