 With spatiotemporal objects like teapots, humans seem to rely on counting criteria that privilege maximal self-connected entities (Spelke 1990, Casati &amp; Varzi 1999). A self-connected teapot is one that cannot be split into two parts that are not connected. In contrast to parthood, which is a mereological concept, connectedness is a topological notion (see Casati and Varzi 1999 for discussion of various postulates for a “mereotopology”, a theory that combines mereology and topology). The maximality requirement prevents counting teapots that are proper parts of other teapots, and the self-connectedness requirement disqualifies sums of parts from different teapots. Casati and Varzi point out that not all kinds of entities, not even all kinds of spatiotemporal entities, come with counting criteria that involve topological self-connectedness. Obvious counterexamples include bikinis, three-piece suits, and broken glasses that are shattered all over the floor. We have to recognize a wider range of counting criteria, then, that guarantee compliance with (32) in one way or other.