AAP 2026 CONFERENCE

Many mereologists think Weak Supplementation is analytic (Simons, 1987; Effingham & Robson, 2007; Varzi, 2008), while its opponents generally rely on denying Extensionality. Weaker alternatives like Strong Company have been proposed, but its models seemed physically implausible without time travel (Simons, 1987; Cotnoir & Varzi, 2021). If charge and mass are intrinsic properties of fundamental particles, however (Lewis, 1991; Bird, 2007), then an Extensionality-preserving physical model of Strong Company exists.

The idea is that calculating mass and charge for isolated fundamental particles requires accounting for self-interactions via perturbative expansions, represented as Feynman diagrams of increasing order. If mass and charge are intrinsic, then these self-interactions must be parts of the particle propagator. Indeed the perturbative expansion generates a weak partial order with Reflexivity, Anti-Symmetry, and Transitivity. If the bare propagator is treated as a top, then the poset forms a join semi-lattice interpretable as parthood. As the sequence is infinite every perturbation order will occur, there are no disjoint parts, so the strongest possible decomposition axiom is Strong Company. Yet two Feynman diagrams which allow the same perturbations are topologically identical, so the model satisfies Extensionality. The intrinsic properties of fundamental particles demotivate the analyticity of Weak Supplementation.