Conway's Proof Of The Free Will Theorem 65 points by ramgorur on Aug 11, 2014 | hide | past | web | favorite | 86 comments

 As the final section shows, this is more about the question of determinism vs indeterminism. Depending on your particular ontological and epistemological leanings, that question and the question of free will may be the same, or conflating the two may be a category error. I personally fall in the latter camp, but this was an interesting foray into the musings of a brilliant mind.
 Whenever I face the arguments of determinism vs. indeterminism, I wonder how indeterminism would be defined in a purely indeterministic world. I don't know. But in this seemingly deterministic universe, we define indeterminism as a negative sense to the deterministic dynamics we observe, but we can't do it in a positive sense. All of our conceptions of "indeterminism" and random/chaos like concepts is all "determinism-biased" in that sense. Maybe, determinism might be a tiny, tiny small subset of a huge set of indeterminism, as if integers are a tiny subset of all real numbers. There's no such a thing as integers vs. real numbers. Integers are also just real numbers. In that sense, determinism might be a small part of indeterminism.
 > In that sense, determinism might be a small part of indeterminism.I agree. The astonishing thing about quantum mechanics to me is that it describes how deterministic laws emerge from completely non-deterministic processes.For example, in quantum electrodynamics, a photon going from A to B, chooses a random path with a well defined probability density assigned to each possible path. When you do the math, it turns out that the shortest path between A and B is the most likely one and that's why the classical "deterministic" law that light goes in straight lines is a good approximation for large distances. Yet the path which the photon chooses to take is completely random, chosen by the photon's free will, if you will.
 But we would still have the concept of determinism in the macro world even if physics turns out not to be deterministic in the small.
 Indeed - and one can eliminate determinism without resort to QM: Classical mechanics is also indeterministic, you just have to know where to look.Read "Causation as Folk Science" by John D. Norton [1]. He sets out a very simple example of a classical system that behaves indeterministically, analogous if not in fact homologous to how the radioactive decay of a single particle cannot be predicted.The apparatus to demonstrate this consists of a dome with a particular curve (see the paper for details). A sphere placed at the apex of the dome will eventually roll off, in a random direction. But we can predict NEITHER when NOR which direction. And yet it is a fully defined classical system.(And see [2], recently discussed here, to see how relevant and frutiful classical mechanics remains to this day.)(Note that a better word than indeterministic might be acausal, which is the word Norton uses when describing the dome. Either way, one need not resort to QM, regardless interpretation, to demonstrate that determinism does not in fact prevail in our universe. We can all behave in ways that are not predetermined.)
 > Classical mechanics is also indeterministic, you just have to know where to look.On the contrary, classical (pre-quantum) mechanics is certainly deterministic. The first real challenge to a strict relationship between causes and effects was QM, which (as you may recall) caused Einstein to begin a long campaign against those ideas -- "God doesn't throw dice," and so forth.> But we can predict NEITHER when NOR which direction.Our inability to predict an outcome doesn't constitute an argument against determinism, only the limits of experimental measurements.> analogous if not in fact homologous to how the radioactive decay of a single particle cannot be predicted.That's simply false. A radioactive decay's timing is certainly nondeterministic, but the direction an observed, macroscopic ball takes is deterministic, even if we don't get the memo.Think a bit harder. If Norton could demonstrate the indeterminism of classic mechanics, as opposed to publishing a philosophical paper on the topic, he would win a Nobel prize for undermining a well-established physical principle. But philosophy isn't science.> We can all behave in ways that are not predetermined.We can all behave in ways that we believe to be nondeterministic, but free will remains an open philosophical question.
 Our inability to predict an outcome doesn't constitute an argument against determinism, only the limits of experimental measurements.I'm not sure how to square that statement with the paper: The paper does sets the equations of motion for an object, equations that completely define the objects motion, but that cannot predict when the object will move. This has nothing to do with the quality of measurement.
 So you're saying the world can be deterministic and you can still have free will? That would mean you would have to believe in something like souls then, right? Something outside of this physical world that influences your physical existence? I'm not questioning your views just trying to understand.
 We consider free will important because we like to think we make our decisions based on our own individual identity, rather than physical properties of the universe that predetermine what we will do.Even if free will exists, our mechanism for arriving at a decision to do one thing over another thing pretty much needs to be context-dependent - i.e. we make that decision based on some line of reasoning (whether correct or not).At the same time, everything we've experienced and consider to be part of our own individual identities, the stuff that defines our free will, is incorporated as a part of that context. So many people argue that free will and determinism are still pretty much compatible.Nevermind all the other crap we like to pretend doesn't influence our decisions like whatever crazy hormones happen to be elevated at the time.
 To me, this argument is a strong defense of the "self", but does not address the "free" part at all. It is like saying that a rock is free to weigh more than a marshmallow because of the complicated history that lead it to being this rock.
 Exactly my thought as well.I believe we keep telling us stories about a "free will" because we're afraid of that thought because we misinterpret it. Most people answer unreflected things like "that would be like living in a prison". Also we have learned to judge everything and everyone. How can we expect people to completely drop all kinds of judgement?
 Why would we stop judging?
 Not sure I understand your question correctly.We should stop judging.Because nobody has been able to show "free will" is more than just another belief (as in religion) and it is therefor no basis for rational discussion. And if free will does not exist, our concepts of "merit" (on the positive side) or "guilt" (on the negative side) are worthless and should be abolished.That's why there should be no judging at all.(Note: No judging does not mean nobody goes to prison for crime. It simply means we must redefine "punishment" as "a neutral sanction" or better: "protection from happening again".)
 > We should stop judging.If there is no free will and we still judge, we cannot not judge!
 Yes, we can!All there needed to be was for the handful of initial variables that were set at the "beginning of our universe" to have such values that their interaction over time would lead us to rational thinking and therefor our understanding that there is no "free" will.Simply put: If I explain to you why free will is an illusion and you stop judging, then it wasn't a "free" will. It was a cause-and-effect situation.
 You should try and get implication and conclusion sorted out. I think you slipped in a negation somewhere.If there is no free will and I stop judging, then yes, obviously we can stop judging.But if there is no free will and after your explanation I still judge, then no, we cannot.
 Let's put it like this:My explanation would be only 1 variable in your system (out of an infinity of others, if you assume that you can always continue to "zoom in").Now, if that 1 variable does anything to your decisions or not depends on all the other variables as well, i.e.: You may have gotten a very religious education which may lead you to accept beliefs put forth by other as "the truth", without questioning. Since one major point of religion is "free will", I'm not sure "my explanation" would do anything to your decision making.
 If there is no free will, then all we do is predetermined and arguing is pointless, because, by definition, it cannot change anything because everything is predetermined.
 The arguing is just 1 variable in the system. It was bound to happen because it was caused by other variables (i.e. us being online, someone posting the article, etc.) and it will interact with other variables to lead to some amount of change. It's not something that "we control". (Our brains do, but they are the result of other variables, such as our genome, environment, etc.)
 I don't get that - with predetermination, there are no variables at all. Its all a mechanism set in motion at the big bang, turning inexorably toward ultimate entropy. We're just some predestined middle state right now, with no choice and no say.
 All that would mean is that you were incorrect before when you had some mystical idea of what choice meant. Choices still matter (in the most literal sense: they are material). If complete determinism is true, the choices we make and the things we say are part of the causal stream that leads to other actions, even if that stream could only ever go one way.On top of that, how would choice make more sense in a random universe?
 Mystical? I think the meaning of 'choice' is well-understood. I believe philosophers have reinvented the meaning so they can put it into their wholly imaginary framework of doubletalk.
 If you mean choice as something external to whatever deterministic/indeterministic framework we use to understand physical systems, it is mystical. If you mean choice as in "I wanted to do something and then I did it", which is the commonly understood meaning of choice, there is literally no conflict with determinism.
 Now how do you stop judging without free will?
 That's an easy one:If somebody explains you the reason why judging does not make any sense and you understand it and apply it to your life, then it wasn't "free will". It was causality - you're doing it because of a "variable" (the explanation) that was part of your "system". Obviously, there is a huge number of other variables participating in your decision, not just one, and you could track them on a micro level (molecular) as well as on an macro level (i.e. your family, friends, wealth, etc.).
 But without free will nobody can decide to tell you something and influence your future decisions. If there is no free will then watching the universe over time is just like playing back a movie, maybe with some unpredictable plot twists due to randomness. Me writing this comment was predetermined - at least with some probability - since the big bang. All the things humans have done, from fighting wars to writing all the books to inventing and building all the human made things in the world, are predetermined. And while I think that there is no free will trying to imagine that everything around me is the result of a mindless process is more than my poor brain can do and therefore in everyday life I just keep pretending I have free will.
 > If there is no free will then watching the universe over time is just like playing back a movie, maybe with some unpredictable plot twists due to randomness.Yes, rational thinking dictates exactly this conclusion (the apparent randomness being introduced by our current understanding of quantum physics).> And while I think that there is no free will [...] in everyday life I just keep pretending I have free will.Well, Rome wasn't built in one day. Our whole culture was built upon the illusion of "free will" (same goes for other beliefs like magic, gods, etc). It's a good exercise to remind oneself about this when we get all worked up over something or somebody.
 I call hypocrisy - convincing folks there is no 'free will' has got to be the ultimate in fooling oneself!
 I don't convince, I argue.If the logic has a flaw, please let me know, I'm interested in being as close to the "truth" as possible.
 The flaw is, what's the point? If its true, it has no effect. If its not, your arguing a falsehood.
 > If its true, it has no effect.As discussed, it would mean, for example, that we cannot judge anyone (and at the same time claim to be rational).To give an example: The death penalty should no longer exist, because it is solely "justified" by judgement along the lines of "person X is evil and therefor doesn't deserve to live". There are no evil people, only people who do what they have to do, given the variables in "their system". That means there should be no "punishment", but emotionally neutral measures to prevent the suffering from happening again (i.e. locking the person up). It's pretty clear to me that a much more humane society will be the result of this understanding. And who wouldn't want that?Edit: "rational" in the sense of "logical".
 If there is no free will, then it is spurious to claim anyone is 'rational'. That loses all meaning.
 > If there is no free will, then it is spurious to claim anyone is 'rational'. That loses all meaning.No, it doesn't. I mean, the rational actor model is evidently false for lots of other reasons, but its a purely mechanistic model but for the utility function (on whose nature it is completely neutral), so rationality is just as compatible with the non-existence of free will as it is with the existence of free will (in fact, rationality requires either that there be no free will or that it be confined entirely within the utility function.)
 If the rock told me that it intuitively perceives itself as being free to weight more than a marshmallow (and I didn't otherwise have reason to believe I was hallucinating), then I would have little trouble conceding that the rock is free to weigh more than a marshmallow.
 A conception of 'free will' that is considered to be impossible if the universe is deterministic has a difficult question to answer: how does non-determinism enable it?Suppose I'm making up my mind whether to buy some item. There is some last-nanosecond non-deterministic quantum event that causes a neuron to fire, that wouldn't otherwise have fired, and I buy the item. What was 'free' about my decision if that quantum event was not caused or influenced by 'me'?Non-determinism informally says that some things in the universe may be unpredictable. If my decisions depend on unpredictable events in the universe, how are they 'free'? It sounds like 'at the mercy of random events in the universe'.So it's not that the world can be deterministic and you can still have 'free will', it's rather that if the world was non-deterministic, you still couldn't have that sort of 'free will'.
 Oh jeez, there's no happy way of looking at this is there.Seriously though -- this is extremely depressing to me, it's literally giving me terrors right now. It's reducing all that I love and value to nothingness. How do you guys deal with this?
 An important thing in what I wrote is that it only applies to certain sorts of free will. The sorts of free will it applies to include the idea of 'free will' that many scientifically educated (and usually philosophically untrained) people have. Let's call it the 'natural' or 'naive' idea of free will. In that view, free will and determinism are incompatible.However, as others have pointed out in parallel answers, there are 'compatibilist' views in which free will and determinism are compatible. The sorts of 'free will' that those views apply are different from the naive idea of free will and the important point to take away from that is: it may not be clear to you or me what the phrase 'free will' actually means.I do not subscribe to compatibilist views, because they define 'free will' as something that I do not believe is worth wanting. However, that begs the question: what is a definition of 'free will' that I do believe is worth wanting? And I have found that I cannot answer that question: I cannot define it satisfactorily in a way that is amenable to philosophical analysis, while all definitions that can be analyzed are unsatisfactory.So it boils down to this: I believe it is important to have 'free will', but I cannot define what it means to have free will. As I cannot become unhappy about not having something that I do not understand clearly enough to reason further about, my life is effectively no different from never having thought about 'free will' at all.So that's how I deal with it. In a way that is unsatisfactory to many people, because it seems to allow for a bit of 'insert magic here' just to satisfy my emotional need for the existence of some intuitive notion of free will. To which all I can say is: yes, I believe that believing "I don't understand" and being happy is better than believing "the best answer we can come up with is depressing" and not being happy.
 I personally go with a computability/compatability argument. If 'you' are some sort of process analogous to a computer program, you can be totally deterministic yet unpredictable. You can't predict in advance the outcome of running some program, c.f. halting problem, without simply running the program slightly faster. Running the program slightly faster is identical to the initial process anyway, since it must get exactly the same inputs. Hence, you are a computational process experiencing itself, everything you feel is valid and no-one can take that away from you :)
 There are varieties of compatibilism (the view that determinism and free will are compatible) that do not require the existence of souls. I'd suggest taking a look at Daniel Dennett's _Elbow Room_ for one example.The Stanford Encyclopedia of Philosophy has an article on the subject: http://plato.stanford.edu/entries/compatibilism/
 Compatibilists redefine free will, similarly to those who redefine "god" as "nature" or "the universe". Sure, anyone can define any term the way they want, but it simply causes confusion to the majority of people who don't hold such definition. Rather, it's best to abandon some terms as fiction, and create new ones surrounding the concept you are looking to address. Better books on the topic are Sam's _Free Will_ or Trick's _Breaking the Free Will Illusion_.http://www.samharris.org/free-will
 i never had the patience to follow that mind juggling, or "word jugglery" as Kant calls it. For me as a programmer free will would mean something like: var a:Int = 2 var b:Int = 3 println("\(a+b)") >> 42 where transistors take the place of neurons
 Other people have answered this well, but I think that the question of determinism vs. indeterminism is essentially the question of an ordered universe vs. a random one (or picking a point between those two extremes). If that's the case, then what we are usually talking about when we speak about somebody acting freely or having free will has little to do with that discussion.To get to your question about what free will would be then: I'm not a huge fan of a pure concept of free will, though we talk about people acting more or less freely often enough that it's worth thinking about. I think then that a useful definition of "free will" might simply be a measure how much somebody's actions are able to be in accord with their desires. How an outside observer would ever gauge that as well as what actions, desires, and the two being in accord would mean are obviously murky philosophical territory, but it's pretty late.To answer at least one obvious rejoinder, actions and desires can certainly be reduced to particles and the like, but they are phenomena that have qualities we wouldn't ascribe to particles. For instance, it makes little or no sense to say that a particle has a nice smile. In much the same way, we generally mean something different when we say a person wants to do something and a particle wants to do something.
 Is there any good definition of free will at all? Given somebody is in situation X and has options A and B then the choice to do one or the other can either be completely at random or on the other extreme depend completely on the situation X (including the person with the brain and all the memories and the complete environment). Or it may be a mix of both where the situation affects the probability distribution. But none of these scenarios matches what I would call free will, making a choice that is neither random nor a deterministic consequence of the situation, but I can not even think of any mechanism outside of the spectrum from randomness to deterministic consequence.
 This issue you're running into is why I think trying to think about free will in that context is a category error. The concept doesn't make sense when it's something that depends on randomness or determinism. Instead, I think it's useful to think about how we use it in actual practice, which is generally something like, "is a person more or less self-directed" where self-directed means that their actions are consistent with their observed character and expressed desires. That's not particularly satisfying if you're raised in a culture that puts a lot of value on free will as a concept, but I think it may be the best we can do.
 The world can be deterministic and still allow free will with respect to a real observer. In some sense it doesn't matter if a person's actions are in principle predictable when there is no observer who can actually make those predictions. You'd have to measure and simulate the entire universe to predict a single particle's future.
 But it would just be an illusion no? If the discovery were made that the universe is entirely deterministic it wouldn't matter whether any one person could, or any number of people, could produce accurate meaningful predictions. The truth alone would VERY disruptive.
 The great Australian philosopher David Stove was of the opinion that the main function of philosophers is to save the rest of us the trouble of thinking about these sorts of things.When a useful professional in another field such as you or I starts wondering about these sorts of issues, he can simply pick up a philosophy book, note that a bunch of smart people have already thought this issue through, put labels on every possible position, argued through the consequences of each, and still failed to come to any consensus about it. And then we can say "Whew, glad someone's already taken care of that" and get back to our useful lives without worrying our pretty little heads about it too much.So if you do find yourself worrying about free will, I suggest reading the vast amount of pre-existing literature on the subject and unburdening yourself of feeling like you should be making progress on it.
 If you want humanity to progress then you should encourage critical and rational reflection. It's the capacity of thinking which society often lacks.
 > The truth alone would VERY disruptive.This is clearly untrue. The discovery has already been made that events in the universe happen in one of two ways:1. "deterministically", the way you think would be VERY disruptive2. determined by chanceThis isn't disruptive; people just ignore it.
 Sources?
 It does matter, because determinism generally (but not always) depends on causation. People making (determined) predictions would still influence the (determined) future actions of other people. Punishing people who acted in a (determined) way would still affect the (determined) actions of other people. Lived experience allows for the possibility of a number of different ontological theories, which is a large part of why there are so many different and conflicting ones.
 I suppose you could call it an illusion, but I don't think that needs to be considered a bad thing. By the same token, your senses are an illusion. That doesn't mean it's unreasonable to say that we do have senses, and it doesn't mean our senses aren't often extremely useful.
 What would be "disruptive" about it?
 it would just be an illusion? no, not necessarily. consider that the deterministic particles in the universe could be receptors and the actual thing that has free will exists outside the universe and sends signals to those receptors in some way. this is where the concept of souls would come in, and that would make determinism and free will compatible.
 In your model, the "deterministic" particles do not actually behave in a deterministic way, unless the thing sending them signals sends those signals in a fully deterministic way. But in that case, there's no reason to bother including it in the model.
 Um, no. The model suggests that particles would be entirely predictable unless acted upon by an outside force. It doesn't matter at all if "signal-sending things" are deterministic or not. This "free will" wouldn't exist in the physical world, it's metaphysics.If the pool table were the universe, the course of the billiard balls is predetermined until the shooter shoots. No shooter, no change.If the solar system were the universe, the planets would be deterministic until the aliens blow up Jupiter. Aliens don't exist? Then the planets would be entirely deterministic for the full course of their lifetime.If the universe were the universe, all particles are completely deterministic, unless spooky ghosts make magic. Whether the spooky ghosts are real is a question of gullibility.
 As I attempt to interpret my parent comment using the framework you provide, I get this:- The particles making up the universe are deterministic, unless free will is exercised.This would amount to a concession that while free will is possible, it has never been used. I don't think that's what parent had in mind.
 The idea that free will is compatible with determinism (this position is called, shockingly, compatibilism) is actually the most popular view in the philosophical debate about free will, and has nothing to do with mind-body dualism.Some ways folks have tried to defend compatibilism (see http://plato.stanford.edu/entries/freewill/ for discussion of what follows): motivating the idea that free will is grounded on choice on the basis of one's desires, or on choice that makes sense given one's values. There are other ways, linked to the idea of it being possible that you had chosen otherwise, and on a metaphysics of modality (i.e., of what it is for something to be possible, or necessary) compatible with determinism.
 I don't follow.How does free will+determinism imply an outside influence?I see no convincing reason that an entirely deterministic thing can't have "free will".Though I don't remember ever having found a definition of "free will" that I've found satisfactory.I don't think compatibilism implies a belief in anything "supernatural" though.(quotes to indicate things potentially not being exactly the right term, or other similar indications)
 Conway's description of entanglement is misleading. FIN does not actually apply here. According to quantum physics, no information is exchanged between the particles. If information is exchanged, it is not limited to any finite speed we know of.The thought experiment he describes is well-known in the popular science press: you create two particles with opposite spins (angular momenta), but such that the spins are not determined. As soon as you measure the spin of one the spin of the other becomes determined -- INSTANTLY. There is no speed-of-light limit here. If you describe the situation as two particles colluding by sharing some "information," then FIN does not apply, as far as we know! (And if there is a limit, it is greater than the speed of light.) A physicist would instead say that no actual information is transmitted, and entanglement cannot be used to transmit information faster than the speed of light.Since the metaphor of wave function collapse as information sharing between particles leads to incorrect physics, I don't think we should read too much into the metaphor of measurements as "free choices" of a particle.
 I'm surprised that people are so determined (heh) to pull determinism out of quantum mechanics. I don't believe in metaphysical souls or free will per se, but I also accept randomness in quantum mechanics (relational interpretation).
 Interesting article. Thank you for posting.I have a very limited understanding of physics but two questions spring to mind:1) Why is there little doubt in the axioms, especially FIN? It requires the concepts of distance and time, either of which might not be applicable to the resulting property.2) Why call the resulting property "free will" or "free whim"? As far as I can tell the proof is for the existence of an additional property to both the experimenter and the particle, but there is no real description of it. This is somewhat unsatisfactory addressed in the last paragraph, but really, why not just call it a "randomness" or "god" instead of "whim"?
 1. Current physics - and in a way it goes back to Descartes and the very first conception of modern physics, the idea that things happened for mechanistic reasons rather than mysterious temperaments. If information can travel instantaneously, doesn't that imply that distance and time are in some sense meaningless? Also, relativity + faster-than-light information implies causality violation, grandfather paradox and all of that. It's not "beyond all reasonable doubt", but standard physics seems to respect it as an axiom.2. Because Conway likes attention.
 If FIN were false it would be possible to transmit information backwards in time by transmitting it faster than light between a transmitter and receiver moving relative to one another.
 2. Because the property under description is qualitatively like what some people think free will is like.
 If I understand this correctly, this proof is used to exclude one of the two given explanations for the "Kochen-Specker Paradox"?The article says the KS "paradox" implies that either> 1. Each measurement of a particle is not independent but rather depended on > context. In other words, the order in which you make measurements matters.or> 2. The particle does not decide what the value of its spin is in any direction > until the experimenter actually makes a measurement!As I understand it, the proof shows that the order in which you take the measurements can't matter, excluding explanation (1), because of the following thought experiment.* Take two particles, entangled and then separated by some distance.* More quickly than information can pass between the particles, measure one particle in three directions in some order, and measure the other particle just once in one direction which you choose right at that moment.The second particle can't be affected by the order in which you measured the first particle's spins, but if I was able to choose a direction in which to measure the second particle's spin, then the second particle was able to choose a result to match the appropriate result from the first particle's measurements.I think I followed this argument up until the last sentence above. What I (mis)understand to be happening here is "spooky action at a distance"; it doesn't at all appear to be a free choice on the particle's part.In essence we established via the KS paradox that our two particles couldn't have "agreed" on their spins ahead of time, because there's no consistent way to assign all of their spins. But then we measured the two particles in the proscribed way and got a result that looks like the particles did agree on their spins beforehand.I believe that this excludes explanation (1) from above, but I don't understand how explanation (2) is consistent with this. If it were the case that the particle was deciding its spin at measurement time (explanation (2)), wouldn't the two particles have to communicate faster than c (or whatever our speed limit is) in order to ensure that they made the same decision? We explicitly ruled out this possibility via the FIN axiom and our experimental setup.The only way I can think of to make this work is to say that the universe doesn't "choose" which result I got until I meet up with my friend who measured the other particle. But this seems to be a far stronger claim than the article makes.What's the right way of thinking about this?
 Talk about the particle "deciding" is coming from a Copenhagen interpretation viewpoint. I find the many-worlds view clearer:When the two particles are set up, their wavefunctions are in sync (or rather, antisync) with each other. Particle A's wavefunction looks like an equal superposition of up and down (at least, when projected onto a single axis; the wavefunction for the full particle incorporating all the possible axes is more complicated); Particle B's wavefunction is the same but 180 degrees out of phase, so that A is up whenever B is down and vice versa.When you make a measurement of particle A, you entangle yourself with it; that is, your own wavefunction becomes in phase with its. (Again, it's still an equal superposition between having measured up and having measured down). When your friend makes their measurement of particle B, they entangle themselves with it in the same way. So when you meet up with your friend, your wavefunctions are in (anti)phase; the universe as a whole is an equal superposition of the world where you measured up and your friend measured down, and the world where you measured down and your friend measured up.(What does being in that superposition look like, subjectively? It looks like a 50% probability of the first world and a 50% probability of the second world. Which agrees with what we measure when performing the experiment)
 Thanks for the reply!> When your friend makes their measurement of particle B, they entangle > themselves with it in the same way. So when you meet up with your friend, > your wavefunctions are in (anti)phase; the universe as a whole is an equal > superposition of the world where you measured up and your friend measured > down, and the world where you measured down and your friend measured up.If we take this perspective, are we still able to rule out possibility (1)? That is, our assumption was that what my friend did couldn't affect my experiment; we used this fact to rule out the possibility that the order of my friend's measurements affected my result. But if in some sense my experiment doesn't "occur" until I meet up with my friend, then this assumption seems not to be true any longer. Which is to say, we could explain this whole thing without requiring any "free will" / "true randomness" on the part of our particles.
 From a many-worlds point of view there's not the same nondeterminism in the physics. There's nondeterminism in our subjective experience, but it's a surface phenomenon rather than something fundamental.So I guess we've sidestepped the question the "theorem" is aimed at, because by adopting this viewpoint we're already assuming that humans don't have any kind of physical nondeterminism (or "free will", if you insist).Personally I think the idea was stupid as stated; having a set of dice inside your head doesn't make you any more likely to have "free will" than if you didn't, and that's all that quantum nondeterminism really means. But I guess some philosophers really did claim that this was support for the notion of free will, so it's worth refuting that as directly as possible.So I guess you're right: if anything, a many-worlds interpretation gives more support to the idea that quantum nondeterminism has something to do with free will, because it means the nondeterminism only comes in when we look at a human's subjective observations. So yes, I think we really do sidestep the claim this way.
 I don't know about all that quantum math craziness or that spin fin twin nonsense but it sounds like Conway shares a long standing sentiment I've had that "free will" is a story we tell ourselves because we want to believe our choices are based on something fundamentally more complex or important than the choices of an animal or a computer. Even if "free will" is a real thing and not just an illusion, what is it really but random in-deterministic variations, or what Conway called whims.I remember when I voiced these opinions in my college philosophy class to a room full of denialists. It's good to know I'm not alone in my thinking in a world where multi-verse and string theory are sooner accepted than the fact that free will is an illusion.
 Well, at the end Conway claims to believe in free will. I don't know what you make of that but it is in the article.
 Your response is ripe with irony.'A world where multi-verse and string theory are sooner accepted ...' indicates a world where there is agency, and thus will. We won't even go near your normative subjective ideas about the 'good'.You can't both deny the existence of free will, and castigate those whom with you disagree. If you're right, then none of us can be wrong -- certainly no more than a plant or a rock or the moon can be wrong.
 This is a very common logical fallacy. Because the concept of "right" itself was created by society itself thanks to deterministic events, to be used in practical applications to judge and be judged, where that judgement is itself deterministic, so your concept of "wrong" and "right" would have to be a different one that the one used by society in order to say "no of us can be wrong".That can sound confusing so I will put a very simple example: A fireman is on front of a fire. The fire needs to be extinguish even if you think the fire is not to be blame for what it did because after all is only a fire, it didn't do it on purpose, but regardless it needs to be extinguish. The same happens with people, they are judged for what they do, for practical purposes, when they commit a crime, they are just like a fire that needs to be put out. But not with water by with judgement.
 > You can't both deny the existence of free will, and castigate those whom with you disagree.They certainly can; in fact they have no choice in that matter according to themselves.
 It is easy to imagine a computer program that is both deterministic and wrong. Why not a person?
 Because a computer program is only deterministic if you look at it in a snapshot view, a human within the context of a "snapshot" could also be deterministic I suppose.Or the other way to look at it, A computer program changes over it's lifespan and when you look at it from that perspective it is not deterministic.
 When one describes a computer program as "wrong" it is within the context of what some other agent wants or expects it to do. As a purely physical process, it can never be wrong or right, it can just be.
 You have defined "wrong" in an incredibly strange and useless way. 2+2=5 is "wrong" regardless what agent you are or what universe you exist in.
 I'm not sure where to start.The first diagram of the proof starts with "there exists some experimenter with at least some free will". That's a problem, as it uses the argument's conclusion as one of its premises.Using a simpler example, it'd be like saying, "To prove that aliens exist, let me show you three simple steps: 1) let's assume aliens exist, 2) ...The second problem here is that he seems to be trying to illustrate that if things cannot be predicted that we have free will. This is a common fallacy in the free will debate. Randomness is an attack on fatalism, but offers ZERO degree of control to humans, and therefore has no place in the free will debate.Finally, if you want to see a much better argument, in the other direction, check out my Two Lever Argument Against Free Will that uses 25 lines of Ruby.
 > it uses the argument's conclusion as one of its premises.His theorem doesn't assert free will. It asserts that if experimenters have free will, then particles have free will. So if it's wrong, then it's not for the reason you give.
 I think he's asserting that if experimenters have free will, then particles do, which means we do as well.This isn't a proof of particles having free will. That's an intermediary step to saying we have it as well, and therefore you can start with a step that says we do.
 You need to read it again. The person you're replying to has correctly stated what is shown.
 Isn't the conclusion, "all particles have free will"? So, the arguments conclusion is pretty far from its premise. "All numbers are larger than 5" is very far from "some number is larger than 5".And, whether or not you call this property "free will" is irrelevant to the proof itself; see the final paragraph.
 The knight's move seems to be the following:1. Experimenters have free will 2. They're made up of particles 3. Those particles therefore have free will 4. Therefore we have free will (that's why it's called a proof of free will)Item #1 above assumes the conclusion.
 Read it again. That's not the argument. The argument is roughly:Either the observer's choice of measurements of the particle is completely determined by prior events, and the observer has no free will, or the observer can at his or her whim pick a way to measure the particle. If the latter, then the particle must be able to, also at whim, pick which spin to be measured at.He never assumes that the observer is made of particles.
 > This theorem states "If there exist experimenters with (some) free will, then elementary particles also have (some) free will."How did you pull (4) out of that?

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