Look at what I've just read on the Internet Encyclopedia of Philosophy: "There are no laws of nature that hold just for the planet Earth (or the Andromeda Galaxy, for that matter), nor are there any that hold just for the Eighteenth Century or just for the Mesozoic Era." I agree that this looks absolutely true, but why is it so? I suppose science cannot prove that there is no fundamental law of physics that holds only in a small part of the universe or only during some short period. Sure, such a law would be unexplainable, at least scientifically unexplainable, but aren't ALL fundamental laws of physics unexplainable? That's why they are fundamental. If the above quotation is only stipulating some meaning of "laws of natures", isn't it arbitrary? Thank you.

It's a good question and I don't think it has an easy answer.

On the one hand, if laws aren't truly "global" (i.e., could hold only at particular times and/or places), then we have a potential problem of arbitrariness. I'm pretty sure this is a true generalization:

All men born in Canada and typing an answer on December 27, 2014 in the city of Washington DC to a question about laws on askphilosophers are wearing cotton sweaters.

On the other hand, I'm quite sure that it's not a law of nature and I can't imagine why anyone would think otherwise. You could just stipulate that all true generalizations are laws of nature, but that seems truly arbitrary, and in particular it seems to ignore all the reasons we think it's worth looking for laws of nature. So from a certain point of view, requiring that laws of nature can't be restricted to particular places or times seems like a way of avoiding rather than introducing arbitrariness.

That said, it hardly follows that we would never have reason to take laws seriously that had some temporal or spatial restrictions built in. This is especially true if we take a more pragmatic view of what a law of nature is. One general approach is David Lewis's "best system" analysis. There are various virtues we want out of generalizations that we call laws of nature. Truth is one. So is the kind of simplicity that we look for in scientific explanations. So is applicability across as much of time and space as possible. And so on. On Lewis's view, the laws of nature are the generalizations that make for the best system overall when measured in terms of these virtues. That might call for trade-offs. We might be willing to give up complete and perfect truth for greater generality, for instance. Lewis hoped that reality would be kind to us by favoring one system as the clear winner. However, there's no guarantee that that's true. More relevant to your point, it could turn out that the best system overall is one that has some spatial or temporal restrictions built in. If the system that resulted still scored high enough on enough of the virtues, the most sensible thing to say might be that there are some generalizations that deserve to be called laws of nature, but that don't hold literally everywhere and everywhen. Perhaps the universe contains subregions (presumably somewhat insulated from one another) whose generalizations are powerful within their appropriate region but not useful elsewhere. Perhaps at some point in its history, the universe changed and generalizations that held before no longer do, but have been replaced with new generalizations. It's hard to see how we can rule out such things a priori.

So I think you're right: we aren't forced to say that genuine laws of nature must apply at all times and in all places. That kind of universality is one among various virtues, but we're not guaranteed to get it. Insisting that if we don't have it, then there simply are no laws of nature does indeed seem arbitrary, and approaches like Lewis's show that admitting this doesn't set us on the road to chaos. As I put in in a talk that I never got around to publishing, we can potentially make sense of a patchwork universe with patchwork laws

I just wanted to add to Allen's remarks (with which I largely agree).

First, the claim that there are no laws of nature that hold just for (e.g.) the planet Earth may require the qualification "no fundamental laws of nature". After all, if it is a law of nature that like electric charges repel, then it is a law of nature that like electric charges on planet Earth repel. The latter is a derivative law, however. So there could easily be non-fundamental laws that hold just for the planet Earth.

Second, on Lewis's own version of the Best System view, the laws of nature must all be truths. There is no trade-off between "complete and perfect truth" and "greater generality." Of course, a modified version of Lewis's account might be more liberal.

Third, it could be that all fundamental laws of physics have no explanations (that's what makes them fundamental, as you say), and yet there is a reason why all fundamental laws of physics cover all of space-time and (to put it roughly) say the same things about every spatiotemporal region. It could be a meta-law of nature that all fundamental first-order laws of physics cover all of space-time and say the same things about every spatiotemporal region. This meta-law would explain why all first-order fundamental laws of physics have these properties. After all, if all of the first-order fundamental laws of physics are like this, then it seems like this fact would not be a coincidence. There would be a common "cause" for all of the first-order laws' being like this.

Finally, notice that we have moved here from laws of nature to laws of physics. Perhaps there are laws of "special sciences" that are restricted in space or in time.

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