 But this common cause certainly cannot be a common thing in the way Boethius described universal things, for, as we have seen, the assumption of the existence of such a common thing leads to contradictions. To be sure, Abelard also provides a number of further arguments, dealing with several refinements of Boethius’ characterization of universals proposed by his contemporaries, such as William of Champeaux, Bernard of Chartres, Clarembald of Arras, Jocelin of Soissons, and Walter of Mortagne – but I cannot go into those details  here.[28]  The point is that he refutes and rejects all these suggestions to save real universals either as common things, having their own real unity, or as collections of several things, having a merely collective unity. The gist of his arguments against the former view is that the universal thing on that view would have to have its own numerical unity, and therefore, since it constitutes the substance of all its singulars, all these singulars would have to be substantially one and the same thing which would have to have all their contrary properties at the same time, which is impossible. The main thrust of his arguments against the collection-theory is that collections are arbitrary integral wholes of the individuals that make them up, so they simply do not fill the bill of the Porphyrian characterizations of the essential predicables such as genera and  species.[29]