Back in 1814, Pierre-Simon Laplace was mulling over the implications of Newtonian mechanics, and realized something profound. If there were a vast intelligence — since dubbed Laplace’s Demon — that knew the exact state of the universe at any one moment, and knew all the laws of physics, and had arbitrarily large computational capacity, it could both predict the future and reconstruct the past with perfect accuracy. While this is a straightforward consequence of Newton’s theory, it seems to conflict with our intuitive notion of free will. Even if there is no such demon, presumably there is some particular state of the universe, which implies that the future is fixed by the present. What room, then, for free choice? What’s surprising is that we still don’t have a consensus answer to this question. Subsequent developments, most relevantly in the probabilistic nature of predictions in quantum mechanics, have muddied the waters more than clarifying them.

Massimo Pigliucci has written a primer for skeptics of determinism, in part spurred by reading (and taking issue with) Alex Rosenberg’s new book *The Atheist’s Guide to Reality*, which I mentioned here. And Jerry Coyne responds, mostly to say that none of this amounts to “free will” over and above the laws of physics. (Which is true, even if, as I’ll mention below, quantum indeterminacy can propagate upward to classical behavior.) I wanted to give my own two cents, partly as a physicist and partly as a guy who just can’t resist giving his two cents.

Echoing Massimo’s structure, here are some talking points:

* There are probably many notions of what determinism means, but let’s distinguish two. The crucial thing is that the universe can be divided up into different moments of time. (The division will generally be highly non-unique, but that’s okay.) Then we can call “global determinism” the claim that, if we know the exact state of the whole universe at one time, the future and past are completely determined. But we can also define “local determinism” to be the claim that, if we know the exact state of some part of the universe at one time, the future and past of a certain region of the universe (the “domain of dependence”) is completely determined. Both are reasonable and relevant.

* It makes sense to be interested, as Massimo seems to be, in whether or not the one true correct ultimate set of laws of physics are deterministic or not. He argues that we don’t know, and that’s obviously right, since we don’t know what the final theory is. But that’s a rather defeatist attitude all by itself; we can look at the theories we do understand and try to draw lessons from them.

* Classical mechanics, which you might have thought was deterministic if anything was, actually has some loopholes. We can think of certain situations where more than one future obeys the equations of motion starting from the same past. This is discussed a bit in the Stanford Encyclopedia of Philosophy article on causal determinism. But I personally don’t find the examples that impressive. For one thing, they are highly non-generic; you have to work really hard to find these kinds of solutions, and they certainly aren’t stable under small perturbations. More importantly, classical mechanics isn’t right; it’s just an approximation to quantum mechanics, and these finely-tuned classical solutions would be dramatically altered by quantum effects.

* General relativity is a classical theory, so it’s also not correct, but we don’t have the final theory of quantum gravity so it’s worth a look. As Massimo points out, there are good examples in GR where traditional global determinism breaks down; naked singularities would be an example. (Basically, determinism breaks down when information can in principle “flow in” from a singularity or boundary that isn’t included in “the whole universe at one moment of time.”) We might sidestep this problem by arguing that naked singularities aren’t physical, which is quite reasonable. But there are much more benign examples, such as anti-de Sitter space — a maximally symmetric spacetime with a negative cosmological constant. This universe has no singularities, but does have a boundary at infinity, so a single moment of time only determines part of the universe, not the whole thing. On the other hand, like the classical-mechanics examples alluded to above, this seems like a technicality that can be cleared up with a slight change of definition, e.g. by imposing some simple boundary condition at infinity.

Much more importantly, these kinds of GR phenomena are very far away from our everyday lives; there’s really no relevance to discussions of free will. GR violates global determinism in the strict sense, but certainly obeys local determinism; that’s all that should be required for this kind of discussion.

* Quantum mechanics is where things get interesting. When a quantum state is happily evolving along according to the Schrödinger equation, everything is perfectly deterministic; indeed, more so than classical mechanics, because the space of states (Hilbert space) doesn’t allow for the kind of non-generic funny business that let non-deterministic classical solutions sneak in. But when we make an observation, we are unable to deterministically predict what its outcome will be. (And Bell’s theorem at least suggests that this inability is not just because we’re not smart enough; we never will be able to make such predictions.) At this point, opinions become split about whether the loss of determinism is real, or merely apparent. This is a crucial question for both physicists and philosophers, but not directly relevant for the question of free will.

The traditional (“Copenhagen”) view is that QM is truly non-deterministic, and that probability plays a central role in the measurement process when wave functions collapse. Unfortunately, this process is extremely unsatisfying, not just because it runs contrary to our philosophical prejudices but because what counts as a “measurement” and the quantum/classical split are extremely ill-defined. Almost everyone agrees we should do better, despite the fact that we still teach this approach in textbooks. Someone like Tom Banks would try to eliminate the magical process of wave function collapse, but keep probability (and thus a loss of determinism) as a central feature. There is a whole school of thought along these lines, which treats the quantum state as a device for tracking probabilities; see this excellent post by Matt Leifer for more details.

The other way to go is many-worlds, which says that the ordinary deterministic evolution of the Schrödinger equation is all that ever happens. The problem there is comporting such a claim with the reality of our experience — we see Schrödinger’s cat to be alive or dead, not ever in a live/dead superposition as QM would seem to imply. The resolution is that “we” are not described by the entire quantum state; rather, we live in one branch of the wave function, which also includes numerous other branches where different outcomes were observed. This approach (which I favor) restores determinism at the level of the fundamental equations, but sacrifices it for the observational predictions made by real observers. If I were keeping a tally, I would certainly put this one in the non-determinism camp, for anyone interested in questions of free will.

* Then there is the question of whether or not the lack of determinism in QM plays any role at all in our everyday lives. When we flip a coin or play the lottery, one might think that the relevant probabilities are “purely classical” — i.e. they stem from our lack of knowledge about the state of the muscles and nerves in my hand and the wind and the coin that is about to be flipped, but if I knew all of those things I could make a perfectly deterministic prediction about what would happen to the coin. (Indeed, a well-trained magician can flip a coin and get whatever result they want.)

This is actually a tricky problem, to which the answers aren’t clear. Yes, there may be a level of classical description in terms of a probability distribution; but where does that probability distribution come from? Physicists disagree about whether or not quantum mechanics plays a crucial role here. Since I have friends in high places, this weekend I emailed Andy Albrecht, who answered and brought David Deutsch into the conversation. They both argue — plausibly, although I’m not really qualified to pass judgment — that essentially

allclassical probabilities can ultimately traced down to the quantum wave function. And indeed, that this reasoning provides the only sensible basis for talking about probabilities at all! (David mentions that Lev Vaidman seems to disagree, so it’s not uncontroversial by any means.) They are both, in other words, firmly anti-Bayesian in their view on probability. A good Bayesian thinks that probabilities are always statements about our fundamental ignorance concerning what is “really” going on. Albrecht and Deutsch would argue that’s not true, probabilities are ultimately always statements about the wave function of the universe. If they’re right — and again, it looks plausible, but I need to think about it more — then QM effects are indeed of crucial importance in accounting for our inability to predict the future in the everyday world.

* I should say something about chaos, which always comes up in these discussions. In classical mechanics, even when the underlying model is perfectly deterministic, it can often be the case that a small uncertainty in our knowledge of the initial state can lead to large uncertainty in the future/past evolution. (E.g. for the tumbling of Hyperion.) This is sometimes brought up as if it causes problems for determinism: “since tiny mistakes propagate, you couldn’t realistically predict the future anyway.” This is about as irrelevant as it is possible to be irrelevant. The Laplacian viewpoint was always that if you had

perfectinformation, you could predict the past and future. But that was always a statement of principle, not of practice. Of course, in practice, you have nowhere near enough information to make the kinds of calculation that Laplace’s vast intellect likes to do. That was perfectly obvious long before the advent of chaos theory. The correct statement is “in a classical deterministic system, with perfect information and arbitrary computing power you can predict the future in principle, but not in practice,” and that statement is completely unaltered by an understanding of chaos.

So where does that leave us? My personal suspicion is that the ultimate laws of physics will embody something like the many-worlds philosophy: the underlying laws are perfectly deterministic, but what happens along any specific history is irreducibly probabilistic. (In a better understanding of quantum gravity, our notion of “time” might be altered, and therefore our notion of “determinism” might be affected; but I suspect that there will still be some underlying equations that are rigidly obeyed.) But that’s just a suspicion, not anything worth taking to the bank. For everyday-life purposes, we can’t get around the fact that quantum mechanics makes it impossible to predict the future robustly.

Of course, this is all utterly irrelevant for questions of free will. (I’m sure Massimo knows this, but he didn’t discuss it in his blog post.) We can imagine four different possibilities: determinism + free will, indeterminism + free will, determinism + no free will, and indeterminism + no free will. All of these are logically possible, and in fact beliefs that some people actually hold! Bringing determinism into discussions of free will is a red herring.

It matters, of course, how one defines “free will.” The usual strategy in these discussions is to pick your own definition, and then argue on that basis, no matter what definition is being used by the person you’re arguing with. It’s not a strategy that advances human knowledge, but it makes for an endless string of debates.

A better question is, if we choose to think of human beings as collections of atoms and particles evolving according to the laws of physics, is such a description accurate and complete? Or is there something about human consciousness — some strong sense of “free will” — that allows us to deviate from the predictions that such a purely mechanistic model would make?

If *that’s* your definition of free will, then it doesn’t matter whether the laws of physics are deterministic or not — all that matters is that there are laws. If the atoms and particles that make up human beings obey those laws, there is no free will in this strong sense; if there is such a notion of free will, the laws are violated. In particular, if you want to use the lack of determinism in quantum mechanics to make room for supra-physical human volition (or, for that matter, occasional interventions by God in the course of biological evolution, as Francis Collins believes), then let’s be clear: you are not making use of the rules of quantum mechanics, you are simply *violating* them. Quantum mechanics doesn’t say “we don’t know what’s going to happen, but maybe our ineffable spirit energies are secretly making the choices”; it says “the probability of an outcome is the modulus squared of the quantum amplitude,” full stop. Just because there are probabilities doesn’t mean there is room for free will in that sense.

On the other hand, if you use a weak sense of free will, along the lines of “a useful theory of macroscopic human behavior models people as rational agents capable of making choices,” then free will is completely compatible with the underlying laws of physics, whether they are deterministic or not. That is the (fairly standard) compatibilist position, as defended by me in Free Will is as Real as Baseball. I would argue that this is the most useful notion of free will, the one people have in mind as they contemplate whether to go right to law school or spend a year hiking through Europe. It is not so weak as to be tautological: we could imagine a universe in which there were simple robust future boundary conditions, such that a model of rational agents would not be sufficient to describe the world. E.g. a world in which there were accurate prophesies of the future: “You will grow up to marry a handsome prince.” (Like it or not.) For better or for worse, that’s not the world we live in. What happens to you in the future is a combination of choices you make and forces well beyond your control — make the best of it!

If I learned there was no such thing as free will, I would live my life very differently. 🙂

I think that the idea of determinism is not well defined. Furthermore, the idea of randomness is even less well defined. On the other hand, I think that uncertainty is something that we can easily quantify, and we deal with it daily in many ways.

One thing I hate to think of is a point particle. Or rather, I hate even more thinking of many point particles. The chance of two point particles colliding is precisely zero unless you assume that they are capable of attracting each other to an infinite extent. But that infinite extent makes points just as nasty as naked singularities. I can accept that there are point-like phenomena associated with a finite force field and that picture breaks down on some scale, but I think that any subsequent renormalization only confirms that the picture is going to be wrong on some scale.

Another thing I hate to think of is plane waves that go on forever. I hate even wave packets that are clumpy but have to be defined way out at infinity to make the math work out right. It is really hard for me to think about how one bit of one real-world wave correlates with another bit of itself, but it must do so to some extent or else it wouldn’t be much of a wave. I bet that the extent is limited and that its limited nature shows up in detectors as imprecise arrival times of peaks and troughs (or imprecise photon arrival times that cannot be attributed to the source).

What I find odd is that the hydrogen atom behaves in ways that suggest mathematical things like Hilbert Space or a space of all possibilities exist in some way. I am certain these things are useful mathematical tools but I fear that they are otherwise physical nonsense. They cannot exist in this world any more than a point particle can.

My thoughts: There’s absolutely no reason to think that physicalism (or determinism) in any way implies that we aren’t free or rational.

Hawking asks whither the laws of physics might “not equally well determine that we draw the wrong conclusion.”

Sure, they might, in one sense. But only in the sense that the laws of physics might determine that a mouse will walk backwards to the edge of a cliff and leap backwards to its death. Such a process is physically possible — and it might be determined by the laws of physics — but as a matter of fact, it doesn’t fit with the emergent structure (e.g., biological structure and psychological structure) of the actual world.

Rationality and freedom (of the compatibilist sort) are emergent physical features, and the development of these features makes it more likely that if we keep working at it, we’ll get an account of physics that’s more or less right.

“The relevant point is that the behavior does follow the physical laws.”

The thing about chaos (or, more generally, situations that are arbitrarily sensitive to initial conditions) is that you cannot show that, at least, not fully. I think that that is why it is improper to dismiss chaos here. (In other words, physics is at its heart about the prediction of consequences of initial actions. If the knowledge of the initial conditions is lost through chaotic evolution, so that you cannot calculate effect from cause, then you cannot be sure that that the physical law is in fact fully being followed. Maybe it is some other law, which also leads to a loss of knowledge of initial conditions.)

Note that this is a fundamental failure. No matter how accurate your measurements are, and how many digits your calculations carry, I can make you lose all precision. If there is a “ghost in the machine,” I suspect that’s where it would enter in.

sprawld says

“Deutsch, Wallace et al. have shown pretty convincingly that you can derive probability amplitudes (mod squared) from MWI + decision theory or symmetry arguments.”

There seems to be a certain amount of credulous hype surrounding the decision-theory “derivation” of the Born rule for MWI. Sean Carroll describes it as “promising”, this commenter says it’s “convincing”. So I would like to point out a few things.

First, if you are going to derive the Born rule from a multiverse theory, then the obvious thing to expect is that Born probabilities correspond to frequencies in the multiverse. If quantum mechanics says that outcome A is twice as probable as outcome B, that should mean that outcome A is twice as common in the multiverse, compared to outcome B.

As things stand, MWI does not offer anything like this. Suppose we pick a basis and decompose the wavefunction, what do we get? *One* copy of each “world”, each of which has a complex number associated with it. If we decompose a reduced density matrix, instead of a full wavefunction, we at least get real numbers that look like probabilities, but so far, they’re still just numbers. Just because you now have a number 2/3 associated with the A-branch, and a number 1/3 associated with the B-branch, does not yet explain why we actually see outcome A twice as often as outcome B.

In my opinion, the logical thing to do would be to bite the bullet of duplicated worlds, and say that there are 2 copies of the A branch, and 1 copy of the B branch. You could get this by having an ontological axiom, that the coefficient of all branches must be equal, so a branch with coefficient 2/3 is actually a sum of two identical state vectors, each with a coefficient of 1/3. Finally this gives you a multiverse with the right multiplicities: outcome A now really does exist twice as often as outcome B.

However, the ideology of MWI advocates is usually that “the wavefunction is everything”, “the theory interprets itself”, etc., so the idea of a special axiom to (1) define what a world is (2) make sure that multiverse frequencies do match the Born rule, is unappealing to them. I can only think of one version of MWI which explicitly talks about duplicated or near-duplicated worlds in order to obtain the Born rule, and that’s Robin Hanson’s “mangled worlds”. (Zurek seems to be edging close to this option, but he doesn’t want to sign on to MWI, instead taking the absurd line that “existence requires redundancy”, so something only exists if it exists several times over.) Hanson’s mangled worlds, as I understand it, involves a dynamically determined preferred basis in which the required multiplicities are obtained by treating a world that is e.g. 99% |dead cat> + 1% |live cat> as a “dead cat” world. So Hanson’s individual worlds are themselves superpositions; a solution to MWI’s problems which might itself be regarded as problematic.

But returning to the mainstream of MWI – if mainstream is defined by public visibility and excited advocacy – that does appear to be defined by this “decision-theory derivation” of the Born rule. So allow me to point out what’s going on here. This perspective involves an explicit repudiation of the idea that Born probabilities correspond to multiverse frequencies. In one of his papers, David Wallace says there is just no answer to the question “how many copies of a given world are there?”

Instead, probabilities are to be obtained from decision theory. Let me sketch how this works. A common decision-theoretic concept is that you are to maximize your expected utility – the benefit you can expect to obtain, given an action – and this is equal to a weighted sum over the various possible outcomes. Each outcome has an intrinsic benefit (its “utility”), and it also has a probability. Winning $1 million in the lottery would be highly beneficial to you, but also highly improbable, which is why buying lottery tickets is not a way to maximize your *expected* utility… Maximizing your expected utility, for a decision theorist, defines rational behavior. So here, finally, we reach how the Deutsch-Wallace derivation of the Born rule is supposed to work. We will examine *rational behavior in the multiverse*, e.g. we will look at quantum game theory. The prescription, be rational, will tell us how we should act in quantum games; we know the intrinsic utilities of the various outcomes; so if we “divide out” the rationality ranking by the intrinsic utilities, the probabilities of the outcomes will be left over, and here we will recover the Born rule.

I fear that in describing this procedure, I have failed to convey the utter absurdity of it. So let’s go back to the big picture. MWI advocates have failed to find a satisfactory way to demonstrate that their multiverse contains two times as many copies of “A” as it does of “B”. So rather than conclude that there is a problem with their theory, they instead conclude that there is a problem with the concept of probability, and cleverly propose to do away with the idea that probabilities have something to do with how often an event occurs. Instead, they shall argue that being rational in the multiverse will require you to act *as if* A has twice the probability of B… I think I’m still not conveying how absurd and desperate a dodge this is.

In any case, I see many people talking about how the Deutsch-Wallace “derivation” is “promising” or “convincing”, and yet I don’t think they really understand what is being proposed, at a fundamental level – this logical inversion which makes probability dependent on rationality, rather than vice versa. Hopefully I have managed to enlighten a few people as to what’s really going on in their arguments.

Typically our reasons for thinking that we have the relevant laws in hand don’t rest on generating an absolutely precise prediction of a final state from an absolutely precise specification of an initial state. Instead, we get close enough, and run things many times, and we eventually decide that the best explanation of the data is the claim that the system follows certain simple laws.

What is often most important for our deciding whether some physical law holds is our knowledge of the domain of applicability of those laws. (Sean has discussed this in several places, e.g., here.)

This allows us to say that even though a system (e.g., a double pendulum) might be chaotic — thus making it impossible to predict its exact behavior — it nevertheless is obeying the laws of classical mechanics. (And the fact that the mechanics tells us that the behavior will be chaotic gives us all the more reason to believe that we’ve got the laws right.)

The usual reason for wondering if there is free will, is that the common notion of morality requires it. If there is no free will, the argument goes, how can we hold people responsible for their actions?

Of course, if there is no free will, then our choice of whether people can be held accountable for their actions also vanishes. Our choice, pro or con, is predetermined, and there is no point worrying about it.

** What happens to you in the future is a combination of choices you make and forces well beyond your control — make the best of it! **

Forces beyond my control would be for example to die in an earthquake .. But that that happened to me was because I was born on earth .. That’s the point of view of Buddhists .. So control it and try to not be born (again) … 😉

Free will, in any real sense, is dead if you accept determinism.

Regardless of whether you can *predict* the future or not, the path of your life and the fate of humanity, is already laid out as surely as the orbit of the moon around the earth.

You can *pretend* that you are making free choices that determine your future, but what choices you make are also determined by the laws of physics, as well as their consequences.

Thanks to Mitchell Porter (#30) for the critique of the (attempted) Decision Theory based derivation of probability in MWI. Personally I think that any such derivation is doomed, for the simple reason that you cannot get (fundamental) probabilities out of a model unless you put (fundamental) probabilities in. This seems so trivially obvious that I am amazed that so many educated people believe the purely deterministic MWI is a sensible idea, unless they really believe in a (super)deterministic universe – and in that case it is not even possible to conclude that logic is correct – so the whole scientific enterprise would be pointless.

But I think this debate always starts with the wrong emphasis – that determinism seems natural (due to Laplace argument etc) – whereas I would say it’s actually much more reasonable to accept that free-will is an obvious feature of the universe, at least since conscious life evolved. Is it not so staggeringly obvious that the behaviour of physical things on our planet is different from the deterministic behaviour on lifeless planets? A Poincaré recurrence cycle of the entire universe would probably happen more often than the Schrödinger equation would produce the works of Shakespeare.

(Super)Determinism is clearly not how the universe works once conscious beings have evolved, and I don’t need an intensive study of tedious theological or philosophical works to deduce that (although I have been unfortunate enough to have wasted time studying some of these in the past)

“What happens to you in the future is a combination of choices you make and forces well beyond your control — make the best of it!”

On the block universe view, which I think you accept, the future (like the past and present) is fixed in 4D spacetime. I imagine many folks would suppose the block universe obviates any notion of real choice, since choices too are equally fixed in spacetime. “Real” choices, “real” freedom, they might suppose, require us to exist outside spacetime, exerting control over it. But since we exist within spacetime, freedom and control can only consist in our participating in certain sorts of fixed patterns in the block universe, those in which the outcomes we want follow from the actions we take in service to our desires. This gets elaborated at http://www.naturalism.org/spacetime.htm but I’d be interested to get your take on it.

I think you are a little bit too hasty in dismissing the idea of simple robust future boundary conditions applying to our universe affecting the fate of “rational” agents.

How is free will “a useful theory of macroscopic human behavior models people as rational agents capable of making choices”? What constraint does free will make on predictions of behavior? Actually, free will is not a theory of behavior at all, since it (by definition) has no constraint. Unless you are using the words “useful” and “theory” in ways that they are not typically used in science, I see no way that your claim can be true.

And if it were true, why not describe other complex systems as having “free will”, like say, the weather? Certainly the ancients thought the weather was driven by will. Why are humans any different than any other complex system that makes “free will” a “useful theory”?

“It wanted to rain today, but it couldn’t quite make the decision. Weather here is so indecisive.”

You’re assuming a libertarian notion of freedom, which is rejected by Sean (and by the majority of people who have thought carefully about this topic). What Sean is advocating is a compatibilist account of freedom, which can indeed be seen a result of constraints.

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Cosmonut @34 is correct to point out that if hard determinism is correct, then all of existence is as pre-determined as a movie on a DVD — from any frame of the movie, there is only one possible next frame. No choices are possible.

I believe free will (and consciousness) is an emergent property — like “solid”. You can’t show me under the microscope anything solid. In fact, the better the microscope, the less “solid” something is. Yet, you will hurt yourself walking into the wall trying to act on the knowledge that it is 99.999999999+% unsolid.

“You’re assuming a libertarian notion of freedom, which is rejected by Sean (and by the majority of people who have thought carefully about this topic). ”

No, I’m not. Free will has no constraint. That doesn’t mean that it isn’t *compatible* with constraint (which is the compatibilist position) but rather that it doesn’t, as a “theory” *offer* any constraint, which means it cannot be a useful theory of human behavior.

Re: 42

The compatibilist account of freedom usually claims that actions are free just in case they are caused by an agents desires, commitments, personality, etc. and they are not the result of external coercion or force. I don’t see that as a “theory of behavior” this differs importantly from other psychological features.

Re: 43

That is not a useful theory of behavior, that is a definition.

Katherine (#24),

From pretty early on in his career, the philosopher of science Karl Popper emphasized precisely this point. (I’ll ignore Conway and Kochen’s use of the term “induction”. 🙂 ) It is a deep issue; I would argue that it is

thecentral issue. Another way of putting it is this: Does the notion of seeking and discovering (usually provisional) solutions to problems really mean anything in a universe that allows no room for making choices that are not predetermined by its past state plus the laws of physics?Obviously as physical beings our actions are “determined” by the laws of physics. Nevertheless I would argue that we have free will in any practical sense, namely:

(1) Given a choice between two alternatives, we are in fact capable of choosing either one; and

(2) No outside observer is able to predict with 100% confidence which of the alternatives we will choose.

As evidence I offer the following experiment, which you can do yourself: prepare two breakfast beverages (for convenience we will label them T and C). Also prepare some quantum mechanical system so that it is in a superposition with two equally likely outcomes upon measurement (e.g. an electron in a superposition of spin up and spin down). Perform the measurement in secret, and based upon the result drink one of the beverages (e.g. if the measurement shows spin up, drink T, otherwise drink C).

At first blush this doesn’t seem to say much about free will, since you’re letting an outside event (the state of the electron) “determine” your choice. If you prefer, you can consider the system (you + electron) to be the agent, In any case, if you perform the experiment you do show that property (1) is true, namely that you are in fact capable of choosing either alternative. Moreover, if the measurement is secret and if our current understanding of quantum mechanics is correct, no outside observer can predict which beverage you will drink, so property (2) is also true. One can argue the metaphysics either way, but I think properties (1) and (2) together amount to free will in any practical sense.

Eric, your definition of free will is circular, given that you used the concept of “choosing” in point 1. Or perhaps you should clarify what “choose” means – can you define it in such a way that it doesn’t apply equally well to the quantum system you’ve described in your thought experiment? Does that system “choose” the state?

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Re: 47

You bring up a good point. I don’t see any circularity in the definition, but I can see that one might think the word “choose” implies more than it ought to. I simply meant that of the two possible outcomes (I drink C) or (I drink T), either outcome is possible. Yes I see that could also equally well apply to a quantum system, so it’s probably not a good choice (:-)) of words. Perhaps “choice” = “outcome” + “consciousness”.

I have no problem with materialism, and am perfectly happy to agree that my “choices” are the product of the states and transitions of all the particles that make up my brain. Nevertheless I think it is an interesting thing that “I” (some system of particles) can act in very complicated ways which seem not to be predictable even in principle. I know that some people prefer to avoid the term “free will” because it seems to imply dualism, but we already have the perfectly good words “materialism” and “dualism”, and I’d hate to simply define “determinism” as “materialism”.