How We May Be Free From Physics

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How We May Be Free From Physics
Chuang Liu

Professor of Philosophy

University of Florida, USA
Our discussion in the first five sections shows that little new can be said about compatibilism, that van Inwagen's argument for incompatibilism still stands, and that the view of free agency for a libertarian has little chance unless she believes that agency contains elements that are not within the natural order. Borrowing from a suggestion from Russell we expanded the Nozick-Kane model of libertarian free agency and connected it to the Wignerian interpretation of quantum measurement. As such, free decisions and choices may well violate the Born rule of probability distribution and yet it is shown how such violations are unlikely to be detected in experiments. This model is probably the only model in which Loewer's van Inwagen style argument for the incompatibility between free agency and quantum indeterminism does not apply, and it is a model in which free agency is not only compatible but necessary. It is compatible with indeterminism and it is necessary for the determinateness of any measurement outcomes.
I. On Frankfurt-type cases and ceteris paribus laws

For the sake of later discussion, let me refresh our memory of van Inwagen's main argument against compatibilism in a simple example. Suppose there is a very simple world, D, in which there are five objects. Physically they can hardly be distinguished from one another and they are no different from perfectly solid (and rigid) pebbles in our world; but one of them has the mental capacity of an ordinary person.1 D may be strange but it is certainly a possible world, and because it is physically so simple only the deterministic (or Newtonian) laws of motion and gravity need to be considered. The intelligent pebble, let us call it Shiren, reports that he can entertain alternative possible directions and/or ways he wants to move in D and can even make decisions about which direction and/or way he wants, but if he has a clear understanding of his predicament, which he must have because he has an ordinary intelligence by our standard and his predicament is extremely simple, he will know that none of his acts can be regarded as free even if he fully feels that some of his moves are the result of his decisions. His reasoning is likely to go as follows.

If D, my universe, is deterministic, which seems obviously true, the law and some event E in the past entails that I moved in a certain direction B at time t. If I had moved in a different direction B' at time t, I would have made 'moving in direction B at time t' false. That implies I would have made either the law false or E otherwise. No one can change the past, so it is not possible for me to have made E otherwise; therefore, I would have made the law false. But no one can made a law of physics false; therefore, I could not have moved in direction B' at time t. Hence, by reason against absurdity, if determinism is true in D, I could not have moved in a different direction than I was determined to move.2
The restriction 'in D' in the last sentence can be removed and a similar argument can be made for any possible world that is deterministic in the sense that the laws and any event in that world together determine uniquely any other events in it. And this is essentially van Inwagen's argument (van Inwagen 1983, ch. III).

The basic assumptions for the argument can be stated roughly as follows.

(1) Free actions (that ground moral responsibility) requires the possibility of real alternatives.

(2) It is not possible to change the past.

(3) It is not possible to violate the laws.
There is a large literature debating the necessity of (1); and the most prominent line is what is known as the Frankfurt-type cases against the “principle of alternative possibilities (PAP)” (cf. Kane 2002, part V.) The point that is common to all the cases is simply this: because one can imagine cases - situations where clever devices are inserted at the right places to eliminate, without the agent's awareness, the relevant alternative possibilities required according to assumption (1) for free decisions - where an agent has obviously made a decision to act in a way that he should be held responsible and yet for him no relevant alternatives exist regarding his decision.

I shall not engage the debate here but ask the following question: do Frankfurt-type cases provide counterexamples to van Inwagen's argument? Van Inwagen certainly does not think so (cf. Van Inwagen (1983) pp. 162-182). His argument as sketched above is for the incompatibility of free will and determinism; it does not say anything about what is necessary for an agent to be held responsible for her actions. Although he believes that to be morally responsible for one's act one must be able not to have carried it out or carried it out differently - and he has arguments for this claim - he concedes that the Frankfurt-type cases make a forceful and appealing rejection to it. If the Frankfurt-type cases are indeed successful, we must admit that one can be morally responsible for one's actions without one's being able to have done otherwise. This means for van Inwagen that one can be held responsible for acts that one has not done freely or, in other words, one does not need freedom of will to be responsible for one's own actions.

This take on the implication of the Frankfurt-type cases, obviously preferred by van van Inwagen, is problematic, to say the least. First, because the agents in most of the Frankfurt-type cases are unaware of the existence of the devices that eliminate their freedom of choice, they made their decision as if they were entirely free. If we compare the actual decision trajectory of a Frankfurt agent with the trajectory of a similar agent who is exactly alike but without a Frankfurt-type device, there is no discernable difference between the two. Hence, if the latter agent can be said to have freely chosen his action, there is no reason for us to say that the Frankfurt agent has not, despite the fact that all the alternative possibilities are removed by the implemented device. And it is this 'free choice' without alternative possibilities that makes it plausible for us to attribute moral responsibility to the agent's action. Second, the two positions, hard determinism and compatibilism are not the negation of each other. Hard determinism is the position that says if determinism is true, there is no free will (no actions are chosen freely) and hence no one is morally responsible for one's actions, while compatibilism says that even if determinism is true, there could be free will and hence one can be morally responsible for one's actions. The Frankfurt-cases arguments are aimed at vindicating compatibilism; they are not aimed simply at refuting hard determinism (i.e. even if determinism is true, agents are still morally responsible for all of their actions). If van Inwagen's interpretation is correct, the latter would have to be the sole purpose of the Frankfurt-type cases. Third, the common sense belief that we cannot be morally responsible for all of our actions must be kept whatever our view on free will is; but if determinism is true, all actions are without alternative possibilities. What distinguishes those actions we are responsible from those we are not, despite the lack of alternative possibilities? It must be something that we judge as having been chosen by us rather than having us been coerced into doing them. This distinction does not exist unless Frankfurt and company are right that there are free choices without genuine alternative possibilities. Therefore, van Inwagen's interpretation is seriously flawed.

If this is so, the answer to my initial question: do Frankfurt-type cases provide counterexamples to van Iwagen's argument should be a 'Yes.' There are freely decided actions for which the agents involved are morally responsible if Frankfurt and his supporters are right, and if so, van Inwagen's argument for incompatibilism is unsound. However, I am yet to be convinced that Frankfurt and his supporters are right, which is a controversy I shall not touch here. The above is a critique of van Inwagen's take on the implication of Frankfurt-type cases only.

Let me return to the main track after this short detour. Assumption (2) is impossible to assail or at least much more difficult to assail than any other assumptions or claims in the whole debate. Even if one can travel back in time, one has to make sure that such journeys change nothing in the past (cf. Lewis 1986, p.67ff); in fact this is part of the consistency condition that makes time travel possible.3 Hence the assumption must be left alone.

Before we consider the possibility of (3) let us consider the following question: could a natural system's complexity, and perhaps some emergent properties in it, make sense of our control over our decision-making processes and actions even if determinism is true? To answer this question, we need to see whether it is true that as we conceptually increase the complexity of a simple possible universe (with the aim of making it more and more resemble our universe as we now know it) whether certain “rooms” or “spaces” open up so that the determinism becomes less stringent.

Let us first make a simple Newtonian universe more complex by adding a large number of similar particles - as large a number as one wants. It's obvious that the determinism remains the same as long as their behavior is similarly governed only by Newton's laws of motion and gravitation. Next let us give the particles more properties, such as electric charges, such that a new force of interaction and a new law of electromagnetism are introduced to the universe. If the law of electromagnetism is as deterministic as the law of gravity, we do not seem to have any reason to suspect that the nature of determinism is changed. The state of this enriched universe is simply defined as the positions and momenta of all the particles and any state at any time is completely determined when the state at another time is given together with the three laws (of motion, of gravity, and of electromagnetism) in the same rigorous sense of entailment (or derivability) as given above. This recipe, or any straightforward variation of it, of making a universe more complex can obviously be repeated as many times as one likes so that the resulting universe looks more and more like the actual world. Notice, the recipe is entirely general and extremely flexible: the denizen of the universe can be physical objects of any kind of (finite) sizes and shapes and possessing any number of properties - mass, charge, properties describable in chemistry, geology, biology, or psychology. Prima facie, as long as the instantiations of these properties in the objects together completely define the state of the universe and the values of these properties change strictly according to deterministic laws, the nature of determinism will remain the same as the strict determinism in the simplest world with which we begin, if determinism holds at all.

I begin the previous sentence with “Prima facie,” but is it in fact true? One can think of different ways to challenge the claim, and one of which is to appeal to the ceteris paribus nature of laws (and regularities) Let us suppose for the sake of simplicity that laws of nature have the logical form:

(4) All Fs are Gs,
where F stands for one property and G another. For instance, Newton's law of gravity can be put into this form by saying roughly “all objects with mass are objects that attract one another with the force of gravity that is expressed in the equation __.” A subclass of laws may however be better represented by a variation of the above form:
(5) Whenever X happens at t, Y happens at t*, t*≥t,
where X and Y are two distinct sets of events (including the singletons) and t and t* two instants in time. A degenerate form of both types of laws are known in the literature as the ‘ceteris paribus laws’ because they are said not to be true by themselves but true ’when all other things - most of which are unaccounted for - are equal.’ Such laws, if they can be regarded as laws of nature at all, are most frequently seen in disciplines of science that deal with complex phenomena (think of evolutionary biology and sociology). It therefore may seem reasonable, nay even natural, to conclude that in a world as complex as ours there are laws of this kind, and if so, the determinism in our world is a ‘softer,’ less strict kind of determinism. But can the notion of ceteris paribus laws create some degree of freedom for options or choice in which we reconcile determinism and free will?

Many generalizations we encounter are of the following kind. Eating amount X of carbohydrate makes you fat. Playing amount Y of violent videogames in adolescence makes someone commit a violent crime in his adulthood. Throwing a lighted match to a heap of dry grass ignites it. Brushing your teeth twice a day, every day, prevents cavities in your mouth. We all know that these and others similar to these are not always true; they admit exceptions. To make them true, we can always say this: all things being equal, eating this much carbohydrate will make you fat; all thing being equal, brushing your teeth twice a day, every day, will prevent cavities in your mouth; and so on. The reason behind our doing this is the following simple fact. For every person at any time, eating amount X of carbohydrate will either make him fat or it will not make him fat. Separate the people (and their circumstances when they consume a lot of sugary stuff) into two classes: those who get fat and those who do not. Then we say the statement ‘eating amount X of carbohydrate will make you fat’ must be true to those cases where the circumstances are exactly the same as the people who get fat (or the intersection of their circumstances) (hence the phrase ‘all things being equal’). The statement, which is purportedly about a law of nature, is therefore made true; but unless we know exactly what those circumstances are that must be kept the same we do not really know what the statement says. Notice, it is not that the statement says something vague or imprecise; no, it is precise because ‘all things’ refers to those and only those circumstances that guarantee the truth of the statement. When all circumstances - whatever they are - are held equal, everyone who eats amount X of carbohydrate will get fat.4 But we do not know in most of such cases what is said by the statement, because we do not know what are the things that ‘all things’ refer to.

Because of this subtle difference between what is said by a ceteris paribus law-statement and what we can know about what is said there, I do not believe that even if the laws of nature in our world include ceteris paribus ‘laws,‘ the determinism we have is any less strict. If our world is deterministic, it entails that for every ceteris paribus law the circumstances that the ‘all things being equal’ phrase refers to are well-defined and determined in a logical sense. We may not and never know what they are, but as far as the laws governing the behavior of the objects in our universe are concerned, the grip is just as strict as the laws that do not have the ceteris paribus clause. To put this matter in another way. Suppose there is an omniscient being who knows all circumstances at all time. For him there are no ceteris paribus laws or such laws are not necessary for him because the above-mentioned difference between what is said and what can be known in a ceteris paribus law-statement does not apply to him. He knows whatever is said about our universe. Is it not obvious that how strict a determinism our world has is not determined by us, who are ignorant of many things, but by him who is omniscient?

Moreover, even if our determinism is less strict because of the ceteris paribus nature of some of the laws, it will not help in giving us a place for free will. What makes such laws govern less strictly is that the ‘law‘ fails to hold when the circumstances are presumably not all the same. One may think that a free agent may be able to exploit such a situation in the sense that he can exert control over his choice in those circumstances in which the grip of the ‘law’ in question is absent. But this can never happen if the laws are truly ceteris paribus because there is a dilemma: if an ordinary agent is able to know when the law holds and when it has exceptions then the law is no longer ceteris paribus for him, such as it could never be to an omniscient being, or if the law is truly ceteris paribus to the agent then whatever room it creates is no use to him. Hence, even if an agent tries to explore the situation, his effort can only succeed by chance; and that is opposite to what we take as evidence of his free agency. We are now back to that dilemma for free will that threatens to exclude it whether or not the world is deterministic. Hard incompatibilists (cf. Pereboom 2001) have compellingly argued that if the world is deterministic, it has no place for free will; but if the world is indeterministic, it has no place for free will either because what happens in such a world happens by shear chance, and chance is perhaps more incompatible with control or choice of free agency. So, to open the world, so to speak, to a softer determinism by evoking the notion of ceteris paribus laws does not work.

However, our recipe I described above can produce a logically possible world in which there is an opening. To a world (/universe) that either has an infinite number of inhabitants or has inhabitants that have an infinite number of properties, determinism may have to loosen its grip. In this world ceteris paribus laws, if there are such, are by default open-ended laws, because the ‘all things being equal’ clause truly refers to an undeterminable set of circumstances that are not merely unknowable to us but unknowable to an omniscient being or unknowable in principle. But on the other hand, open-endedness is the least problem for such a world; an infinite world is difficult to deal with conceptually unless some restrictions are implemented. Strictly speaking one cannot even define a state of this universe at any instant of time because it would involve an infinite number of numbers, which is not a determinant. Because of that one can not conceive of laws in that world in any ordinary sense, i.e. in terms of nomological connections among states. The most natural restriction one would assume if one has to deal with such a universe is a segregation condition of some sort. If this universe can be roughly divided into two parts, one populated and the rest almost empty, then we can just deal with the populated part and ignore for all practical purposes the rest. If one thinks that our world is such an infinite universe and the laws governing the populated part in which we inhabit are all strictly deterministic, then the rare intrusion of things from the nearly vacuous part that is the rest of our universe may serve to loosen the grip of this determinism. This seems reasonable but again it does nothing to help us rehabilitate the compatibility between determinism and free will, because whatever model one conceives in the attempt to bridge such occasional intrusions from the outside with the incidents of free decision is bound to appear implausible if not downright ridiculous.

To summarize, the existence of ceteris paribus laws in a world by itself does not make it less deterministic, and even if the world is less deterministic (than the simplest possible world with only two particles and Newton's laws), because for example that it is infinite in some sense, the ‘softer’ determinism would not provide any room for free will to make compatibilism more plausible.

II. How violating laws, if possible, makes room for freedom

We agree as most do that we cannot change the past. What happened cannot be changed even if one can travel back in time. But can we violate laws of nature? And if in some sense we can, would our ability to violate laws help us to reconcile determinism with free will? But do we really feel that we have violated any laws every time we make a decision that we think is entirely up to us; that is to say when we think we have made a free decision and thereby we are fully morally responsible for what happened as a result of that decision? ‘No, absolutely not!’ would be the usual answer. If this is correct, then who cares even if we are able to violate laws in some sense? I do believe there is a lot of truth in this simple, common-sense, observation, which will be shown by the end of this essay. In the meantime, let us press on.

To find out whether an agent (i.e. a human being or a rational being) can violate a law of nature in the sense of doing something to render a law false at some instant of time we must first know what laws are. I can only briefly review some settled views on laws here, but such a review should suffice because what we need is not a particular view in all its details but some common features of laws that different views can agree to. For example, it should not matter much for our purpose whether laws are regularities of some sort (one view) or relations among universals (another view) as long as they are made out to support counterfactuals.

Let us go back to the two forms I mentioned earlier for laws, (4) and (5). A law-statement is either of the form ‘all Fs are Gs’ or of the form ‘whenever X happens at t, Y happens at t*,’ where the first form quantifies over things as well as events while the second only events. So, laws are at least regularities that are represented by statements of type (4) (or (5)). Not all regularities are laws; lawlike regularities must be distinguishable from accidental ones in any adequate theory of laws. One of the prominent features of laws that distinguish them from mere regularities is that laws support counterfactual statements and mere regularities do not. To account for such a feature (and some others features) two theories are prominent in the literature: the (sophisticated) regularity theory and the universalist theory, the most widely discussed of the former belongs to Lewis's Best-system theory and the most widely discussed of the latter the Armstrong-Dretske theory. Racially different ontologies separate the two theories. Lewis and the rest of the regularitists think that laws are nothing but regularities that have some extra logical or epistemological features, while Armstrong and the rest of the universalists think that universals, besides things and/or events, exist in reality and laws are special relations among these universals (some think they are contingent while others think they are logically necessary relations).

To distinguish a law from a mere regularity, the regularitists can be seen as using the formula:
(6) Law = Regularity + X,
where X is a set of constraints of some sort that does not temper with the ontology. Most such theories take X to consist of epistemological conditions (cf. Ayer 1963, Skyrms 1980, Urbach 1988), but Lewis's is different (cf, Lewis 1973, 71ff); the constraints in his theory are logical and pragmatic. Here is a very brief sketch of Lewis's theory with a remark on its connection to his metaphysics. Imagine the totality of all facts in our world, some of which are particular and some are general (i.e. regularities). These facts are logically related: one fact entails another and are entailed by yet another; but some facts, specially some of the general facts, entail a lot more other facts than others. Imagine an axiomatized system over all the facts of our world that is structured as a hierarchy of entailment: the more general facts that entail more other facts are towards the top and the less general that entail less are towards the bottom. Now imagine many alternative such systems, some of which are very informative, meaning containing a lot of propositions for particular facts, while some are very simple, meaning containing mostly highly abstract and general propositions. (As two extremes: the most informative system is the one that contains no truly general proposition but only propositions of particular facts; and the simplest system is one that contains one or a few propositions that are true of everything in our world. From a practical point of view neither is useful to us.) What we want is a system that has the best balance of simplicity and informativeness (which Lewis calls ‘strength’); and a law of nature is an axiom or a theorem of such a system. This is the skeleton of the theory and we can see that the additional component X contains only logical elements - the axiomatization - and pragmatic elements - the standards for simplicity and strength.

How can laws in the Best-system theory support counterfactuals? Here is a brief, perhaps too brief, answer. Logical systems of the above-mentioned kind exist in almost all logically possible worlds. The possible worlds that are close to our world (the actual world) differ from it mostly in particular facts. A possible world that contains a different number of people and/or trees and/or dogs and/or rivers, etc. is closer to us than one that contains dogs that design computers while humans only bark and fetch, and so on; and this latter world is closer to us than a world that contains birds that fly faster than the speed of light. Intuitively we only regard the first kind of possible worlds as close to us, whereas those worlds in which dogs design computers or birds fly superluminally are likely to be worlds that do not obey the same set of laws in our world. A difference of particular facts does not affect the structure of the axiomatic system. Hence, our axiomatic system that give us our laws in our world is shared by all the possible worlds that are close to us. That means the laws are also shared among such worlds. And if so, what is made true by laws in our world is also true in those worlds; and that grounds the truth/falsity of our counterfactual statements. Quite generally, if something that is not a M were to be a M, would it also be a R (given ‘all Ms are Rs’ expresses one of our laws)? The answer is yes from the Lewis theory, because the possible world in which a non-M object in our world is a M-object is a world that differs from ours only in particular facts, and hence our law, all Ms are Rs, is also its law; and because of that all Ms are Rs in that world, and therefore something in our world would be a R if it were a M.

We are now ready to examine Lewis's notorious claim that there is a sense in which one can violate a law of nature (cf. Lewis 1981). Recall in that little argument Shiren gives at the beginning of this essay. One of the key premises is that no one can violate a law of nature. If one can, that argument is no longer sound, but that means van Iwagen's famous argument for incompatibilism is unsound because Shiren's argument is a simple instance of van Inwagen's. It may seem obvious that in order to violate a law, one must be able to do something at time t to make the law fail at least at t or do something that causes an event at time t that makes the law fail at least at t. Either way, to violate a law is to be able to do something that, directly or indirectly, causes an instance of a law's failure. This, Lewis thinks, is impossible and I agree. However, Lewis thinks that there is at least one other way that one can violate a law. A law can be violated, in what Lewis regards as a ‘weak‘ sense, if one is able to do something such that the law would have failed if he did it. The simple verbal formulation of the two senses - the strong and the weak - of the notion may not be ideal to convey the differences between them, but a careful reading of Lewis's article should yield the following implications.

With the strong sense, the relation between one's action and the violation of a law is primarily a causal one: the action causes, directly or indirectly, the violation; and because of this causal relation, the fact about the action entails the fact about the violation. With the weak sense, there is no causal relation between one's action and the violation, and yet the fact that one did the act entails that the law in question would have been violated. If I am able to violate a law in the weak sense, it may still be impossible for me to do anything to ‘break‘ the law's grip on the processes of events, and yet there must be something such that if I did it this or that law must have been violated (though not at all by what I have done). It also follows from the difference that all instances for the strong sense are those future directed causal sequences, or simultaneous events, such that if I am able to violate a law, my act is either the law-breaking event or the cause of some later law-breaking event. All the instances for the weak sense are, on the contrary, past directed: my 'law-violating' acts indicate that the law in question must have been violated at some point in time before my act.

What would be an example of the violation of a law in the weak sense? There is at least one class of examples of which the following is quite typical. Suppose it is a law that nothing move faster than the speed of light. The law would have been violated if I did observe an object that moves faster than the speed of light. What I did - observing that an object moves faster than the speed of light - does nothing to violate the law in question nor does it cause anything else to violate it, and yet if I did it the law would have been violated, because it is logically impossible for there to have been no breach of that law and yet I observed an superluminal object.

What does this all mean? Why is the violation of a law in the weak sense less severe than the one in the strong sense, and how could the former happen if the latter as Lewis says could not? I am not sure I see a good answer on behalf of Lewis except perhaps the following. Seeing a superluminal object is less radical an event than accelerating an object over the speed of light. Therefore a possible world in which the former happens is less different (or closer) to our world than one in which the latter happens. While we can never accept the latter world as close to us, we perhaps can accept the former as close enough, and yet the law in question is violated in that world.

Does Lewis's conception help to rehabilitate free will and therefore support compatibilism? And if it does then how? Here is how I think it might work. Laws and facts in the universalist ontology are creatures of different metaphysical species; but for a regularitist like Lewis, they are metaphysically the same. They differ in the logical status in the axiomatized system. When we look at possible worlds that are ordered according to their closeness to our world we usually find those worlds that differ only in singular facts but in no laws much closer than a world that differ in at least one law. But this does not have to hold absolutely. Ask yourself which of the following worlds differs from our world more. In one world a few pieces of metal - they are true metal by their chemical composition - fails to conduct electricity for no reason at all but everything else is the same as in our world; and in the other world all metals conduct electricity and everything else is the same as in our world except creatures designing computers all physiologically like dogs and a popular type of pets are physiologically no different from humans.

What is the relevance of the above to solving the free will problem and compatibilism? A complete and accurate answer to this question may be difficult to come by but the following case should suffice for a start. Suppose determinism is true and it so happens that the last meal my mother ate before I was born was of such amount and composition that together with all the laws that govern whatever is relevant to my growth and development such that it is entailed that I would be sitting here writing this essay at this moment. But just at this moment I could have decided of my own free will to stand up and walk to the kitchen and brew a cup of coffee, etc., in other words, I could have decided right now to take a break and taken it. Suppose again that it has been found out which of those laws alluded above must have been violated in order for this to have happened; and it turns out that the most severe consequences of such a violation is that several other people would have had some events in their lives slighted altered, most of which are on the magnitude of standing a few feet away from what he or she actually stood at a certain moment or being indoors rather being outdoors which is where they actually were or …, the most dramatic being that one person missed one of her daily commuting train and had to take another train 15 minutes later.5 Now is the world in which I did take the break and thereby had several laws violated that bear no more than the above-mentioned consequences a closer possible world to our world than a world in which it is impossible for me to take the break and no law was violated? Lewis can be interpreted as saying ‘yes‘ to this question, and it is in this sense Lewis's soft determinism helps compatibilism.

Therefore, if laws of nature are what Lewis and company say they are and free actions as they are described in common sense are indispensable, then deterministic reality must be such that given any event at time t, another event at another time t* can only be determined up to a point by the laws.

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