Hi Gottfried,

Yes, I would say that generalisation is the origin of all rational activity. Though the word which sounds better to me is "analogy". I think that humans, as intelligent creatures, see similarities in things, which in turn point to the fact that the compared objects are analogous in some respect. This is the first step of simplification and abstracting away. Then we infere some conclusions about this comparison.

In some way nothing is similar and everything is unique. But if we want to say anything about anything, we have to start theorizing - hence we bear a lot on these (over)simplifications.

In fact, there is an entire school in cognitive science which believes that when we are doing maths, we always use some metaphores. Indeed, a symmetry, as you put it, or analogy, is a kind of a "metaphorical mapping of one into another (and vice versa)", since we don't fully present the one and the same object both times on both sides of the equasion - those two guys share some relation. And this relation, the equivalence, is a kind of metaphorical mapping, as Lakoff and Johnson would believe.