Friday, February 8, 2008

Magic and Humean theories of causation

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.


Mike Almeida said...

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.

Alex, I'm pretty sure you have not shown you have a magical power. At best, I think, what you have is a possible magical power. Your chanting I here, in our world, will have no such effects, nor will it have such effects in any nearby worlds. So the counterfactual is false here. But there is a world w (perhaps) in which you (i.e. your counterpart) makes such a chant and the counterfactual is true. But what is magic here, in our world, is not magic everywhere. It is not magic in w, for instance, where the laws are apparently very different.

larryniven said...

I haven't done much reading in this area, but I wonder if you can explicate a bit further what you mean by "A causes B if and only if A type events always cause B type events." The word "always" here is my concern: if it deals with hypotheticals (i.e., "A causes B iff at any given time an A type event were to happen, it would cause a B type event"), then I don't think this works at all, for relatively obvious reasons (e.g., someone could utter your incantation after the aliens were extinct). However, if it doesn't deal in hypotheticals (i.e., "A causes B iff every time an A type event actually happens, it causes a B type event"), I bet you could've come up with a much simpler situation (which, granted, would have been less entertaining). There may, of course, also be some alternative interpretations I'm not seeing.

David said...

Would the case you imagine support counterfactuals? In nearby worlds to w, you chant a slightly different incantation, but everything else in w remains the same. But the political events in Andromeda don't change, even though your incantation does.

David said...

If you answer this point by saying that the relevant possible worlds are those in which the different incantation you chant continues to encode correct information about Andromeda, then why should think these worlds are close enough to w to be relevant for counterfactuals?

Alex said...

I don't think I agree with your argument. You claim that, in the world where you utter the incantation, the incantation would have to be included into Humean law because, even though the law becomse more complicated, it would make the universe that much simpler to understand. I don't think this is true. It would certainly make Andromedan politics easier to understand, but then we would have to explain this magic power of yours. Let's divide this explanation into two possibilities; either your chant was just (i) an extremely unlikely coincidence, or (ii) you actually have a magic power.

If (i) is true, then there is no need to include your statement in the laws of the universe because it was, in fact, just a coincidence. Since it was just bizarre luck that led you to be correct, your chanting will not always be correct, so you chanting (Event A) will not always contain information about any event B, so your chanting doesn't actually cause anything.

If (ii) is true, you suddenly have to explain the workings of your magic power, which could easily complicate the universe far more than the universe would be uncomplicated by knowing the history of Andromedans. One way of arguing this is to say that your demonstrating an unrepeatable example of magic shows the universal existence of magic, whereas the history of Andromedans is just some small amount of information and not as essential as the inner workings of the universe.

P.S. Nice name.

Alexander R Pruss said...


"It would certainly make Andromedan politics easier to understand, but then we would have to explain this magic power of yours."

However, the Humean / Lewisian approach is not about explanation. It is, rather, about an optimal balance of informativeness and brevity. By adding a law relating the incantation and Andromedan politics, we can describe both my incanting behavior and Andremedan politicking behavior in somewhat more than the length it would take to describe the incantation (the "somewhat more" is the need to describe how the correlation works; but if the amount of politicking is large, then this "somewhat more" is proportionately small).


Let w* be a world just like ours except that I chant this particular incantation--in particular it has the same politics in Andromeda as our world. Then, in w*, there is a law relating my incantation and Andromedan politics. There is, thus, magic in w* (in the paradigmatic sense of incantations affecting things far away with no intermediate causes). Moreover, w* is the world that would be actual were I to chant this incantation. So, if the incantation is within my powers, so is the magic.


The Humeans do want "always" to mean "actually always". However, one doesn't want the correlation to hold trivially because neither event occurs--indeed, to be charitable, we should suppose that the correlated events happen not rarely (this is clearer on Lewis's view).

MG said...


Just to drop a friendly note, there are some comment responses to your comments about the fillioque up.