Compositional objects are wholes instantiated by collections of parts. If an ontology wishes to permit the inclusion of compositional objects it must define which collections of objects are to be considered parts composing a whole. Mereology, the study of relationships between parts and their wholes, provides specifications on how parts must relate to one another in order to compose a whole.
Mereology of material objects
Ontological disputes do not revolve around what particular matter is present; rather, the center of disputation is what objects can be said to be instantiated by a given collection of matter. The token objects posited by a given ontology may be classified as instances of one or more distinct object types. As the types of objects accepted proliferate, so do the possible tokens that a given collection of matter can be said to instantiate. This creates variations in size between ontologies, which serve as an arena for disputes among philosophers. The ontologies of present concern are those that include compositional objects among posited types. Compositional objects are objects made of a collection of one or more parts . These objects seem to be included in any intuitively constructed ontology as objects ordinarily encountered are doubtless composed of parts. For example, any ontology that affirms the existence of tables, rabbits, or rocks necessarily commits to the inclusion of some compositional objects. The specification of ‘some’ compositional objects foretells the point of attack suffered by these theories. Clarification demands that these theories provide a means to account for which compositional objects are included and which are excluded. One may include tables and, presumably, chairs, but what about the composition of the table and surrounding chairs? What characteristics of a collection of parts determine that they form a whole?
Mereological Nihilism
Mereological nihilism is an extreme eliminative position. Mereological nihilism denies that any objects actually instantiate the parthood relation appealed to in theoretical descriptions of mereology. If there are no relationships that count as parthood relationships, then there are no composite objects. One may initially seek to reject such a position by pointing to its counterintuitive conclusions. However, there are other mereological positions that prove equally counterintuitive and so a more substantial rebuttal is required. A principled rejection of mereological nihilism is put forward those committed to atomless gunk. A mereology is gunky if every part is itself a whole composed of further parts. There is no end to the decomposition of objects, no fundamental part or mereological atom. There is no place for the atoms posited by mereological nihilism in gunky ontologies. This causes a problem because if all that exists are atoms, but there is nothing like an atom that exists within an ontology, then nothing can be said to exist (Van Cleve, 2008). Noting the appeal of accepting that things do exist, one must reject mereological nihilism in order to maintain a gunky ontology. Not everyone will strive to maintain a gunky ontology and so mereological nihilism is still potentially a viable position.