Strange Parts: The Metaphysics of Non‐classical Mereologies

Abstract

The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, the paper considers an alternative approach that focuses the blame on antisymmetry but allows us to keep natural supplementation axioms. Third, we look at counterexamples to the idempotency of composition and the associated ‘parts just once’ principle. We explore options for developing weaker mereologies that avoid such commitments.

Are The Statue and The Clay Mutual Parts?

“…We'll return to the above supplementation principles in §5, but first I want to consider an argument for Mutual Parthood similar to the one above that is presented by Simons (: 228–229), and endorsed by Thomson () and Cotnoir ().…”

“…Assuming that Moderate Pluralism is true, we can ask what relations hold between coincident material objects such as the statue and the clay? Many moderate pluralists claim that the clay constitutes the statue. Some moderate pluralists, notably Cotnoir (, , ; see also Cotnoir and Bacon ), Hawthorne (), Hovda (), and Thomson (, 1988), have argued that the statue and the clay are mutual parts, endorsing

Mutual Parthood: If x and y are distinct coincident objects, then x is a part of y and y is a part of x.

…”

Part and Whole, Again1

“…Note that a compositional pluralist would treat the exploration of alternative formal systems (e.g. my own , Cotnoir ) as characterizing different composition relations, rather than as competing attempts to characterize the One True Composition Relation.) While composition CEM obeys unrestricted composition, what I've called composition ordinary does not; it takes more for the latter to obtain.…”

Structural universals

“…For formal discussion of non‐classical mereology that is relevant to the metaphysics of structural universals, see Cotnoir () and Mormann (). See also the Philosophy Compass article on non‐classical mereologies by A. J. Cotnoir (). For discussion of supervenience principles of structural universals within a context that allows for non‐classical mereologies, see Bader (, pp.…”