Is a cap a hat?

I get enormous pleasure from reading things like this, and I don’t quite understand why. It kind of feels like these technical definitions with clear and precise terminology are carving reality at the joints.

So my internal mental models become more compact, my thinking is now a little bit clearer and that feels really good. I still don’t quite get it though. I wonder - is it a joy unique to systematizers or does everyone get it?

(Also careful readers will note an inconsistency in the definitions below - it’s still a better map and still feels good. And it may be resolvable - if you, dear reader, know, or investigate and come to a definitive conclusion, please let me know .)