On What Grounds What

TL;DR: In this article, the authors show that a manifold is a manifold of events with certain fields defined on the manifold, and that the manifold is an independently existing structure that bears properties.

Abstract: ion: The grounding relations are relations of abstraction. The derivative entities, in order to be an ‘‘ontological free lunch’’ and count as no further addition, ought to be already latent within the substances. In other words, the grounding relations should just be ways of separating out aspects that are implicitly present from the start.37 Here is the sort of picture of substances that these diagnostics converge upon: Priority Monism: There is exactly one substance, the whole concrete cosmos. Insofar as there can be no difference in the world without a difference somewhere in the cosmos, priority monism delivers a complete roster of substances.38 This roster is trivially minimal, since the only proper subset of {the cosmos} is Ø, which obviously is not complete. Moreover, this roster is clearly metaphysically general—the ways the cosmos could be just are the ways the world could be.39 And this roster is empirically specifiable since advanced physics is field theoretic physics, and field theory has a natural monistic interpretation in terms of a spacetime bearing properties.40 These diagnostics also converge on: Thick Particularism: Substances are thick particulars (concrete things). 37 Scaltsas imputes a similar view to Aristotle: ‘‘for Aristotle a substance is complex, not because it is a conglomeration of distinct abstract components like matter, form, or properties; a substance is complex because such items can be separated out by abstraction, which is a kind of division of the unified substance’’ (1994: 109) 38 To see the bite of completeness, note that a pluralistic roster comprising point particles in spatiotemporal relations would fail completeness if the whole had emergent features, as are arguably present in entangled quantum systems (Schaffer forthcoming–a: §2.2). 39 In contrast, a pluralistic roster of mereological simples fails generality, since the world could be gunky. That would be a way the world that could be that is not a way that any roster of simples could be (Schaffer forthcoming–a: §2.4). 40 For instance, general relativistic models are triples, where M is a four-dimensional continuously differentiable point manifold, g is a metric-field tensor, and t is a stress-energy tensor (with both g and t defined at every point of M). The obvious ontology here is that of a spacetime manifold bearing fields. Thus Norton notes: ‘‘a spacetime is a manifold of events with certain fields defined on the manifold. The literal reading is that this manifold is an independently existing structure that bears properties’’ (2004). Quantum field theory invites a similar monistic reading. As d’Espagnat explains: ‘‘Within [quantum field theory] particles are admittedly given the status of mere properties, ... But they are properties of something. This something is nothing other than space or space-time, ...’’ (1983: 84) See Schaffer (manuscript) for some further defense of the spacetime-bearing-fields view of what is fundamental. on what grounds what 379 That is, substances have both a that-aspect—the thin particular, the substratum—and a what-aspect—the thickening features, the modes (c.f. Armstrong 1997: 123–6). Plugging in priority monism, the that-aspect of the cosmos is spacetime, and the what-aspect of it is its fields. So among the derivative categories are those of substratum and mode: Substratum and Mode as Derivative: substratum and mode are abstractions from thick particulars. Another derivative category will be the partialia, abstracted via: Universal Decomposition: The cosmos may be arbitrarily decomposed into parts. From priority monism plus universal decomposition, the entirety of the actual concrete mereological hierarchy of thick particulars is generated (whether or not the world is gunky). Wholes are complete and concrete unities, and partialia their incomplete aspects, arising from a process of ‘‘one-sided abstraction’’ (Bradley 1978: 124). With the partialia thus grounded, it remains to ground abstracta (such as numbers and possibilia) in the actual concrete realm. Here matters are too complicated to discuss further within the scope of this paper. But perhaps I have said enough to illustrate how at least one of the many possible neo-Aristotelian programs might look. To conclude: metaphysics as I understand it is about what grounds what. It is about the structure of the world. It is about what is fundamental, and what derives from it.41