>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.