Mereology and the Möbius Inversion: Do Different Methods Find the Same Parts?

Accounting for what the parts contribute cannot, by itself, justify the decomposition it presupposes. The older theory of parts and wholes started from parts it was already given, a wheel and a car, and asked how they compose. The sciences set beside one another here were not handed their parts, and a second job then says what the chosen parts contribute. Abel Jansma showed that this second job, as genetics, information theory, and game theory have been doing it, is one piece of mathematics, Möbius inversion, and the inversion takes the parts as already chosen. Whether different procedures for selecting parts find the same parts, and what an agreement between them would establish, is the question. Three rings are his picture. Any two come apart, and the three do not. Usefulness for prediction, correspondence to something in the world, and constitution can be separated where the rings cannot. To decline the last of these is not to call the parts unreal. What an agreement can return is evidence for a correspondence it does not establish, a conclusion about the methods, and a conclusion about the assumptions that made the agreement possible.