Lewis's Plurality of Worlds and the Immanence of Properties in Southeast Asian Buddhist Metaphysics — Epoche C1
The two doctrines being compared David Lewis holds that the property of being a donkey simply is the set containing every donkey there is or could have been, scattered across the whole plurality of possible worlds; the Pali Abhidhamma holds that each of the ultimate constituents of experience possesses a sabhāva , an own-nature that makes it the kind of thing it is and distinguishes it from every other. The two claims look designed to repel one another. A set is not in its members, so a property that is a set cannot be in anything, and a doctrine of natures that are in their bearers appears to have nothing to gain from it. This essay argues that the appearance is misleading, but that the usual way of saying so is misleading too: the comparison that works is not with the sets, and the correction runs on both sides. The terms need fixing before anything is built on them. A possible world , for Lewis, is not an abstract representation but a concrete cosmos, spatiotemporally and causally isolated from ours, as real as ours and differing only in what goes on inside it — the position he calls modal realism and defends at length in On the Plurality of Worlds (1986). Possibilia are the inhabitants of all these worlds taken together. An immanent property, in the sense at issue since Aristotle, is one that exists only in its instances and is wholly present in each; a transcendent one, in the Platonic manner, exists independently of them. And a dhamma , in the Abhidhamma, is one of the irreducible momentary constituents into which the tradition analyses experience — not a substance underlying experience but an event or factor of which experience is composed. What follows from identifying a property with a set The first thing the comparison needs is an accurate statement of Lewis's account, because two claims commonly attached to it are not his. Lewis's identification is austere: a property is the set of its instances across all worlds, so property identity is set identity, and two properties are the same exactly when they have the same members. Three consequences follow directly, and they are not the ones usually advertised. The account is coarse-grained, not fine-grained. Any two properties instantiated by exactly the same possibilia are one property. Being triangular and being trilateral are had by the same possible things in every world, so on this account they are the same property. Worse, every necessarily uninstantiated property — being a round square, being a prime number greater than every prime — has the empty set as its extension, so all of them are the same property. This is the standard objection to intensional accounts, and it runs opposite to the claim, made in compressed presentations of Lewis, that identifying properties with sets of possibilia makes them "fine-grained enough to capture subtle distinctions". It does the reverse: moving from actual to possible instances makes the account finer than a class nominalism restricted to actual things, but still far coarser than our talk of properties requires. There is no trans-world identity, and none is needed. Lewis denies that any individual exists in more than one world; individuals are worldbound, and what we say about how a thing might have been is made true by its counterparts elsewhere, things resembling it sufficiently in the respects a context makes salient. So the assertion that a property "instantiated in one possible world is the same property as one instantiated in another" misstates the geometry twice over. Properties on Lewis's account are not located in worlds at all: a set whose members are spread across the plurality is not itself an inhabitant of any of them. There are far too many properties for any of them to be special. If every set of possibilia is a property, then properties are as numerous as the subsets of a proper-class-sized totality, and the overwhelming majority are gerrymandered collections with nothing in common. Lewis calls these the abundant properties and accepts them without embarrassment, precisely because they are cheap. Cheapness is the point at which the received reading and the essay's thesis both go wrong. An abundant property does no metaphysical work: it cannot ground similarity, because most sets group together things that are not similar; it cannot ground causal powers, because the set is not in the thing. If the Abhidhamma's sabhāva were to be modelled on anything of Lewis's, it could not be modelled on these. The elite minority: Lewis's natural properties Lewis himself saw this, and the resource the comparison actually needs is the one he introduced to solve it. In "New Work for a Theory of Universals" (1983) he argues that a nominalism which recognises only abundant properties cannot do several jobs at once, and that a distinguished minority of natural , or sparse, properties must be admitted. The jobs are specific. First, duplication: to say that two things are exact duplicates is to say they share all their perfectly natural properties, and without a distinguished class the notion collapses, since any two things share indefinitely many abundant properties and differ in indefinitely many others. Second, intrinsicness: an intrinsic property is one a thing has in virtue of how it is in itself, and this can be defined in terms of duplication. Third, lawhood: a regularity counts as a law only if it can be stated using natural predicates, otherwise every gerrymandered summary of the facts would qualify. Fourth, content: what makes an interpretation of a language or a mind the right one is partly that it assigns natural properties to its predicates. The sparse properties are thus the ones that carve reality at its joints, in Plato's image, which Lewis borrows without endorsing Plato's ontology. Lewis is deliberately permissive about their underlying nature: naturalness may be taken as primitive, or explained by Armstrong's immanent universals, or by tropes. What matters for present purposes is