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The Humean view prevailing today is that laws of nature are mere regularities of the empirical events. However, there seems to be a difference between post factum regularities, like the Titius-Bode rule of planetary distances, and strict laws like universal gravity that operate without exception insinuating themselves into every occurence that falls under them. Even when they break down it is not through miraculous exceptions, but by being subsumed under another equally strict law. They manifest in a way suggesting that they somehow "constitute" reality rather than reflect its regularities.

Unfortunately, the Stanford article is more about defining what laws "are" than explaining how they might operate. There are two classical explanations, Kant's and Plato's. On Kant's account strict laws are inserted into phenomena by our mental faculties. It is hard to maintain today as a general explanation, if anything relativistic and quantum laws operate despite our mental a priori, not because of them. And even universal gravity according to Kant is empirical, not a priori.

Plato's view is of course that laws are ideas governing other ideas in the realm of ideas, and real things "imitate" ideas. "Back to Plato" movement got some momentum lately. Armstrong, Dretske and Tooley describe laws as relation among universals, which link properties of particulars. But it appears they replace imitation with "then a miracle occurs", which relates universals to particulars, or to us for that matter.

According to Hillary Putnam, "realism is the only philosophy that does not make the success of science a miracle". But on Humean account of laws as brute facts realism appears to lose its explanatory power. The exceptionless lack of miracles is itself a miracle, we might as well accept the brute fact of scientific success. If the miracle argument is taken seriously it leads much further than generic realism. Isn't Platonism the only philosophy that does not make the success of realism a miracle?

Is the miracle argument valid in its inference to "best explanation" for the laws of nature? If so, is there a way to avoid "miracles" without resorting to Platonism, or at least to provide a credible replacement for imitation? What are the modern non-realist accounts of the operation of natual laws and success of science in discovering them?

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I don't think humeanism is the prevailing form of realism today. You are right that the "no miracle" argument is an argument to the effect that the modal aspects of laws (their being necessary, governing rather than descriptive instances) should be taken seriously, and that the argument plays against humeanism. The emphasis is indeed on explanatory power, which is generally assumed to require some "modal force".

However there are other accounts of laws that you do not mention:

  • primitivism, according to which laws are not analysable, but govern the universe. It looks like a non-solution at first sight, but Maudlin has interesting arguments in "metaphysics within physics". The principle argument is roughly that you need ontological primitives anyway, and that explanation, counterfactuals, dispositions and causality can be grounded in laws of nature (so it is a good primitive).
  • dispositional monism, which is conversely an attempt to ground laws in causality. The view is that properties should be identified with their causal profile, and that laws describe the essence of properties. The position attempts to "put back laws inside the universe" so to speak, and to take the advantages of both humeanism (only concrete facts) and universalism (explanatory power), without the inconvenients. You can read Bird's "nature's metaphysics" on this.

Edit: also note that your formulation does not do justice to kantian philosophy. The idea is not that laws are inserted into the phenomena but that laws are a way for us to categorize the phenomena and have cognitive access to them. For the kantian it is no miracle that phenomena obey to laws, because if they did not they would not be intelligible to us. It should be noted in this respect that the Schrödinger equation in quantum mechanics can be fully derived from a priori invariance principles alone (unitary invariance by spatial rotation, temporal translation...). The same goes for conservation laws in general, as Noether's theorem shows. Indeed a law which vary in space and time or a system whose state evolution depends on the choice of a coordinate system seems hardly intelligible. There is certainly some a priori in laws.

  • I agree that phenomena have to obey some laws to be intelligible, but gravity, Newtonian or relativistic, is not one of those, and neither are many others that Kant classified as empirical. Noether's theorem only shows that symmetries generate conservation laws, symmetries and invariance principles themselves are empirical regularities, and so is the Schrödinger equation. That phenomena obey equations is not a priori either. Even Newton's laws of motion that Kant originally thought were a priori turned out to be so only relative to a restricted mode of describing phenomena that he assumed. – Conifold Dec 17 '14 at 21:36
  • I am not a specialist in kantian philosophy, I don't know if he would say that all laws are completely a priori, but I don't think so. He would say that some principles such as the principle of causality are. I think the idea is that such principles are like "fishnet" to catch the phenomenal (which is what Wittgenstein says about causality). Regarding conservation laws and symetries: the invariance by time-translation seems a-priori. Laws are not supposed to vary in time (or we talk about states instead). – Quentin Ruyant Dec 18 '14 at 0:48
  • @conifold: Noethers theorem generate conservation laws from symmetries of an underlying space; its taken as intuitively plausible, I think, that space and its symmetries are more fundamental than conservation laws; recall, that Newton before going on to posit his laws, first declares how he understands space, time and their relationship. – Mozibur Ullah Dec 18 '14 at 18:34
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    Also, physical space and time isn't Kants concern, but the actual experience of them, their qualia if you like; we don't after all experience the curvature of time and space, and nor do we experience quantum stuff directly - we just know that its there, and have a theory about it; this view is the phenomenological view in philosophy. – Mozibur Ullah Dec 18 '14 at 18:37
  • @Mozibur Ullah I agree in principle, but his goal was explaining science of his day, so he had to identify what is studied in science with "qualia", or "phenomena" in his own word. It turned out to be too narrow, hence his explanatory strategy can not be used anymore without some major revisions. – Conifold Dec 18 '14 at 22:26
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The universe does not obey our laws. The universe does what the universe does. "Gravity" is sometimes called a law, but it is more accurately described as a model to describe the world which has been so sufficiently tested that there is no reasonable reason to question it.

Many of these stricter models (rephrased from "stricter laws") stem from the nature of science. Scientists generally appreciate stricter laws.

Consider: photons used to have a "position." Now days we accept that that they are better modeled as a quantum wave. However, in the middle of that process, there was a period where we had to accept a fuzzy law that "photons have a position, except in these funny situations where they appear to not have a position." Scientists spent very little time suggesting that the photons should be arrested for their bad behavior, and spent their time working hard until they had a strict model that could supercede the previous one.

One of the great successes of science is the concept of the random variable. Scientific measurements are always made with an error range around them. Consider that science, and indeed logic itself, would gravitate towards modeling the portion of life which can be modeled as an equation plus a random factor.

If one wishes to take a non-realist bent on the situation, one only needs to have a reason to converge on a roughly realist outcome. One only needs a slight fraction of miracle (such as a virgin birth) to be not 100% realist. It would be trivial to define a world which was purely thought, but which nearly all thinking entities agreed upon a portion of our existence.

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    I agree that scientists strive to produce stricter models, so finding them wouldn't be a surprise on the assumption that they are "out there". But if the nature was truly random no amount of effort could produce strict laws, not even approximate ones. The question is in what sense are they "out there" to explain the successes. – Conifold Dec 17 '14 at 21:15
  • scientists (at least this one) prefer consistent models and, after that, simple models. "strict laws" ain't quite the same. – robert bristow-johnson Dec 17 '14 at 21:23
  • @robert bristow-johnson Strict more or less means strictly predictive, and that takes priority even over consistency and simpicity. – Conifold Dec 17 '14 at 23:38
  • @Conifold: There is often apparent local structure in random noise (the infamous "monkeys at the typewriter" argument). I think the philosophers would have a hard time disagreeing with the statement that we are not impartial observers, but rather part of the system. If our consciousness is not impartial, but rather gravitates towards local structure which is explainable by laws, it would not be unusual for us to observe more "laws" than actually exist from an impartial observer's point of view. – Cort Ammon - Reinstate Monica Dec 18 '14 at 1:35
  • @Cort Ammon Observing more "laws" than actually exist is interesting, could you elaborate or give reference? I don't think I understand what "consciousness... gravitates towards local structure which is explainable by laws" means. – Conifold Dec 18 '14 at 22:22
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Among complete idealisms, there is a trend that moves away from 'imitation' toward some kind of interrelation, which to me captures the modern impression of intersubjectivity that increasingly pervades our experience of mental activity. It is hard to accept that as the Kabbalah says, and Plato would surely agree, "Where God's gaze is withdrawn for but an instant, existence ceases." Instead, we recognize that feedback loops run the universe.

To put it short and cute, Leibnitz and Whitehead both float models of how regularities in interaction are maintained based on "continual negotiation between all those concerned" in a sort of Grand Moot of All Particles. Each attendant part is reflected in each other part, with more clarity the more closely related are the parts, and it can only do things that do not overly surprise any of its observers. Of course making that any clearer and less anthropomorphic is like nailing jelly to a tree.

This seems bizarre at first blush, but the way it fits in with quantum mechanics and other theories of how things work on a small scale, is almost prescient. We know now that if you strictly limit the involved observers, reality does not have to behave particularly consistently, and as you add observers, you add constraints, until you reach the point where there are so many possible paths of observation that things smooth out into what we think of as normal macroscopic behavior.

One way to look at general relativity is to say gravity happens because less time passes when there are a lot of particles present. Gravity correlates to slowing time proportional to mass. But who says which way the causation flows? This is the kind of thing you might expect to proceed from the idea that time is 'harder to do' when there are more interactions, as monadic 'reflection' vaguely implies. Particles move closer together because less time passes where there are more of them. So movement toward one another tends to be faster than movement away from one another.

  • I am not familiar with Whitehead's views but Leibniz's is "pre-established harmony" between reality and mind. That's essentially just imitation, just mediated by God. I am not sure how adding observers would increase regularities in observations though, and microscopic behavior seems to be pretty regular too, not just macroscopic. – Conifold Dec 17 '14 at 21:23
  • 1) Monads are plural, whereas under 'imitation' the form is singular. Every monad is reflected on the 'surface' of every other monad... Basically, Plato lacks any ability to explain why the participants care about one another. They are tied back to the form, but they only look up, not sideways. 2) Not being able to locate a particle, and then having it decide at some point to 'be' somewhere is not very regular. "Quantum foam" is not a metaphor for predictability. – user9166 Dec 18 '14 at 16:35

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