On Philosophy

May 21, 2007

Natural Law

Filed under: Epistemology,Metaphysics — Peter @ 12:00 am

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.



  1. OK, just to liven things up a bit, I am basically a rationalist, and I believe that my position is justified by recent discoveries such as the Church-Turing thesis. Take any system; a bicycle, for example. The bike is in some number of states, whether you just care about measurable ‘bike states’ such as position of each wheel or whether you want to include every quantum state. Now, cut the bike in half and the number of states doesn’t get halved, but decreases logarithmically. Cut it again, and again. Soon you have a very few number of states and soon it will converge to lots of systems of one state each. But the universe as a whole will have the same number of states because the new relations among those parts hold (are) state. From just that we can infer an enormous amount of information about the “natural laws” I have worked up a mathematical notation for representing systems based on this (it’s the eventual topic of my own blog.) We needn’t do experiments to determine that states decrease logarithmically, nor, I believe, do we need to experiment to know that the universe is a state machine. So, my position is purely rational; Hume and crew didn’t have access to computer science techniques or advanced mathematics, and neither did their opponents. Hume won by default because he put the burden of proof on the rationalists and they didn’t have the necessary tools with which to respond. A kind of condescending tone (Peter? :) ) has kept the status quo by filtering dissenters.

    Comment by Bruce — May 21, 2007 @ 2:55 am

  2. I don’t see how this law is supposed to exist independantly od the universe. If it is true then like any other law it is simply a true description, not something that forces the universe to be a certain way under its own power.

    But I doubt that it is a true description of our universe due to quantum mechanical effects, because you cannot pull apart a quantum mechanicical system like you can a classical system. (If you pull apart a quantum mechanical system you lose the ability to be in certain joint states, because the state of a muti-part quantum system is more than the sum of the state of its parts.)

    Comment by Peter — May 21, 2007 @ 8:08 am

  3. Actually, to say that a system changes state in this or that way, or that it can be in x number of states is a description and can be true or false (I prefer accurate/inaccurate but true/false works too). But to say that it has states at all isn’t a description because it tells you nothing new. For example, if I say that a property of a particular brand of pencil is its color and that it can be red, blue, or gold you know that the color property carries three states (one ‘trit’). If the pencils were all gold then there would be only one state (zero bits). Furthermore, the fact that the matter is arranged into pencil form is a state because the same matter could have been arranged otherwise. That all carries information. But if I say “I have a system and it can be in x number of states” I’ve told you nothing about the system; that isn’t a description. In fact, think about your conception of possible universes. Do you imagine that they are in one or more states? Can you imagine a possible universe for which “it is in one or more states” does not apply?

    As for quantum states, quantum weirdness arises when we treat an n-state system as if it had more than n states.

    Comment by Bruce — May 21, 2007 @ 12:11 pm

  4. Being in a state is in quantum physics, equivalent to saying that the quantum state of the system is currently an eigenvector of some observable. If you say the system can be in X states then you have told me a lot about it, or at least a lot about the observable you are measuring the system with. Indeed this is a description that can be true or false.

    And quantum weirdness turns out to be the way things really are. Our intuitions about the way nature works, even intuitions such as “there are a definite number of particles present” turn out just to be just rough approximations. The rationalist mistake is to assume that the universe must conform to certain abstract truths which seem too intuitive to be false. But it turns out tha the universe is under no such compulsion, and that mathematical and logical facts are just another way of describing how the uiverse works, which the actual operation of the universe may validate or invalidate.

    Comment by Peter — May 21, 2007 @ 3:13 pm

  5. I agree with everything you said, but you haven’t addressed my point. Yes, “this system has n possible states” is information. What isn’t information is “this system is a state system.” All systems, all possible universes, are state systems. Universes that don’t change have only one state (zero bits) but they are still state systems.

    Because the sentence “a universe (or any system) is a state system” carries no information about that system, it’s clear that we are not claiming that “the universe must conform to certain abstract truths.” We aren’t saying anything!

    Here is a concrete question to see if you really disagree with me: Are there any possible universes that are not state systems?

    I don’t think that the concept of a non-stated universe even makes sense. “S has state” just means “S has some differentiable or internally observable property” In other words, “The universe is a state system” isn’t a special claim about the universe, it’s a tautology.

    Comment by Bruce — May 21, 2007 @ 3:55 pm

  6. It depends how you define what a state is. A superposition is not a definite state, classically. So thus even our universe is not a state system. Or if you define state to mean: has one of a finite many configurations that is also not a true description of the universe, as even a single electron can be in an infinite number of possible superpositions of its spin alone.

    Comment by Peter — May 21, 2007 @ 4:01 pm

  7. Of course I don’t mean a simple classical state, but defining state using the principle of charitable interpretation, is there a possible universe that isn’t described by states?

    Comment by Bruce — May 21, 2007 @ 4:10 pm

  8. I don’t see why there couldn’t be. (It seems perfectly possible to me that there might be universes which in no way can be described as having states, although putting what such a universe might be like into words is obviously tricky.)

    Comment by Peter — May 21, 2007 @ 4:13 pm

  9. Yes, it would be quite tricky, at least without sounding theological. Certainly it undermines the concept of a “functional property.” Any functional property can be used to store state. Any ‘observable’ is store of state. Interacting with such a system would have to happen without changing our state — but isn’t that what an interaction is? Our state is mapped to the state of the observed in some way? In other words, propositions about such a system are completely unverifiable, unfalsifiable, and really have to be accepted on pure faith. No?

    Comment by Bruce — May 21, 2007 @ 4:26 pm

  10. Well I don’t think it is necessary to define observation in that way either. Who knows how observation would work in such a universe. Certainly we can’t say definitively that it must require that the observer has a state which changes by interacting. The observer may be stateless as well, or may adopt multiple states, or be indeterminiate in state. For all we know the statless nature of such a universe may be that it appears to have states to the observers within it.

    Comment by Peter — May 21, 2007 @ 4:38 pm

  11. I know from theology debates that we won’t be able to resolve this about possible universes. But I don’t think that it is controversial to say that our universe is state-based and that a property that didn’t store state (even if it had only one state, i.e., zero bits) is unobservable and useless to posit over. But consider this: If there are two types of universe: state-based and “wholly other”, then the determination of what type of universe we have is a bit of information — state! That type of argument makes it hard to imagine that non-stateness has any meaning.

    Comment by Bruce — May 21, 2007 @ 4:56 pm

  12. Sure I would grant that it is likely that our universe has some kind of quantum state. And you have omitted the possibilty that there might be universes that are in some kind of superposition of having state and not having state, having both state and no state, and so on.

    Comment by Peter — May 21, 2007 @ 5:07 pm

  13. Anways your initial argument was that our unverse necessarily had to obey some kind of law about the way that the states of complex system relate the state of simpler systems, namely that the number of states of system a+b = the number of state of a * the number of states of b. Not only is that not necessarily true; our universe necessarily doesn’t have to obey any laws, but in fact it doesn’t obey that particular law. Thus any such law is at best a true description of the universe and not some external force acting on it to make it some particular way, which was my initial claim.

    Comment by Peter — May 21, 2007 @ 5:11 pm

  14. OK, big misunderstanding here. ‘No-state’ and ‘non-state-based’ are very different. ‘No state’ or ‘multi-state’ or ‘indeterminate state’ are still state based descriptions. I’m talking about a universe where the very concept of state cannot be used in valid descriptions. ‘Superposition of states’ is still a description based on states. If states apply at all, then the logarithmic rule I used above applies.

    BTW, by ‘no state’ you probably mean no BITS. The concept of zero states doesn’t exist. Zero Bits = One State.

    Comment by Bruce — May 21, 2007 @ 5:19 pm

  15. No, I’m not misunderstanding you, I am talking about a universe which is both non-state based and state based, at the same time. Logical laws are not something that can be asusmed to be true in all universes either. So while that possibility is nonsensical in our universe it is perfectly viable for other universes.

    Comment by Peter — May 21, 2007 @ 5:47 pm

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