Great comment. I'll share a potential practical "definition" that popped into my head that is clearly different from the topological approach. If one starts wi

Great comment. I'll share a potential practical "definition" that popped into my head that is clearly different from the topological approach. If one starts with the idea of a hole as: "something that an entity can fall into or through", then it becomes very clear that a cup has a hole and a plate doesn't. An ant can fall into a cup from one side, but there is no way for an ant to fall into or through a plate. For falling "into" something, clearly some conception of "height" is important for this definition. Perhaps its related to being able to draw certain lines -- ones that are nearly parallel and of a relatively large length -- from one boundary to another surface of the object. For falling "through" something, I'm drawing a bit of blank right now, but I think there is some fairly simple definition that can clearly express this idea. I would argue the above is pretty close to what humans naturally consider as holes. --- EDIT: Thinking about this a bit more... I think we can simplify the above by viewing holes as "openings". This covers both cases of "falling into" or "through", and removes the distracting reference to gravity. It should be possible to come up with some sort of fairly practical definition of "opening". I think it has do with relatively sizing and geometry of the "cavern" that the hole leads to. However... inherently, there is no sharp line we can draw here, as the difference between a small scratch or dent and an actual cavernous hole is just a matter of degree. It seems, like many things in life, the distinction will remain a bit fuzzy and is not perfectly resolvable.