>It's just like if you were a biologist and you'd just learned about "animals" and "vertebrates": you'd have to learn about some animals that aren't vertebrates.
John, this example is a bit confusing: animals are a more generic structure than vertebrates (vertebrates are animals with a specific structure in them - they are animals with vertebrae), so
preorders \\(\rightarrow\\) animals
posets \\(\rightarrow\\) vertebrates
So following the logic, to learn more about vertebrates, one should look for vertebrates which *aren't* animals, with attached interpretation - to learn more about vertebrates, look for some artificial structures which have spine-like support in them.