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

Region R Question: How many objects — entities, things — are contained in R? Ignore the empty space. Our question might better be put, 'How many material objects does R contain?' Let's stipulate that A, B and C are metaphysical atoms: absolutely simple entities with no parts whatsoever besides themselves. So you don't have to worry about counting a particle's top half and bottom half as different objects. Perhaps they are 'point-particles', with no length, width or breadth. Perhaps they are (...) extended in space without possessing spatial parts (if that is possible). Never mind. We stipulate that A, B and C are perfectly simple. We also stipulate that they are connected as follows. A and B are stuck together in such a way that when a force is applied to one of them, they move together 'as a unit'. Moreover, the two of them together exhibit behavior that neither would exhibit on its own — Perhaps they emit a certain sound, or glow in the dark — whereas C is.. (shrink)

Very close analysis of Baruch Spinoza's wording in describing individuals rather than things. Individuals, but not collections such as a political state or club, each have their own specific conatus, or essence. Collectivities, like nations or institutions, fail to meet this necessary condition of individuation.