 Generally speaking, such further principles may be divided into two main groups. On the one hand, one may extend M by means of decomposition principles that take us from a whole to its parts. For example, one may consider the idea that whenever something has a proper part, it has more than one—i.e., that there is always some mereological difference (a “remainder”) between a whole and its proper parts. This need not be true in every model for M: a world with only two items, only one of which is part of the other, would be a counterexample, though not one that could be illustrated with the sort of geometric diagram used in Figure 1. On the other hand, one may extend M by means of composition principles that go in the opposite direction—from the parts to the whole. For example, one may consider the idea that whenever there are some things, there exists a whole that consists exactly of those things—i.e., that there is always a mereological sum (or “fusion”) of two or more parts. Again, this need not be true in a model for M, and it is a matter of much controversy whether the idea should hold unrestrictedly. 