Structural properties, mereology, and modal magic

Why is it that whenever a structural property (e.g., hydroxide) is instantiated, its constituent properties (e.g., hydrogen) are instantiated as well, by proper parts of the original object? By developing a suggestion from Lewis (Australas J Philos 64(1):25–46, 1986), Hawley (Australas J Philos 88(1):117–133, 2010) rises to this explanatory challenge by taking structural properties to be mereologically composed by their constituents, and by taking composition to be analogous to identity (Lewisian weak CAI). However, setting up a plausible framework for composition and CAI claims about properties, I will argue that structural properties are not identical to their constituents, at least not in any sense robust enough to warrant an Hawley-style argument—and perhaps not identical to them in any sense whatsoever. More generally, core principles of extensional mereology are in danger when applied to structural properties, which may force an extensionalist to either reconsider the application altogether, or reconsider mereological monism, thus granting the mereology of structural properties a peculiarly non-extensional status. Finally, although this debate has been traditionally framed as a debate about universals, an appeal to structural tropes can reconcile, at least to some extent, the mereology of structural properties with Lewisian extensional mereology—(weak) CAI included.