Monists and pluralists disagree concerning how many ordinary objects there are in a single situation. For instance, pluralists argue that a statue and the clay it is made of have different properties, and thereby are different. The standard monist’s response is to hold that there is just a single object, and that, under the description “being a statue”, this object is, e.g., aesthetically valuable, and that, under the description “being a piece of clay”, it is not aesthetically valuable. However, Fine (...) provided an ontological reading of the expression “an object under a description”: the theory of rigid embodiments. The debate between monists and pluralists reduplicates in the domain of ordinary occurrences, like walks and conferences. Specifically, they disagree whether an occurrence in progress (also called “process”) like John’s walk that is happening at tn is identical to some completed occurrence (also called “event”) like John’s walk that happened between, e.g., t1 and tn. Under the adoption of the pluralist’s position, the article aims to provide a novel theory of ordinary occurrences that develops the ontological reading of “under a description” to account for occurrences in progress and completed occurrences. As a first result, we formulate a theory according to which both occurrences in progress and completed occurrences are rigid embodiments. As a second result, we argue that the suggested theory is explanatorily powerful to the extent it solves two puzzles that we call “the Puzzle from the Completion of a Process” and “the Metaphysical-cum-Semantical Puzzle”. (shrink)