Monday, March 20, 2006

Is Modality Supervenient?

I'm wondering whether the modal facts supervene on the non-modal facts. Another way to put the question is to ask whether the intrinsic (non-modal) facts about our world determine its position in modal space. Or could there be a world that is non-modally identical to ours, but located elsewhere in modal space, so that various counterfactual claims would turn out differently?

That would seem odd. Supervenience makes more sense. The way the world is should determine how things would have been (insofar as those facts are determinate at all). If it's true that I would be struck by lightning were I to step outside, then this must be true in virtue of features of the actual world: the gathering clouds, the lingering molecules that would be displaced by my movement and set off a chain of events that would culminate in a lightning strike. Whatever. The modal facts are not independent of these facts. Counterfactuals do not get to float free of the actual world.

We can see this even within a standard "possible worlds" framework, for there (if I understand it correctly) our position in modal space is determined by various "similarity" or "resemblance" relations. The closest possible worlds are those that are most like our world. Hence the cause of the counterfactual lightning strike must have its basis in features that also exist in our world. (If the lightning just appeared ex nihilo, or from an entirely novel basis, the world would be too different from our own to qualify as the truthmaker for my counterfactual claim. The worlds where I step outside without being struck by lightning would be "closer" to actuality, so the counterfactual would be false -- as is almost certainly the case in fact.)

On the other hand, I think my concept of objective chance is an irreducible primitive (or, at least, it isn't reducible to 'frequency' facts). Compare two worlds where God flips a coin three times and it comes up 'heads' on each. These worlds might differ in their modal properties - perhaps in the first world it is a fair coin, and had a 50% objective chance to land heads each time, whereas in the second world the coin is biased towards heads. We can't tell this just from frequency data. But we can deny frequentism without giving up supervenience, because presumably there are other physical facts about the world which determine the objective chances here. (Perhaps the second coin is asymmetric and imbalanced, and this fact about its physical constitution explains why it is a biased coin.)

Could we bypass such considerations by looking at more fundamental entities? Let's say God creates a very simple universe containing a radioactive atom which decays after five seconds. Could there be another universe identical to that one in all intrinsic respects, except that the atom has a different chance of decaying at any given moment? (It still decays after five seconds. It's just that this event was more or less "unlikely" than in the first case.) It isn't clear to me how one could have such "objective chances" floating free of the actual nature and constitution of the object. There must be some actual difference underlying any modal difference; perhaps the two worlds have different laws of nature, or the atoms are constituted slightly differently, or whatever. But they couldn't be exactly the same in all actual respects and yet differ in their modal properties. I can't make any sense of that. So I guess I'm happy to hold that modal facts supervene on the non-modal facts. (That's good, it makes them less mysterious. Free-floating facts are just weird.)

This isn't to deny that modal deviancy is possible. Rather, we must simply recognize that it will be grounded upon quirky or 'deviant' features of the actual world. (Recall my discussion of the lightning strike, above.)

7 comments:

  1. Great post, Richard! Very thought-provoking, by which I mean it makes my head hurt. :)

    I had an idea about this:

    Let's say God creates a very simple universe containing a radioactive atom which decays after five seconds. Could there be another universe identical to that one in all intrinsic respects, except that the atom has a different chance of decaying at any given moment? (It still decays after five seconds. It's just that this event was more or less "unlikely" than in the first case.) It isn't clear to me how one could have such "objective chances" floating free of the actual nature and constitution of the object.

    It seems to me that there's one easy way out of this: one could argue that probability is only a meaningful concept when applied to an ensemble of possible worlds, not when applied to a single possible world. For example, there could be two sets of possible worlds, A and B, all of which are initially identical. But after five seconds, the atom has decayed in (say) half of the A worlds, and only one-third of the B worlds. One could use this fact to calculate the probability of the atom "having been going to decay" in any world from either of those sets.

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  2. Thanks Adam. I'm not sure I understand your suggestion, though. How do we choose which background set of worlds to use? It seems that by arbitrary selection we could manipulate the so-called "objective probabilities" to come out any way we want them to. For example, let A be the set of worlds which contain flying pigs, plus the actual world. We now conclude that pigs should almost certainly fly, and it's an incredible fluke that our world turned out to lack flying pigs. This seems absurd, and completely unrelated to our intuitive notion of "objective chance". (Also, how are you going to get different results for two physically identical worlds? Couldn't they be associated with the same background sets?)

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  3. Oops, too late at night for me to read properly. Sorry about that. I see you suggest that we take sets of worlds with identical histories (or at least some identical moments). But then my final question still stands. My two physically identical worlds will be associated with the same sets here. So we can't get 'objective chances' that fail to supervene on those physical facts. (That is to say, you cannot have a difference in chances without there being some underlying physical differences.)

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  4. I think it's true that there must be some physical difference between two worlds for there to be a difference in probabilities. But (if we live in an indeterministic world, which seems to be the case), that difference need not be something that was detectable before the fact, or even something that existed before the fact.

    One could say that in half of the worlds from my set A, after five seconds a brute fact just "pops up" (not very technical language, I know), for no prior reason at all, and causes the atom to decay. In the other half of A-worlds, no such brute fact occurs, the atom doesn't decay, and that's just the way things are. It's strange, I know, but then quantum mechanics all by itself should make us suspect that something deeply counter-intuitive is going on.

    A possible fault with my original post that hadn't occurred to me before concerns just how similar two possible worlds have to be to be included in the same ensemble of probabilities. Do they necessarily have to be atom-for-atom identical, with indeterminism alone making the subsequent difference between them? Or is it enough to say that they're very similar, that they occupy nearby positions in the phase space of possible worlds? And if so, how "nearby" do they have to be? (Your flying pigs example prompted this line of thought.)

    I should note, however, that it's not necessarily controversial to claim that, given one ensemble of worlds, it was unlikely that flying pigs would evolve in our world; and given a different ensemble, it was very likely indeed. This would only seem strange if one held to the view that probability inheres in a single possible world; in my view, it would just inhere in an ensemble of worlds and that's all there is to it.

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  5. >And if so, how "nearby" do they have to be?

    You could say their relevance is determined by how similar they are (in degree rather than catagory). So a flying pig’s world is less relevant than one basically identical to our world except for a recent random decay of an atom.

    Just saying "all the worlds with identical histories to now" would be one approach (i.e. worlds where there has as yet been no divergence) or you could talk about degrees to which universes are included in the set (similar to the approach - you are a lot like me a chimp is a bit like me a cat is a little less like me)

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  6. I have wondered about this kind of claim myself and felt attracted to it, indeed, for the kinds of reasons you mention.

    However, note that the obtaining of supervenience relations is itself a modal state of affairs.

    Supervenience claims are plausibly equivalent to claims about what is necessary. So in claiming that modal facts supervene on actual facts, one has not thereby committed oneself to the possible existence of a complete account of the modal facts in terms of the non-modal facts. On the contrary, you have committed yourself to the existence of at least one modal fact -- the supervenience fact -- that is independent of such an explanation. ...I think. There must be at least one remaining modal fact, which is not itself grounded in actual facts -- i.e. the supervenience fact.

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