Remark 1: Under this approach, the whole universe of discourse (for mass nouns and their predicates) is specified by a single Boolean algebra, with uniformly defined join (sum), meet (intersection), and order (parthood). Predication is defined in terms of Boolean intersection (or equivalently, order or parthood in the case of definite subjects). This works with mass nouns and predicates that are homogeneous (i.e., refer distributively and cumulatively). But mass nouns like furniture are clearly not homogeneous. And a predicate like made by John isn’t homogeneous either. When something is made by John (e.g., a piece of furniture), it doesn’t imply that any part of it (e.g., some wood used to make it up) is also made by John. For the reasons given in section 2, the Boolean approach may ascribe incorrect truth-conditions to sentences like This is furniture, Some furniture is made by John, and The furniture is made by John. For instance, [this] ≤ [furniture] does not guarantee that what is demonstrated is furniture, since a piece of wood may be a part of a piece of furniture without being furniture. So there are mass nouns and predicates to which the approach doesn’t seem to apply, even though the same difficulties with negation appear with them. If in the examples above we replace gold by furniture and in the safe by made by John, we meet the same problems with negation. (If there are two pieces of furniture, only one of which is made by John, is it true or false that The furniture is made by John?) So an appropriate solution had better not be tied to the assumption of  homogeneity.[14]