Because of the way we talk about natural law many come to think of it as something that exists in addition to the physical components of the world, as if natural law was some kind of extra force that makes the physical components of the world behave as they do, and that without it there would be no order in the world. This is a mistake; there is nothing extra that corresponds to natural law, and certainly nothing that makes things behave as they do. It is muddled thinking that leads to such a conception of natural law, and such muddled thinking often leads to other mistakes as well. Hopefully by achieving a better understand of what natural law us we can eliminate some of the confusions that lead to a poor understanding of it.
Of course first it is necessary to show that this understanding of natural law really is a misunderstanding. But that is easy to do. Suppose for a moment that it is the correct understanding, that there is something in addition to the physical components of the world that makes them behave as they do. We can call this thing X. But then the fact that X always makes the physical components of the world obey the same laws is another natural law. And thus there must be something that makes X follow this natural law in addition to it (by the same reasoning that led to a positing of X in the first place). We can call this thing Y. But by the same reasoning we can then establish that there must be a Z forcing Y to behave as it does, and so on ad infinitum. Clearly this infinite regress is absurd, and the only way to avoid it is to suppose that at some step there is nothing external that makes that thing behave as it does. But if we accept that that is possible then by Occam’s razor we should simply accept that at the very first step, and hold that there is nothing outside of the physical components of the world that makes them behave as they do. That contradicts our original premise that natural law (X) was in fact something extra in addition to the physical components of the world. Thus, by contradiction, we can conclude that there is nothing in addition to the physical components of the world that makes them behave as they do.
This same conclusion can be reached simply by considering what we might call the order of dependence that holds between specific physical events and natural law. We deduce that a certain regularity (natural law) holds by observing a large number of individual physical events, each of which adheres to the regularity. But note: this is an inference, we don’t become absolutely certain that the regularity always holds (really is a natural law) by observing a number of specific events, we only become justifiably more confident that it holds. A natural law can be a true description only if every physical event, at every time, past, present, and future, conforms to that natural law. The key point here is that every natural law is a description of a universal ordering of events. And descriptions do not make things happen; my shirt may be validly described as green, but the fact that my shirt can be described as green doesn’t make it reflect a certain color of light, rather the fact that it reflects a certain color of light makes calling it green a true description.
The illusion that natural law exists in addition to the physical components of the universe arises, I think, from how we use natural law. We take what we consider to be natural law and the initial conditions and then deduce some further facts from them. It thus seems like the natural laws are something existing in addition to the initial condition that force the outcome to be a certain way. Of course this is a misunderstanding. First of all this is not real deduction. The conclusions may very well turn out to be false, even if our initial observations are flawless and the natural law has been perfectly correct up to this point. It is better to think of this situation as another kind of induction, from past observations, represented by what we think of as natural law, to future observations, what we think of as conclusions. Obviously such induction is not an example of facts following from other facts, but rather a statement as to what we can reasonably expect. And secondly it can’t, even in principle, be a valid deduction because it is a fact that a natural law holds only if every particular sequence of events is in agreement with it. Thus to reason from a natural law to conclude that a particular sequence of events will occur is circular reasoning, because it would be to deduce that a particular sequence of events will occur on the basis of the assumption that that very sequence of events will occur (among other assumption).
Obviously such an understanding of natural law is contrary to how it was seen at the dawn of modern science by the rationalists (Descartes, Spinoza, Leibniz). These philosophers thought that you could simply see the truth of natural law by direct intellectual perception, thus avoiding the threat of circularity and giving a more reasonable foundation to the position that natural law was its own thing that existed in addition to particular events. Of course historically the empiricists won this debate, with most of the rationalists claims about the philosophy of science being tossed into the dustbin, where they remain (because it turns out that we don’t have such a faculty of intellectual perception, just a faculty of reason). Obviously I’m not trying to launch an attack on the rationalists; there is no point as they have been refuted by others before me. I am simply trying to illuminate a certain confusion about natural law, which may lead to an adoption of certain rationalist positions, which would be unfortunate.