mereology

Mereology is the branch of philosophy and ontology that studies part–whole relations and the ways in which objects are composed from parts. In most frameworks the parthood relation is primitive: if x is a part of y, one writes P(x, y). A part that is not identical to the whole is called a proper part.

Key notions include overlap, where x overlaps y if there exists some z that is a part of both x and y; disjointness, where no part is shared; and fusion (often called the mereological sum), the object whose parts are exactly the union of the parts of the given collection. A fundamental principle in many theories is the extensionality axiom: if two objects have precisely the same parts, then they are identical.

Mereology also distinguishes between sums and composition. Some theories accept unrestricted composition, which says that for any collection of parts there exists a fusion having those parts; others reject this in favor of restricted composition. The debate touches on the existence of atomic parts (atomicism) versus “gunk,” where every part has further parts and there are no atoms.

Historically, mereology traces to early intuitions about part–whole relations and was formalized in modern times by figures such as Leśniewski, with influential discussions in contemporary analytic metaphysics by scholars like Peter van Inwagen. Related issues include the logic of parthood, the relationship between mereology and set theory, and applications to the ontology of material objects, mind–body philosophy, and formal ontology in AI and knowledge representation.

Overall, mereology provides a framework for analyzing how complex things are built from simpler parts and how those parts interact to form wholes.