"Mereology" (from Greek meros, "part") is the theory (often formalized) of part, whole, and cognate concepts. The notion of part is almost ubiquitous in domain of application, and for this reason Edmund Husserl assigned its investigation to formal ontology. Aristotle observed that the term part was used in various ways, as for a subquantity, a physical part (leg of an animal), a part in definition (animal is part of man), a part in extension (man is part of animal). Part concepts had obvious applications in geometry and were among Euclid's undefined terms. Several senses of "part" are expressible using the preposition "in," but not all uses of "in" express parthood.

Until the twentieth century it was generally assumed that the concept of part was sufficiently clear not to require elucidation, but gradually the need for a formal treatment became apparent. Euclid's maxim that the whole is greater than...