mereology (from Greek meros, ‘part’), the mathematical theory of parts; specifically, Lesniewski’s formal theory of parts. Typically, a mereological theory employs notions such as the following: proper part, improper part, overlapping (having a part in common), disjoint (not overlapping), mereological product (the ‘intersection’ of overlapping objects), mereological sum (a collection of parts), mereological difference, the universal sum, mereological complement, and atom (that which has no proper parts). Formal mereologies are axiomatic systems. Lesniewski’s mereology and Goodman’s formal mereology (which he calls the Calculus of Individuals) are compatible with nominalism, i.e., no reference is made to sets, properties, or other abstract entities. Lesniewski hoped that his mereology, with its many parallels to set theory, would provide an alternative to set theory as a foundation for mathematics. Fundamental and controversial implications of Lesniewski’s and Goodman’s theories include their extensionality and collectivism. Extensional theories imply that for any individuals, x and y, x % y provided x and y have the same proper parts. One reason extensionality is controversial is that it rules out an object’s acquiring or losing a part, and therefore is inconsistent with commonsense beliefs such as that a car has a new tire or that a table has lost a sliver of wood. A second reason for controversy is that extensionality is incompatible with the belief that a statue and the piece of bronze of which it is made have the same parts and yet are diverse objects. Collectivism implies that any individuals, no matter how scattered, have a mereological sum or constitute an object. Moreover, according to collectivism, assembling or disassembling parts does not affect the existence of things, i.e., nothing is created or destroyed by assembly or disassembly, respectively. Thus, collectivism is incompatible with commonsense beliefs such as that when a watch is disassembled, it is destroyed, or that when certain parts are assembled, a watch is created. Because the aforementioned formal theories shun modality, they lack the resources to express the thesis that a whole has each of its parts necessarily. This thesis of mereological essentialism has recently been defended by Roderick Chisholm. See also ESSENTIALISM , EXTENSIONALISM , METAPHYSICS , SET THEOR. J.Ho. & G.Ro.