Carving up the network of powers

Do powers have parts? Mereological thinking is typically guided by two different metaphors: building vs. carving. The building picture treats wholes as constructed from fundamental bits; the carving treats wholes as the result of carving some interconnected space. After considering some suggestions for how to view powers as built from other components, I'll opt for the carving picture, and suggest that a mereology of powers can be generated by carving and underlying space of an interconnected web of fundamental powers. The space of powers is a network of manifestation/triggering connections that can be modelled graph-theoretically along the lines of Bird (2007) and Tugby (2013). The identity of a fundamental power is importantly tied up with its position in the overall structure. I'll consider the idea that powers are completely identified by their position in the structure (as pandispositionalists have thought), which then places limits on the sorts of structures that powers theorists can help themselves too. I'll also consider another novel suggestion on the identity of powers borrowed from non-wellfounded set theory. I’ll show how to identify principles governing ‘carving’ the web into groups of closely connected powers, such that one group can naturally be called ‘part’ of another group, and explore the resulting mereology.