Distributivity and Cumulativity

Abstract

The following four chapters take up the features of quantities of matter that distinguish them from individuals by their mereological structure. This structure is reflected in the character of certain predicates expressing the property of being a particular kind of substance, say water, and exhibiting one or more phases, such as being liquid and being gas. Such predicates seem to ascribe an amorphous character to their subjects, which authors have tried to more precisely capture in terms of a distributive and a cumulative condition, formulated in terms of the mereological part relation and sum operation, respectively. These conditions are presented in this chapter and generalised to apply to relational predicates. This generalisation is obviously needed for relational predicates like “is the same substance as” and “is warmer than”. But substance and phase predicates, by contrast with the monadic predicates “is a time” and “is a spatial region”, are also taken to be relational, standing between a quantity and a time. The relational interpretation follows the chemist’s understanding of the permanence of matter throughout chemical change, which has been standard at least since the time of Lavoisier. Aristotle and the Stoics can be reasonably interpreted, it seems, to have thought that the distributive condition holds of substance and phase predicates, as discussed in Chap. 5. Whether the conditions can be upheld from a modern perspective is discussed in Chap. 7.