The study of part-whole relationships. Formal theory of the relationship between part and whole, a branch of ontology, mereology is the philosophical theorizing of ontological relationships. Mereology and ontology inform each other. Presumably there are applications in cognitive psychology, computer science, physics, and any other discourse concerned with defining a universe of existence.
Questions that might prompt mereological inquiry:
- What is the relationship between a part of X and X as a unity?
- Is a whole a composition of its parts, or is there more to a whole than the sum of its parts?
- Is the composition of X an essential feature of X?
- In the study of X, what can we consider to be the atomic building blocks of the structure that X comprises? For example, what is the atomic unit of the human body? And, how are these atomic units related to the human body as a structure or system?
- Do atomic units characterize (or are they characterized by) the system?
Some notable figures include Alfred Tarski and Nelson Goodman, more recent contributors include David Lewis and Peter Simons.
(Personally, I think that mereology is a high-point of philosophical abstractness and obtuseness, and that a formalization of the relationship of abstract parts to abstract wholes is going to offer little in the way of practical benefit. This is, of course, one standard objection to a formalization of anything, and mereology is not without its detractors.)