A true polyhierarchy really needs its individual hierarchies to be independent or orthogonal. Types in one should be independent of types in the other. That there is in one hierarchy the type ‘Volt’ should have no implications whatsoever on the color hierarchy. In conception, at least, these hierarchies are going to synthesize. That is to say, there will be Ford Explorers, Ford Focuses etc. from one hierarchy, and red, green, blue from the other; and then, implicitly (and explicitly, if there is literary warrant) all combinations are acceptable eg red Explorers, green Explorers etc. If the hierarchies are not orthogonal, this will be violated. For example, if an envisaged car hierarchy had, of itself, the category ‘red Explorer’, that category could not be combined with the color green-the notion of a green red Explorer is a nonsense. This is because the hierarchies are not orthogonal, The orthogonality requirement points to something else. Each of the component hierarchies has differentiae, the differentiation predicates that do the divisions down the levels. The types of one hierarchy must not be used as the differentiae in another (because that removes full synthesized combinations below).