Classical mereology and restricted domains

Classical Mereology, the formal theory of the concepts of part, overlap and sum as defined by Lesniewski does not have any notion of being a whole. Because of this neutrality the concepts of Mereology are applicable in each and every domain. This point of view is not generally accepted. But a closer look at domain-specific approaches defining non-classical (quasi)-mereological notions reveals that the question of whether something belongs to a restricted domain (and, thus, fulfills a certain criterion of integrity) has come to be mixed up with the question of whether it exists. We claim that the structural differences between restricted domains are not based on different mereological concepts, but on different concepts of being a whole. Taking Classical Mereology for granted in looking at different domains can shed more light on the specific nature of these domains, their similarities and differences. Three examples of axiomatic accounts dealing with restricted domains (linear orders of extended entities as they can be found in discussions of the ontology of time, topological structure and set-theory) are discussed. We show that Classical Mereology is applicable to these domains as soon as they are seen as being embedded in a less restricted (or even the most comprehensive) domain. Each of the accounts may be axiomatically formulated by adding one non-mereological primitive to whatever concepts are chosen to develop Classical Mereology. These primitives are strongly related to the domain-specific notions of integrity or being a whole. (C) 1995 Academic Press Limited