The matching of parts of things

An axiomatic treatment of the relation part of is shown to lead naturally to an account of the ways in which parts of things are matched. The determination of matchings by the properties of parts and by the relations between parts is discussed and shown to be relevant to certain classificatory problems in science. The connexions between matchings and symmetries of parts are explored, and a general account is given of the ways in which ambiguities in the matching of parts may be resolved.