Friends of primitive powers and dispositions often contrast their view with an alternative view, usually attributed to Lewis, on which modal facts about powers, dispositions, laws, counterfactuals etc. are grounded in facts about other possible worlds. But Lewis never held that alternative view – nor did anyone else, as far as I know. The allegedly mainstream alternative is entirely made of straw. The real alternative that should be addressed is the reductionist view that powers and dispositions are reducible to ultimately non-modal elements of the actual world.
Unlike in the case of reference magnetism, the exegetical question is straightforward. Lewis nowhere suggests that natural modality is grounded in other possible worlds.
On the contrary, he declares it an a priori truth that "any contingent truth whatsoever is made true, somehow, by the pattern of instantiation of fundamental properties and relations by particular things" in the actual world ("Humean Supervenience Debugged", p.225). Lewis's hypothesis of Humean Supervenience is a stronger and more speculative version of this assumption, adding that the relevant fundamental properties are all properties of spacetime points and that the only fundamental relations are spatiotemporal relations.
Recall Lewis's most memorable definition of Humean Supervenience:
Humean supervenience is named in honor of the greater denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. (But it is no part of the thesis that these local matters are mental.) We have geometry: a system of external relations of spatiotemporal distance between points. Maybe points of spacetime itself, maybe point-sized bits of matter or aether or fields, maybe both. And at those points we have local qualities: perfectly natural intrinsic properties which need nothing bigger than a point at which to be 1instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else supervenes on that. (Introduction to Philosophical Papers II, pp.ix-x)
No mention here of other possible worlds.
So when it comes to natural modality – powers, dispositions, laws, chance, counterfactuals, and the like – Lewis's position is simply a form of reductionism: he accepts that there are truths of these kinds, but holds that they are ultimately made true by non-modal features of our world. Much of Lewis's work in metaphysics can be seen as filling in the details.
Why do people get this wrong? Where do the rumours come from that Lewis wanted to ground modal truths in truths about other worlds? I don't know. I can think of two explanations.
The first is a deep conviction that modal facts can't possibly be reduced to ordinary non-modal facts, combined with the knowledge that David Lewis (whose work one hasn't actually read) endorsed "modal realism", the view that other possible worlds are just as real and concrete as the actual world. This suggests that Lewis might have proposed the realm of other possible worlds to ground modal facts.
Barbara Vetter nicely expresses something like this in "'Can' without possible worlds" (2013, p.1):
The world (the actual world, which we inhabit), for Lewis and his followers, is modally empty: it contains 'a vast mosaic of local matters of particular fact, just one little thing and then another. ... we have an arrangement of qualities. And that is all.’ (Lewis 1986, ix f.) Modality, for Lewis and Lewisians, has to come from outside that mosaic if it is to be real: it has to be outsourced to other possible worlds.
That modality could be real but reducible – Lewis's actual view – doesn't seem to cross her mind.
A second possible explanation is that people misunderstand the role of possible worlds in Lewis's semantic analyses. In Counterfactuals (1973), for example, Lewis invokes possible worlds to express truth-conditions for counterfactuals: roughly, 'if A then B' is true at a world w iff B is true at all the closest A-worlds to w. One might think this biconditional ('...iff...') specifies the metaphysical grounds for the truth of counterfactuals: what makes it true that I would hurt my head if I were to bang it into the wall are certain basic relations between possible worlds.
This is clearly not how Lewis himself understood the analysis, as he explicitly says (in the introduction to Philosophical Pappers II) that the analysis supports Humean Supervenience. How is that supposed to work?
For a start, note that the "closeness" in Lewis's analysis is an internal relation insofar as the relative closeness between three worlds w1, w2, w3 is a matter of the intrinsic nature of these worlds (unlike closeness between cities). Second, recall that for Lewis what possible worlds there are is not a contingent matter: the space of worlds is fixed once and for all (Plurality, p.80). So whether the actual world is closer to some world w2 than to another world w3 depends only on the intrinsic properties of the actual world. Invoking the other worlds is just a convenient shortcut to isolate the relevant intrinsic properties. In "Ordering semantics and premise semantics" (1981), Lewis actually shows how one could equivalently do without the shortcut.
A comparison may help. Lewis analysed belief in terms of (centred) possible worlds: you believe a proposition just in case the proposition is true at all your doxastically accessible worlds (e.g. Plurality, pp.27-36). But he did not hold that in order to have a belief one must stand in a mysterious, substantive relation to other possible worlds; the possible-worlds analysis was not meant to provide the metaphysical grounds for beliefs. Instead, Lewis held that to have a given system of beliefs and desires is to be in a state with a characteristic causal role (e.g. Plurality, pp.36-40). The possible worlds are just a convenient way of picking out the relevant roles.
In any case, the idea that counterfactuals have uniform metaphysical grounds is absurd. Any truth p is logically equivalent to if p then actually p.
So these are the two explanations I can think of for the widespread assumption that Lewis held modal facts to be grounded in facts about possible worlds. Am I missing something?
Of course, there's another relevant consideration: the supposedly Lewisian idea is really unappealing. (There's a reason why practically nobody ever endorsed it!) Presenting it as the main rival to anti-Humean primitivism therefore makes primitivism look sensible and attractive.
But it's not the main rival. The real rivals are Humean reductionism and Humean projectivism. Forget about the possible worlds.