Wednesday, April 8, 2009

Lewis and Vague Laws of Nature?

Sometimes people seem to assume that David Lewis took the notion of law of nature to be (somewhat) vague (which I take to mean that 'x is a law of nature at @' has borderline cases), but does Lewis say that explicitly anywhere? (On the face of it, it would seem to be in contrast with the best system thesis being expressed as a biconditional, but, on the other hand, Lewis seems to concede that strength and simplicity are somewhat vague criteria.) And would any other sophisticated regularity theorist be happy with that?

(Crossposted at It's Only A Theory)


  1. Not sure that the following nails it down, but it is suggestive. "Counterfactuals" p.74:

    "I adopt Ramsey's 1928 theory of lawhood, glossed as above, because of its success in explaining some facts about laws of nature. ... (6) It explains why lawhood has seemed a rather vague and difficult concept: our standards of simplicity and strength, and of the proper balance between them, are only roughly fixed." (p.74)

    That does seem to be saying that the extension of "x is a law" is vague in virtue of the fact that in the criterion for bestness are "only roughly fixed"---and that it's a virtue of the best system account that it makes it possible to say this.

    Why would this conflict with expressing the best-system idea as a biconditional though? I guess the idea is that we claim "x is a law of nature iff x is a theorem of all the best systems". And the RHS and LHS can both be borderline for some values of x.

    On the sort of view of vagueness that Lewis (and many others) like, that's perfectly compatible with the biconditional being (determinately) true. In supervaluational lingo, the idea would be that "best system" and "law" are penumbrally connected, so that the two halves of the biconditional have the same extension on any precisification of the language.

  2. Hmmm... maybe the quote doesn't really do that much after all. "Has seemed vague..." is after all compatible with the seemings being wrong!

  3. Hi Robbie,

    Thanks for your helpful comment. As you say in your second comment, that passage does not seem to amount to a claim that 'x is a law of nature' is vague only that it seems vague. I was wondering whether Lewis is more explicit somewhere else or if that passage is the source of the assumption I was talking about.

    Btw, (let me do a bit of x-phi here) I must confess I don't share at all Lewis's seeming. If laws of nature are supposed to be mind-independent (which, I take, is one of the advantage Lewis view is supposed to have over "epistemic" regularity accounts of laws of nature), shouldn't Lewis claim that there are objective criteria of simplicity and strength and that our vague criteria track those objective criteria more or less reliably? So, shouldn't the vagueness of 'x is a law of nature' be merely epistemic? (I have a strong feeling Lewis is giving us a typical Lewisian runaround here)

  4. Here's what seems to be a interesting statement of position (from "Humean supervenience debugged):

    "I suppose our standards of simplicity and strength and balance are only partly a matter of psychology. It's not because of how we happen to think that a linear function is simpler than a quartic or a step function; it's not because of how we happen to think that a shorter alternation of prenex quantifiers is simpler than a longer one; and so on. Maybe some of the exchange rates between aspects of simplicity, etc., are a psychological matter, but not just anything goes."

    So he's open to quite a bit of objective explication of the constituent virtues determining "bestness". He does seem to think that there's some kind of non-objective ingredient---in *part* they're a matter of psychology (esp. wrt balancing off).

    "If nature is kind, the best system will be robustly best--so far ahead of its rivals that it will come out first under any standards of simplicity and strength and balance. We have no guarantee that nature is kind in this way, but no evidence that it isn't. It's a reasonable hope. Perhaps we presuppose it in our thinking about law. "

    So (i) this seems to commit him to claim that actual laws of nature aren't indeterminate---that there'll be a clear winner in our actual situation; and (ii) I guess the thought is that however we vary whatever the "psychological" component determining best theory (the "standards"), the same theory will win out.

    What he says next is intriguing:

    "I can admit that if nature were unkind, and if disagreeing rival systems were running neck-and-neck, than lawhood might be a psychological matter, and that would be very peculiar. I can even concede that in that case the theorems of the barely-best system would not very well deserve the name of laws. But I'd blame the trouble on unkind nature, not on the analysis; and I suggest we not cross these bridges unless we come to them."

    The first sentence I think alludes to the "psychological determination"---I guess the thought is that if "best" for me incorporates one standard of balance, and "best" for you incorporates another, in this situation the "laws" for me would be different than they are for you. And Lewis is suggesting that in this case we might get something like presupposition failure (see the end of the first package)---meaning that here we've got no laws at all.

    An intriguing idea suggested by this (though typically Lewis doesn't straight out endorse it---just says he's "can even concede" it) is that whenever we get near to a case where you might get indeterminacy mattering, you won't get indeterminate laws---you'll get no laws at all (nothing that deserves the name "law"). I guess the idea would be, roughly, that it's analytic of "law" that psychological factors should be irrelevant to what counts as a law. (I'm supposing that whenever indeterminacy threatens variation in "standards" could resolve it one way or another---that's deniable I guess).

    "(Likewise for the threat that two very different systems are tied for best. (See Armstrong (1983, pp. 70-71); van Fraassen (1989, pp. 48-49).) I used to say that the laws are then the theorems common to both systems, which could leave us with next to no laws. Now I'll admit that in this unfortunate case there would be no very good deservers of the name of laws. But what of it? We haven't the slightest reason to think the case really arises.)"

    The third-to-last sentence is as close to an endorsement of the "no laws" position as I can find. And to repeat, the idea would be that when indeterminacy might threaten, we say that there are no laws at all (not even the theorems that are common to all the best candidates).

    I think this is a pretty dodgy view, in comparison to the indeterminacy alternative. I reckon it's going to give pretty counterintuitive results about nested counterfactuals, for example---where the indeterminacy alternative would give more plausible results.

    I'm also not really seeing what his grounds for optimism are that in the actual situation we get a unique best candidate, to be honest.

  5. Robbie,

    I must confess--every time I read 'HS Debugged' I'm more puzzled. First, as I think suggest in your previous comment, Lewis seems to ultimately deny that there can be nomic indeterminacy. So, if there is any vagueness about what the laws are, its source seems to be largely epistemic (as I was suggesting in my earlier comment)--if our standard of simplicity and strength diverge, there is still a fact of the matter as to what the laws are. What I find really bizarre if Lewis's account is to be interpreted as a form of nomic realism is that Lewis suggests that, if we can't agree as to what system is the best, then there may be no laws. This seems to be analogous a metaethical realist claiming that, if people widely disagree about moral principles, then there may be no moral principles. (Analogously, Lewis seems to assume that widespread intersubjective agreement is somehow evidence of the objectivity of the standards, but as far as I can see part of the worry is that our standards of simplicity and strength are anthropocentric and widespread agreement among humans would not dispel the worry any way)

    Second, I find the whole "desert" terminology very telling. Lewis repeatedly talks of 'law' as "a name" some true universal generalizations deserve and other not. To me that sounds a lot like what a naive regularity theory would say ('Law' is some sort of honorific title we confer to those universal generalizations that play a special role in our system of beliefs).

    Third (and I'm going to stop after this), I really don't know what to make on Lewis's remarks about Nature being "unkind" and "blaming" Nature not the analysis when we can't agree on what the best system is. Why would you "blame" nature??? To me this sounds like 'my analysis of laws (despite all wiggle room I've left for myself) has still some pretty weird consequences so I'll start talking metaphorically and hope someone will believe that I'm saying something profound'. So, supposedly nomic facts supervene on Humean facts. But, in some cases, if the BSA is correct, no nomic facts supervene (despite being presumably a lot of really nice widespread regularities; so many in fact that we cannot even find one single way to describe them all in the best possible way). And it is a pretty weird consequence, but it is not to be blamed on the BSA but on nature's unkindness. If you really believe that it is plausible to maintain that under those circumstances there genuinely would be no nomic facts, why is there someone/something to "blame"? Even Lewis couldn't swallow that but even that it is not the BSA's fault it is Nature's fault!!! ;-) But can Lewis do so in a principled manner? The only principled reason I can think of is--if we find ourselves in the situation described by Lewis (widespread disagreement as to what the best system is)would this bizarre consequence arise no matter what analysis of laws of nature one adopts? But, clearly, the answer is 'no'. If, say, the likes of Armstrong, Tooley and Dretske are right no matter how much we disagreed about which system is the best there could (and plausibly would) still be laws of nature even if we might have a hard time figuring out what they are (in which case Nature may be unkind epistemically but not metaphysically so to speak). So, in what sense is Nature to blame?

  6. Hi Gabriele,

    I don't know whether I'd have described Lewis's system as "nomic realism" in any very strong sense to begin with.

    It does seem worth distinguishing

    (1) nomic realism-nonrealism about the property *X is a law of nature of W*, where W is a name of a specific world, and X a variable.
    (2) nomic realism-nonrealism for "X is a law of nature of world x" for variable X and x.

    It seems to me that what Lewis is claiming as an advantage of his system is that "the laws of nature of A" where A names our actual world don't in any significant sense depend e.g. on our dispositions to find things simple.

    That's compatible with thinking that what counts as "the laws of nature of W" for some non-actual situtation W might depend on what someone or other finds simple. If you think that occurred, then you might be in a position to say that the relation "X is a law of x" is somehow mind-dpt.

    I think what Lewis really wants to resist, throughout, is the mind-dependence answer to issue (1). Re issue (2), he seems to vacilate a bit---and perhaps the "no laws" idea is meant to secure a certain kind of non-mind-dependence in the relation as well as the actual-world property. Like you, I find the strategy dubious (and I have to say, I don't really know how to make the talk about "realism" or "mind-dependence" precise).

    Re your second point. I wonder whether "what it takes to deserve the name law" should be fleshed out in terms of the BST directly, or rather, in connection to the analysis of counterfactuals, dispositions, causation, etc etc. You might then take Lewis to be saying: well, being a theorem of best theory can play this role, and so we should bestow on it the honorific title. (Of course, people like Armstrong and van Fraassen say precisely that BST-laws can't play this role---but here Lewis is just going to take them on). Thought of that way, the picture doesn't seem unattractive to me.

    I think, like you, that the "blaming" stuff doesn't do much work for him. I don't really know how to unpick the metaphors, but one idea would be for him to say: look, my philosophical theory of laws has lots of nice consequences. Admittedly it returns certain counterintuitive results (maybe: that if situation x had been the case, there would have been no laws of nature). But why should its admitted counterintuitiveness with respect to certain far-fetched possibilities outweigh its advantages in other respects?

    The two main problems I see with this strategy are (1) that I simply can't see why the relevant possibilities are "far fetched" (I can't even see the case for them being non-actual). And (2) I also think that bad results aren't going to stop with counterfactuals involving statements about laws in their consequents (which I personally could live with) but also counterfactuals with consequents about causation, disposition, and various nested counterfactual claims.

    I think a position that said there were laws at "balanced" worlds, but it was indeterminate what they were, would fare better. Maybe it turns out that there's some "mind-dependence" we're committed to there (*maybe*---I don't fully understand the indeterminacy-to-nonrealism path that Lewis seems to see). But we can still say non-crazy things about what causes what at the world, what counterfactuals are true there etc. I wouldn't think of this as an unattractive package to endorse.