Lattices are also ordered (by intellectual descent) with respect to early explorations in philosophy, such as using transitivity on "Socrates is a man" and "All men are mortal".

Without lattices, we would never have had the ambiguous phrase "computer scientists commonly choose models which have bottoms, but prefer them topless" occurring in a serious textbook.

Edit: agreed, intellectual descent is only partially ordered, but the interval between aristotle's example syllogism and lattices contains a chain. Guess I should've said "also comparable (by."