[ouid]

Trying to study a very abstract concept without any examples is almost useless. There is, perhaps, some philosophical sense in which we could only be writing down mathematics for god to read, but humans searching the proposition space necessarily move heuristically. Formal generalization is fine (and even great) for working with objects, but pretty terrible for recognizing them. For example, (and also meta-example), most people do not need to spend a lot of time convincing themselves that the pigeonhole principle is true, at least in the finite case, but show most people a problem that it solves, and they will be unable to do so.