Humean theories of causation make causal facts supervene on facts about correlations between events. The simplest theory was Hume's: A causes B if and only if A type events always cause B type events. Perhaps the best contemporary version is Lewis's: (1) the laws of nature are true propositions which optimize a balance of brevity and informativeness; (2) similarity of worlds is defined in large part by local sameness of law; (3) counterfactuals are defined in terms of similarity of worlds; and (4) causation is defined in terms of counterfactuals.
I claim that if Humean theories of causation are true, then I have a magical power—the power of causing events in another galaxy just by muttering incantations. Let's suppose that the Andromeda Galaxy contains a billions of intelligent aliens, whom I shall call Andromedans, who are going to have a long and exceedingly complex political future, but a finite future with a finite description of it being possible. The events I can magically cause are the political activities of the Andromedans. (If Andromeda has no intelligent life, I can modify the example.) I now claim that if Humean theories of causation are true, there is a long incantation that has the following two properties: (a) it is physically possible for me to chant it, and (b) if I chanted it, the chant would be the cause of every major political event among the Andromedans from now until the end of Andromedan history. If that's not enough to establish I have a magical power, I don't know what is.
Now my argument. There are infinitely many incantations that it is possible for an analog being like me to chant. Fine details of the tone, timbre, etc., of an incantation can be used to encode information. It is easy to come up with very simple ways of encoding information in a chanted incantation, and still keep the incantation within my physical powers. Let Q be a detailed and correct description of the political future of the Andromedans in a simple and straightforward language L. Then, Q is a very, very long but finite text. However long Q is, we can encode it with a simple encoding scheme into an incantation I that it is physically possible for me to chant. (I don't mean I know how to intentionally chant it; but it is possible for me to chant it, perhaps by accident.)
Let w be a world as much like ours as we can make it but where I chant I. What would w be like? Well, presumably, all the Andromedan events described in Q would still happen in w. However, in I, these events would be foreshadowed by being encoded in I. If there are enough of these events (that's why I assumed that the Andromedans will have a long and exceedingly complex political future; moreover, to ensure that there are enough events, I need only be sufficiently detailed in Q), then this correlation will be one that the Humean will have to take cognizance of and make be a part of the laws—making it be a part of the laws does increase the complexity of the laws, but the gain in informativeness is worth it. So, in w, there will be a Humean law about the correlation between aspects of I and aspects of the Andromedan political future. Moreover, on Humean views, this law will support counterfactuals (laws do, of course) and will (on Lewis's view we can insert "therefore" here) be such as to ensure causation between the aspects of I and the Andromedan political events therein described. Hence, in w, I cause the Andromedan events if Humeanism is correct.
Thus, it is physically possible for me to do something, viz., chant I, which is such that were I to do it, I would be causing all Andromedan political events.
And this is absurd. So Humean theories of causation are false.