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Magnetic laws

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I’ve been thinking more about the problem of fit I posted last week. Specifically, I’m trying to work out how a response appealing to reference magnetism would go.

Recall the puzzle: how is it that when we select hypotheses that best exemplify our theoretical values, we so often hit on the truth? A simple example: emeralds, even those we haven’t observed, are green, rather than grue. And lo, we believe they are green, rather than believing they are grue. It seems things could have been otherwise, in either of two ways:

  1. There might be people who project grue rather than green, in a world like ours.
  2. Or there might be people who (like us) project green, in a world where emeralds are grue.

Those people are in for a shock. Why are we so lucky?

A response in the Lewisian framework goes like this. Not all properties are created equal: green is metaphysically more natural than grue. In particular, it is semantically privileged: it is easier to have a term (or thought) about green than it is to have a term (or thought) about grue. This should take care of possibility 1. If there are people who theorize in terms of grue rather than green, their practices would have to be sufficiently perverse to overcome the force of green’s reference magnetism. There are details to fill in, but plausibly it would be hard for natural selection to produce creatures with such perverse practices.

But this still leaves possibility 2. Given that our theories are attracted to the natural properties, even so, why should a theory in terms of natural properties be true? The green-projectors in the world of grue emeralds have just as natural a theory as ours, to no avail.

But even though 2 is possible, we can still explain why it doesn’t obtain. What we need to explain is why emeralds are green—and we shouldn’t try to explain that by appeal to general metaphysics, but by something along these lines: the electrons in a chromium-beryllium crystal can only absorb photons with certain amounts of energy. That is, we explain why emeralds are green by appeal to the natural laws of our world.

Generalizing: “joint-carving” theories yield true predictions because their predictions are supported by natural laws. Why is this? On the Lewisian “best system” account of laws, it is partly constitutive of a natural law that it carve nature at the joints: naturalness is one of the features that distinguishes laws from mere accidental generalizations. So, much as reference magnetism makes it harder to have a theory that emeralds are grue than it is to have a theory that emeralds are green, so the best system account makes it harder to have a law that emeralds are grue than it is to have a law that emeralds are green. Then the idea is that, since our theories and our laws are both drawn to the same source, this makes it likely that they line up. Furthermore, since the laws explain the facts, this explains why our theories fit the facts.

Something isn’t right about this story; I’m having a hard time getting it clear, but here’s a stab. There’s a general tension in the best system account: on the one hand, the laws are supposed to explain the (non-nomic) facts; on the other hand, the (non-nomic) facts are metaphysically prior to the laws. But metaphysical priority is also an explanatory relation, and so it looks like we’re in a tight explanatory circle. (Surely this point has been made? I don’t know much of the literature on laws, so I’d welcome any pointers.)

This is relevant because the answer to the problem of fit relies on the explanatory role of laws—a role that seems difficult for the best systems account to bear up. But I feel pretty shaky on this, and would appreciate help.


Written by Jeff

March 2, 2009 at 8:44 pm

7 Responses

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  1. We know about laws because of regularities, and the regularities are true because of the laws. Part of the problem is we have to know what a law is. A law might not explain anything if it is just a generalization for regularities. Then specific regularities will be evidence of the law, but they will also be true because of the law.

    I just wrote a post about something similar. Observation in science is theory-laden, but it gives us evidence of that assumed theory when it corresponds with it appropriately. The theory itself has to have causal connections involved. If I drop an object it will fall partially because I am a solid object just like the object I drop. The theory of solidity is assumed by the observation, but the observation also gives evidence of the theory. Without the theory we couldn’t explain the observation as well.

    Although there is a circularity involved, we can still have evidence and counterevidence. If I can’t drop an object because I can’t touch it, that could give us evidence that the object isn’t solid.

    The argument isn’t “A is true, so A is true.” Instead it is something more like: “A is assumed to be true. If no reductio ad absurdum can be derived, we will continue to assume A.” The circularity isn’t as big of a problem when we just take something as an assumption rather than a “proven fact.”

    If we want to say that something like solidity is a proven fact, then this can become more difficult to explain. I suppose we could turn the same argument into a kind of Disjunctive Syllogism. We can “assume not-A. If no reductio ad absurdum can be derived, then Not-A is a legitimate assumption.” So, an assumption can be taken to be a proven fact when its negation leads to an absurdity.

    James Gray

    March 3, 2009 at 7:41 pm

  2. Hi Jeff,

    Is it essential to the Lewis’s view of lawhood that the non-nomic facts are ‘metaphysically prior’ to the laws? Followers of Lewis typically say as much, but I see no aspect of Lewis’s view that commits them to this claim.

    Lewis thought that the laws of a world *supervene* upon the non-nomic facts of that world, of course. But as is well known, supervenience is not sufficient for metaphysical priority.

    And as you note, Lewis arguably thinks that a necessary condition for an empirical generalization to be a law is that its predicates correspond to properties that are sufficiently natural. But something’s being a necessary condition for something else isn’t sufficient for metaphysical priority, either.

    Alex S.

    March 8, 2009 at 11:28 am

  3. […] problem of fit and magnetic laws. AKA why when we pick a hypothesis are we so often right? (In Peirce this is termed the logic of […]

  4. That’s an interesting thought, Alex. (Glad you dropped by!) But I think the best system (BS) view has got to go beyond mere supervenience. For example, Shoemaker would say that the laws supervene on the non-nomic facts (because they’re metaphysically necessary!), but that doesn’t make him a best system theorist. I thought that BS was supposed to be an account of what it is to be a law, which is stronger than a mere supervenience account. And I thought it would have to be a kind of (metaphysical) explanation of why the laws are whatever the laws are. It’s hard for me to understand the view otherwise.


    March 10, 2009 at 4:13 pm

  5. […] does this matter? It’s relevant to my criticism last week of Lewis’s “best system” account of laws (not just my criticism). Briefly, I […]

  6. […] leave a comment » Does the universe come “facts first” or “laws first”? That is, in terms of metaphysical priority, do the non-nomic facts determine what the laws of nature are, or are the laws at the ground floor determining what the non-nomic facts are? (Or maybe neither grounds the other; I’ll ignore this view for now.) The best-known example of a facts-first theory is Lewis’s “best system” account: to be a law of nature is to be a member of the set of generalizations over the non-nomic facts that has the best balance of simplicity and strength. Here are two rough-and-ready arguments against an account like that. The first is the circularity argument I gestured at a few weeks ago: […]

  7. Hi Jeff!

    I’m late to the party here, but in case you’re still looking for pointers: I think similar points were made both by Armstrong (in §4.2 of What is a law of nature?) and by Dretske (‘Law of Nature’). Here’s the quote from Dretske:

    To say that a law is a universal truth having explanatory power is like saying that a chair is a breath of air used to seat people. You cannot make a silk purse out of a sow’s ear, not even a very good sow’s ear; and you cannot make a generalization, not even a purely universal generalization, explain its instances. The fact that every F is G fails to explain why any F is G, and it fails to explain it, not because its explanatory efforts are too feeble to have attracted our attention, but because the explanatory attempt is never even made. The fact that all men are mortal does not explain why you and I are mortal; it says (in the sense of implies) that we are mortal, but it does not even suggest why this might be so. The fact that all ten tosses will turn up heads is a fact that logically guarantees a head on the tenth toss, but it is not a fact that explains the outcome of this final toss. On one view of explanation, nothing explains it. Subsuming an instance under a universal generalization has exactly as much explanatory power as deriving Q from P & Q. None.

    I don’t know of any Humean who has discussed this argument at length, but both Loewer (‘Humean Supervenience’) and Earman (‘A Primer on Determinism’, p. 103) touched on it briefly, and both responded (I think) by appealing to unification as a source of explanatory power. The Loewer quote is:

    It is likely that he would similarly complain that L-laws don’t really explain since a the fact that a regularity is an L-law is a complex state of affairs constituted in part by the regularity. But the argument isn’t any good. If laws explain by logically implying an explanandum – as the DN model claims- then the state of affairs expressed by the law will in part by constituted by the state of affairs expressed by the explanandum. How else could the logical implication obtain? In any case, L-laws do explain. They explain by unifying. To say that a regularity is an L-law is to say that it can be derived from the best system of the world. But this entails that it can be unified by connected it to the other regularities implied by the best system. I suspect that Armstrong thinks that L-laws don’t explain because he thinks that laws explain in some way other than by unifying. I will return to this point later when we discuss his own view of laws.

    Hope these are relevant!


    Yu Guo

    November 16, 2009 at 7:08 am

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