An extensionalist’s guide to non-extensional mereology

Formal mereology should be of interest to metaphysicians because it allows us, in a rigorous way, to determine the consequence relations between metaphysical theses and theories, many of which are of metaphysical interest. Take, for example, the many and various puzzles of constitution, and the metaphysical theories that have been advanced to solve them. Ideally, it should be possible to analyse these puzzles and their solutions in a formal way — to describe, for example, the puzzle of Dion and Theon, or of the statue and the clay, as a set of logically inconsistent propositions in a formal mereological language. By doing that we could more easily explore the space of possible solutions, since every solution would consist in denying one of those propositions. Ideally, it should be possible to state some (but not all) of the content of metaphysical theories concerning the part-whole relation formally, and that would enable us to better evaluate objections to those theories, since it would give us procedures for determining what is and what isn’t a consequence of such a theory. Formal mereology is a great tool, and it should be used.