The Elusive Essence: Why Lewis's Mereological Nominalism Fails to Grasp Intrinsic Properties — Epoche C1
David Lewis identified the property of being red with the class of red things — not a universal shared by them, not a quality inhering in each, but the collection itself. This note asks whether that identification can support the distinction between a thing's intrinsic properties, which it has in virtue of how it is in itself, and its extrinsic ones, which it has in virtue of how it stands to other things. The conclusion defended here is that it cannot, and the thesis of the earlier version of this note is therefore upheld. But the route to it must be rebuilt, because the objection usually offered — and offered in that earlier version — is one Lewis had already answered, and the answer is decisive. The failure lies elsewhere, and finding it is more instructive than the objection it replaces. The view, stated as Lewis states it Three preliminaries fix the target. A universal , in the sense at issue since the mediaeval debates, is a single entity wholly present in each of the many things that share a quality: one redness, in every red thing at once. Nominalism is the denial that there are such entities. Class nominalism is the particular denial that says a property just is the class of things that have it, so that sharing a property is nothing more than joint membership. Lewis's version is set out in "New Work for a Theory of Universals" (1983) and in the first chapter of On the Plurality of Worlds (1986); the earlier version of this note attributed it to Parts of Classes (1991), which is not where the theory of properties appears. That book has a different job, and it is the job that earns the label in this note's title. In it Lewis shows that a class is the mereological fusion — the whole composed of parts, in the sense of the formal theory of parthood — of the singletons of its members. Classes, that is, are not a further kind of thing beyond wholes and parts, save for one addition: the singleton-forming function itself, which Lewis cannot reduce and takes as primitive. So Lewis's account of properties is mereological at the base, and it is fair to call it mereological nominalism provided one remembers that a primitive was required to get there. That the parsimony is purchased with a primitive is the pattern this essay will find repeated at the decisive point. One further clarification, because "parsimony" is doing rhetorical work in the earlier version that it cannot bear. Lewis does not eliminate abstract entities; he accepts classes, which are as abstract as anything in the debate. What he eliminates is a second category — universals — alongside the classes he was going to accept anyway. The saving is real but narrower than "grounding properties in concrete particulars" suggests. Why the coextension objection fails as usually stated The standard objection to class nominalism, pressed by D. M. Armstrong (1978), is that distinct properties can have exactly the same instances. His stock case is a world in which all and only the creatures with hearts are the creatures with kidneys; the classes are then one class, so the properties are one property, which is absurd. The earlier version of this note ran the same argument with Korean stone: if the class of objects carved from granite were identical to the class of objects weighing over $500\,\mathrm{kg}$, then Lewis must call those one property. The argument is valid and its conclusion is unacceptable. It nevertheless does not touch Lewis, and the reason is the doctrine the earlier version treated as an embarrassment. Lewis's classes are not classes of actual individuals. They are classes of possibilia : all the individuals there are at any possible world, where on his modal realism the other worlds are concrete entities of the same kind as this one, differing from it only in not being the one we are part of. A property, for Lewis, is a class drawn from that whole population. Once the domain is enlarged in this way, accidental coextension stops identifying properties. Suppose that here, as a matter of fact, every granite object weighs more than $500\,\mathrm{kg}$. There is nevertheless a world containing a granite pebble of $200\,\mathrm{g}$, and that pebble belongs to one class and not the other. The classes differ; the properties differ. The same reply disposes of the case of the stone Buddha and the celadon vase. Being carved from granite and being fired clay are different classes because their memberships diverge somewhere in modal space, whether or not they diverge here. Coextension in the actual world is simply the wrong test, and any objection built on it fails. Two further claims in the earlier version fall with it, and should be withdrawn plainly. The first is that on Lewis's view an uninstantiated property does not exist, so that "being a perfectly spherical golden mountain" is nothing. It is not nothing: there are golden mountains at other worlds, and the class of them is a perfectly good property that happens to have no actual members. The second is that this creates trouble for Lewis's modal realism. The relation runs the other way. Modal realism is what supplies the extra members that keep distinct properties distinct, which is precisely why Lewis, having accepted the plurality of worlds for independent reasons, could afford so austere a theory of properties. What the modal move does not fix That settles the easy case. Two residues survive, and they mark where the account genuinely strains. The first is necessary coextension. If two properties cannot possibly diverge, their classes of possibilia are the very same class, and Lewis must identify them. Being triangular and being trilateral are one property; every truth of mathematics expresses the same property as every other; the property of being a thing at all and the property of being self-identical coincide. Lewis accepted this consequence rather than avoiding it, and it is a genuine cost, because we plainly reason with these as different, taking one as a premise for the oth