 Numerical difference does not map precisely onto essential difference. The failure of numerical sameness may be due to one of two causes. First, objects are not numerically the same when one has a part that the other does not have, in which case the objects are essentially different as well. Second, objects are numerically different when neither has a part belonging to the other. Numerical difference thus entails the failure of numerical sameness, but not conversely: a part is not numerically the same as its whole, but it is not numerically different from its whole. Thus one thing is essentially different from another when either they have only a part in common, in which case they are not numerically the same; or they have no parts in common, in which case they are numerically different as well as not numerically the same. Since things may be neither numerically the same nor numerically different, the question “How many things are there?” is ill-formed as it stands and must be made more precise, a fact Abelard exploits in his discussion of the Trinity.