An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

Part is not a univocal term. Uses of parthood and composition that do not obey any supplementation principle have a long philosophical tradition and strong support from contemporary physics. We call such uses potential parts. This paper first shows why potential parts are important and incompatible with supplementation, then provides a formal mereology for such parts inspired by the path-integral approach to quantum electrodynamics.