The Problem with Complete States: Freedom, Chance and the Luck Argument

The Problem with Complete States: Freedom, Chance and the Luck Argument Richard Johns Department of Philosophy University of British Columbia August 2006 Revised March 2009 The Luck Argument seems to show that libertarianism is false, since indeterministic free will is impossible. We should be wary of this argument, however, since a very similar argument shows that indeterministic causation 1 is impossible. Further, since chancy events require causes, but are not determined, it would also follow that chancy events do not exist. If we are to conclude that free actions are all deterministic (or nonexistent), then the same reasoning should also persuade us that events with physical chances do not exist. The Luck Argument, in its various formulations, assumes that a human being, like any physical system, has a set of complete (or exact, or precise) possible states. The same assumption drives the similar argument against indeterministic causation. This spells disaster for both free actions and chancy events, as these require causes. The assumption that physical systems have precise states should therefore be subjected to the closest scrutiny, which is not usually the case. On the contrary, it enjoys a wide and uncritical acceptance. 1 The term causation is used in a number of ways, but I shall specify my meaning below. 1

I. THE LUCK ARGUMENT The Luck Argument has various formulations, but we will focus on van Inwagen s. He begins by considering a particular freely performed action. Let us suppose, to use van Inwagen s example, that Alice freely chose to tell the truth. Van Inwagen then imagines that God rolls back the universe to precisely the state it had just before Alice s decision to tell the truth, and then lets it run forward from there a second time. If we suppose that Alice s action is not determined by the prior history of the world, then it could have been otherwise, even holding the past fixed. In that case, on this second run, Alice might tell a lie instead. Van Inwagen then imagines that God repeats the experiment over and over again, endlessly. At this point, he seems to assume that the truth-telling event is chancy, as he states that the proportion of truth-telling outcomes will almost surely settle to some limit, such as 0.7. (This surely requires the extra assumption that the event has a precise physical chance.) If we are watching these trials, van Inwagen says, we will be convinced that the outcome on any particular trial is a matter of pure chance, and thus beyond Alice s control. Other formulations of the Luck Argument do not involve rolling back the universe to an earlier state, but the differences are irrelevant to the criticism I will make. In some versions, for example, one considers parallel universes, that are exactly like this universe up until just before Alice s decision. In other words, the universes all share the same precise state at every moment before her deliberation begins. Then, assuming determinism is false, Alice s counterparts in other universes may lie even though Alice tells the truth, and the argument proceeds as before. The different versions of the Luck Argument all crucially involve the notion of a precise state, either explicitly or implicitly. Since my criticism of the argument is based on its dependence on this notion, the differences between the formulations are unimportant here. Note that, if the Luck Argument is modified by putting Alice and her copies into merely roughly the same state, then it collapses. For whatever reason, our intuition that Alice s real action is beyond her control disappears. 2

II. CAUSATION I claimed above that indeterministic causation and chancy events are impossible in a system with precise states. In order to present this claim clearly, and argue for it, I must say what I mean by causation. I will not give a theory of causation, since this is unnecessary for my present purpose. Also, I hold that the English term cause has a number of meanings, and I do not wish to denigrate those that differ from the one that is relevant here. The meaning of cause here is (at least roughly) Aristotle s notion of efficient cause, as the thing that produces or brings about some event. Like G. E. M. Anscombe, I see the efficient cause as some sort of ontological source of its effect, i.e. I hold that the effect comes from the cause, as a baby comes from its parents. I also see efficient causation as a physical relation, as Phil Dowe does, that is independent of human activities such as explaining and controlling things. In particular, a cause and effect must be physically joined through spacetime by a continuous causal process. So-called causes by omission and double prevention, therefore, are best seen not as literal causes, but rather as instances of some broader notion. A closed causal process, or system, is one in which the later time slices are caused by the earlier ones. More precisely, if the real history of the system is arbitrarily partitioned into time slices, then each time slice arises from its immediate chronological predecessor. Thus, in a causal system, there are no events from nowhere, which appear all by themselves without any source. When two causal systems interact, then events may occur in each that are (at least partially) caused by events outside that system. These are still not events from nowhere, of course, since they come (partially) from the other system. I hold, as a matter of fact, that there are no uncaused events in this sense. One crucial feature of causation that is often missed is its intimate connection to real existence. Only real, concrete events can be causes and effects. If we say that C caused E, we are committed to the real existence of both C and E. This is in sharp contrast with necessitation, since non-actual states of affairs can necessitate each other. For example, as I sit here in Vancouver, the non-actual state of affairs of my being in Outer Mongolia right now necessitates my being in Asia. The requirement for causes and 3

effects to be concrete is easily overlooked in the case of deterministic causation, where it is easy to confuse the causal relation C caused E with the causal conditional C, if it occurred, would cause E (the latter is really the determination relation, which doesn t require real existence). But the requirement is much clearer in the case of indeterministic causation, since C caused E is obviously different from: C, if it occurred, might cause E. I claimed in the introduction that both free actions and chancy events must have causes, in this sense. They must not be events that arise all by themselves, unassisted, from nowhere. I will now argue for this. The first claim, regarding free actions, is commonplace. While freedom is hard to define, one clear idea is that a free agent is in control of his actions. (Were this not the case, they would not really be his actions at all.) Thus a free action must come from the person, and thus be (efficiently) caused by the person in some way. I am not talking about what is called agent causation here, but just ordinary event causation. The causes of a free action will include psychological states of the agent, such as beliefs, desires and character. The second claim, while less frequently made, is no less obvious. Consider a physical experiment in which the chance of some outcome X is 2/3. If this experiment is repeated exactly, say a trillion times, then we are rightly confident that the proportion of X-type outcomes will be close to 2/3. Now suppose that each outcome, though chancy, were uncaused. In other words, we suppose that each outcome of the experiment appears all by itself, from nowhere, with no physical connection to the physical apparatus in which it occurs. It then follows that the aggregate of one trillion outcomes also appears from nowhere. 2 Yet this is absurd. How can an uncaused event be so reliable? After all, an uncaused event is not controlled by anything, so there is nothing in the world to dictate this relative frequency of 2/3 for X-type outcomes. The silliness of this becomes even clearer when we consider that, in some other apparatus, the relative frequency of X will reliably take some other approximate value, say around 0.316. If these aggregate 2 I am aware that such composition inferences are not all valid, but this one surely is. It is no different from the following: If every person in this room is from Portugal, then the aggregate of the people is also from Portugal. 4

outcomes appear out of thin air, then how are they (almost) always correctly matched with their respective experimental set-ups? One might respond to this argument by agreeing that its conclusion is true, indeed trivially so. Yet one might insist that chancy events, while having causes, are nonetheless not fully caused. They are partially caused, and partially from nowhere, perhaps. As far as I can tell, however, this intuition arises from confusing causation with determination. It is of course true that chancy events are only partially determined by their causes. The determination relation certainly comes in degrees in fact physical chances are simply degrees of determination! 3 But causation is never a matter of degree. C cannot partially cause E, because E cannot partially occur. (C might be partial cause of E, in the sense that C was merely part of the cause of E, but that s an entirely different matter. Such partial causes are ubiquitous even in deterministic systems.) III. INDETERMINISTIC CAUSATION We now come to the central claim of this paper, that the assumption of precise states rules out indeterministic causation. The whole concept of indeterministic causation obviously relies on a sharp distinction between causation and determination. As stated above, I understand causation to be a relation between concrete events. Determination, by contrast, is a logical relation between propositions, so that C determines E just in case the maximal (true) proposition describing C logically entails all true propositions describing E. 4 States are also logical entities, propositions in other words, that stand in logical relations (such as consistency and consequence) to each other. The fact that two systems that are numerically distinct can be prepared in the same state also shows them to be abstract entities. States may be more or less precise, leading to the distinction between macrostates and microstates. The macrostate of a flask of gas, for example, will partition 3 This is argued in Johns, A Theory of Physical Probability, U. of T. Press, 2002. 4 One may wonder where the laws of physics appear in this definition. I regard laws to be propositions about the behavior of a system that are logical consequences of its dynamical nature. This nature is of course a partial cause of that behavior, so that (in short) the laws are part of the causes. See Johns, op. cit. for more details. 5

the space within into little cubes, and specify the mean pressure and temperature in each cube, whereas the (more precise) microstate will specify the position and momentum of each molecule. The is more precise than relation is just logical entailment, of course, as the less precise state can be inferred from the more precise one. Given a particular concrete system, and a time, there are then many states for the system at that time, with varying degrees of precision. These are (partially) ordered by logical consequence. The most precise state, assuming that this exists, will be the maximum of the set of states, under this ordering. One could also define it as the logical conjunction of the states. This I will call the maximal state. This state is more commonly referred to as the complete state of the system at that time. But what is meant by this, if not that it is the maximal state under logical consequence? In fact the concept of completeness, in general, is quite different from that of maximality. The term complete suggests perfection, as if the concrete time slice of the system at time t and the maximal state at t are identical twins, exactly mirroring each other. Maximality does not entail completeness (at least not obviously), since there may be inherent limits to the description of concrete systems in abstract terms. In that case, the best possible description will not exactly correspond to the real system, and so will be incomplete. With this noted, let us for now assume that maximal states are complete, and see where this leads. (It leads, as stated earlier, to the impossibility of indeterministic causation, but let us now prove this.) Suppose that the maximal states of a system are also complete. This means that the maximal possible histories of the system, which are built in some way from the states (or vice-versa) are also complete. Now we allow the concrete dynamical system to evolve freely for a period of time, and compare that real, concrete history RH to the corresponding possible history, PH say. By hypothesis, they are exactly alike, with no differences at all. Now, the concrete history RH contains causation the later stages were caused by the earlier ones. Indeed, if the system is isolated from its surroundings, then the earlier stages are a total cause of the later ones. Hence, by hypothesis, PH must contain some exact duplicates of these causal relations. 6

Here we hit a problem, however. For the properties of a possible history are not changed by that history becoming the actual history. So, even before the evolution of the concrete system occurred, these mirrors of the causal relations must already have been present in PH. Thus, from PH we can infer that if the start of it is concretely realised, then (in the absence of external inference) the rest of the history will be caused to occur as well. In other words, the causal relations in PH are deterministic. We see, in other words, that the assumption that states are complete leads to causation existing in possible histories, which leads to causation being a necessary relation. It s a very simple argument, proving beyond doubt that indeterministic causation cannot ever occur in a system with complete states. For the sake of clarity, however, let s run the argument again, contrapositively. (Feel free to skip the next paragraph.) Let s now suppose that the concrete system is indeterministic. Then, as before, we prepare the system in some state and allow it to evolve freely in time. The real history that emerges corresponds to some possible history PH, but there is at least one other possible history PH that agrees with PH in some initial segment. Had the causal evolution gone differently, then PH rather than PH would have been the actual history of the system. We immediately see that the causal relations that exist in the real history cannot correspond to anything in PH. For, in that case, such relations would also exist in PH, so that from the shared initial segment of these histories one could infer, with certainty, two incompatible outcomes, which is absurd. Let me consider a couple of possible responses to the argument. (1) The relation that exists in the possible histories is not causation, but possible causation, probable causation, or some such thing. This will not do. For the relation that exists in the concrete history is simply causation, not possible or probable causation. The later stages of the real history really occur. They don t possibly, or probably, occur. They fully exist. But we cannot have any such fullness in the possible histories. 7

(2) The possible states and histories are slightly incomplete, by omitting causal relations. But this is a very small matter. They are, as it were, 99.998% complete, so that this proof has no interesting philosophical consequences. It is true that this proof gives no indication of how much is missing in the maximal state. But for this reason we have no assurance that what s missing is trivial either. Moreover, the gap shown between the concrete and the abstract is likely to be philosophically important wherever causation is a central concept. In the Luck argument, in particular, the worry is that Alice doesn t have control over her choice, that it doesn t come from her. In this context an assumption of complete states is disastrous, from a libertarian point of view, since it rules out the very kind of causation that is necessary for free will! IV. CONCLUSION We have seen that the Luck Argument depends on an assumption that every concrete system has a set of complete or precise possible states. I have attacked this assumption by showing that entails the impossibility of indeterministic causation. Now, since the existence of indeterministic causation is a fundamental component of libertarianism, we see that the idea of complete states is inconsistent with libertarianism. One cannot, therefore, assume the existence of complete states when arguing against libertarianism. To do so is to beg the question. Finally, I note that my thesis in this paper is very close to the familiar idea that indeterminism requires indeterminacy. Objective indeterminacy has always been a tricky idea to defend, since indeterminacy seems properly to belong to representations, descriptions, etc., rather than the world. Having proved that maximal states are often incomplete, however (in the indeterministic case that is) we now have a straightforward way to understand objective indeterminacy. For while descriptions in general cannot be considered objective, since they are not determined by the world, maximal descriptions are indeed objective. While there are many true descriptions of something, there is only one maximal true description. Hence the maximal true description supervenes on the 8

physical facts. And the incompleteness of such descriptions means that the world itself is undetermined by them. Moreover, we have shown that such objective fuzziness is a necessary condition for indeterministic causation. 9