The objective method [i.e. the method of philosophy which starts from the object and proceeds to the subject] can be developed most consistently and carried farthest when it appears as materialism proper. It regards matter, and with it time and space, as existing absolutely, and passes over the relation to the subject in which alone all this exists. Further, it lays hold of the law of causality as the guiding line on which it tries to progress, taking it to be a self-existing order or arrangement of things, veritas aeterna, and consequently passing over the understanding, in which and for which alone causality is. It tries to find the first and simplest state of matter, and then to develop all others from it, ascending from mere mechanisms to chemistry, to polarity, to the vegetable and animal kingdoms. Supposing this were successful, the last link of the chain would be animal sensibility, that is to say knowledge; which, in consequence, would then appear as a mere modification of matter, a state of matter produced by causality. Now if we had followed materialism thus far with clear notions, then, having reached its highest point, we should experience a sudden fit of inexhaustible laughter of the Olympians. As though waking from a dream, we should all at once become aware that its final result, produced so laboriously, namely knowledge, was already presupposed as the indispensable condition at the very first starting-point, at mere matter. With this we imagined that we thought of matter, but in fact we had thought of nothing but the subject that represents matter, the eye that sees it, the hand the feels it, the understanding that knows it. Thus the tremendous petitio principii disclosed itself unexpectedly, for suddenly the last link showed itself as the fixed point, the chain as a circle, and the materialist was like Baron von Munchhausen who, when swimming in water on horseback, drew his horse up by his legs, and himself by his upturned pigtail. Accordingly, the fundamental absurdity of materialism consists in the fact that it starts from the objective; it takes an objective something as the ultimate ground of explanation, whether this be matter in the abstract simply as it is thought, of after it has entered into the form empirically given, and hence substance, perhaps the chemical elements together with their primary combinations. Some such thing it takes as existing absolutely and in itself, in order to let organic nature and finally the knowing subject emerge from it, and completely to explain these; whereas in truth everything objective is already conditioned in such manifold ways by the knowing subject with the forms of its knowing, and presupposes these forms; consequently it wholly disappears when the subject is thought away. Materialism is therefore the attempt to explain what is directly given to us from what is given indirectly. Everything objective, extended, active, and hence everything material, is regarded by materialism as so solid a basis for its explanations that a reduction to this (especially if it should ultimately result in thrust and counter-thrust) can leave nothing to be desired. All this is something that is given only very indirectly and conditionally, and is therefore only relatively present, for it has passed through the machinery and fabrication of the brain, and hence has entered the forms of time, space, and causality, by virtue of which it is first of all presented as extended in space and operating in time. From such an indirectly given thing, materialism tries to explain even the directly given, the representation (in which all this exists), and finally the will, from which rather are actually to be explained all those fundamental forces which manifest themselves on the guiding line of causes, and hence according to law. To the assertion that knowledge is a modification of matter there is always opposed with equal justice the contrary assertion that all matter is only modification of the subject's knowing, as the subject's representation. Yet at bottom, the aim and ideal of all natural science is a materialism wholly carried into effect. That we here recognize this as obviously impossible confirms another truth that will result from our further consideration, namely the truth that all science in the real sense, by which I understand systematic knowledge under the guidance of the principle of sufficient reason, can never reach a final goal or give an entirely satisfactory explanation. It never aims at the inmost nature of the world; it can never get beyond the representation; on the contrary, it really tells us nothing more than the relation of one representation to another.- Arthur Schopenhauer, The World as Will and Representation, vol. 1, sect. 7 (tr. E.F. J. Payne)
Isaac Newton believed that F=ma was a law of nature. Leave aside for the moment the question of whether he was right - some philosophers might think that, although it turned out simply to be an approximation that worked well for matters of ordinary experience, it still counts as a legitimate law. That's not what I'm concerned with right now. What I'm concerned with is what it means to claim that F=ma is a law of nature. Because of this, I may sloppily speak of F=ma as having a referent when, according to some theories I will be considering, it might not have one at all. Since F=ma is merely a convenient example, this should not undermine the argument.
Those who accept the governing conception of laws of nature hold that the claim that F=ma is a law of nature is the claim that there is some thing or collection of things in the universe or some property or collection of properties of the universe and/or its contents that makes objects accelerate at a rate of F/m whenever a force is applied. They further claim that, strictly speaking, this thing or collection of things or property or collection of properties is the law.
In order to claim this, they must claim either (1) that the collection of symbols "F=ma" (in some context) refers to the law (or would refer to the law if such a law existed), or (2) the sentence "F=ma is a law of nature" contains some sort of idiom, so that we actually mean "F=ma describes the effects of a law of nature." I claim that both of these analyses are implausible.
(1) claims that "F=ma" refers to something very different than, for instance, "f(x)=y+5" or "y=mx+b", but why should this be so? Shouldn't all equations refer (if they refer at all) to the same sorts of things? Shouldn't an equation be a type of mathematical object, and shouldn't all of these refer to equations? One response would be to simply claim that the thing that makes objects accelerate at a rate of F/m is an equation, a mathematical object. This, however, does not seem to me to have much inherent plausibility. A better try would be to say that in the context of physics the reference passes beyond the equation to the law which makes the world obey the equation. This idea will be dealt with in our treatment of (2), to which we now turn.
(2) seems implausible, if for no other reason, simply because this doesn't strike me as the way we talk. If you were to ask a physicist who, sadly, had had little exposure to philosophy of science or metaphysics, whether F=ma was a law or merely described a law, I expect you would get a funny look. Nevertheless, let's consider for a moment the view that, whatever the syntax may indicate, it is true, at least in some contexts, that the referent of F=ma is an equation or some such mathematical object, and this object describes a law of nature. What sort of thing might this law be? Remember that we are claiming that the law, whatever it is, makes objects accelerate at a rate of F/m. The law is one of the things in the universe, but it is clearly not a physical object or a force or a quantity of energy. Although people who call themselves physicalists might believe in it, it is not really physical in the ordinary sense of the word. Rather, as I have argued before, it is at least something very like the Heraclitean logos, or perhaps even something more like a conventional deity. Philosophers who believe in a more Aristotelian theory according to which the law is a collection of potentialities, where potentialities are properties of physical things, will be in a somewhat better position to continue maintaining physicalism.
Suppose that there was such a thing. Do we really mean to make a metaphysical assertion about its existence when we say "F=ma is a law of nature?" I am highly doubtful of such a thing. Rather, "F=ma" is a description, and a law is simply an accurate description which has certain properties that I won't attempt to specify here.
A few days ago, I talked about the classical assumptions relevant to wave-particle duality, in part 1 of this series. I hope to build up to discussing the relevant philosophical questions, most of which probably won't come in until part 4. But first, here and in the next part, I'm going to briefly discuss the important experiments in the development of wave-particle duality, because however it's interpreted in the philosophical discussion, it can't run afoul of these. This post is mostly physics; however, there's no math whatsoever. As always, suggestions about how to improve the physics to philosophy ratio would be appreciated.
Part 2: Wave-Particle Duality of Light
Last time, we talked about some observations that, under the classical assumptions about waves and particles, would definitively establish a phenomena as a wave or particle phenomena. These were:
O1) Interference and/or diffraction phenomena (implies wave)
O2) Travels faster in matter of higher difference densities (implies wave)
O3) Interaction occurs only with discrete amounts of energy (implies particle)
O4) Highly localized interaction in space (implies particle)
Why Is Light A Wave?
Initially, light was thought to be a particle, but in the 1660’s that Robert Hooke suggested a wave theory. Experimental evidence came around the start of the 1800’s, when Thomas Young observed interference patterns of light in his famous double slit experiment. The wave nature of light was further confirmed when it was observed that light travels faster in glass than in air (glass being a denser medium). These two observations (corresponding to O1 and O2) convinced physicists that light was indeed a wave, and the theory to explain light as a wave wasn’t long in coming. Maxwell found his famous wave equations, which included light as a type of electromagnetic radiation. Experimentally this was supported when it was shown that radio waves (certainly a type of electromagnetic radiation) have similar properties to light waves. The disagreement seemed to be settled- light was definitively a wave, and furthermore, electromagnetic radiation.
Note, however, that both of these observations deal with how light travels- it interfering with other light waves while traveling, and how fast it travels. This will be relevant in future sections.
Why Is Light A Particle?
Before too long, though, it was discovered that there was a major problem in physics, in classical thermodynamics, which seems at first to be irrelevant to light, but is actually related. Thermodynamics is basically statistical mechanics with a heavy emphasis on temperature, and statistical mechanics is applying Newton’s Laws to a system through statistics. For example, if you had a box with 10,000,000 particles in it, you might just care about the average speed of the particles and its standard deviation, instead of wanting to know the speeds of all the individual particles.
In thermodynamics, a blackbody is an ideal system that absorbs all radiation that falls on it, and then radiates some energy back. Although it is an ideal system, it can be accurately approximated in laboratories. As a blackbody is heated, the amount of energy radiated increases and is concentrated in shorter wavelengths, according to classical thermodynamics (the Stefan-Boltzmann Law). There is a spectral distribution formula relating the power radiated from a blackbody to the wavelength (the Rayleigh-Jeans Law).
In theory, a graph of the power vs. the wavelength should look approach infinity at zero and approach zero at infinity. The experimental results agreed as it approached infinity extremely well, but as the wavelength became small, instead of approaching infinity, it crested an approached zero- a very different behavior than expected. Furthermore, the theory was founded on classical mechanics and statistics. Statistics, with its rigorous mathematical formulation and proofs, is certain- so that implies there is a problem in Newton’s Laws, the very foundation of physics. Since these experiments were done in the ultraviolet range, this was known as the ultraviolet catastrophe.
Then, Max Planck wrote down an equation that fit the experimental curve, which required the use of a constant (Planck’s constant- h). He then tried to find a way to “derive” this equation classically. Using similar techniques to what was used in thermodynamics, Planck broke the energy spectrum down into discrete amounts, parameterized by h, and then proceeded with the normal derivation. At the end of derivation of this type, one would take the limit as h approaches 0 to recover a continuous energy spectrum. (This is similar to integration, where one sums the area of rectangles of a finite width, and then takes the limit as the width of the rectangles approaches 0). However, if Planck didn’t do this last step and let energy spectrum remain discrete, it matched the fit equation. Furthermore, when h did approach 0, he recovered the classical equation. This shows that, for a given frequency f, energy comes in “packets” of size hf.
However, this is the same as O3 above, which implies particle behavior…however, some physicists suggested that the proper response was to say that localized energy wasn’t exclusively a particle phenomena, but perhaps under certain situations, waves could display it also. This is equivalent to changing the definition of a particle from P1 and P2 to just P1, where as in the last section, they are defined as:
P1) A particle is localized in space
P2) A particle exchanges energy at a point
However, another famous physicist, Albert Einstein, proved that waves also display O4, whose derivation (described in part 1), relies only on P1.
The photoelectric effect is that, when light is shines on metallic surfaces, electrons are emitted. Physicists have created an apparatus to do more experiments on this effect. Basically, light (or any type of electromagnetic radiation) shines on one metallic plate (the cathode) and a distance away from it is another metal plate, which can absorb electrons (the anode). Then wires, resistors, etc are added to create a voltage across these plates, and physicists run experiments to test the correlation between the current in the system (caused by the electrons emitted from the photoelectric effect) and the voltage. A positive voltage causes electrons to be attracted to the anode, but a negative voltage repels the electrons from the anode. When the voltage is negative, only the electrons that are emitted with enough initial kinetic energy to overcome the voltage difference make it to the anode.
Classically Newton’s Laws and our understand of the nature of atoms (as negatively charged electrons around a positive nucleus) combine to make certain predictions.
1) There should be a maximum voltage such that all the emitted electrons make it to the anode (since a positive voltage attracts the electrons). Increasing the voltage beyond this does not increase the current any further.
2) If one increases the intensity of the light hitting the cathode, corresponding to increasing the amount of energy hitting the cathode, while keeping the frequency of the light constant, this should increase the maximum kinetic energy of the electrons emitted, and thus electrons should be emitted with higher speeds. Hence, there should be no minimum voltage beyond which no electrons are emitted- at any voltage, if you increase the intensity of the light enough, there should eventually be an electron emitted with enough kinetic energy to make it to the anode.
3) Finally, one can calculate the length of time light of a given intensity needs to shine on the cathode before enough energy is gathered for an electron to be emitted. Lower intensities should have a longer delay than higher intensities, but eventually an electron should be emitted.
However, of the three predictions, only (1) was verified experimentally. Regarding (2), physicists noted that there was a minimum voltage beyond which no electrons were emitted (however long they waited). Even worse, for (3), physicists noted that either the electrons were emitted virtually instantaneously immediately or not at all (however long they waited); their predictions of several hours were completely rebutted by experimental evidence.
Einstein proposed taking Planck’s quanta of energy literally- that light was really packets localized in space that have discrete amounts of energy, which he called photons. Einstein proposed that instead of a wave uniformly and constantly hitting everything on the metallic surface, what really happened is that individual photons collide with individual electrons and transfer their energy to them. If they give the electrons enough energy, the electrons escape from their orbits and are emitted. For a given frequency of light, the extra energy a photon transfers to the electron (beyond escaping the orbit) is converted to a specific amount of kinetic energy. This means that there is a limit on the initial maximum kinetic energy an electron leaves with, and if that’s not enough to overcome voltage to get to the anode, then the electron won’t make it, ever. Thus, Newton’s Laws plus the quantized energy predicts that there will be a minimum voltage (remember negative voltages repel the electrons) beyond which no electrons will make it to the anode, as observed. For the timing- if the energy is great enough, as soon as the photon strikes the electron it will be emitted. This will happen with the first photon that hits an electron; they don’t need to accumulate over time. Thus, there is no measurable lag. However, if the energy of a photon isn’t enough to give the electron enough kinetic energy to escape, photons striking the electron won’t knock it out, no matter how long you wait. There will never be a situation where you will have a steady supply of electrons emitted after several hours because the energy doesn’t accumulate continuously until an electron is emitted (the energy dissipates between when one electron hits and the next).
Overall, this implies O4, that light is localized in space. If physicists rejected this from the definition of a particle, they’d have no definition left. Thus, they were forced to accept some sort of wave-particle duality, at least for light.
Before we discuss interpretations of wave-particle duality, and the issues of properties iit raises, we’re going to look at wave-particle duality with respect to matter next in part 3. This is because it gives us a clearer view of the nature of the waves involved, and also because we know from relativity that light is something special.
Note, for the future sections, that all of this particle behavior observations deal with light interacting with something, and not with how it travels.
Hello world!
For those of you who missed the announcement, I am Lauren, Kenny's fiance, and now a guest blogger here. As Kenny mentioned, I'm majoring in physics, math, and philosophy, so one thing that I'm hoping to discuss on this blog is philosophical issues related to physics. As you can probably guess from the title, the first thing I've decided to try is wave-particle duality, an aspect of quantum mechanics. In particularly, wave-particle duality raises interesting questions about the relationship between properties and objects, whether there is one "thing" with wave properties and particle properties, or whether there is a particle and a wave that are related somehow.
However, before I begin, I'd like to take a moment to discuss methodology. Before one can talk about the meaning of different ideas of physics, it's important to have a firm grasp on the experiments that led to these ideas. The experiments place boundaries on what interpretations of the results are valid; if an interpretation conflicts with an experiment, we must reject it in favor one that doesn't. (However, the interpretation of those experiments is dependent on some earlier ideas, so we have to beware of circular reasoning...but that is another post for another day.) Therefore, before getting to the philosophical meat of the issue, I'll be taking a brief detour through the physics. I'm going to try to keep the physics discussions on a not very technical level (which is helped by the fact that Kenny doesn't have this set up to handle math equations well). However, please feel free to tell me if you want more or less detail in the physics explanations; I'll be happy to adjust.
To this end, here are the parts I foresee for this series:
1) What are particles and waves
2) Experimental evidence for wave-particle duality for light (massless particles)
3) Experimental evidence for wave-particle duality of matter (has mass)
4) What can this mean? (Philosophical part)
I apologize for two whole sections of mostly physics before the philosophy; I'll try to incorporate philosophical questions into those as I write them.
Part 1: Classical assumptions: What are waves and particles anyway?
Before discussing wave-particle duality, however, it’s important to understand what waves and particles are. To interpret whether an experiment shows a wave property or a particle property, we have to determine what those properties are first. Physical definitions are abstracted, through a long process, from basically everyday experiences. For example, there seem to be two ways of transporting energy- for example, one could throw a rock at something and knock it down, or one could drop the rock in water and watch the waves spread out and move things like leaves sitting on the water, even a far way away. The first corresponds roughly to "particle" and the second corresponds roughly to "wave".
Let’s look at dropping the rock in the pond. We notice:
1) The waves spread out in all directions, and gradually dies out instead of ending abruptly.
2) The waves seem to have a regularly, curvy-like shape that repeats (sinusoidal). If we’re really good at throwing rocks and throw several in at the just right times, we see that we can get interesting combinations of these shapes that don’t look very much like the shape from just one rock, but if we throw any one rock in, we basically get this shape.
3) If we put a leaf on the top of the water and drop a rock in, at the end of the wave passing by, the leaf is in more-or-less the same place, implying that at the end of everything, the water hadn’t had a net motion.
Now let’s look at throwing the rock. We notice:
1) Unlike waves, the rock doesn’t seem to spread out much as we throw it. It has a definite stopping point, the edges of the rock.
2) The path of the rock in our example does seem to be regular, but it’s not periodic like the waves.
3) The rock definitely ends up in a different place than when it began.
Over time, these definitions became slightly more refined.
Classically, the definition of a wave became:
W1) Energy is spread continuously in time and space
W2) Its propagation obeys, or it is made out of components that obey, the wave equation (a second order differential equation.)
W3) Propagation occurs within a medium
And for the particle-
P1) A particle is localized in space
P2) A particle exchanges energy at a point
Letting x be a phenomena, and Wx = x is a wave and P = x is a particle, the classical assumptions about waves and particles can be summarized as:
1) Wx if and only if (W1 & W2 & W3)
2) Px if and only if (P1 & P2)
3) For all x, (Wx or Px)
Everything is either a wave or a particle.
4) For all x, not (Wx & Px)
Nothing is both a wave or a particle.
Finally, let’s take a look at what tests can be used to determine if something is a particle or a wave. We’ll discuss 2:
O1) Interference and/or diffraction
The continuous spread of energy means that if we block most of a wave, but let part of it through, it’s going to have to “spread” out after it’s let through, because otherwise it would have a discontinuous drop to zero. This phenomena is called diffraction. Similarly, if you let two parts of a wave through, they’ll both spread out, and then start overlapping with each other to make bigger peaks and deeper troughs than just one of them had, which is interference. (W1->O1). However, a single particle only exchanges energy at a point, so one particle cannot display interference and diffraction, which are patterns of the exchange of energy observed over space. Additionally, a stream of particles wouldn’t create interference or diffraction patterns. If one shoots a bunch of particles at a gap in the wall, one will get a pile of particles behind the gap; they’re not going to spread out immediately beyond the gap. (P2-> ~O1). Thus, the observation of interference and/or diffraction proves something is a wave.
O2) Faster in matter of difference densities
Consider if a phenomena was made of a bunch of particles. For a phenomena to be observed a long distance away, at least some of those particles would have to move over there, because the particles are localized. Now, if there’s a lot of other particles in the way, it’s going to take them longer to get there, because they keep getting bumped around (like it takes longer to get anywhere in a crowd). It takes longer for a single particle, or a stream of them, to travel the same distance in a denser medium. Hence, O2 -> ~P, or consequently, that something is a wave. To double check, we can experiment with waves. If we take our experiment with dropping a rock in water, and repeat it with oil and other liquids, we’ll find that waves go faster in denser mediums. So far, everything is consistent.
O3) Interaction in only discrete amounts of energy
Waves have a continuous distribution of energy in space and time. So, a wave can transfer any amount of energy in its range. However, particles can have distinct values of energy. Now, for something like throwing a rock, you can throw a rock with a lot of different energies, so observations on a series of rocks could mimic observations on a wave. However, if we observe something that can only have distinct values, classically it cannot be a wave, and so must be a type of particle that has distinct energy values.
O4) Localized interaction
Waves spread out continuously through space and time. A wave, therefore, should interact everywhere along its' front; there's a wide spatial range of where energy is to cause interactions. However, particles must have localized transfer of energy. So one test is to look at the interaction pattern of a phenomena when it encounters a wide strip of possible interaction points- whether it strikes them all, or whether it hits some and misses some. In the first case it would provide evidence for a wave (although not conclusive proof, since it could be a really dense uniform spray of particles). However, in the second case (ignore apparatus error) would be conclusive evidence for particles.
That's probably more than enough for this post, although it's been mostly definition. Next I'll talk about what the experiments show for light.
It is popularly believed that if a theory has theological implications, then the theory is somehow "unscientific." A post (NOTE: MovableType won't let me link directly to this post because the URL contains an unescaped ' contrary to the HTTP spec so the above link goes to the daily archive) at the Florida Student Philosophy Blog challenges this claim. I think the article is unnecessarily long and involved, but I'm quite impressed with the insight. The argument is a reductio that works more or less like this:
That's rather a beautiful proof, isn't it? Of course, the proponent of the strict separation of science and theology is free to respond by further refining his notion of 'implication' to mean something narrower than logical implication, but I've never heard any such account.
Update (10:20 PM PDT): As Richard (of Philosophy, etc.) points out below, the comments to the linked post are worth reading and discuss precisely the point I just mentioned: the fact that the best response for the opponent to make is to simply state that he doesn't mean logical implication (the modal stuff is not needed - if God exists, then any proposition implies that God exists in the strict logical sense; I should have seen this immediately, and I think it makes the argument slightly less impressive, though the discussion is still of interest). He should set up something else as what he really means by implication. My own suggestion (similar to some of those made in the comments) is that he might use something like a Bayesian theory of evidence: that is, if P(S|H&B) > P(S|B) (where S is some supernatural claim, H is some hypothesis, and B is our background knowledge) then H is not a scientific hypothesis. Of course, it would be much more reasonable for the critic to say that even if P(S|H&B) > P(S|B), to infer S from H is not to make a scientific inference, because we have left the subject matter of science. If this was the claim, then the ID proponents would be exactly right to call the claim that the evidence supports some kind of designer a scientific claim, but discussion of the identity of the designer unscientific - even though the inference is obvious it is, according to this idea, an unscientific inference. But the previous claim, that H is unscientific because it provides evidence for a supernatural claim, seems to me to be the worst kind of dogmatism - it is to specify in advance as methodology what science can and can't find. Besides, it's impossible to uphold: for instance, the fact that natural laws hold consistently and tend to be mathematically elegant tends to provide evidence for the God of traditional monotheism over and against Zeus and friends, a theological claim. Furthermore, these people tend to think that scientific evidence against God is ok. So what we should really say is that as long as our hypothesis itself is entirely natural, it can be a scientific hypothesis (though it is not automatically a good one), but conclusions about the supernatural may still be able to be drawn (by philosopher-theologians) from the hypothesis.
In metaphysics, libertarianism is the view that human beings (and other free beings) are free because they can do otherwise. Determinism is the view that the conjunction of the laws of nature with all the facts about the configuration of the world at some time t entail all the facts about the configuration of the world at all times. Compatibilism is the view that free will and determinism are logically compatible, and incompatibilism is the view that they are not. Libertarianism is generally taken to entail incompatibilism, and is contrasted with compatibilist theories of free will. However, in her recent paper "The Non-Governing Conception of Laws of Nature" (in Philosophy and Phenomenological Research 61), Helen Beebee points out that Humean supervenience theories of the laws of nature seem able to be deterministic without contradicting libertarianism: according to Humean supervenience theories, laws are purely descriptive, they don't actually make anything happen. The laws of nature will include future facts, since they are summaries of everything that happens in the world, but they won't make things happen that way. This seems to make it metaphysically possible for me to do otherwise, even if the laws are in fact deterministic. It still won't be physically possible for me to do otherwise, but this isn't because the laws of physics prevent me from acting - the laws of physics don't do anything, other than describe - rather, it's because if I had done otherwise, the laws would have been different.
Note that if God exists and has middle knowledge, he will still be able to ensure, among other things, that the fundamental laws of physics are simple, mathematically formulable, finitely axiomizable, etc. Alternatively, if Lewis's plurality of worlds exists, there will still be some "well-behaved" worlds where the laws have these properties.
Of course, Humean supervenience theorists can't explain why the universe exhibits regularity, but nomic realists can't explain why there are laws and why the laws are as they are, so they aren't doing much better. Besides, theists can explain why the universe exhibits regularity, regardless of their theory of lawhood.
Another interesting point here is that Humean supervenience will require that there be facts (in the present) about what human beings will do in the future (otherwise laws that quantified over all time would lack truth values). This has its own problems for free will. On the whole, however, a very interesting (and, in my view, quite possible correct) idea.
D. M. Armstrong is the best known proponent of a currently quite popular understanding of natural laws. Laws so understood are, as a result, called Armstrong-Laws, or A-Laws for short. These are distinguished from L-Laws, named for David Lewis. L-laws are identical to regularities in events (but not all regularities are laws). Unlike L-Laws, A-Laws are actual metaphysical entities, which exist independently of their instances. That is, according to this theory, the Law of Universal Gravitation is a thing out there in the universe (not in the mind) which actually makes massive objects move toward one another. The attraction (no pun intended) of A-Laws is that they seem to explain why there should be regularity in the world at all, whereas L-Laws simply state the regularities. Armstrong-type theories posit that there is actually something out there which makes the regularities occur. Now, despite Armstrong's naturalist/physicalist claims, this thing must be transcendent and non-physical (not any more so than Armstrong's "states of affairs," but that's another story).
Philosophers usually talk for simplicity about laws of the form "all Fs are Gs" or "all Fs are followed by Gs," but, of course, the real laws that physicists talk about are not like this at all. The real laws are things like F=ma or K=(1/2)mv^2. (Note that I say the real laws are like this - we don't actually live in a Newtonian universe, so these are not examples of actual natural laws, or at least not fundamental ones - macrophysics is usually considered by philosophers to be one of the "special sciences" like geology or psychology, and these are supposed to follow from the true theory of microphysics, whatever that might be.) It is not clear to me (perhaps because I haven't read the positive part of Armstrong's book What is a Law of Nature? - I've only read the critique of "naive regularity theory" so far) how Armstrong's specific claim (not held by all Armstrong-type theories) that laws are relations between universals is supposed to deal with these sorts of laws, which aren't actually about Fs being Gs. As a result, there doesn't seem to be any reason why we should posit multiple laws of nature: why not just conjoin them?
If we do this, we've got a transcendent, non-physical entity responsible for the orderliness and regularity of the world, "and this all men call God." Hmm...
Of course, if you are concerned about confusing this entity which, for all we know, is impersonal with personal conceptions of God or with some religious theory, you might not want to give it that name, but at the very least you've got the Heraclitean logos (not to be confused with the Johannine logos), a fundamental ordering principle of the universe, and this certainly seems to be a god-like thing. Of course, if we were actually positing God in a more traditional sense, he is supposed to be a necessary being and to create freely, so this would explain why the laws are as they are, but, whatever the case, we seem to have here at the very least something that might be reasonably described as an impersonal, disinterested (small-g) god, and maybe we've got a good deal more than that.
(For the record, I believe in a sort of regularity theory instead, despite believing that God wills at every moment that the laws hold; this is because I believe that laws are strictly identical with true law statements, where these statements are purely descriptive in nature, or something like that.)
A thought occurred to me just now as I was reading the end of Sydney Shoemaker's "Causality and Properties" and thinking, as usual, of a Berkeleian response. What, we ask, are the truth-conditions or truth-makers for statements about natural laws and causality? Shoemaker has a story about properties being defined in terms of dispositions to act a certain way in the presence of certain other properties, and he thinks we can flesh out these statements in this way. For Berkeley, of course, the properties of physical objects can have no causal efficacy. Instead, Berkeley takes these statements to be simple counter-factuals: because of a constant conjunction between perceptions of pens being dropped and perceptions of pens falling, we conclude that when pens are dropped they fall, and therefore make statements like "if I dropped this pen it would fall." Simple, right? Wrong...
According to Berkeley, let it be remembered, our perceptions are implanted directly in our minds by God, and are a language by which he speaks to us. This means that the statement above should be equivalent to the statement "if I were to form the volition to drop this pen, God would respond by implanting in my mind perceptions of the pen falling." This is a counterfactual of freedom! This seems to mean that, in order for us to have knowledge of causal statements and natural laws, we need to have middle knowledge about God, which is certainly even more problematic than God having middle knowledge about us!
Can this problem be avoided? I think it can. Recall that Berkeley thinks that our perceptions form a language and, in addition to his many statments (in, for instance, the Third Dialogue) to the effect that natural laws are to be interpreted counterfactually, he also refers in the Principles to Newton's Principia as the best grammar manual of the perceptual language. If this is correct, then we ought to suppose instead that statements about causation and natural laws are statements about grammar.
Will this save us? It seems so. Consider the statement "transitive verbs in English are followed by their direct objects." This is a true statement about grammar. But one might think that this translated into some statement like "if Kenny, a native speaker of English, were to utter a syllable pattern corresponding to an English transitive verb (while speaking English), he would soon after utter a syllable pattern corresponding to an English noun, which he would intend as the direct object of said verb." This is a counterfactual of freedom. However, it seems that the latter sentence might actually be false. That is, from the perspective of free will, etc., there is no reason why I can't utter nonsense instead of following the rules of English grammar. This does not undermine the truth of the grammatical statement above. The same should hold with regard to natural laws and God's freedom. God is perfectly free to utter nonsense, but there are nevertheless rules of the grammar of the perceptual language, and true statements about these rules are true statements about natural laws.
Disaster averted.