Mereology (from the Greek meroV, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratic atomists and continuing throughout the writings of Plato (especially the Parmenides and the Thaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium), and Boethius (especially In Ciceronis Topica).

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Mereology has also occupied a prominent role in the writings of medieval ontologists and scholastic philosophers such as Garland the Computist, Peter Abelard, Thomas Aquinas, Raymond Lull, and Albert of Saxony, as well as in Jungius’s Logica Hamburgensis (1638), Leibniz’s Dissertatio de arte combinatoria (1666) and Monadology (1714), and Kant’s early writings (the Gedanken of 1747 and the Monadologia physica of 1756). As a formal theory of parthood relations, however, mereology made its way into modern philosophy mainly through the work of Franz Brentano and of his pupils, especially Husserl’s third Logical Investigation (1901). The latter may rightly be considered the first attempt at a rigorous formulation of the theory, though in a format that makes it difficult to disentagle the analysis of mereological concepts from that of other ontologically relevant notions (such as the relation of ontological dependence). It is not until Le´sniewski’s Foundations of a General Theory of Manifolds (1916, in Polish) that the pure theory of part-relations as we know it today was given an exact formulation. And because Le´sniewski’s work was largely inaccessible to non-speakers of Polish, it is only with the publication of Leonard and Goodman’s The Calculus of Individuals (1940) that this theory has become a chapter of central interest for modern ontologists and metaphysicians. In the following we shall focus mostly on contemporary formulations of mereology as they grew out of these recent theories—Le´sniewski’s and Leonard and Goodman’s. Indeed, although such theories came in different logical guises, they are sufficiently similar to be recognized as a common basis for most subsequent developments. To properly assess the relative strength and weaknesses, however, it will be convenient to proceed in steps. First we consider some core mereological notions and principles. Then we proceed to an examination of the stronger theories that can be erected on this basis.