> That's because the article doesn't think that can happen.

I don't see what else he could mean by "lattice" or "partial ordering", except an admission that this can and does happen. Help me understand.

> I fail to see how being a lattice allows there to be two elements where each is greater than the other. My criticism doesn't depend on partial vs. strict ordering

Isn't that exactly what a lattice allows? The absolute ordering of Lisp and Haskell is undefined, while both are greater than some (like Cobol), and probably less than others. Users of either might think theirs is greater, but each has features the other doesn't, which is what makes the ordering merely partial.