David Lewis, answered from the texts and cited to the page.
Everything contingent that obtains in our world supervenes on the Humean mosaic — the distribution of point-sized perfectly natural properties and relations across the spatiotemporal manifold, together with the spatiotemporal relations themselves.1 Fix the mosaic, and you fix everything else: the laws of nature, the chances, the causal facts, the dispositions, the mental states, the moral facts.2
The mosaic does not "produce" the rest through some additional necessitation or biasing; the rest is just patterns in the mosaic, supervening as a photograph supervenes on its dots. I do not claim that Humean supervenience is necessarily true — it is meant as a contingent thesis about worlds like ours, with no claim about how things must go in any possible world.3
And I do not claim certainty that physics will vindicate it: "Really, what I uphold is not so much the truth of Humean supervenience as the tenability of it. If physics itself were to teach me that it is false, I wouldn't grieve." The interest of the program is to show that a metaphysics in this spare style can discharge its debts — that laws, causes, chances, minds, and values can be reconstructed in the vocabulary of arrangements of local qualities.
If quantum entanglement or some successor physics forces fundamental non-local relations into the inventory, we move to whatever better supervenience thesis emerges from better physics; the deflationary spirit survives the revision.45
Humean Supervenience is yet another speculative addition to the thesis that truth supervenes on being. It says that in a world like ours, the fundamental relations are exacdy the spatiotemporal rela¬ tions: distance relations, both spacelike and timelike, and perhaps also occupancy relations between point-sized things and spacetime points.Papers in Metaphysics and Epistemology, p. 236
In "Counterf ctual Dependence and Time Arrow" I offer an account of that sensitivity. Given causation, or rather causal dependence, we can proceed to causal analyses of various things; for instance seeing, in "Veridical Hallucination and Prosthetic V ion," or what else you can do if you can freely ra e your hand, in "Are We Free To Break the Laws?" Next, persistence through time.Philosophical Papers Vol II, p. xiii
Humean Supervenience is meant to be contingent: it says that among worlds like ours, no two differ without difference in the arrange¬ ment of qualities. But when is a world like ours? I used to say: when it's a world of the "inner sphere", free of fundamental properties or rela¬ tions that are alien to our world. Sally Haslanger (1994) has shown that this answer probably won't do.Papers in Metaphysics and Epistemology, pp. 237–238
I'll give the beginning of a solution to the problem that plagues Humean analyses, and I'll say why that beginning is not good enough. And then I'll come at last to the good news: thanks to a suggestion by Michael Thau, I think I know how to complete the solution. The resulting rescue of Humean chance won't give us all we might wish, but I think it gives us enough. So the key idea in this paper is Thau's.Papers in Metaphysics and Epistemology, p. 235
Some stick close to the original idea but seem too weak; others seem strong enough but out of touch with the original idea. A useful notion threatens to fade away into confusion. I offer this diagnosis of the trouble. There really is just one simple, easy, useful idea. However, it is unavailable to those who assume that all modality must come packaged in boxes and diamonds.On the Plurality of Worlds, pp. 22–23
The organizing program of my metaphysics from the early 1980s onward, and the framework within which the Best System Analysis of laws, the counterfactual analysis of causation, the Principal Principle on chance, and the functional analysis of mental content are all developed. The standing critics are the necessitation theorists of laws (Armstrong, Dretske, Tooley); the dispositionalists (Bird, Mumford, Ellis) who locate modal force in irreducible powers; and the entanglement-physics objectors (Maudlin most prominently) who argue that quantum mechanics already shows the mosaic must include fundamental non-local relations. Within the broadly sympathetic literature, Barry Loewer, John Hawthorne, and (with reservations) Jonathan Schaffer have worked out particular pieces of the program. The "tenability" framing is genuine: I uphold the program as a worked example of what a thoroughgoing Humeanism would look like, not as a thesis I think the next century of physics is obliged to vindicate.