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.
In a way making a forum post is an example of the very kind of thing that I’m criticising—it’s a piece of freeform expression, and it’s a medium in which mistakes creep in easily.
I think you’re right to disagree with my statement there. The key thing isn’t the presence of mathematics—it’s the existence of some kind of set rational process—the “established systematic guidelines” that you mentioned.
DuncanS:
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.
In a way making a forum post is an example of the very kind of thing that I’m criticising—it’s a piece of freeform expression, and it’s a medium in which mistakes creep in easily.
I think you’re right to disagree with my statement there. The key thing isn’t the presence of mathematics—it’s the existence of some kind of set rational process—the “established systematic guidelines” that you mentioned.