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Le libre arbitre

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Jean-Baptiste Guillon

Chapitre 7

How the Laws Constrain: Causation, Counterfactuals, and Free Will

Kadri Vihvelin

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1The free will/determinism problem is usually presented as a problem about the compatibility of laws of a certain kind – deterministic – with a special property of human beings: free will. And many people think, sometimes on the basis of argument, sometimes because it just seems obvious to them, that determinism is incompatible with free will. Some say that determinism rules out not just free will but also moral responsibility. Others disagree, claiming that we might be morally responsible even if deterministic laws rule out all alternative possibilities and thus all free will. And so the debate goes, always for very high stakes because free will and moral responsibility matter a great deal to us.

2I want to take a different approach. I think the problem is more general. I think that the free will/determinism problem is, most fundamentally, a problem about the (apparent) conflict between the way things are at a deterministic world and our commonsense beliefs about causation, our causal powers, and the causal powers of ordinary objects like hammers and baseballs. In order to make progress on the free will/determinism problem, we must first understand causation better. To understand causation better, we need to understand the relation between causation, counterfactuals, and the natural laws.

3I think, for reasons I will give later, that we should be surprised by how quick we are to conclude that the truth of determinism means the absence of free will. After all, we already know that we are physical beings in a physical world, subject to the same laws that apply to everything else in the universe. We know that the laws set limits on our abilities, our possibilities, and on our powers of choice and agent-causation. (We don’t think our causal powers somehow transcend the laws or include the power to break or change the laws.) We accept these limits while still believing that we are agents with free will. Yet determinism, when explained in a philosophy or science classroom, tends to make us think we have no free will.

4We need an explanation for why we move so quickly from our cheerful acceptance of the fact that our powers of free will and agency are limited without being eliminated by the physical world and its laws to the conclusion that if these laws turn out to be deterministic then we have no free will at all.

  • 1 In this essay, I use ‘compatibilist’ to refer to someone who believes that the truth of determinism (...)

5I’d better put my cards on the table. I’m a compatibilist.1 I think that we do have free will – and by this I mean, among other things, that we are often in situations where we are able to choose and act otherwise. I think that we have causal powers – of choice and action – that we are free to use or not use as we please. I think, and have argued at length in many places, that there are no good arguments for the dire conclusion that the truth of determinism means the absence of free will and the absence of these causal powers. But I do not deny that incompatibilist intuitions are powerful.

  • 2 Hobart 1934.

6In his classic defense of compatibilism, R.E. Hobart famously said that our incompatibilist intuitions are due to “our natural want of the analytic imagination”.2 He compared our failure to understand how we might be free-willed agents at a deterministic world to the failure of a group of village folk to understand how a steam engine works. Even after they had listened to a long lecture on how the parts fit together to make the engine work, they asked if there was a horse inside.

  • 3 For discussion of this objection, see Velleman 1992.

7There is clearly something to Hobart’s diagnosis. The “Disappearing Agent” objection to the Causal Theory of Action is a classic case of Hobart’s Horse Inside the Engine mistake.3 But I don’t think that this is all there is to it. Determinism is a thesis about the laws. It is not a thesis about causation or causal explanation. And yet a very common response to determinism is to think that it undermines our commonsense beliefs not only about free will but also about causation. Why is this? I will be arguing that the answer lies in an assumption we make about counterfactuals.

  • 4 Lewis 1979.
  • 5 Bennett 1984.

8That’s the first part of this essay. The second part is an argument that we should reject the current dominant theory of counterfactuals – David Lewis’s theory4 – in favor of a theory that holds the laws fixed. I will be recommending the Simple theory once defended by Jonathan Bennett.5 I do not claim that the Simple theory makes it easier to defend compatibilism. I think that compatibilism is true, but I don’t claim it is easy to defend. My claim is that, for reasons that have nothing to do with the free will/determinism problem, we should reject Lewis’s miracle-permitting theory in favor of Bennett’s Simple theory. We should adopt Bennett’s Simple theory because it is a better theory of counterfactuals. But I also think, and will briefly argue, that the Simple theory provides us with the tools we need to think more clearly about the free will/determinism problem.

9I will begin by saying something about our beliefs about our causal powers, and how we acquire these beliefs.

1. How Experience Teaches

10When we try to figure out what to do, from deciding what to have for lunch to the big decisions that shape our lives, we assume that we are choosing from some range of alternatives. And we assume that we are able to choose any of these alternatives and that it’s up to us which one we choose. We believe that we have the power to decide by using a process of conscious rational deliberation, but we also believe that whether we use this power is up to us.

11Even when we aren’t trying to decide what to do, we think of ourselves as agents with the power to do things that make a difference to the world around us. Our powers are limited by the size and shape of our bodies, by our skills and physical capacities, and by the situations in which we find ourselves. And, of course, by the laws of nature and the past. We can’t make bread from stone, part the Red Sea, or run faster than the speed of light. And we can’t do anything to change the past, including those actions we now regret. Nevertheless, within these broad limits, we believe that we have the power to move our bodies in ways that cause some things to happen and prevent other things from happening. By throwing a baseball, you are able to break a window. By catching the ball before it reaches the window, I am able to prevent the window from breaking. We think of these powers of causing and preventing as being under our control in the following way: When we cause or prevent an outcome, we didn’t have to do what we did; what we did was up to us; we were able to do otherwise; doing otherwise was in our power; we had a choice.

12We also believe that we sometimes have control over outcomes that we ourselves do not cause. To continue with the baseball story, suppose that I see you lift the baseball and take aim at the window. I am standing between you and the window, catcher’s mitt in hand, and I have plenty of time to raise my mitt and intercept the ball. But I think it would be fun to watch the window breaking, so I don’t. I don’t cause you to throw the ball, and it doesn’t seem right to say that I cause the window to break. But it does seem right to say that I allowed it to break. And part of what we believe, when we believe this, is that I had the power to do something that would have prevented the window from breaking.

13In addition to our view of ourselves as agents with the power to make a difference – by causing or preventing, doing or allowing – to what happens in the world around us, we also think that we are agents with respect to our future selves. We don’t think of ourselves as being stuck with being the kind of person we are in the way we are stuck with some of our physical attributes. We think that we have at the power to change ourselves, to learn from our experiences, and to improve our character. We think that we have a choice, or at least some choice, about who we turn out to be.

14What these ways of thinking about ourselves as causes have in common is that they assume some difference between what we actually do (how we actually deliberate, choose, act, and cause) and what we are able to do (our powers of deliberation, choice, agency, and causation).

15Our belief that we have powers which are ours to use or squander is not just a belief we have when we occupy the standpoint of first person deliberation. It’s a belief we have when we look back and judge that we made a wrong or foolish choice or missed a great opportunity. And it’s a belief that we have about others.

16These beliefs – let’s call them beliefs about our powers of agent-causation – matter to us. Very different views of life have in common the idea that we live a good life by making the most of what has been given to us – our genetic endowment, the family we were born into, our talents, opportunities, and the chances that come our way in life. We admire those who have done much with little and we criticize those who have wasted great native talents and frittered away their abundant opportunities.

  • 6 Gopnik, Meltzoff, and Kuhl 1990, Chapter 3, “What Children Learn about Things”, especially “Making (...)

17How do we acquire these beliefs about our powers? Here's my small, not very controversial, conjecture: We acquire these beliefs at the same time, and in the same way, that we acquire our beliefs about causation more generally.6 We begin, as babies and young children, by learning that we are able to control the movements of our bodies and to use them to manipulate nearby objects and to thereby cause changes in these objects and in our environment. A baby uses her hands to pick up a rattle and discovers that when she shakes the rattle, it makes a certain kind of noise. She moves her hands a certain way, the noise starts; she stops moving them that way, the noise stops. She shakes her teddy bear; no noise. She squeezes the teddy bear; a different kind of noise. And the baby thereby learns both that the teddy bear and the rattle make these kinds of sounds when manipulated a certain way and that she is able to produce these sounds by manipulating them in these ways. By experimenting in these ways, we gradually learn the truth of counterfactuals of the following kind: "If I had not moved my body like that, that object (that rattle, that teddy bear) would not have done that.”

  • 7 What I have just argued should be understood as an empirical claim about how we in fact (typically) (...)

18As we learn more about the causal powers of the particular objects around us and, at the same time, about our own causal powers, we acquire beliefs in more counterfactuals, and we progress from beliefs about particular objects to counterfactual generalizations about similar objects. We acquire this counterfactual knowledge not only by noticing which manipulations produce changes in which kinds of objects, but also by noticing how objects of certain kinds persist unchanged, or change on their own, in the absence of our interventions. We learn that scissors are good at cutting paper, not so good at cutting cloth or wood. We learn that balls tend to roll down sloped surfaces unless blocked by some other object. And so on.7

19As our ability to predict the characteristic behaviors of objects increases, we acquire the ability to prevent things from happening. We see a ball rolling down a hill; we put our foot in front of it, preventing it from reaching the bottom. We see a plate teetering on a counter, and grab it before it falls and breaks. An older child might realize that a younger child is in danger, and reach out and grab the child before she falls or touches something sharp or hot. And once we understand what it is to prevent something from happening – that is, once we understand how to anticipate an outcome that would have happened, had we not intervened – we can also understand what it is to allow an outcome. For to allow an outcome is to fail to prevent some outcome that we could have prevented. More specifically, when we allow an outcome, there was some way of moving our bodies such that we were able, then and there, to move our body that way, and had we done so, the outcome would not have occurred.

  • 8 In Vihvelin and Tomkow 2005, we offer an account. For some further thoughts on the do/allow distinc (...)

20The do/allow distinction is thought to be a philosophically problematic one, and I do not claim here to have given a philosophical account of it.8 My claim is only that our ordinary talk about what people do and cause appears to be committed to such a distinction, and that our ordinary beliefs about what people allow are tied to beliefs about the outcomes they could have prevented, and that this 'could' is the 'could' of a power of agent-causation.

21I think that we apply the same distinction when we think about our powers with respect to our future selves. We speak of people overcoming adversity and a terrible childhood, and making their own character by "sheer force of will" (and a bit of luck). But we also speak of people who let their characters deteriorate and allow themselves to fall into bad habits.

  • 9 Chisholm 1964.
  • 10 See Vihvelin 2013 for argument that the possession of these agential powers is compatible with dete (...)

22To sum up: I have described our commonsense beliefs about the ways in which we are actual and potential causes of a wide variety of events and states of affairs. The most interesting metaphysical commitment of these beliefs is that we have, somehow or other, causal powers that persist during times that we are not exercising them. This belief is, I have argued, a highly robust one, and one that is embedded in our ordinary talk of allowing various kinds of things to happen – undesirable consequences, our own actions, the evolution of our future selves. But it is also not articulated, in crucial respects, in the way that commonsense beliefs tend to be. Nothing that I have said supports the claim that commonsense has a metaphysical view about the nature of these powers or about what the laws must be like in order for us to have these powers. Nothing that I have said supports the claim, famously made by Roderick Chisholm,9 that the powers that I’m calling our ‘powers of agent-causation’ are like the power “which some would attribute only to God: each of us, when we act, is a prime mover unmoved”. So far as commonsense is concerned, it might be that our causal powers require determinism or indeterminism or are compatible with both.10

2. Determinism and the Three Stages of Denial

23And yet when we learn what the thesis of determinism says, and are asked to take seriously the thought that science might tell us that determinism is true, we respond with horror and what I call the three stages of denial.

  • 11 van Inwagen 1983, Beebee and Mele 2002, Beebee 2011.
  • 12 Lewis 1979, Earman 1986.
  • 13 Vihvelin and Tomkow 2016.
  • 14 For more on determinism, and for why determinism should not be confused with various claims about c (...)

24Determinism is defined in the literature in one of two ways. The Entailment definition says that determinism is the thesis that for every time t, there is some proposition S about the state of the world at t which, together with some proposition L about the laws of nature, entails every true proposition about the state of the world at every other time.11 The Modal definition says that determinism is the thesis that, for any two worlds w1 and w2 that satisfy the same set of laws L as our world, and for every time t, if w1 and w2 are alike at t, they are alike at all other times; if w1 and w2 are different at t, they are different at all other times.12 The Modal definition is stronger; if a possible world is deterministic according to the Modal definition, then it is also deterministic according to the Entailment definition, but not vice versa.13 But it doesn’t matter which definition is used, so long as it is clearly explained.14

25The first stage of denial is the Incredulous Stare: Determinism can’t be true; it literally makes no sense. The second stage is Misinterpretation and Epiphenomenalism: Determinism is understood as almost-determinism: all events are governed by deterministic laws except for our choices. If almost-determinism were true, we would still have free will but no freedom of action. We would still be able to deliberate and make choices, but none of our choices would make any causal difference, not even to the movement of our own bodies. The third stage is Fatalism: Everything that happens – including our own thoughts, choices, and efforts – is necessary; everything that doesn’t happen is impossible. We have no free will and no causal power. It isn’t really us – or for that matter, horses or steam engines or baseballs – that does the causing. It’s “just the laws making everything happen”.

26I’m not making this up. I’ve been teaching the free will/determinism problem in an introductory semester-long class to undergraduates for almost twenty years. It took me awhile to recognize it, but I am now confident that I am correctly reporting a common reaction.

27The horror and the shock come in the move from a claim I call the No Exception thesis to either the Entailment or the Modal definitions of determinism. The No Exception thesis says that we are no exception to the laws that govern everything else in the universe: we are free to do only those things permitted by the laws; everything we do, including the things we do with our minds/brains, falls within the scope of the laws. The No Exception thesis does not provoke any of the three stages of denial. It is the explanation of the difference between a deterministic and non-deterministic system of laws, and, especially, the difference between a deterministic and non-deterministic world, that triggers the panic.

28My question, again, is: Why this response?

29Some readers might not be persuaded that there is anything problematic because they already think that some more sophisticated version of the third stage is the correct response So I will say a bit about why I think this conclusion is not warranted.

3. How the Laws Constrain

30We begin our philosophical theorizing with some commonsense data, which we ignore at our peril. Here is one datum about the laws of nature, which any adequate theory of laws must accommodate, somehow or other.

31The laws constrain us – and everything else in the universe – in a substantive way. There are some things we are not able to do because of the laws. Knowing what the laws are gives us useful, non-trivial information about what we are able to do. This is distinct from two other kinds of constraints – the constraints of logic, broadly understood, and the constraints that distinguish individuals from one another.

32It is logically impossible to: square the circle, stay home all day while also leaving the house that day, bring it about that there are exactly 10 people in a certain room at a certain time and also fewer than 8 people in that room at that time. We are not able to do or cause any of these things. If we tried, we would fail, no matter how hard we tried, no matter how many times we tried, no matter how ingenious our efforts were. Nor would we be able to do something logically impossible if the laws of nature were (somehow) different; our inability is due to logic (broadly understood), not the laws.

33It isn't logically impossible for me to speak Chinese, walk a tight-rope without falling more or less immediately, or run a mile in less than five minutes. Nor do the laws of nature rule this out, for the world is filled with Chinese speakers, tight-rope walkers, and fast runners. And I might even acquire these abilities myself, some day. But I'm nevertheless not able to do these things now. If I tried, I would fail, and my failure wouldn't be a mere fluke or something we might write off as bad luck. I would fail no matter how hard I try, or how many times I try. I would fail because I don't, given the way I am now, have what it takes to do any of these things. Given the way I am now, the laws preclude my doing any of these things.

34It isn't logically impossible for me to accelerate to a speed faster than the speed of light, but the laws say that no one – and nothing – does. And because of this no human being is able to win a race with a light-beam, no matter what. It makes no difference how good a runner you are, how long you train, or how hard you try. Your failure is actually and counterfactually guaranteed, by the laws. There are possible worlds where the laws of physics are different, and even different enough to permit faster than light acceleration. And there may be possible worlds where you – or your counterpart – is able to run faster than the speed of light. But the laws that govern the actual universe – our laws – dictate that you will never acquire this ability. Nor are you able to acquire this ability. There is nothing that you are now able to do – in the way that you are now able to take a Chinese course, join a circus class, or start running every day – such that, if you did it long enough, and seriously enough, you would eventually acquire the ability to run faster than the speed of light.

  • 15 Swartz 1986, Beebee and Mele 2002.

35It is sometimes said that if Hume is right about the laws, then the laws do not impose any constraints on what we are able to do because the laws are mere "constant conjunctions" or global patterns of events. By acting in certain ways we (and horses, steam engines, and billiard balls) make it the case that the laws are what they are, rather than the other way around. That is, the laws don't "dictate" or “govern" or in any way constrain our behavior, and we are free to do whatever we like, whenever we like.15

  • 16 van Inwagen 1983.
  • 17 Lewis 1973.
  • 18 Lewis 1981.

36This is a mistake. A Humean need not take issue with van Inwagen's example of the bureaucrat who orders an engineer to build a spaceship capable of travelling faster than the speed of light. The engineer explains that it's a law of nature that nothing goes faster than light. The bureaucrat concedes that this presents a problem but counsels perseverance: "if you work hard, and are very clever, you'll find some way to go faster than light, even though it's a law of nature that nothing does."16 Nor does David Lewis, the most prominent contemporary defender of a Humean account of lawhood – the "Best System" account17 – respond to van Inwagen’s Consequence argument by explaining that the argument is guilty of some kind of mistake about the nature of the laws.18

  • 19 I’m not claiming that every Humean theory of laws satisfies this (and other) conditions of adequacy (...)

37Any adequate account of laws must draw a distinction between the history of particular fact at a world and the laws of that world.19 For instance, it may be true that no one ever has or ever will read all of the Oxford English Dictionary aloud. But this proposition, even if true, is not a law. And any adequate account of laws must be able to make sense of the idea that worlds with different histories of particular fact share the same laws. And that's enough to provide us with the resources for saying the things we want to say about how the laws limit our causal powers.

38We can define a set of propositions L, such that L is the set consisting of all and only the laws of our world, and we can define a set of worlds w, such that w includes all and only the worlds where all and only the members of L are the laws. Call the members of w the 'physically possible worlds' (relative to our world). Given this distinction between what actually happens (the total history of events at our world), and what is physically possible (the total history of events at some physically possible world), we can define a physically possible event or sequence of events E as follows: E is physically possible iff there is some physically possible world where E occurs. And we can define a physically impossible event or sequence of events as follows: E is physically impossible just in case there is no physically possible world where E occurs.

39With this in place, we can now understand how the laws constrain.

40Nothing in the universe, including us, has the ability (or power, capacity, capability, disposition, and so on) to do or cause any event or sequence of events that is physically impossible.

41So, for instance, suppose that it is true that no one ever has, or ever will, read all of the Oxford English Dictionary aloud. But since this isn't a law there are physically possible worlds where someone succeeds in accomplishing this apparently pointless task. It doesn't follow, of course, that any actual human being has the ability to read all of the Oxford English Dictionary aloud. But if we lack this ability, it is not because of the laws. By contrast, it is both true and a law that nothing accelerates to a speed greater than the speed of light, so there is no physically possible world where any human being runs faster than light. And every human being lacks this ability, and lacks it because of the laws.

42What I have just said should be uncontroversial. You should agree regardless of what you believe about the nature of laws and regardless of your view concerning the free will/determinism problem. You should agree that the laws impose substantive, non-trivial limits on what we are able to do regardless of whether you are a compatibilist or an incompatibilist.

43But there are limits to how the laws constrain. The laws do not dictate all the details of the initial conditions of the universe, nor do they dictate all the details of how the world must be at any given time. This is so even at a deterministic world. If we claim that a person at a deterministic world has the ability, at a particular time, to refrain from doing what she actually does by doing something else instead, we do not thereby contradict the uncontroversial claim, described above, about how the laws constrain. The incompatibilist needs an argument for the claim that at every deterministic world there is an additional constraint, and that this additional constraint robs us of the free will we would otherwise have, rendering us always unable to do otherwise.

  • 20 van Inwagen 1983.
  • 21 Vihvelin 2013.

44There are, of course, such arguments, most notably the Consequence argument.20 I think, and have argued, that these arguments all fail.21 But that is not the question that is my present concern. In my experience, the uninitiated – my students – don’t need to be given an argument for incompatibilism. Once they understand what the thesis of determinism says – and it does take them awhile to grasp that – they are already incompatibilists, of a particularly extreme variety.

45My question, again, is, why do they respond this way? Why is compatibilism a belief that has to be acquired, by hard work? Shouldn’t the truth be easier to believe? And even if I am wrong, and the philosophical truth of the matter is that free will is incompatible with determinism, why do so many people respond to the thesis of determinism in the way that they do? Why do they think that the truth of determinism would mean that our commonsense beliefs about causation are all false?

4. Counterfactuals

46One natural thought is that our resistance to determinism can be explained by our experience of making choices. When we try to decide what to do, it seems to us that we are able to choose and act in any of two or more incompatible ways, given the entire state of the world at the time just before we decide.

  • 22 Holton 2009.

47But this is not something that experience can tell us; at best experience can tell us that we are able to choose either of two or more incompatible courses of action given our current beliefs, desires, and intentions (and perhaps some other psychological facts about us). Richard Holton has suggested that our experience of choice might give rise to the belief that determinism is false by way of an illicit inductive leap from the belief that we can do otherwise, given our beliefs, desires, and intentions, to the belief that we can do otherwise, given the entire state of the world just before we choose.22 This may be true. But it doesn’t explain what I’m trying to explain. I’m not trying to explain why we believe that determinism is false (so far as our choices are concerned). I’m trying to explain why we think that it must be false in order for us to have free will and the causal powers that we have taken for granted for most of our lives.

48I think that the explanation lies in certain counterfactuals that we assert, entertain, and believe true in situations that I call choice situations. Choice situations may be, but need not be, situations in which we have the experience of making a choice.

49We have the experience of making a choice in situations where we don’t immediately know what to do; situations in which we need to make up our mind by considering our options and choosing the one we think best, or right, or which most appeals. You are standing before the counter at the ice-cream parlor, gazing at the 25 different flavors, trying to decide which one you want. You are at a fork in the road, faced with a choice between the scenic winding coastal route and the boring but speedy freeway. You are faced with a more difficult decision, between competing job offers, or houses.

50But choice situations also include situations in which we don't stop to think, either because the situation calls for a quick response or because we already know what to do. We learned, long ago, that touching a hot pot without oven mitts is a bad idea, that stopping at red lights is a good idea, and so on. I count these as choice situations because even if we did not act by first considering the alternatives and making a decision, it seems that we could have done so.

51Some more examples: You are driving your car when a squirrel suddenly runs in the path of the car; to avoid hitting the squirrel, you could apply your brakes, swerve, or keep driving in the hope that the car will pass over the squirrel without hitting it. You have less than a second to decide. You keep driving. You walk into a room just in time to see a child reaching for the knife that has been left on a counter. Without pausing to think, you run over to stop the child.

  • 23 For an excellent account, by three leading psychologists, of some recent research about the “scient (...)

52Choice situations are ubiquitous. We’ve been in choice situations our entire lives, from the time we were babies, performing simple versions of scientific experiments in our attempts to find out how the world works.23 We learned about causation by being in choice situations.

53What all choice situations have in common is that we believe that certain kinds of counterfactuals are true. When we deliberate, even briefly, for the purpose of deciding whether to do A or to do B, we begin our decision-making by asking certain kinds of counterfactual questions: What would happen if I did A? What would happen if I did B? More generally, what would the world be like if I did A? What would the world be like if I did B? We are good at entertaining and evaluating these kinds of counterfactuals, and we think of them as objective in certain kinds of ways. We use them as the basis of our advice to others, and as the basis for some of our interventions with others. (We run over to stop the child from grabbing the knife because we believe that if she got hold of it, she would probably hurt herself). We use them to criticize ourselves, and others, for making foolish decisions and poor choices.

54Nor is our knowledge of counterfactuals limited to counterfactuals about the choices of agents. As I pointed out earlier, we acquire knowledge of our own causal powers at the same time, and in the same way, as we acquire knowledge of the causal powers of the things around us – by acquiring knowledge of certain kinds of counterfactuals.

  • 24 Kim and Maslen 2006.

55Being good at counterfactual thinking is not the same as having a theory of counterfactuals, but if any theory of counterfactuals could be attributed to common sense, it might be the view that counterfactuals are like short stories.24 We evaluate the counterfactual if A had been the case, then C would have been the case by imagining a situation as much like the actual situation as possible given the truth of A, and we use our knowledge of how the world works, as well as our knowledge of particular facts, to figure out whether C would also be true. We don’t worry how A got to be true; we just imagine that it is. Thinking this way works just fine so long as we are not thinking in terms of determinism or entire possible worlds, as opposed to small parts of worlds (the child and the knife, the squirrel and the car).

56But in order to understand determinism, we must first understand the philosophical concept of a possible world, and we must understand the difference between a deterministic world and a non-deterministic world. And once we understand this, we realize that our counterfactual short stories must be embedded within entire possible worlds. And then we put two and two together and conclude that we have been counterfactually reasoning as if determinism is false. We have been assuming that our counterfactual short story can be “added” to the actual past and the actual laws. But this is possible only if the actual past and laws permit this counterfactual divergence from past history; that is, it is possible only if the actual world is not deterministic.

  • 25 I will be arguing later that there is no actual conflict and that our commonsense beliefs about cou (...)

57My claim is that our strong resistance to determinism– what I’ve been calling ‘the three stages of denial’ – is due to the conflict between determinism and this assumption about counterfactuals. Our common sense knowledge of a significant set of counterfactuals seems to commit us to a claim about counterfactuals that entails the falsity of determinism.25 This claim – let’s call it Fixed Past and Laws – says that the counterfactual if A, it would be that C is nonvacuously true only if the truth of A is compatible with the actual laws and the actual past prior to A.

58If determinism is true, there are no possible worlds that share our laws and our past. But we know that we make and criticize choices – our own and those of others – by using counterfactuals that we evaluate by holding fixed our knowledge of past facts as well as the laws, and we can’t imagine doing it any other way. More generally, we evaluate counterfactuals about events like the child’s dropping the knife or the squirrel’s sudden dash onto the road by holding fixed the laws and the past, and we can’t think of any other way to do it. So our first response to determinism is to deny that it could possibly be true. This is a perfect instance of Hobart’s “natural want of the analytic imagination”.

  • 26 Holbach 1770. “Man in running over…the route which nature has marked out for him, resembles a swimm (...)

59Our second response – and first step in the direction of incompatibilism – is to understand determinism as ‘almost-determinism’, making an exception for our own choices. This is a step backward from our earlier endorsement of No Exception, but it is a natural reaction. For experience tells us that we choose, and we choose between alternative actions A and B by evaluating counterfactuals about what would happen if we chose A, and what would happen if we chose B. So there must, it seems, be possible worlds with our past and our laws where we choose A and there must also be possible worlds with our past and laws where we choose B. But this doesn’t help. We now reason as follows: “Okay, so determinism doesn’t mean I have no free will. But determinism means that my choices never make any difference to the physical world. For if I chose otherwise, the laws and the past, including the entire state of my brain and body, would still be the same. And if my brain doesn’t tell my body to move differently, it won’t move differently.” And thus the second stage of denial is an epiphenomenal version of dualism. Our choices have no sufficient physical causes but they also have no physical effects.26

60We move to the third stage when we come to understand that determinism is a thesis without any exceptions; if determinism is true, then everything we do, including every decision and choice we make, is constituted or realized by physical events and processes that instantiate strict deterministic laws. Our philosophy professor will try to explain that this doesn’t preclude our decisions and choices from being causes as well as effects, and will try to explain some version of compatibilism. But we will remain dismayed, for it will now seem that there are no non-vacuous counterfactuals. And it will seem that we cannot deliberate in the way that we are accustomed to doing. And while we might nod and agree that, of course, we still make choices, and our choices still cause our bodies to move in the ways appropriate to action, this won’t mean what it used to mean. For causes are not what we thought they were, for they are no longer associated with non-vacuously true counterfactuals. We don’t have the causal powers we thought we had; nor do horses, steam engines, or baseballs have the causal powers we thought they had. The causal power in the universe is located in the laws and the remote past, not in us. We will reluctantly conclude that determinism is true and free will is an illusion.

61This is the end of the free will part of my paper. I turn now to counterfactuals.

5. Determinism and Counterfactuals

62Suppose that determinism is true. We still need a theory of counterfactuals. Even if we decide that the truth of determinism means the absence of free will, we still need to make decisions, and we make decisions by evaluating counterfactuals. And we still need to make causal judgments about a wide range of events not limited to the actions of human agents. And causal judgments typically go hand in hand with counterfactuals.

  • 27 Loewer 1996.

63It remains an open scientific question whether determinism is true.27 And even if determinism turned out to be false in the way that libertarians hope, we cannot base our counterfactual thinking on this assumption: the counterfactuals that we believe true are not limited to counterfactuals about the choices of agents with free will. We need a theory of counterfactuals that is general enough to work at deterministic as well as non-deterministic worlds and general enough to apply to events like heart attacks, earthquakes, and plane crashes as well as the free choices of agents.

64If determinism is true and A is any proposition that is actually false, there are no possible worlds with our laws and past history prior to A where A is true. We must give up at least one of:

Fixed Laws: If A, the laws would still be exactly the same as the actual laws.

Fixed Past: If A, the past prior to A would still have been exactly the same as the actual past.

  • 28 Lewis 1973, Lewis 1973B, Lewis 1979.

65Until David Lewis came along28, everyone who thought about counterfactuals assumed that we must retain Fixed Laws. The reigning assumption, in those days before possible worlds semantics, was that the truth-conditions of a counterfactual are given by the existence of some valid deductive argument: the counterfactual Antecedent > Consequent is true iff the consequent logically follows from the antecedent, the laws, and some true statements about the particular facts. But it was well-known that there was a problem. If all true statements are eligible to be included, the premise set is inconsistent. For the true statements include the negation of the antecedent and the logical consequences of the negation of the antecedent. But restricting the set of eligible premises to exclude inconsistent premise sets does not suffice to yield the right counterfactual results. Consider any dry well-made, well-placed match of which it’s true, on some particular occasion, that if the match had been struck, it would have lit. The statement that the match lights follows from a consistent premise set that includes the antecedent, the laws, and some truths about the match – that the match is dry, well-made, in the presence of oxygen, etc. So far so good. But the statement that the match does not light also follows from a consistent premise set that includes the antecedent, the laws, and some truths about the match – that the temperature of the match never rises above room temperature. So the account also tells us that if the match had been struck, it would not have lit. We need some way of restricting the set of true statements that are eligible to be included in the premise set so that the fact that the match is dry (well-made, etc.) is eligible but the fact that the match stays at room temperature is not eligible.

66Goodman, who is credited with discovering the “problem of cotenability”, was pessimistic about solving it:

  • 29 Goodman 1947.

In order to determine the truth of a given counterfactual it seems we have to determine, among other things, whether there is a suitable S that is cotenable with A… But in order to determine whether or not a given S is cotenable with A, we have to determine whether the counterfactual ‘If A were true, then S would not be true” is itself true…Thus we find ourselves involved in an infinite regress or a circle; for cotenability is defined in terms of counterfactuals, yet the meaning of counterfactuals is defined in terms of cotenability. In other words, to establish the truth of any counterfactual, it seems that we first have to determine the truth of another. If so, we can never explain a counterfactual except in terms of others, so that the problem of counterfactuals must remain unsolved.29

  • 30 Stalnaker 1968 and 1984; Lewis, ibid.
  • 31 Collins, Hall, and Paul, 2004.

67The first step in solving the problem of cotenability came with the possible worlds semantics for counterfactuals developed independently by Lewis and Stalnaker.30 The problem of providing a formula for specifying the set S of cotenable premises is replaced by the problem of specifying the set W of worlds relevant for the evaluation of the counterfactual. If determinism is true, the set W is limited to worlds with our laws and a different past (prior to the time of the antecedent) or worlds with our past and different laws; we must choose between keeping Fixed Laws and keeping Fixed Past. This gives us no reason to reject Goodman’s assumption that the laws (except for the special case of contra-legals) are always cotenable with the antecedent. But the philosophical orthodoxy has changed since Goodman wrote. David Lewis has persuaded many, and especially philosophers who work on causation and counterfactuals, that it is Fixed Laws that must go. It is now almost a platitude in certain circles that the correct way to evaluate counterfactuals, at least in so-called “standard contexts”, is by not permitting “backtracking” counterfactuals31; we must reason counterfactually in a way that preserves the past (or at least most of the past).

  • 32 Vihvelin 2000, and 2013.

68For a long time I was convinced by Lewis’s theory (for reasons having to do with counterfactuals and causation, not free will) and I defended Lewis against various charges.32 I now think this a mistake. There is a better theory of counterfactuals – better both in terms of what it tells us about counterfactuals and also better in terms of what it tells us about the relation between causes, counterfactuals, and laws. In order to explain why I think this, I must first explain how it came to be that Lewis persuaded so many of us that the closest counterfactual worlds are worlds where the occurrence of a small “divergence miracle” means that the laws are different from our laws.

6. How Lewis Persuaded Us: Counterfactual Knowledge and Time’s Arrow

  • 33 Stalnaker 1968 and 1984.
  • 34 Lewis 1973.

69The starting point for thinking more rigorously about counterfactuals is the possible worlds semantics and logic developed independently by Stalnaker33 and Lewis34. The basic idea is simple and maps onto our ordinary way of thinking about counterfactuals. When we try to decide what would happen if, for instance, I dropped my pen (or a bird suddenly flew into the room or the fire alarm went off), we do so by imagining a situation very like the actual situation, but which is just different enough so that the antecedent is true. In possible worlds language, this comes out as:

  • 35 This is rough, since Lewis rejects the Limit assumption – that there is a closest set of worlds. Hi (...)

A > C is true iff C is true at the A-worlds most similar to the actual world.35

70Different theories of counterfactuals may be understood as offering different accounts of the relevant notion of similarity (or ‘closeness’, as it is sometimes called); these are, in effect, rival solutions to Goodman’s problem of cotenability.

71The simplest theory – the one that seems closest to our ordinary counterfactual thinking – says that the most similar A-worlds are worlds that are exactly like ours with respect to the past (prior to A) and the laws. But, as we saw, that won’t work. Even if we live at the kind of world that libertarians think is ours, there will be non-vacuously true counterfactuals (like the one about the bird flying into the room, or the fire alarm going off) and we have no reason to suppose that the antecedent of each of these counterfactuals is an event that lacks a deterministic cause.

  • 36 Ibid.
  • 37 Ibid, p. 92. “Somehow we do have a familiar notion of comparative overall similarity, even of compa (...)
  • 38 Ibid, p. 75. By ‘miracle’, Lewis meant an event that is miraculous by the standards of our laws.

72In the book in which he introduced his logic for counterfactuals,36 Lewis told us that we are to use our ordinary notion of comparative overall similarity, the one that we use when we say things like “Seattle is more like San Francisco than it is like Los Angeles.”37 And he said that while similarity with respect to the laws is important, so is similarity with respect to matters of particular fact or true generalizations that are not laws. This opened the door, for the first time, to the rejection of Fixed Laws and to the idea that a “small localized inconspicuous miracle” might mark the transition from a past that matches the actual past to a counterfactually different future.38 But Lewis left the details unspecified.

  • 39 Fine 1975.

73Kit Fine famously replied with the counterfactual if Nixon had pressed the button, there would have been a nuclear holocaust.39 Since any world with a nuclear holocaust is vastly different from the world we fondly hope is our own, Lewis’s similarity metric appears to tell us that this counterfactual is false. But it is easy to stipulate that the facts are such that the counterfactual is true.

  • 40 Lewis 1979.
  • 41 I was among those convinced and I even used Lewis’s theory to defend a bold kind of compatibilism I (...)
  • 42 Though not entirely. The groundwork was laid in Lewis 1973, especially in Chapter 3 (“Comparisons”) (...)

74Lewis responded to Fine’s objection with his 1979 “Counterfactual Dependence and Time’s Arrow”.40 The arguments that convinced many of us41 to give up Fixed Laws are mostly found there.42

75Lewis had two arguments – his ambitious and complicated time’s arrow argument and an epistemic argument.

76The epistemic argument was that if we don’t hold all, or at least most of the past fixed (at the expense of the laws, if determinism is true), we will have no idea how to evaluate any counterfactuals.

  • 43 Goodman 1947.

77For instance, consider Goodman’s example of a counterfactual truth we seem to know.43 I am holding a dry well-made match in this room – a room with oxygen, no wind, and conditions favorable in every way. I don’t strike the match. It seems true that if I had struck it, it would have lit. But if we evaluate this counterfactual by holding the laws rather than the past fixed, how can we say that it would light? After all, if determinism is true, then every world with our laws is a world where the past is different all the way back to the Big Bang. At some of these worlds the struck match lights, but at others it fails to light because it is wet or defective or not surrounded by oxygen or something else goes wrong. On what basis do we say that some of these worlds are more similar to our world than others? So it seems that the most we are entitled to conclude is that if I had struck the match it might have lit and it might not have lit.

  • 44 Bennett 1984, Horwich 1987, Goggans 1992, Price 1992, Vihvelin 1995, Elga 2000, Mackie 2014, Tomkow (...)
  • 45 Bennett 2003, Chapter 13. For a close examination and critique of Bennett’s rejection of his earlie (...)

78The key claim of the time’s arrow argument was that the counterfactuals that we ordinarily use are temporally asymmetric in a way that is not the product of stipulation but is in response to a pervasive but contingent fact about the world. Even though every detail of Lewis’s argument for this claim is vulnerable to criticism (and has been criticized44), the claim itself was striking and it seemed that there was something right about it. It was the combination of the purely negative epistemic argument against Fixed Law theories with the complex and ambitious time’s arrow argument that did the trick. Even Bennett eventually gave up his Simple theory in favor of a theory that permits counterfactual miracles.45

79The time’s arrow argument had many moving parts.

80First, Lewis claimed that counterfactuals are temporally asymmetric.

If the present were different, the future would be different; and there are counterfactual conditionals, many of them as unquestionably true as counterfactuals ever get, that tell us a good deal about how the future would be different if the present were different in various ways…

Not so in reverse. Seldom, if ever, can we find a clearly true counterfactual about how the past would be different if the present were somehow different. Such a counterfactual, unless clearly false, normally is not clear one way or the other. It is at best doubtful whether the past depends counterfactually on the present, whether the present depends on the future, and in general whether the way things are earlier depends on the way things will be later.

  • 46 Lewis 1979, p. 32.
  • 47 He was referring to instances of the following kind of “backtracking” counterfactual reasoning: “Ji (...)
  • 48 Lewis 1979, p. 35.

81His example was of typing words on a page. If Lewis were typing different words today, different words would be on the page tomorrow. But there is no “clearly and uncontroversially true”46 counterfactual about how yesterday would have been different, if he were typing different words today. Lewis acknowledged that we sometimes assent to backtracking counterfactuals – counterfactuals that say how the past would have been different if the present were different.47 But, he insisted, these are all “non-standard” contexts (“standard” being the default resolution of the vagueness of counterfactuals, the one that we revert to in the absence of contextual clues that the speaker intends something else). He also said that the asymmetry does not hold in all possible conditions – it might not hold in a time machine, or at the edge of a black hole, or at a possible world consisting of a solitary atom in the void.48

  • 49 It is misleading because Analysis 1 is silent on the subject of miracles. If determinism is false i (...)

82Second, Lewis argued that, subject to these qualifications, counterfactuals are temporally asymmetric in a way that corresponds to a theory that he called ‘Analysis 1’ (which is the theory usually attributed to him and called, somewhat misleadingly, ‘the local miracles theory’).49 Analysis 1 is a three-part account; it says that the counterfactually closest worlds have exactly the same past as the actual past until the beginning of a transition period that starts shortly before the time of the antecedent, differ from the actual world during the transition period only as much as they must to permit the antecedent to hold, and conform to the actual laws at all times after the time of the antecedent. Lewis said that we need a transition period to ensure a “smooth” transition from the actual past to the counterfactual future. If the unstruck match is a foot away from a striking surface at t, we do not evaluate ‘if the match had been struck at t…” by considering worlds where the match travels a foot in no time at all.

83Third, Lewis argued that the temporal asymmetry of counterfactuals, as revealed by our use of Analysis 1, explains our ”time’s arrow” belief that the past is in some sense “fixed” while the future is “open”. He considered the claim that our time’s arrow belief is explained by our belief that determinism is false but dismissed this on the ground that our belief in time’s arrow is more robust than our belief that determinism is false. He rejected several other hypotheses, concluding that our belief in time’s arrow is explained by the fact that counterfactuals are (contingently) temporally asymmetric. Since the temporal asymmetry of Analysis 1 is stipulated, it can’t be the last word.

  • 50 Lewis assumed determinism in his discussion of the Nixon counterfactuals. He later extended his dis (...)

84The last part of Lewis’s time’s arrow argument was the most complex. He used Fine’s Nixon counterfactual – intended as a counterexample to his original account – to defend the claim that the temporal asymmetry of Analysis 1 is the product of a temporally neutral similarity metric together with a contingent fact about the world that he called ‘the asymmetry of overdetermination’. He began by saying that the lesson of the Nixon counterfactual is that we should not use our offhand judgments of overall similarity of worlds but, rather, whatever similarity metric gets the right verdicts for uncontroversial counterfactuals like the one about Nixon. He applied Analysis 1 to that case, and showed that it yields the right verdict. Analysis 1 says that the most similar worlds where Nixon presses the button are worlds with exactly the same past as the actual past until the occurrence of a small miracle – probably a neuron firing differently in Nixon’s brain – causes him to make the fateful decision to press the button.50 After that, events take their lawful course and the nuclear holocaust ensues.

85Lewis’s temporally neutral similarity metric goes like this: The most similar worlds are those which maximize exact match of particular fact taking into account not only the past but also the future; if it takes a small miracle to achieve a large spatiotemporal region of exact match of fact, so be it. Worlds with a small miracle are more similar than worlds with a big miracle (or many little miracles). Approximate similarity counts for little or nothing. It will be useful to have a name for this similarity metric; let’s call it ‘MaxiMin’.

  • 51 By ‘world like ours’ he means worlds where counterfactuals are temporally asymmetric in the way the (...)
  • 52 Lewis 1979, p. 49.
  • 53 Lewis 1979, p. 49.

86Lewis then used the Nixon counterfactual to argue that the temporally neutral MaxiMin picks out the same set of worlds as the temporally biased Analysis 1. He pointed out that only a small miracle (that extra neuron firing in Nixon’s brain) is required to set the counterfactual course of events in motion, but it takes a huge miracle (or many little miracles) to get the counterfactual sequence to converge back to the exact course of events at our world. The fatal signal must vanish on its way from the button to the rockets, Nixon’s fingerprints on the button must disappear, the click of the button on his tape-recorder must be erased, the light waves flying out the window bearing the image of Nixon’s finger on the button must be stopped, Nixon’s memories must be erased, and so on. Lewis said that the moral is that divergence from a world like ours51 is easier than perfect convergence to it. If determinism is true, then it takes a miracle to achieve either divergence or convergence, but “convergence takes very much more of a miracle.”52 The temporal asymmetry of counterfactuals is, he claimed, due to the fact that “the appropriate standards of similarity, themselves symmetric, respond to this asymmetry of miracles”.53

  • 54 He pointed out that overdetermination of the future by the present – the victim whose heart is simu (...)

87Lewis made one more explanatory claim: that the asymmetry of miracles is explained by a de facto temporal asymmetry he called ‘the asymmetry of overdetermination’. Lewis defined a determinant of a particular fact as a set of conditions that are together minimally sufficient, given the laws, for that fact. At a deterministic world, facts have later as well as earlier determinants. Lewis’s claim was that at the kind of deterministic world ours might be facts typically have multiple simultaneous later determinants, but usually only one earlier determinant at any given time.54

  • 55 Lewis 1979, p. 50.

Whatever goes on leaves widespread and varied traces at future times…It is plausible that very many simultaneous disjoint combinations of traces of any present fact are determinants thereof; there is no lawful way for the combination to have come about in the absence of that fact… If so, the abundance of future traces makes for a like abundance of future overdeterminants.55

88Since it takes a miracle to break the link between a determinant and that which it determines, the miracles required for divergence from our past are small but the miracles required for convergence to our future are big. So the asymmetry of overdetermination explains the asymmetry of miracles. And the asymmetry of miracles, together with the temporally neutral MaxiMin, explains why we evaluate counterfactuals in the temporally asymmetric way specified by Analysis 1. Or so Lewis argued.

7. Why We Should Not Be Persuaded

89What is remarkable is the speed with which Lewis dismissed all Fixed Law theories. He had just one argument – the epistemic argument, which says that if we hold the laws fixed, we won’t have any idea how to evaluate any counterfactuals, including the uncontroversially true ones, like the Nixon and match counterfactuals. By contrast, Analysis 1 makes it easy to evaluate these counterfactuals.

90If we find this argument persuasive, it is because we are assuming, with Lewis, that the correct similarity metric is one that compares worlds with respect to similarity of particular fact during all time – past, present, and future. If determinism is true, this means that a Fixed Law theory tells us to compare worlds with different histories all the way back to the beginning of time. And if that’s the case, it’s hard to see how a Fixed Law theory can tells us which worlds are most like our own.

  • 56 Bennett 1984.

91The epistemic argument fails against Bennett’s version of a Fixed Law theory, his Simple theory.56 The Simple theory says that the most similar worlds are worlds with the same laws as our world and which are otherwise most like our world at the time of the antecedent. About the match, it says that the relevant worlds are ones where the match and its surroundings are almost exactly the way they actually are – the match is dry, well-made, in a room with oxygen and without wind or rain, and so on. This gives us the right results; at these worlds, my striking the match is followed by its lighting. About Nixon, the Simple theory says that the relevant worlds are ones where everything at the time of Nixon’s button-pressing is almost exactly the way it actually was; the Doomsday machine is in perfect working order, as is Nixon’s tape recorder, and so on. More generally, since we know about the past by knowing its many traces in the present, the Simple theory provides us with the same epistemic access to many counterfactuals as Analysis 1.

  • 57 “Seldom, if ever, can we find a clearly true counterfactual about how the past would be different i (...)

92The Time’s Arrow argument was based on a claim that seems right (and which some Lewis critics have not appreciated) – that there is a striking temporal asymmetry in the counterfactuals we think true. There are lots of true forward-tracking counterfactuals – counterfactuals that say that if the present were different in some relatively specific way, the future would also be different in some relatively specific way. But specific backtracking counterfactuals are either false or not clearly true.57

93Reflection on this temporal asymmetry might seem to support:

No Backtracking: Where A and C are both false, and the time of A is later than the time of C, it is never true that if A, it would be that C.

  • 58 It was this temporal asymmetry of counterfactuals that was the basis of Lewis’s hope that causal de (...)

It is No Backtracking that underlies the appeal that Lewis’s theory of counterfactuals continues to have.58

94Is No Backtracking true? We will take this up in a moment. There is an important preliminary point. Even if No Backtracking is true, it does not support Lewis’s theory in the way that he claims.

95There are two ways in which a counterfactual may be fail to be true. Thus, where A and C are both false:

(1) If A were the case, then it would be that C

may fail to be true because:

(2) If A were the case, it would (still) be the case that not-C

or (1) may fail to be true because:

(3) If A were the case, it might be the case that C and it might be the case that not-C

Both (2) and (3) entail that (1) is not true, but they are inconsistent with one another. If (2) is true, (3) is false, and vice versa.

96No Backtracking says that any instance of (1) is not true if the time of A is later than the time of C. But are these backtrackers not true because (2) or because (3)? The answer is important because it makes a difference to the way in which counterfactuals are temporally asymmetric.

97If backtrackers are never true because (2), then No Backtracking tells us:

Fixed Past: If the present were different in any way, the past would (still) be exactly as it actually was.

98On the other hand, if backtrackers are never true because (3), No Backtracking tells us:

Indeterminate Past: If the present were different in any way, the past would be different, but not in any very specific way.

99Fixed Past says that the past is counterfactually independent of the present; it would be the way it is no matter how the present is. Fixed Past is inconsistent with Fixed Law theories. Indeterminate Past, on the other hand, makes the weaker claim that the past depends on the present only in non-specific ways. Indeterminate Past is consistent with Fixed Law theories of counterfactuals, including the Simple theory.

  • 59 “In reasoning from a counterfactual supposition about any time, we ordinarily assume that facts abo (...)

100Contrary to what is sometimes claimed (and contrary to what he sometimes says59), Lewis does not hold Fixed Past. His claim is a more complicated one: he says that the past is counterfactually fixed, but only up to a certain point – the beginning of the transition period. During the transition period and until the time of the antecedent, Lewis holds that the past is Indeterminate:

  • 60 Lewis 1979, p. 40.

We should sacrifice the independence of the immediate past to provide an orderly transition from actual past to counterfactual present and future. This is not to say, however, that the immediate past depends on the present in any very definite way, There may be a variety of different ways the transition might go, hence there may be no true counterfactuals that say in any detail how the immediate past would be if the present were different.60

101Lewis suggests that it is only the “immediate past” that is Indeterminate, but he cannot mean this. The length of the transition period will vary, depending on the counterfactual.

If dinosaurs ruled the earth, there would be no internet.

102In order to evaluate this counterfactual in a way that permits a “smooth” and “orderly” transition (no big miracles), the transition period must stretch back in time for millions of years.

103Lewis’s Analysis 1 thus requires us to think of the past as Fixed to a certain point in time and Indeterminate thereafter, with the relevant point in time depending on the counterfactual we are entertaining.

104Everything said so far is consistent with the truth of No Backtracking. But No Backtracking is false. There are clearly and uncontroversially true counterfactuals that say how things would have been different – would have to have been different – earlier if things had been different later. To see this, consider first this counterfactual:

If Kennedy had run for a second term as President, he would have won.

105This is a counterfactual about which reasonable people may disagree, depending on their beliefs about the political facts. But in ordinary contexts no one would propose that the closest worlds where Kennedy runs for a second term are worlds where Kennedy was assassinated in 1963 but rises from his grave to run again in 1964. In arguing the matter, we consider worlds where Kennedy was never killed in the first place. And that commits us to the clearly and uncontroversially true backtracking counterfactual:

If Kennedy had run again for President (in 1964), he would have to not have been killed (in 1963).

106Nor would Lewis disagree. Worlds where Kennedy is killed in 1963 and later rises from his grave to make a second bid for the presidency are worlds with a big miracle, and big miracle worlds are not among the closest worlds, according to Lewis. Nor could he claim that in asserting the backtracker we are switching to a “non-standard resolution”, for the backtracker falls within the scope of the transition period that his Analysis 1 requires.

  • 61 Bennett 1984 and Mackie 2014 both criticize Lewis on this point.

107Neither of these two objections – that No Backtracking doesn’t entail Fixed Past and that No Backtracking is false – counts against Lewis’s claim that counterfactuals are temporally asymmetric. Lewis can still plausibly claim that if dinosaurs now ruled the earth, this might have come about in any of a variety of different ways. And it is also plausible that if Kennedy had run again for President, this might have been because the assassination attempt failed or because he never made that trip to Dallas in November 1963, or… And he can still claim that we evaluate counterfactuals by holding fixed as much of the past as is possible without some large miracle (resurrection from the dead, dinosaurs popping into existence ex nihilo). That is, he can restate Analysis 1 to clarify that ‘short’ means “as short as can be without a large miracle”. But what he cannot claim is that our belief in time’s arrow – our belief that the past is “fixed” in some way that the future is not – is explained by our belief that the past is counterfactually fixed.61

108But note where we are now. We began with Lewis’s initial and plausible observation that counterfactuals are temporally asymmetric. Lewis used this observation to support his claim that the asymmetry is the kind specified by No Backtracking and Fixed Past, and he used these claims to argue that we (standardly) evaluate counterfactuals in the way specified by Analysis 1 and that this explains our time’s arrow belief. But No Backtracking and Fixed Past are false, and our belief in the temporal asymmetry of counterfactuals isn’t what explains our time’s arrow belief. The epistemic argument against Fixed Law theories fails; at least one Fixed Law theory – the Simple theory – remains a contender. Given all this, do we have any reason to believe that we evaluate counterfactuals according to Analysis 1?

  • 62 Lewis 1979, p. 33. Wilson 2014 criticizes this argument at pp. 263-268.

109Lewis offers one other argument. We ordinarily feel free to use whatever we know about the past in our counterfactual reasoning. “If I were acting otherwise just now, I would revenge a wrong done me last year - it is absurd to even raise the question whether that past wrong would have taken place”.62

110But this argument fails. We evaluate counterfactuals by considering worlds where the antecedent is true without any gratuitous departures from actuality. It is sometimes true – as in the case of the Kennedy and dinosaur counterfactuals – that we have to suppose a difference in facts about the past going back a long time – a year, millions of years. But in many cases we have no reason to suppose that a past fact would, or even might, have been different. The present includes Lewis’s memories of the past wrong. In the absence of reasons for thinking that Lewis’s memory would have been faulty, we should assume that the past wrong would still have occurred, had Lewis been acting otherwise. But reasoning in this way about the fixity of some past facts does not commit us to the claim that the entire past is counterfactually fixed. Nor does it commit us to the claim that the past is counterfactually fixed until the occurrence of some small miracle at some point in the recent or not so recent past.

111Lewis had one last argument – the ambitious Asymmetry of Overdetermination argument, which was supposed to show that the temporal asymmetry of Analysis 1 is not stipulated but is the product of the temporally neutral MaxiMin and the contingent asymmetry of overdetermination.

  • 63 Price 1992.
  • 64 Elga 2000.
  • 65 Horwich 1987.
  • 66 Lewis 1979, Postscripts D. and E. See also Schaffer 2004.

112This argument has been the subject of much discussion. It has been argued that the asymmetry of overdetermination is not general enough to support the kind of temporal asymmetry that Lewis needs for his counterfactual analysis of causation.63 It has been argued that it isn’t always true that a convergence miracle must be a big one.64 It has been argued that it is psychologically implausible that we have developed such a complex similarity metric and implausible that all competent users of counterfactuals have the kind of sophisticated knowledge (of the overdetermination and miracle asymmetries) required for the use of this metric.65 I do not have the space here to discuss these objections or Lewis’s response.66

  • 67 Lewis 1979, p. 43.

113My criticism is a simpler one. Lewis offers the Asymmetry of Overdetermination as an explanatory claim. The explanandum is, in the first instance, the asymmetry of miracles, and, in the second instance, our evaluation of counterfactuals according to the temporally biased miracle-permitting Analysis 1. If we don’t use Analysis 1 in the first place, the explanation is not needed. If we evaluate counterfactuals according to a theory that doesn’t permit miracles – a Fixed Law theory – there is no miracle asymmetry to be explained. Lewis had only one argument against Fixed Law theories – the epistemic argument. But that argument fails against the Simple theory. The Simple theory generates the correct verdicts for the uncontroversially true counterfactuals, like the match and Nixon counterfactual, and therefore passes Lewis’s own test for how we should think about similarity. (“we must use what we know about counterfactuals to find the appropriate similarity relation, not the other way around.”67) Lewis’s only positive argument for Analysis 1 was based on the claim that counterfactuals are temporally asymmetric in certain kinds of ways. But, as we saw, there is more than one way that counterfactuals may be temporally asymmetric, and Lewis did not show that counterfactuals are temporally asymmetric in the Fixed Past way stipulated by Analysis 1. In the absence of any good reason to reject the Simple theory, we have no reason to accept Lewis’s claim that we evaluate counterfactuals according to a theory that permits miracles. And if that’s so, the Asymmetry of Overdetermination explanation is beside the point.

8. Some Reasons to Prefer the Simple Theory

  • 68 Bennett 1984, p. 74.
  • 69 Cf. my discussion of How Experience Teaches, above, or Gopnik, Meltzhoff, and Kuhl 1999. Even if Le (...)

114The first reason is that it is simple, unlike either Analysis 1 or MaxiMin which require us to balance different similarity respects – smallness of miracle against size of region of exact match of particular fact. The Simple theory says that the closest worlds are worlds with exactly our laws – no messing about with miracles – and which are otherwise most like our world at the time of the antecedent. If the time of the antecedent is the present, then we “put away our history books and crystal balls, using only our capacity for causal inference in both temporal directions.”68 This makes the Simple theory a more plausible candidate as an explanation for how we actually learned to use counterfactuals, from the time we were babies, to figure out the causal facts about the objects around us.69

115Objection: Didn’t you say that we evaluate counterfactuals by holding fixed the laws and the past? Wasn’t this your explanation of the Three Stages of Denial?

  • 70 Thanks to Helen Beebee for pressing me on this point.

116Reply: No, I was careful not to say this. I said that we are – and have been from an early age – competent users of counterfactuals without having any articulated theory of how we do this, much less any articulated theory of the truth-conditions of counterfactuals. My claim was that our response to determinism is explained by what happens in the philosophy classroom when we are first introduced to determinism and forced to take seriously the thought that it might, for all we know, be the truth about our world. We respond by articulating, for the first time, a theory of counterfactuals - the Fixed Past and Laws theory, which says that Antecedent > Consequent is true only if there is a world with our laws and past where the Antecedent is true. I did not say it then, but I will say it now: Fixed Past and Laws isn’t just a bad theory of counterfactuals; it is not a theory that we ever used.70 We make a mistake when we attribute this theory to ourselves, but it is not a crazy mistake, given that the counterfactuals we are most familiar with – choice counterfactuals and counterfactuals about alternative behaviors of nearby agents and objects – can be evaluated while ignoring the past. (We don’t have to provide a ‘back story’ to figure out what would have happened, going forwards, had the agent or object done otherwise.) But ignoring the past is not the same as holding it fixed. And holding some past facts counterfactually fixed is not the same as holding the entire past fixed. The fact that we can also understand and evaluate backtrackers (like the one about Kennedy) shows that we don’t think that all of past history is counterfactually fixed.

  • 71 See Bennett 2003, pp. 219-221 and pp. 234-240 for discussion of counterexamples and problem cases, (...)

117Taking determinism seriously means facing up to the fact that we cannot evaluate counterfactuals by limiting our attention to worlds with the same laws and same past. Something’s got to give. The correct theory of counterfactuals must be a theory that gives up either Fixed Past or Fixed Laws. The Simple theory says that it is Fixed Past that must yield; Lewis argued that it is Fixed Laws that must go. (And, though he did not advertise it, he also rejected Fixed Past.) Both theories are able, with some adjustments71, to account for the counterfactual data – the forward-tracking counterfactuals that are as clearly and uncontroversially true as counterfactuals ever are. But the Simple theory has the theoretic virtue of simplicity, and because of this it is more plausible that it is the theory that we actually use.

118The second reason for preferring the Simple theory is that its similarity metric is temporally neutral, permitting counterfactual reasoning in both temporal directions. It is therefore able to accommodate the plausible claim with which Lewis began, about the way in which counterfactuals are temporally asymmetric, without requiring it, as Analysis 1 does. And because the Simple theory doesn’t stipulate a temporal asymmetry, it does not need to provide an explanation for why we evaluate counterfactuals in this temporally asymmetric way. It leaves it open, in a way that Lewis’s theory does not, what the correct explanation of this temporal asymmetry is. It thus has the theoretic virtue of modesty, of assuming no more than is required to explain the counterfactual data.

119The third, and most important, reason for preferring the Simple theory is that it takes the laws seriously – by holding them counterfactually fixed. This should be our default assumption, when looking for a theory of counterfactuals. We shouldn’t accept miracles unless we have to. This is so regardless of whether our philosophical view of the laws is Humean or nonHumean. There is a tight link between laws and counterfactuals; the laws tell us not only what actually happens but what would happen even if things were different. When we believe that something is a law, we believe that it would hold no matter what else happens, no matter what we do or try to do. When we consider counterfactuals for the purpose of making decisions about what to do (and not to do – better not step off that balcony without a safety net!), we rely on our knowledge of the laws.

  • 72 “The violated deterministic law has presumably not been replaced by a contrary law. Indeed, a versi (...)
  • 73 Lewis 1981 distinguishes a Strong ability to perform actions which would either be or cause law-bre (...)

120The Simple theory accounts for these commonsense beliefs in a simple and straightforward way: by telling us that the worlds most similar to ours are always (except for the special case of counterlegals) worlds with exactly our laws. Lewis can account for our commonsense beliefs as well, but only in a more complicated way, and only up to a point. He is able to account for the role of laws in our counterfactual thinking so far as the future (relative to the time of the antecedent) is concerned. And, depending on your view of the nature of laws, he may be able to dismiss worries about how to think about the laws at his small miracle worlds.72 But he isn’t able to endorse the commonsense platitude that the laws – all the laws – would hold no matter what happens. And he has to draw some fine distinctions to avoid having to say that the ability of a free deterministic agent to act otherwise is not an incredible ability to break the laws.73

121It is sometimes thought that Lewis’s theory of counterfactuals is a consequence of Lewis’s Humean view of laws, and it has even been said that a compatibilist who is a Humean about the laws must be a “local miracles compatibilist”. This is a mistake. It is true that Lewis’s view of the laws was one of the factors that led him to his theory of counterfactuals:

  • 74 Lewis 1973, p. 73 and p. 74.

I doubt that laws have as much special status as has been thought…Laws are very important but great masses of particular fact count for something too; and a localized violation is not the most serious sort of difference in law.74

122This way of arguing for a miracle-permitting theory of counterfactuals would not appeal to someone with a nonHumean view about the laws. But it is by no means mandatory for a Humean to accept Lewis’s theory of counterfactuals – either the Analysis 1 version or Maximin. It is worth remembering that until the time of Lewis’s Counterfactuals (1973), everyone assumed that the laws are always cotenable with the antecedent of a counterfactual – that is, that the laws are counterfactually fixed. And in those days almost everyone held the Humean view that laws are a subset of the true universal generalizations.

123To sum up: The third reason for preferring the Simple theory to Lewis’s theory is that, in the absence of very good reason for rejecting the counterfactual fixity of the laws, we should prefer a Fixed Law theory of counterfactuals. Since Lewis doesn’t give us a good reason to reject Fixed Laws, we should prefer the Simple theory.

9. Concluding Remarks

124What does all this have to do with free will and the free will/determinism problem?

125At least this. In order to understand the truth about free will and determinism, we need to understand counterfactuals. I have argued that our beliefs about free will and our agent causal powers are closely connected with our beliefs about certain kinds of counterfactuals – the counterfactuals that we assert and believe true in choice situations – and I have argued that there is an apparent tension between these counterfactuals and the truth of determinism. When we engage in counterfactual reasoning in choice situations, it seems that we assume that both the laws and the past are counterfactually fixed. But if determinism is true, then either the past is not counterfactually fixed or the laws are not counterfactually fixed. We are faced, it seems, with a hard choice. Lewis persuaded many of us that the lesser evil is to keep the past (or at least most of the past) fixed, at the cost of a small miracle. But this, I have argued, is a mistake. In arguing this, I have not appealed to my belief that free will is compatible with determinism or even my belief that the existence of ordinary sorts of causal powers (of baseballs, horses, and steam engines) is compatible with determinism. I have appealed only to the kinds of considerations that count in favor of a theory of counterfactuals. I have argued that the Simple theory, which keeps the laws counterfactually fixed, is a better theory of counterfactuals. If it is the better theory of counterfactuals, then it is the one we should use when we think and argue about the free will/determinism problem.

126As I said, I do not claim that the Simple theory makes it easier for us to defend compatibilism. But I do claim that the Simple theory provides us with the resources for thinking more clearly about the free will/determinism problem. In order to think clearly about the problem, we must take determinism seriously. Determinism isn’t just the claim that there are laws of nature that describe general truths about the way the world is; it is the claim that the laws, somehow, circumscribe the ways the world can be.

127Humeans are often accused of not acknowledging this, but that’s not fair. Here is Lewis’s definition of determinism:

  • 75 Lewis 1979, p. 37.

A deterministic system of laws is one such that, whenever two possible worlds both obey the laws perfectly, then either they are exactly alike throughout all of time, or else they are not exactly alike through any stretch of time. They are alike always or never. They do not diverge, matching perfectly in their initial segments but not thereafter; neither do they converge.75

128By explicitly quantifying over nomologically possible worlds, Lewis captures the modal commitments of determinism. His definition makes clear how much we are assuming when we assume for the sake of any philosophical argument that determinism is true.

129Given this understanding of the modal commitments of determinism, we might expect Lewis to agree that there are counterfactual commitments as well. If determinism, as Lewis understands it, is true, it seems reasonable to suppose that Counterfactual Determinism is true as well.

Counterfactual Determinism: If the world had been different in any respect at any time, then it would have been different in some respect at every moment in the future and the past.

130But Lewis denies Counterfactual Determinism. He agrees that if the world (assuming determinism) were different now, it would also be different in some respect at every future time. But he denies that if the world (assuming determinism) were different now, it would also be different in some respect at every past time.

  • 76 Bennett 1984, p. 68.

131The Simple theory, by contrast, affirms Counterfactual Determinism. As Bennett says, “It seems to me just plainly true that if the actual world is deterministic then if a certain pebble had rolled at a moment when in fact it did not roll, the entire previous history of the world would have had to be different.”76

  • 77 A shorter version of this paper was presented at the Free Will and Causation conference at the Coll (...)

132In affirming that determinism entails Counterfactual Determinism, the Simple theory provides us with a unified framework for addressing questions about how, if at all, we can have the free will we think we have, and the agent causal powers we think we have if determinism turns out to be the truth about our world. More generally, it provides a unified framework for addressing more fundamental questions about how steam engines, horses, and baseballs can have the kind of causal powers we think they have if determinism is true. And it is only by having answers to these hard questions that we can hope to provide a compatibilist solution to the free will/determinism problem in a way that avoids the usual charges of “wretched subterfuge” and “quagmire of evasion”.77

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Notes

1 In this essay, I use ‘compatibilist’ to refer to someone who believes that the truth of determinism is compatible with our having the free will we think we have, including the ability to do otherwise. I use ‘incompatibilist’ to refer to someone who believes that the truth of determinism is incompatible with our having the free will we think we have, including the ability to do otherwise.

2 Hobart 1934.

3 For discussion of this objection, see Velleman 1992.

4 Lewis 1979.

5 Bennett 1984.

6 Gopnik, Meltzoff, and Kuhl 1990, Chapter 3, “What Children Learn about Things”, especially “Making Things Happen” and “Kinds of Things”, pp.73-82.

7 What I have just argued should be understood as an empirical claim about how we in fact (typically) acquire our causal beliefs. I’m not claiming that there is no other way to acquire causal beliefs. I’m not making the claim, endorsed by von Wright 1973, that the concept of causation “is connected with features peculiar to action”. Nor do I endorse the claim, by Menzies and Price 1993, that “a causal relation exists between two events just in case it is true that if a free agent were present and able, she could bring about the first event as a means to bringing about the second.” For discussion of some empirical research on the causal counterfactual reasoning abilities of young children, see German and Nichols 2003.

8 In Vihvelin and Tomkow 2005, we offer an account. For some further thoughts on the do/allow distinction, see Vihvelin 2014.

9 Chisholm 1964.

10 See Vihvelin 2013 for argument that the possession of these agential powers is compatible with determinism as well as indeterminism and that they may be understood as dispositions or bundles of dispositions, differing in complexity but not in kind from the dispositions of natural objects like horses, steam engines, rocks, and lumps of sugar.

11 van Inwagen 1983, Beebee and Mele 2002, Beebee 2011.

12 Lewis 1979, Earman 1986.

13 Vihvelin and Tomkow 2016.

14 For more on determinism, and for why determinism should not be confused with various claims about causation (or physicalism or naturalism), see Vihvelin 2013 and Vihvelin 2017.

15 Swartz 1986, Beebee and Mele 2002.

16 van Inwagen 1983.

17 Lewis 1973.

18 Lewis 1981.

19 I’m not claiming that every Humean theory of laws satisfies this (and other) conditions of adequacy for lawhood. See, for instance, Armstrong 1983 for a critique of a Humean theory that he calls “the Naïve theory”.

20 van Inwagen 1983.

21 Vihvelin 2013.

22 Holton 2009.

23 For an excellent account, by three leading psychologists, of some recent research about the “scientist in the crib”, see Gopnik, Meltzoff, and Kuhl 1999.

24 Kim and Maslen 2006.

25 I will be arguing later that there is no actual conflict and that our commonsense beliefs about counterfactuals are consistent with the Simple theory.

26 Holbach 1770. “Man in running over…the route which nature has marked out for him, resembles a swimmer who is obliged to follow the current that carries him along...he sometimes consents, sometimes does not consent to glide with the stream which, notwithstanding, always hurries him forward.”

27 Loewer 1996.

28 Lewis 1973, Lewis 1973B, Lewis 1979.

29 Goodman 1947.

30 Stalnaker 1968 and 1984; Lewis, ibid.

31 Collins, Hall, and Paul, 2004.

32 Vihvelin 2000, and 2013.

33 Stalnaker 1968 and 1984.

34 Lewis 1973.

35 This is rough, since Lewis rejects the Limit assumption – that there is a closest set of worlds. His official account says that A >C is non-vacuously true iff there is some world where A and C are both true that is more similar to our world than any world where A is true and C is false.

36 Ibid.

37 Ibid, p. 92. “Somehow we do have a familiar notion of comparative overall similarity, even of comparative similarity of big, complicated things like whole people, whole cities, or even – I think – whole possible worlds.”

38 Ibid, p. 75. By ‘miracle’, Lewis meant an event that is miraculous by the standards of our laws.

39 Fine 1975.

40 Lewis 1979.

41 I was among those convinced and I even used Lewis’s theory to defend a bold kind of compatibilism I called “Libertarian Compatibilism” (Vihvelin 2000). In brief, my claim was that even if determinism is true, we are sometimes able to choose otherwise, given the actual past up to the time of our choice; our choice is the small miracle. I now think that my claims in that paper were mistaken. This wasn’t entirely because I was relying on Lewis’s theory of counterfactuals, but that was part of it. For discussion of the question of whether a “local miracle compatibilist” must say that a free agent’s choice is the divergence miracle, see Beebee 2003 and Graham 2008.

42 Though not entirely. The groundwork was laid in Lewis 1973, especially in Chapter 3 (“Comparisons”), in which he discussed the problem of cotenability) and Chapter 4 (“Foundations”), in which he argued that the “limited vagueness” of overall similarity of worlds “accounts nicely for the limited vagueness” of counterfactuals”.

43 Goodman 1947.

44 Bennett 1984, Horwich 1987, Goggans 1992, Price 1992, Vihvelin 1995, Elga 2000, Mackie 2014, Tomkow 2013, Wilson 2014, Vihvelin and Tomkow 2015, Vihvelin and Tomkow 2016, Dorr 2016.

45 Bennett 2003, Chapter 13. For a close examination and critique of Bennett’s rejection of his earlier theory, see Tomkow 2013. Bennett 2003 rejects his earlier Simple theory, but falls short of endorsing a Fixed Past theory. The theory that he endorses appears to be neutral between three different ways of spelling out the details of what he calls “forks” – indeterministic forks, small miracle forks, and “exploding difference” forks. An “exploding difference” fork takes place when two worlds with the same deterministic laws are “invisibly unalike” but “alike in every respect we would ever notice or think about” for “aeons” and then suddenly, legally and improbably, diverge. An “exploding difference” theory of counterfactuals is a Fixed Law theory.

46 Lewis 1979, p. 32.

47 He was referring to instances of the following kind of “backtracking” counterfactual reasoning: “Jim and Jack quarreled yesterday, and Jack is still hopping mad. We conclude that if Jim asked Jack for help today, Jack would not help him. But wait: Jim is a prideful fellow. He never would ask for help after such a quarrel; if Jim were to ask Jack for help today, there would have to have been no quarrel yesterday, in which case Jack would be his usual generous self. So if Jim asked Jack for help today, Jack would help him after all.” Lewis’s claim was that this kind of reasoning is a departure from our counterfactual norm. “we easily slip back into our usual sort of counterfactual reasoning and implicitly assume once again that facts about earlier times are counterfactually independent of facts about later times”. (Lewis 1979, pp. 33-34.) For criticism of Lewis’s use of “Downing scare stories”, see Bennett 1984, pp. 69-72 and Bennett 2003, pp. 205-209.

48 Lewis 1979, p. 35.

49 It is misleading because Analysis 1 is silent on the subject of miracles. If determinism is false in the way that libertarians hope, Analysis 1 allows us to evaluate choice counterfactuals by holding fixed both the past and the laws. But if determinism is true, Analysis 1 tells us that if Lewis had been typing different words (or a bird had suddenly flown into the room, or the fire alarm gone off), most of the past would have been exactly the same but the laws would be just different enough to permit a “divergence miracle” shortly before Lewis’s choice, or the bird’s flight, or the sounding of the fire alarm.

50 Lewis assumed determinism in his discussion of the Nixon counterfactuals. He later extended his discussion to the indeterministic case. See Postscript D, pp. 58-66.

51 By ‘world like ours’ he means worlds where counterfactuals are temporally asymmetric in the way they actually are.

52 Lewis 1979, p. 49.

53 Lewis 1979, p. 49.

54 He pointed out that overdetermination of the future by the present – the victim whose heart is simultaneously pierced by two bullets – is a relatively rare occurrence.

55 Lewis 1979, p. 50.

56 Bennett 1984.

57 “Seldom, if ever, can we find a clearly true counterfactual about how the past would be different if the present were somehow different. Such a counterfactual, unless clearly false, normally is not clear one way or the other.” Lewis 1979, p. 32.

58 It was this temporal asymmetry of counterfactuals that was the basis of Lewis’s hope that causal dependence could be analyzed as a certain kind of counterfactual dependence. For it appears to be a contingent fact about our world that causes are always temporally prior to their effects; backwards causation is not conceptually incoherent nor, so far as we know, ruled out by the actual laws. Lewis’s hope was to show that the contingent temporal asymmetry of causation is due to the contingent temporal asymmetry of counterfactuals, and to show this he needed to defend, not only a counterfactual analysis of causation, but also an explanation of the facts that make it the case that counterfactuals are temporally asymmetric in the right kind of way. This was a proposal of staggering ambition, and even if it did not ultimately succeed, we have much to learn from how and why it failed.

59 “In reasoning from a counterfactual supposition about any time, we ordinarily assume that facts about earlier times are counterfactually independent of the supposition”. (Lewis 1979, p. 33.) “We very easily slip back into our usual sort of counterfactual reasoning and assume once again that facts about earlier times are counterfactually independent of facts about later times.” (Lewis 1979, p. 34.)

60 Lewis 1979, p. 40.

61 Bennett 1984 and Mackie 2014 both criticize Lewis on this point.

62 Lewis 1979, p. 33. Wilson 2014 criticizes this argument at pp. 263-268.

63 Price 1992.

64 Elga 2000.

65 Horwich 1987.

66 Lewis 1979, Postscripts D. and E. See also Schaffer 2004.

67 Lewis 1979, p. 43.

68 Bennett 1984, p. 74.

69 Cf. my discussion of How Experience Teaches, above, or Gopnik, Meltzhoff, and Kuhl 1999. Even if Lewis is right in his claim (Lewis 1979, Postscript E) that even “ignorant folk” have the knowledge of the Asymmetry of Overdetermination that his account requires because it is “common knowledge” that events leave “many and varied traces”, it seems highly implausible that babies and young children have this knowledge. The Simple theory requires them to know far less, and is for this reason more psychologically plausible.

70 Thanks to Helen Beebee for pressing me on this point.

71 See Bennett 2003, pp. 219-221 and pp. 234-240 for discussion of counterexamples and problem cases, and for suggested remedies.

72 “The violated deterministic law has presumably not been replaced by a contrary law. Indeed, a version of the violated law, complicated and weakened by a clause to permit the one exception, may still be simple and strong enough to survive as a law.” (Lewis 1973, p.75.)

73 Lewis 1981 distinguishes a Strong ability to perform actions which would either be or cause law-breaking events from a Weak ability to act so that some law would have been broken, and claims that his compatibilism commits him only to the claim that a free deterministic agent has the Weak ability. See Beebee 2003 for critique; see Graham 2008 for defense of Lewis.

74 Lewis 1973, p. 73 and p. 74.

75 Lewis 1979, p. 37.

76 Bennett 1984, p. 68.

77 A shorter version of this paper was presented at the Free Will and Causation conference at the Collège de France in Paris in September 2016. I am grateful to Claudine Tiercelin and Jean-Baptiste Guillon for their hosting of this splendid conference and to all who participated for their helpful comments. I am grateful also to Terrance Tomkow, for hours of extremely valuable discussion about the counterfactuals part of the paper.

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University of Southern California

© Collège de France, 2017

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