Monday, April 10, 2006

Are Laws Internal to Worlds?

Our world is governed by various natural and physical laws, e.g. that nothing can move faster than the speed of light (FTL). Are such laws internal to this world, or are they instead extra-worldly modal facts, perhaps arising due to our position in modal space? (On the latter picture, the no-FTL law might simply consist in the fact that nothing in our spatio-temporal world actually does move FTL, and that the same holds for all "close" possible worlds. But this seems to reverse the order of explanation found in common sense, i.e. that there are no close FTL worlds precisely because of the no-FTL physical law.) Is this even a substantive difference?

It seems to me that there is a sense in which the physical laws fail to supervene on the physical world. I assume that the true physical theory is underdetermined by the totality of our world's actual spatiotemporal properties. Consider a possible alchemic law of nature (A) If a tonne of pure lead is moulded into a particular shape X, then it will transmutate into pure gold.

Given that the antecedent conditions are never satisfied in the actual world, it seems that both (A) and its negation are consistent with the actual physical phenomena. Presumably (A) is false, but it could be true of a world otherwise identical to our own, couldn't it? (It might require special exceptions to be made to other physical laws which would normally lead us to predict that lead atoms won't magically turn into gold. But I mean to allow for all that.) The only difference is not really about what happens in this world, but rather what would happen if we moulded a tonne of lead into shape X. That is, what happens in the nearest possible world where those antecedent conditions are satisfied.

To accommodate the two possibilities, we will need 'duplicates' of our world to fill the two positions in modal space. One will be near a world where X-shaped lead turns into gold, and the other will be near a world where X-shaped lead does nothing much of interest. The former duplicate is a world governed by natural law (A), and the latter is not.

The choice of whether to describe the law as internal to the world will mainly have significance for supervenience claims. I previously claimed that counterfactual truths supervene on the actual physical facts. But this is only true if we include the physical laws within our supervenience basis, as the example of X-shaped lead makes clear. (Whether it's true that "if I were to mould a tonne of lead into shape X, then it would turn to gold" is not fixed solely by the actual spatiotemporal facts. It depends which of the physical duplicates our world is, i.e. where it's situated in modal space, or - equivalently - whether the world is governed by law A.)

If we want to include the laws in our supervenience basis, then we should hold that the laws are internal to worlds. This also allows us to avoid the puzzling situation of admitting multiple identical worlds into our modal space. Instead, we can say that the worlds - though having identical spatiotemporal properties - have distinct laws, and so truly differ from each other in at least this respect.



  1. Given that the antecedent conditions are never satisfied in the actual world, it seems that both (A) and its negation are consistent with the actual physical phenomena. Presumably (A) is false, but it could be true of a world otherwise identical to our own, couldn't it?

    In order to be certain that this is true, don't you have to hold that members of natural kinds don't have any of their dispositional properties essentially?

    If members of natural kinds (say, lead) have dispositional properties (say, chemical stability) essentially, then it may very well turn out that (for example) any possible world where you have X-shaped lead is a possible world where that lead will not transmute into gold. There might be possible worlds where leaden stuff does that, but that would be a possible world with an alien substance, unknown in our world, not a possible world with lead.

    It's open to you to claim that members of natural kinds only have dispositional properties contingently. But that will require some argument; it's certainly not obvious to me, at least, that certain chemical dispositions aren't part of the essence of (say) salt or gold or lead, or that certain biological dispositions aren't part of the essence of (say) slugs or tigers or bats.

    Alternatively, it's open to you to claim that falling under a natural kind can entail having certain dispositional properties, but deny that natural kind membership supervenes on the "totality of our world's actual spatiotemporal properties," i.e. you could have possible worlds with perfectly identical "actual spatiotemporal properties," but have one of them containing lead and the other containing an alien substance that's like lead except it transmutes under the right (as-yet unfulfilled) conditions. But you'd have to give me some pretty burly argument to convince me that natural kind terms aren't part of the basic description of the properties of the world as we know it. I don't know how you'd even begin constructing a complete description of a world without ever using a natural kind term. ("Well, you see, these two worlds are exactly identical in their physical properties. But in W1 there is water and in W2 there is not." Well, then, they're not exactly identical in their physical properties.)

  2. I'm inclined to think that so-called "essences" are merely a matter of description. A semantically neutral description of a world would invoke only qualitative terms, not rigid designators (like many natural kind terms seem to be).

    In any case, I think it's enough for my purposes to note that there could be a world just like ours in all its intrinsic and non-dispositional qualities, but for the corresponding substances in question to have different dispositional qualities. That would show that the dispositional properties fail to supervene on the non-dispositional. (Note that if we accept your account of natural kind terms, then they cannot feature in a purely non-dispositional account of the world.)

  3. Richard,

    If I accept your claims of non-supervenience, it's unclear to me that this demonstrates anything remarkable about natural laws. It would demonstrate nothing, in particular, about whether natural laws apply necessarily or only contingently to the stuff our world is in fact made of (lead, gold, atoms, quarks, matter, whatever). At the strongest it would demonstrate that there are possible worlds made of alien stuff that behaves according to correspondingly alien laws. But it tells us nothing about the modal status of "Lead does not transmute into gold just by being put into such-and-such a shape." Since pretty much all of our natural laws are already expressed using natural kind terms, it'd be hard for world-descriptions that systematically exclude them to tell us anything about the natural laws.

    Second, why should we accept that a "purely non-dispositional account of the world" is even possible? What sort of purely non-dispositional properties do you have in mind? As an exercise, just try describing what qualities water and XYZ have in common with each other, without mentioning any dispositional properties at all. (Transparency, tastelessness, odorlessness, wetness, etc. are all qualities typically mentioned here, but none of them will do for your purposes: they all involve dispositions. Water, for example, is odorless whether you're actually sniffing it or not, and XYZ would still be transparent even when it's dark.)

  4. We can work will all the properties that are realized throughout the entireity of *actual* history. That gives us plenty to work with. Every sensation that water actually causes, every chemical reaction it actually undergoes, etc.

    I'd add that mostly everyone accepts that the laws of nature are contingent, and that there *could* have been a law according to which lead would transmute into gold. So I'm presupposing that common background. My particular question is whether those laws are consistent with our actual spatio-temporal distribution of intrinsic (and non-dispositional) properties. If so, that would seem to spell trouble for what's sometimes called "Humean supervenience" (namely, that these limited properties entail all truths whatsoever).


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