DuncanS:

Someone once said that all science is either physics or stamp collecting. It's close - you have to have some organising principles of decent mathematical quality to do reasoning with any certainty. Without that, stamp collecting is the limit of the possible.

I disagree with this. In many areas there are methodologies that don't approach a mathematical level of formalization, and nevertheless yield rock-solid insight. One case in point is the example of historical linguistics I cited. These people have managed to reach non-obvious conclusions as reliable as anything else in science using a methodology that boils down to assembling a large web of heterogeneous common-sense evidence carefully and according to established systematic guidelines. Their results are a marvelous example of what some people call "traditional rationality" here.