  This solves the problems encountered above by the purely mereological approach and the purely set-theoretic approach. Indeed, what precedes suggests that mass predication (to be M), like count predication or adjectival predication, is well rendered in terms of set membership. The purely set-theoretic approach has problems with definite descriptions because it just uses sets, avoiding sums. But as we saw earlier, mass nouns have the property of cumulative reference. If there is some clay in two cups, then one can refer to all of the clay as the clay in the two cups. This suggests that portions of clay can be summed, and that the set of portions of clay should have the structure of a join semi-lattice. When this is guaranteed for any mass noun M, the semantic value of definite descriptions can easily be specified. The description the M that Q denotes the sum of everything that is some M that Q. It is such a sum that is weighted in The gold on the table weighs fifty grams. And it is such a sum whose identity over time is asserted in The clay that was on the desk on July 1st is identical with the clay that was on the  table on July 2nd. (Another treatment of identity over time is presented in  section 9.) 