> I think this implies a meaning of "the" that doesn't actually exist in modern english.

> "The" often refers to a group or category.

But this does not hold for the meaning of Latin "alter, altera, alterum" (the other one), from which the German and English word "Alternative"/"alternative" is derived.

Our language started out as a bad habit shared between French soldiers and English barmaids. And the barmaids were speaking a language that started as a bad habit shared between Viking raiders and Anglo-Saxon villagers.

Meanings have shifted since Roman times.