The Seduction of Elegance: Shared Mathematics and the Parts of the World

ML and AI systems are often large and hard to interpret, yet useful. It is easy — perhaps even seductive — to confuse structure for the parts, especially when structure is found through an opaque training process. A black hole, defined by its boundary, invites a similar seduction. Its entropy is proportional to that surface's area, an exact relation without an inventory of what fell in. Physics cuts space into subsystems. Biology too names its parts. Many fields score what the parts contribute with one mathematics of mereology. Despite these futuristic topics, the study of parts and wholes is as old as philosophy itself. Plato's Statesman considers the name "barbarian," and from it the expectation of one kind. But sharing scores is not equivalent to finding the same parts. Even independent methods can produce an epistemically empty agreement when the representation used to compare them erases the differences at issue. The mathematics agrees because each field handed it an order. A structure or mathematics can be useful, or match a division the system has, or be the inventory. One does not automatically describe another. Wimsatt counted it false or misleading to take the entities a powerful decomposition yields as all that matters. Indeed, usefulness does not hand us correspondence. Correspondence does not hand us the inventory. Agreeing on a quantity of the whole is agreeing about the whole. This paper argues against seduction in mereology, which has legitimate promise in many fields. One must not mistake local success for an ontological one.