One of the central projects of philosophy since the seventeenth century has been the attempt to reconcile our self-image as human beings with the picture of the world emerging from the natural sciences. We understand ourselves as beings with intrinsic moral worth who make free, conscious choices. And we assume that these choices can be morally right or wrong. These are assumptions that would have been shared by many of the pioneers of modern science, such as Galileo, Descartes, Newton, and Boyle. By and large, the scientists of the seventeenth and early eighteenth centuries had no doubts that the traditional humanistic assumptions of consciousness, rationality, free will and moral worth were true, any more than they doubted the existence of God. Descartes made the shocking suggestion that the body is no more than a complex machine, but he argued that thinking and language cannot be accounted for in mechanical terms, and attributed them to a non-material soul that freely chooses how to direct the body. By the end of the eighteenth century, a great deal had changed. The French physicist Laplace, who polished up the rough spots in Newton's mechanics, when asked by Napoleon (then First Consul of the Republic) what place God played in his system, answered "I have no need of that hypothesis." Napoleon did not ask about free will. But the reasoning behind Laplace's reply leads to conclusions just as destructive to the idea of free will. Laplace viewed the laws of nature as a comprehensive deterministic system, one by which a sufficiently powerful mind, supplied with a complete knowledge of the laws of nature and the state of the universe at one time, could derive what its state would be at any subsequent time. Unlike Newton and Descartes, Laplace believed that a law-governed world must also be deterministic, with no room for either miracles or free will. And by Laplace's day, and particularly in post-revolutionary France, such a view was no longer either shocking or uncommon. Free Will and a Law-Governed Universe Since the time of Laplace, the idea that a law-governed universe must also be a deterministic universe has become a fairly common assumption; and as a result, free will and all that depends upon it have often fallen into doubt and disrepute. And chief among the things that seem to depend upon free will is the possibility of moral responsibility. It seems misguided, perhaps even nonsensical, to praise or blame people for doing things they could not help doing. And some have argued, in a similar vein, that one cannot have a duty to do something unless one is actually capable of doing it: in the words of Laplace's German contemporary, the philosopher Immanuel Kant, "'ought' implies 'can'". If this is correct - if ethical notions like duty and responsibility make sense only if there is free will - then determinism would imply that all such ethical talk is literally nonsense. Now, many philosophers who believe in determinism have tried to make the pill easier to swallow by arguing that the notion of "freedom" that is opposed to determinism - what philosophers call libertarian free will (no relation to the political or economic views by the same name) - is not really something we should care so much about, and that the notions of "freedom" that really matter for things like moral responsibility are, in the end, compatible with determinism. This view, called Compatiblism, is widely held by contemporary philosophers, and there have been some truly admirable efforts to make a case for a Compatiblist notion of "freedom" that salvages much of our humanistic self-image. But compatiblism is not my quarry, either here or in Laws, Mind, and Free Will. My claim, rather, is that, if one has a proper understanding of what natural laws are, it turns out that a commitment to the existence of such laws does not imply determinism, and is fully compatible with a commitment to libertarian freedom. Laws and their Philosophical Interpretations What led to the striking discontinuity between the assumptions of the scientists of the seventeenth and early eighteenth centuries and those of the nineteenth and twentieth? The answer is to be found, not so much in developments within science itself, as in a change in how philosophers and scientists came to understand the nature of laws. Descartes, the originator of the modern notion of "laws of nature", thought of them as literally legislated by God, who could then change them, set them aside, or assign some of His creatures a principle of spontaneous choice distinct from those laws. This view was one largely shared by Newton, who did not discuss principles of human action, but regarded miracles as being of great importance, both to mechanics and to theology. Newton's interest in providence and miracles had roots in his theology. (Newton wrote, but never published, a great deal on theology and Biblical interpretation-far more than he wrote about physics, and almost as much as he wrote about alchemy.) But it was also connected to issues in his mechanics. One of Newton's great accomplishments, of course, was his discovery of a universal law of gravitation that could explain why the planets move in the elliptical orbits that Kepler had described. Indeed, Newton's laws provided an elegant proof that a planet should move around the sun in a perfect Keplerian orbit. Yet Newton saw two problems with his own proof. First, while the proof should work perfectly for a two-body system - a sun and a single planet, operating in a vacuum - Newton thought that, in a solar system with several planets, all exerting gravitational force upon one another, these forces should cause the orbits to deviate from perfect ellipses. Yet the data showed that they did not. Second, Newton believed that space was not empty, but consisted of a fine aether - something very diffuse, but still capable of causing friction. If this were the case, it would cause the orbits of the planets to decay, again something not borne out by the observational data. In short, given Newton's laws and assumptions, the actual orbits of the planets were more perfect than they should be. There is evidence from Newton's notes and correspondence that at times he took this to be reason to believe that God must periodically intervene, either through miracles or through general Providence, in order to keep the planets in perfect Keplerian orbits. While Laplace did not have original accomplishments to rival Newton's, he did work out the kinks in Newtonian mechanics, and brought it close to its final polished form. And one of the things he proved was that, contrary to Newton's assumptions, the gravitational interactions of the planets in fact cancel each other out in the long run. Thus, his famous quip, "I have no need of that hypotheses (i.e., God)", may have been a reference to a very specific hypothesis of Newton's: namely, that the only thing that can account for the regularity of planetary orbits is some action by the Almighty. It is debatable whether Laplace was actually an atheist - he attended mass regularly, and was a lifelong member of the Catholic Church. But there seems to be good reason to believe that he was a determinist - one who believed that everything that happens in the world is completely determined by a combination of natural laws and prior conditions. Indeed, Laplace is credited with one of the most eloquent expositions of determinism, in the image of what subsequent generations have come to call "Laplace's Demon". We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. -Pierre Simon Laplace, A Philosophical Essay on Probabilities The basic idea here is straightforward. Suppose there is a being far more intelligent than ourselves - God, or an angel or demon - who knows (a) all of the laws of nature, and (b) the complete state of the world at a given time (say, 5PM Eastern Standard Time on Tuesday). Laplace's claim is that such a being could, from this information, calculate the precise and complete state of the world at any later time (say, 10AM on Friday). And in order for such a calculation to be guaranteed to be accurate, it must also be the case that the combination of the laws of nature and the initial state description determines with absolute certainty all that will follow. There cannot be any anomic (lawless) factors, such as free will or miracles, that could nudge events in some other direction. It is important to stress that the laws Laplace was dealing with were more or less the laws Newton had discovered, such as the inverse square law of gravitation. Newton and Laplace agreed on what the laws were. What they disagreed about was whether a commitment to those laws, or any set of laws, implies determinism. The dispute is therefore not a dispute within science, but rather is a dispute about the philosophical interpretation of science - and, more particularly, of the nature of scientific laws. Our question then - and one of the principal questions I address in Laws, Mind, and Free Will - is this: does a commitment to scientific laws, properly understood, entail a commitment to determinism, and hence a denial of free will? In the two centuries since Laplace, there has been a widespread assumption that the answer to this question is "yes". I, however, think that this conclusion is misguided, and based upon a misunderstanding of the nature of scientific laws. Philosophers of science have produced a number of accounts of the nature of laws. Some of these imply determinism, while others do not. The most influential twentieth-century account of laws did imply determinism, which may account for the widespread assumptions in favor of determinism in our lifetimes. But that account has largely been rejected by contemporary philosophers of science. And on its most important successor theory, a commitment to laws of nature does not imply a commitment to determinism, and hence is compatible with free will. A Digression - Quantum Indeterminacy Of course, one familiar contemporary argument against determinism is based in claims about Quantum Mechanics: namely, that Quantum Mechanics reveals that, at its most fundamental level, the universe is not deterministic, but probabilistic. I say this is a claim about Quantum Mechanics, rather than a claim of Quantum Mechanics, because there are in fact a number of different interpretations of Quantum Mechanics. Some of them, notably the Copenhagen interpretation endorsed by Bohr and Heisenberg, posit that the universe itself is truly random. But there are others, notably the hidden variable view favored by Einstein, that hold that the underlying reality is deterministic, and only appears probabilistic because we do not see the whole picture. So it seems to me that the argument from Quantum Mechanics is less compelling than it at first might appear. Moreover, true randomness does not provide a basis for free will, either. To say that the ultimate causes of my actions are random is not the same thing as to say that they are freely chosen. Indeed, it is not clear that talk of "free choice" makes any more sense in a world of quantum randomness than in a deterministic world. The good news is that even the non-probablistic scientific laws, such as the law of gravitation, do not require a deterministic interpretation, either. And indeed, it is not clear what sense it would make to call them "deterministic". But before I can argue this point, I must first explain why it ever seemed otherwise. The Mainstream View of Laws in 20th Century Philosophy of Science Through much of the twentieth century, the prevailing view of scientific laws in philosophy of science was one developed by proponents of a style of philosophical analysis called Logical Empiricism. Part of the Logical Empiricist project was to interpret scientific claims in the formalism of a quantified predicate logic. First, laws were understood to be universally quantified claims - things with a form like (for every x )(if x is a P, then x is a Q). Second, the x' s in question were understood to be individual material objects, and the Ps and Qs to include such things as the actual behavior of those objects. So, very schematically, the gravitation law might be thought to claim (or at least imply) something like this: (for any two objects x and y with mass)(if the initial relation of x and y at t 1 is R 1, the relation of x and y at a later time t 2 will be R 2). Third, laws were taken to be "materially true" - that is, true in every actual case. This may sound obvious and trivial, but it has the important consequence that any exception to a law-claim also amounts to a falsification of that law-claim. This overall view of natural laws is called the Empiricist account of laws. If the Empiricist account of laws were correct, a commitment to anything like the scientific laws we believe to be true of the world would imply a denial of any morally significant free will. For if it were correct, then anything to which even one law applied would have its behavior determined by that law, and our bodies are made up of material particles to which those laws apply. Of course, if we are (or have) immaterial souls, those would not be governed by physical laws, and hence we might be able to think free thoughts. But we could not put them into action, at least not in the material world, because our bodies would be caught up in the inexorable grip of natural law. As a result, anything we did would be deterministic, and not under our free control. And this is enough to call into serious question whether the can really be such a thing as moral responsibility. So, if you accept the Empiricist account of laws, the road to determinism is both short and straight. And with it comes a denial of free will. It is thus no surprise that, through much of the twentieth century, there was a great deal of concern that our deeply-held humanistic assumptions might prove incompatible with our best understanding of contemporary science. Problems with the Empiricist Account of Laws Now, if one thinks about actual laws, even in physics, one cannot help but be struck by how little they look like the Empiricists' logical reconstructions. What Newton's gravitation law actually states is this: two objects with mass exert a gravitational attraction upon one another proportional to the product of their masses and inversely proportional to the square of the distance between them. Or, as an equation: F = G(m 1 x m 2 )/r 2. ( F is the force exerted, m1 and m2 are the masses of two bodies, r is the distance between them, and G is the gravitational constant.) The inverse square law does not say anything directly about the actual behavior of objects - that is, about their motions - but only about the force they exert upon one another. Nevertheless, this does provide the basis for many calculations and even theorems about motion. Newton, for example, provides an elegant derivation of the elliptical Keplerian orbits of the planets from the inverse square law plus simple assumptions about the inertia of the bodies. But this falls short of the Empiricist's criteria for the truth of laws. If the Empiricist account were correct, then (a) the gravitation law would describe (exactly) how bodies actually behave, and (b) any deviation from this in the actual behavior, however tiny, would mean that the "law" was false. But in fact, nothing ever behaves exactly in a fashion that can be derived from the inverse square law, or any other physical law. And so, if one were to adopt the Empiricist account of laws, all of the laws actually found in the sciences would turn out to be false. To see why this is so, consider a simple experiment. Take two pieces of paper of equal mass. Crumple one tightly into a ball, and fold the other into a paper airplane. Hold them an equal distance from the Earth, and drop them. Of course, they do not fall in equal times, as one would predict from the inverse square law, as interpreted by the Empiricist account as a universal claim about how bodies actually behave. Is this a refutation of Classical Mechanics? No, because what the inverse square law makes claims about is gravitational force, and not the actual motions of bodies. Gravitational force is one factor that contributes to those motions, but it is not the only such factor: things like aerodynamics, mechanical collision, and magnetism play roles as well. Of course, objects fall differently in a vacuum. But remember that on the Empiricist interpretation, even a single exception falsifies the law. And the problem lies, not with the law, but with the Empiricist interpretation. Moreover, almost all physical interactions involve particles with both mass and charge, which are covered by distinct laws, and hence none of these interactions will take place exactly as either law, in isolation, would lead us to predict. Now, this does not add up to a case for indeterminism in Classical Mechanics. But it does two important things. First, it shows that there is something deeply wrong with the Empiricist understanding of laws. And so, if the reason for believing that a commitment to laws implies a commitment to determinism is simply that this would be true on the Empiricist account, then that argument for determinism need not be taken seriously. Second, it shows that laws are a kind of piecemeal affair - what Nancy Cartwright calls a "patchwork of laws". (1) Each law describes one regular possible partial contributor to real-world behavior, and says absolutely nothing about what other contributors there might be. The gravitation law says nothing about whether there is also electromagnetic interaction, or vice-versa, and neither says anything about what else might be on the list of possible causal factors. Moreover, nothing about any of the laws says that all of the other causal factors must also be lawlike. The questions of whether there are probabilistic laws (like those of Quantum Mechanics) or causal factors that are not lawlike at all (like free will and miracles) is left open. An Alternative Conception of Laws The foregoing suggests the basic lineaments of an alternative conception of laws that has a growing following in philosophy of science. This is sometimes called the "causal account of laws". As a point of departure, consider a natural reading of Newton's inverse square law of gravitation. What does this law claim? What it seems to claim is that there is a gravitational force (F, in the equation) that is proportional to the product of the masses of two objects and inversely proportional to the square of the distance between them. This force is one among many factors that will contribute to the actual behavior of the bodies in question. As there are more than two bodies in the universe, there will be additional gravitational forces acting pairwise on bodies. There is also the inertial force that was known to Newton, as well as forces discovered after his time, such as electromagnetism. The gravitation law does not tell us what other factors there may be, and indeed that is part of the genius of such laws: they pick out real and sometimes fundamental causal factors while leaving open the question of what others there may be. While it is natural to characterize law in terms of "forces" in fundamental physics, that characterization may seem a bit strained when we come to the laws of chemistry, much less biology or the human sciences. Philosophers of science have thus been wont to use other, more general, terms to characterize this basic view of laws, such as that laws express "causal powers" or "causal capacities". Or, as I prefer to put it, "potential partial contributers to real-world behavior". We may refer to such views generally as the "causal account" of laws. Free Will and the Causal Account Now, there is a feature of this causal account which is very significant in its implications for free will. And this is the idea that each law (gravitation, electromagnetism, etc.) speaks only to its own domain, and leaves open the question of what other factors there might be that contribute to the real-world behavior of objects. In science, this is crucial in leaving open the question of what additional laws there might be. But if the gravitation law says nothing about what other laws there might be, it also says nothing about what non -lawful factors might exist that could influence real-world behavior. And thus it says nothing about free will (or miracles). And if it says nothing about freedom, pro or con, it is compatible with free will. Of course, another of Newton's great contributions was the idea that we can sum forces. That is, if a body has multiple forces acting upon it - gravitational interactions with one or more bodies, magnetic interactions, inertia, and so on - we can (in principle) combine these through vector algebra to determine what their combined effect upon real-world behavior will be. And one might suppose that this brings determinism back into the picture: even if each law, individually , does not determine real-world behavior, the combination of all lawful interactions does. But this would be a misunderstanding. What really determines the behavior of an object is the combination of all the forces acting upon it. And there is a subtle (and natural) error in assuming that the summation of lawlike forces is the same thing as the summation of all forces. But an error it is. The idea of summation of forces in no way excludes forces that are spontaneous rather than lawful - say, free will or miracles. Nor does the commitment to particular laws, or any set of laws, or even to the proposition that laws {L 1 ,.,L n } are all of the laws that exist, preclude the possibility that there are also non-lawful causal factors, such as free will and miracles. Implications So, where are we now? On the Empiricist interpretation, laws are universal and deterministic, and this would mean that we cannot act freely in the material world. (Though we might be able to think freely without putting it into action if we are immaterial souls.) But the Empiricist interpretation will not work, for reasons having nothing to do with free will. And we should not be bothered by the fact that so grossly erroneous a characterization of laws would imply determinism and the denial of free will. The other interpretation of laws I have sketched here, sometimes called the "causal account", takes laws to express something on the order of causal capacities of objects - or, as I prefer to put it, potential partial causal contributors. But on the causal account, each law is absolutely silent on what other causal factors might exist, and even if we have a complete list of all the causal factors that are lawful, these in no way exclude the possibility of additional factors that are spontaneous, such as free will. (Or-and this would please Newton-miracles.) Does this prove that we really have free will? No. There might be other reasons to think our behavior is determined rather than free. And the fact that free action is compatible with natural laws does not imply that we are free; the natural laws are equally compatible with our actions being fully determined, or, in the case of some laws, random. What it is intended to show is this: If you feel you have reason to believe in free will, but are worried that this belief is incompatible with a belief in natural laws, you can breathe a sigh of relief. On the best sorts of account of the nature of laws we have today in philosophy of science - some version of the causal account - laws are compatible with freedom. *** (1) Nancy Cartwright, "Fundamentalism vs. the Patchwork of Laws," Proceedings of the Aristotelian Society, volume 94, 1994, pp. 279-292.