  This knowledge of causal laws is knowledge of what a given agent is suited to do, but it is knowledge of what it will actually do only for the most part. This is not knowledge of what it will do most of the time, or even frequently, but of what it will do of itself as long as nothing is present to prevent it from doing it. It occurs through knowledge of “material definitions” which depend on prior, “formal definitions.” The formal definition of a thing specifies its function, and involves a final cause, while its material definition specifies how it must be constructed so as to perform that function, that is, to be an efficient cause of certain effects. The formal definition tells us what the exemplary form is, while the material definition specifies how that form and its causal activity are actually realized in matter. (The distinction between formal and material definition relies on an interpolation from Alexander/Philoponus's commentary in the text of James's translation of Posterior Analytics II 19. From Aquinas on people were aware of this error in the translation.) Knowledge of mathematical truth occurs without any efficient or final cause in the picture, and we can see triangles, for instance, as they really are in themselves with a direct mental view, rather than attempting to reconstruct them, as we do in the case of thunder, for instance, where we know that some physical arrangement is producing a noise (has that as its function, as it were), but cannot view that physical arrangement directly. Thus mathematical demonstrations are higher (potior) than natural demonstrations, since what they show is always the case, and they are more easily known. (Grosseteste (1981) I 18, lines 119-126.)