  Albert the Great, with his more Aristotelian metaphysics, had argued that a demonstration of the highest sort would have the definition of the attribute as its middle term. This sort of definition is sometimes called a causal definition, and is the rough equivalent of a real definition for an attribute. In actuality, an attribute is an accident, and so has no proper real definition, indicating what it is entirely in itself, since what it is involves its belonging to an appropriate subject, and it actually belongs to such a subject only under favorable conditions. So a “real” definition for the attribute would have to express things extrinsic to the attribute, its subject and that which brings it to actuality in the subject. For this reason, Ockham insists that the definition of an attribute is a nominal definition, not a real one, and Aquinas holds that the conclusion of a demonstration of the highest sort will be per se both in the second way (presupposing the subject) and the fourth (indicating efficient causation) (Aquinas, Commentary on P.A. I 10). Albert's preference for the definition of the attribute follows Averroes's opinion that the highest sort of demonstration should demonstrate not a mere potentiality, but an actual state of affairs. Aquinas and the others who held to his view recognized that a demonstrable attribute in a natural thing would have to be a potentiality, though, of course, an actuality could be demonstrated in a mathematical demonstration, where efficient causation is not at issue, and an occurrent attribute can be shown to inhere in the subject necessarily and at every time.