Mathematician says he’s proven free will

Matthew Cobb called my attention to an interview with John Horton Conway in Notices of the American Mathematical Society. Conway is a famous mathematician at Princeton who says he’s proven that free will exists.

I haven’t seen his formal treatment of the Free Will Theorem, so I can’t say I can evaluate it—much less understand it. From the interview it sounds simply like a refutation of pure physical determinism, which most of us who accept quantum mechanics don’t see as problematic. The question is whether our behaviors and “choices” can be influenced by quantum dynamics, but even if that were true it wouldn’t prove “free will” exists in any meaningful sense.  But the proof of “free will” is also connected with the bizarre phenomenon of quantum entanglement.

Talking to interviewer Dierk Schleicher, Conway explains his proof:

My friend Simon Kochen taught me one thing about quantum mechanics which I understood, and I find that many physicists don’t understand that one thing (of course, they understand many things that I don’t). And that one thing we were able to pursue until we had this great theorem. If we make reasonable assumptions, including the assumption of free will, this one thing tells us that the little elementary particles are doing their own thing all over the universe. One atom is deciding to move a little bit leftwards and another to move a little bit rightwards. And it all very nearly cancels out, but not quite. And here [points to Schleicher] is what we call a life. You might be a robot, but I doubt it. I rather suspect you to have the same kind of consciousness as I have. And that is probably a manifestation of the freedom of the particles inside you: they do their own thing.

 . . . Schleicher: Could you make a simple statement about what exactly, or intuitively, the Free Will Theorem says?

Conway: Yes. [Throws a piece of paper.] I just decided to throw that piece of paper on the floor. I don’t believe that that was determined at the start of the big bang, 14 billion years ago. I think it’s ludicrous to imagine that the entire development of the universe, including, say, this interview, was predetermined. For the Free Will Theorem, I assume that some of my actions are not given by predetermined functions of the past history of the universe. A rather big assumption to make, but most of us clearly make it. Now, what Simon and I proved is, if that is indeed true, then the same is true for elementary particles: some of their actions are not predetermined by the entire past history
of the universe. That is a rather remarkable thing.

Newton’s theory was deterministic. In the 1920s, Einstein had difficulties believing that quantum mechanics was not deterministic. That was regarded as a defect of quantum mechanics. Certainly when I tried to learn quantum mechanics and didn’t succeed, I thought it was a defect. It’s not a defect. If the theory could predict what one of those particles could do, then that theory would be wrong, because, according to the Free Will Theorem—supposing we do have free will—a particle doesn’t make up its mind what it’s going to do until it does it or until shortly before it does it.

Let me describe the theorem this way. Suppose there is only a very tiny amount of free will in humans: you can press either button A or button B in a manner that is not predetermined. That is a very tiny part of what we normally consider free will for humans. And if we have that tiny amount of free will, so do the elementary particles, in a sense that a particle in response to some experiment can choose which path, C or D, that it follows. It has free action. It chooses C or D in a manner that is not a predetermined function of all the information in the past history of the universe.

Schleicher: You believe that humans have free will.
Conway: I do. Strict determinism tells us that all of our actions are predetermined by the past history of the universe. I don’t know, maybe it is. I can’t disprove it. I can prove that I can’t disprove it. I can prove that you [points to Schleicher] can’t disprove it either. But I believe anyway that humans have free will.

It seems, then, that  because particles have free will (i.e., purely indeterminate behavior, for they certainly don’t have minds), we must too. But what makes me think that I don’t understand Conway’s proof of free will comes from the way it’s characterized in, say, Wikipedia:

The free will theorem of John H. Conway and Simon B. Kochen states that, if we have a certain amount of “free will”, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen’s paper was published in Foundations of Physics in 2006. . .


The proof of the theorem relies on three axioms, which Conway and Kochen call “fin”, “spin”, and “twin”. The spin and twin axioms can be verified experimentally.

  1. Fin: There is a maximum speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.
  2. Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0).
  3. Twin: It is possible to “entangle” two elementary particles, and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. This is a consequence of (but more limited than) quantum entanglement.

In their later paper, “The Strong Free Will Theorem,” Conway and Kochen weaken the Fin axiom (thereby strengthening the theorem) to a new axiom called Min, which asserts only that two experimenters separated in a space-like way can make choices of measurements independently of each other. In particular, they are not asserting that all information must travel finitely fast; only the particular information about choices of measurements.

The theorem

The theorem states that, given the axioms, if the two experimenters in question are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments. Since the theorem applies to any arbitrary physical theory consistent with the axioms, it would not even be possible to place the information into the universe’s past in an ad hoc way. The argument proceeds from the Kochen-Specker theorem, which shows that the result of any individual measurement of spin was not fixed independently of the choice of measurements.

My view that this is all about determinism, and not really “free will” in the only meaningful sense it can be taken in such a context—that is, dualistic or libertarian free will of the human mind—is buttressed by a critical assessment, also on Wikipedia:

Conway and Kochen do not prove that free will does exist. The definition of “free will” used in the proof of this theorem is simply that an outcome is “not determined” by prior conditions, and some philosophers strongly dispute the equivalence of “not determined” with free will. Some critics argue that the theorem only applies to deterministic models.Others have argued that the indeterminism that Conway and Kochen claim to have established was already assumed in the premises of their proof.

I warmly invite philosophers, mathematicians, physicists, or anyone who thinks they really understand the Free Will Theorem to explain it in the comments, but be aware that this will certainly be a very hard thing to do. I’m looking for clarity here—not just for readers, but for myself. In the end, I can’t believe that quantum mechanics can prove that we have libertarian free will.  And if we’re compatibilists and believe in a kind of free will that isn’t libertarian or dualistic, then we don’t need quantum mechanics or mathematics to show it.


  1. Posted June 27, 2013 at 11:07 am | Permalink


  2. Posted June 27, 2013 at 11:10 am | Permalink

    If free will exists, then homosexuals could just choose to be straight, you could choose to believe the sky is green, or choose to feel certain that you recognize your mother’s face.

    • Michael Fisher
      Posted June 27, 2013 at 1:25 pm | Permalink

      I think that we agree that everything is determined from the Big Bang

      Not that I like it ~ I want a loophole to exist, but I can’t imagine what a legitimate [non-woo] loophole looks like. I would like it to be true that brains can control events, but brains would seem to be just a higher order implementation of fields, forces & particles.

      That said…

      There may come a time when we have a technology that could reconfigure our beliefs & perceptions. It may be possible then for a person to CHOOSE to flick a switch that instantly achieves the necessary changes in mind states, hormones & etc. for your three examples to happen. However this wouldn’t demonstrate that we had free will.

      So I don’t like your examples. There may be people out there [for all we know] who can control their mind states to such an extent that your examples are within their grasp. Not that that would demonstrate free will either.

      I’m altogether unhappy with the concept of free will because it smells like an example of a *wrong question* being asked due to relying on faulty axioms

      • Posted June 27, 2013 at 2:41 pm | Permalink

        I don’t think we do…


      • Posted June 27, 2013 at 7:48 pm | Permalink

        Yeah. I don’t think any of us “agree that everything is determined from the Big Bang.” Certainly not our host.

      • Dominic
        Posted June 28, 2013 at 2:21 am | Permalink

        “I’m altogether unhappy with the concept of free will because it smells like an example of a *wrong question* being asked due to relying on faulty axioms”

        I agree – the concept is meaningless – unless you postulate a sort of mitotic universe that splits constantly whenever there is an ‘alternative molecular path’. If you could direct your consciousness along those paths, that might mean ‘free will’. As it is, we cannot go back & re-run so alternatives do not really exist as far as I can see.

      • Posted June 28, 2013 at 6:58 am | Permalink

        We sort of do have the tech to change our beliefs.

        Squirting cold water in your left ear allows you to believe something that you initially rejected.

        Something like that shouldn’t happen if we have “free will”, since “free will” assumes that decisions are made by “you” and not by physics.

  3. eric
    Posted June 27, 2013 at 11:10 am | Permalink

    I agree with the core criticism (indeterminism /= free will). But if I’m understanding the theorem right, there is another very basic logical error in his argument.

    He wants to know if human behavior is indeterminant; call that A. Another issue is whether subatomic particle behavior is indeterminant; call that B. His theorem seems to be:

    P1: A -> B. (if humans have it, particles must too)
    P2: B (particles have it)
    C: Therefore A. (humans have it)

    That plain doesn’t work; its not the way the modus ponens operator works. He can’t get from P1 and P2 to C.

    • darrelle
      Posted June 27, 2013 at 11:20 am | Permalink

      I don’t know if his explanation in the interview was incomplete, or if he just didn’t do a good job of explaining it, but I had the same problem with it you so clearly stated here.

    • Nikos Apostolakis
      Posted June 27, 2013 at 12:29 pm | Permalink

      He makes it clear that he *assumes* free will for humans in the interview. He doesn’t claim that he has proven free will for humans, merely that if humans have free will then so do elementary particles.

      At least that’s how I understood it.

      To quote from TFA (my emphasis):

      The theorem states that, given the axioms, if the two experimenters in question are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments.

      • eric
        Posted June 27, 2013 at 5:58 pm | Permalink

        Yes, but that’s completely backwards. He’s assuming the main point of contention about free will in order to prove a relatively uncontested point that most people (who understand modern physics) already accept as true.

        I have to think Darelle is correct. This is such an obvious flaw in his reasoning that I have to think he’s not expressing his proof to laypeople very well.

    • Posted June 27, 2013 at 2:54 pm | Permalink

      Yeah, I understood it the same way.

      I’ve mentioned this work in the comments here several times before. I thought it was relevant because P2 is clearly ludicrous, and not P2 implies not A by standard logic. That is, I thought the work suggested that the authors thought free will didn’t exist. But I guess the authors don’t see it that way.

      • eric
        Posted June 27, 2013 at 6:00 pm | Permalink

        Did you mean P1 is ludicrous? Particles being indeterminate is pretty much the only part of his proof that’s reasonable.

    • Posted June 28, 2013 at 5:10 pm | Permalink

      That’s “abduction” not deduction.
      A->B; B; therefore A is classic abduction. What it means is that A is *one possible* explanation/cause of B but not necessarily the actual one.

  4. Posted June 27, 2013 at 11:11 am | Permalink

    It’s simply an argument for the large-scale effects of indeterministic quantum processes (as you say). It has nothing to do with free will.

  5. NewEnglandBob
    Posted June 27, 2013 at 11:16 am | Permalink

    The free will theorem sounds like doublespeak.

  6. Chuck O'Connor
    Posted June 27, 2013 at 11:16 am | Permalink

    Don’t get it.

    • Posted June 27, 2013 at 11:53 am | Permalink

      Makes two of us!
      I totally don’t get the axioms and then again am no mathematician

      • Posted June 27, 2013 at 1:24 pm | Permalink

        When people start talking about axioms, we should be carefull. This because, axioms are fundamental assumptions, i.e. they cannot be formally derived from other prepossitions. By defintion we can choose any abitrary axiom, and derive valid conclusions from it.

        With “formally” I mean pure logical deduction, as oposed to empirical induction.

        In empirical science we “derive” axioms or postulates from observations, and from these axioms we can derive theorems, which can be tested empircally. And if these theorems are refuted, we have to look for other “axioms”.

        • Dominic
          Posted June 28, 2013 at 1:36 am | Permalink

          Sort of, ‘my axiom broke & the wheel fell off’?

          • Posted June 28, 2013 at 1:38 am | Permalink

            Yes, indeed. If you choose the wrong axioms, you might derive logically valid conclusions, but if those axioms are not grounded in reality, you risk that your wheel might fell off.

            • Posted June 28, 2013 at 6:14 am | Permalink

              My axiom broke and the “real” fell off?

        • TJR
          Posted June 28, 2013 at 3:02 am | Permalink

          It also seems very odd to call them axioms. They are assumptions rather than axioms, shirley?

          • Posted June 28, 2013 at 9:47 am | Permalink

            Axioms *are* assumptions. In factual science and related fields (as opposed to formal ones) they are chosen to systematize consequences that are worth pursuing.

    • Dominic
      Posted June 28, 2013 at 1:35 am | Permalink

      Will is in prison – unjustly – & they want to free him! Well, it sounds equally plausible…

  7. eric
    Posted June 27, 2013 at 11:19 am | Permalink

    Another issue (and I’m not sure if or whether he addresses it) is that statistical mechanics renders a lot of indeterminancy just plain irrelevant. Krauss states that something like 99% of the mass of a proton is the result of the constant, stochastic formation and elimination of virtual particles: yet that mass is very exact and very constant. Likewise, alpha decay can occur via quantum tunneling, but that doesn’t mean I can teleport across a room.

    I very much doubt anyone would find it satisfactory if there was a theory that showed macroscopic me had as much free will as I had ability to teleport across a room via quantum tunneling.

    • Torbjörn Larsson, OM
      Posted June 27, 2013 at 2:24 pm | Permalink

      A small nitpick: since the quark-antiquark and gluon-antigluon pairs have a lot (the bulk) of relativistic energy, I don’t think they are virtual any more than the more readily visible net quark triplet.

      Short-lived, surely. But virtual particles have no determinate energy et cetera of themselves, these “impulse-response like” disturbances* need to sum to particle type ripples to get that**.

      [** I’m trying to channel Matt Strassler’s articles on the subject of virtual vs real particles.

      * And I gather virtual particles are what pops out as Green function solutions to field excitations. Ergo, more like contingent impulse responses than particle pulses/ripples.]

    • Kevin Henderson
      Posted June 27, 2013 at 3:21 pm | Permalink

      If someone showed there was a verifiable theory that macroscopic objects could teleport across a room that would change the way we understand physics.

      At present, statistics physics suggests it is essentially impossible for macroscopic objects (10^23 particles) to teleport macroscopic distances.

  8. Posted June 27, 2013 at 11:21 am | Permalink

    I will not claim I fully understand his theorem without reading the paper (and I’m not particularly motivated to read it because I expect equivocation). I am a mathematician. I also agree with your primary assessment that “libertarian free will” (LFW) for human behavior and a non-deterministic universe aren’t the same thing. In fact, that’s why I don’t want to read the paper–I’m rather mad about the equivocation on the term “free will” here.

    I want to highlight a conditional here: “The theorem states that, given the axioms, if the two experimenters in question are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments.”

    On Harris’s conception of the incoherence of free will, the two experimenters have no LFW to make such choices in the first place. It appears his theorem hinges upon that conditional, and if so, he’s assumed what he’s claiming to have proved (perhaps because of a desire to equivocate by him or someone else involved).

    Also, as a mathematician, I want to point out that many mathematicians fail to recognize in operation that their results are only true against the underlying axioms. The ones he’s put out here appear reasonably sound, but look how they stack the deck: finite speed of information propagation plus a situation in which there is entanglement with “spooky action at a distance.” QM seems to be holding up with those, but there are lots of more reasonable things to say (e.g. about locality) than “voila! Free will exists!” based upon the result.

    Not buying the conclusion, but I will admit that Conway is a mathematician way above my pay grade. I just suspect equivocation on hot-button terminology more than anything here, for whatever set of reasons he might have.

    • Torbjörn Larsson, OM
      Posted June 27, 2013 at 2:13 pm | Permalink

      I think this is another way of describing the modus operandi of Conway as I know it.

    • TJR
      Posted June 28, 2013 at 3:09 am | Permalink

      Indeed. Its just yet another different definition of “free will”.

    • Posted June 28, 2013 at 6:46 am | Permalink

      Logically, the theorem really is bullet-proof and the axioms it rests on seem sound. To me, it’s just a very strong and sophisticated broadside against determinism, and this is especially true since Conway’s explanation assumes free will of experimenters in an idealized situation, and does not seem to prove it. In summary, I think the theorem seems to say that measured behavior of certain particles are strongly influenced by decisions of experimenters. Not sure this is that hotly contested…

  9. josh
    Posted June 27, 2013 at 11:21 am | Permalink

    I really don’t see what Conway is on about here. As I read it, IF humans have non-deterministic free-will, then the universe, which they can affect, isn’t completely deterministic…. Duh. Maybe I’m missing something.

  10. H.H.
    Posted June 27, 2013 at 11:23 am | Permalink

    If “we” don’t determine our own behavior, at least in part, then what does? Does it make sense to say that “our” brain makes decisions without “our” input? Perhaps the confusion lies in not in how free will is defined, but in how we are defining “we.”

    • jarkenny
      Posted June 27, 2013 at 11:44 am | Permalink

      Awesome. That is a very important point. Has the discoveries of physics and neuroscience made ordinary language obsolete?

    • eric
      Posted June 27, 2013 at 12:00 pm | Permalink

      If “we” don’t determine our own behavior, at least in part, then what does?

      The complaint about the “quantum indeterminancy” defense of free will is that the non-determinant factor is essentially random. And random action is not what philosophers or the public typically mean when they talk about free will.

      If I rolled a die and let that dictate my actions, I would in some important sense be no freer than a robot, would I? In fact we can program computers today that use random functions to dictate responses. Unless we are willing to believe that those types of programs have human-style free will (and let’s face it, nobody believes that), the quantum indeterminancy argument is pretty much a dead end. (All IMO.)

      • Kevin Henderson
        Posted June 27, 2013 at 3:28 pm | Permalink

        Quantum indeterminancy is not fundamental to helping understand free will. If one assumes that everything is deterministic…even quantum indeterminism, we are left with the hypothesis that all prior events determine future events, ergo no free will, since we are made of matter (and not immaterial stuff).

        However predicting any future is important for free will. If one cannot predict future events and if one cares about the future of events (humans only) then free will is turned back on. Distinguishing between free will and unpredictability for humans has yet to be shown be anyone.

      • cherrybombsim
        Posted June 27, 2013 at 4:08 pm | Permalink

        If you roll a die, the outcome is not inherently random, it is determined by the forces acting on the die. The outcome is *functionally* random, because we can know more practical information about its behavior from probability theory than we can by calculating the forces (in most cases). The inherent randomness of quantum interactions is not exactly a settled question, btw. We may just not know enough. Computers do not generate random numbers, they generate numbers deterministically that behave as if they were random.

        • eric
          Posted June 27, 2013 at 6:05 pm | Permalink

          Yes, I know, but that’s not the point. Substitute “hypothetical philosophically perfect random number generator” for “die” and my point still applies.

      • MNb
        Posted June 27, 2013 at 4:43 pm | Permalink

        “random action is not what philosophers or the public typically mean”
        Perhaps those philosophers and the public are wrong. Wouldn’t be the first time.

        “those types of programs have human-style free will”
        Why should this be any less credible than a completely deterministic robot-style model of the human brain?
        I don’t find Conway’s argument convincing (yet?) as presented here and some objections made above are relevant, but not yours imo.

  11. Posted June 27, 2013 at 11:23 am | Permalink

    Not a terribly new idea. I recall a sci-fi short story (perhaps a novel) I read in the early 70s about an astronaut on a sleeper-ship being woken by others who left earth centuries later but who overtook his ship because they could travel faster than light; their ship’s FTL drive was an application of “electron psychology”.

    Who knew… ?

    sean s.

    • phillupino
      Posted June 27, 2013 at 3:48 pm | Permalink

      Yes, wouldn’t that be something. IF the particles had free will, that would clear up one of the weirdness in the double slit experiment in QM. where,as if, the particle “knows” it is being watched, collapses the wave function and the screen loses the interference pattern. By the way, my physics instructor went ballistic on me. Just wondering.

  12. Gasper Sciacca
    Posted June 27, 2013 at 11:24 am | Permalink

    Any one who has studied quantum mechanics already knows the universe is not predetermined in its details. However, that is only in the details. The ultimate fate of the Universe is probably predetermined.

    I’m with Professor Coyne, this has nothing to do with free will. If some of our decisions are in fact influenced by quantum probability, all that means is that they are arbitrary and not the result of free will.

    • eric
      Posted June 27, 2013 at 12:17 pm | Permalink

      Clearly some human-level decisions are influenced by quantum probability. Here is an example:

      1. Physicist observes a new, single particle decaying. Records lifetime as “12” (arbitrary units).

      2. Physicist publishes lifetime = 12 plus or minus error bars. Many people read it (okay, “many” may be the unrealistic part of the example…)

      3. All human actions that reference “lifetime = 12” – the tip-tapping on keyboards, the words coming out people’s mouths, etc., future publications – can now be considered macroscopic actions that were highly dependent on an essentially quantum mechanical, probabilistic outcome.

  13. jarkenny
    Posted June 27, 2013 at 11:41 am | Permalink

    Does anyone really believe that all behavior was predetermined at the Big Bang? Maybe some Calvinists.

    The old vocabulary of free and determined is simply useless in the present context. We need to seek a new terminology.

  14. Posted June 27, 2013 at 11:42 am | Permalink

    Conway’s gone after this with too much conclusion baked in prior to stating the premises.

    But, what else could he do?? He cannot control Conway!

    A priori he thought about throwing a piece of paper as a future demonstration. Then he did it.

  15. Ray
    Posted June 27, 2013 at 11:49 am | Permalink

    Conway is not proving that humans have free will. The theorem ASSUMES humans have free will, and it concludes that IF humans have free will (suitably defined,) so do subatomic particles.

    I don’t know where you get the idea that Conway thinks he’s proving that free will exists, rather than assuming it as a premise. It’s right there in the interview:

    “If we make reasonable assumptions, including the assumption of free will …” (emphasis mine.)

    • darrelle
      Posted June 27, 2013 at 12:23 pm | Permalink

      If you take “proven” in this context to be the rigorous mathematical definition of proof then you are trivially correct. However, if you read the OP it seems rather clear that Jerry actually did understand what you pointed out here. And it also seems rather clear that Conway thinks that his work here lends support to the concept of human free will that he stated he believes in.

      With all that in mind it seems rather clear that “proven” was not intended by Jerry to be interpreted as the strict mathematical definition. Though often fraught with peril there are other legitimate contexts such as “common colloquial usage” and “literary license.” Though we might not always approve, or think it well done, it seems only fair to at least attempt to understand the context that the author has created before criticizing him.

      • Ray
        Posted June 27, 2013 at 1:05 pm | Permalink

        Well, if that’s the case, Jerry is at least being misleading to use “proof” in a colloquial sense in such close proximity to an actual proven mathematical theorem, which has nothing whatever to do with Conway’s reasons for believing that free will exists.

        Even so, I just don’t see it. It looks for all the world like Jerry thinks the “free will theorem” is supposed to prove that free will exists.

        Perhaps Jerry can clarify what he’s trying to say in the OP.

        • John Scanlon, FCD
          Posted June 28, 2013 at 7:03 am | Permalink

          It wasn’t Jerry that named it the “Free Will Theorem”, that’s what it said on the box Conway sold it in.

          • peterr
            Posted June 28, 2013 at 4:29 pm | Permalink

            Is it your experience that every theorem named “x theorem” is a theorem that proves the existence of “human x”? Not mine.

            For example, an object or being with the name “human Fermat’s Last” probably has never come to be, named that by anybody. And the corresponding theorem seems to prove the non-existence of something, not the existence of anything.

            It looks a lot to me like the Conway/Kochen theorem similarly proves the non-existance of something, roughly, in the physics interpretation, anything in its past which determines some aspect of spin of a particle.

    • Posted June 28, 2013 at 6:57 am | Permalink

      Suppose it is true that if humans have free will, then elementary particles have free will. But free will, as we understand it, is a pretty complicated thing. In fact, it is absurd to imagine that elementary particles have any kind of will, let alone free will. So, since the conclusion is absurd, some of the premises must be wrong as well, for example, the idea that humans have free will.

  16. Matt D
    Posted June 27, 2013 at 11:57 am | Permalink

    I don’t understand this at all, but I won’t claim it’s false because of that.

  17. JimV
    Posted June 27, 2013 at 12:00 pm | Permalink

    I doubt if there are any logic errors in Conway’s results and I don’t see any from what has been cited here. He states that he believes in human free will as an opinion, and states that starting with that opinion as an axiom plus some other reasonable axioms he can prove that elementary particles are not deterministic (which we already knew empirically based on QM).

    My own opinion, as expressed before, is that I could theoretically design a robot whose actions would be predictable in cases where there was a clear best action, but in thousands of cases which were not calculable or too close to call, would be indeterminate – so I don’t see why billions of years of natural selection couldn’t and wouldn’t evolve a similar system (there are advantages to being unpredictable).

    So I agree with Conway’s opinion that human actions are not always determinate and would not necessarily be the same in all cases if we could “replay the tape”. If that is what he means by “free will” than I am on-board with him. (I’m sure he will be grateful to hear that.)

    • MNb
      Posted June 27, 2013 at 4:54 pm | Permalink

      I think yours is the correct approach. The real question is if free will still has a meaning within a scientific model of the brain. I am also sympathetic to Jarkenny, who states that a new terminology would be handy. Because this

      “not really “free will” in the only meaningful sense it can be taken in such a context—that is, dualistic or libertarian free will of the human mind”

      is only defining a term away. “The only proper definition of X is dualistic; in scientific theories there is no room for dualism; hence X doesn’t exist”.
      Well, the definition might be wrong. Or we might have to use a new terminology.

      • darrelle
        Posted June 28, 2013 at 5:56 am | Permalink

        “. . . in scientific theories there is no room for dualism . . .

        As far as how science works, the process, there is room for dualism, or just about anything else you can imagine, in scientific theories. Or hypotheses anyway. You can test such hypotheses.

        In the sense that there is already lots of evidence that dualism is not accurate, and therefore there is no good reason to test for it anymore, that could certainly make sense. But, it might still make sense to test for it if only to demonstrate to people who still accept it that it is not accurate.

  18. Posted June 27, 2013 at 12:04 pm | Permalink

    There’s an article in the Notices of the AMS examining what the free will theorem actually proves.

    The link is from the wikipedia entry

    • peterr
      Posted June 30, 2013 at 11:38 am | Permalink

      Tomulka has been trying to point out in several places over 3 or 4 years that the theorem is false. It would seem likely, from the comment at the very end of the paper cited, that the axiom MIN can be interpreted in at least two ways. When interpreted in the way different from the way the theorem’s other author, Kochen (and presumably also Conway), takes it, that new ‘theorem’, not the one of Conway/Kochen, turns out not to be a theorem.

      This little dispute points out, if it was ever needed, that all these papers are embedded in assumptions about how physical statements are supposed to be converted into pure mathematics. Too bad Conway/Kochen did not include a dictionary for those mathematicians who haven’t read much physics. Tomulka et al could then spend their effort explaining why their interpretation of axiom MIN is the reasonable one.

  19. Posted June 27, 2013 at 12:44 pm | Permalink

    Show Mr. Conway this case, and ask him what he thinks:,,20073583,00.html

  20. Posted June 27, 2013 at 1:15 pm | Permalink

    One should not confuse “proving the free will theorem” with “proving that free will exists.” The first of those is a straight forward piece of mathematics, and “free will theorem” is just its name.

    Whether free will exists is a contentious question, and it depends on what we mean by “free will.” Whether or not the free will theorem is even relevant depends on what we mean by “free will.” Much of the disagreement over whether free will exists is really a disagreement over what we mean by “free will” and the free will theorem does not settle that disagreement.

    • MNb
      Posted June 27, 2013 at 4:55 pm | Permalink


  21. Rob King
    Posted June 27, 2013 at 1:19 pm | Permalink

    The Kochen-Specker theorem–which puts consciousness at the heart of the quantum measurement problem–lies at the heart of this idea. The maths can be pretty intimidating but some elements of the idea are not that hard to grasp. Kochen Specher shows that the E.P.R. assumption–that there really is an underlying deterministic reality– that we are simply not getting at–is false.
    Put simply, it looks like God does play dice and plays them really really sneakily. Einstein was apparently wrong and hated it.
    Ok, lets say this is true–and I freely (hmm) confess that this is outside of my pay grade. What follows? I submit–absolutely nothing whatsover of any philosophical or moral interest in to the issue at hand. I am a big (10^26) bunch of subatomic particles and lets say each one is a really truly random system. So what?
    I do a much much simpler demo for the students where I get 100 dice (not 10^26 dice–becuase I dont have a galaxy sized lecture hall) and bet whatever is in my wallet against a penny from a person in the audience that they cannot roll 100 6s.
    I always get a taker. It never happens. It never will. It will not happen in the lifetime of a universe. If someone says– “do you KNOW this” with that particular emphasis (and funny expression) that you only get from 1st year philosophy undergards I say, yes I do–as much as I know anything. I will bet my house against whatever you put up as collateral that it wont happen. What else do you want form the word “know”?
    I then get someone to roll the dice, put aside the 6s and roll the rest until there are 100 6s. Takes about 20 goes. Always has, always will. That’s what evolution by natural selection looks like. Order from chaos. Sure as sure can be.
    Randomness does not get you freedom–the size of casinos proves this on a rough level to anyone who can do sums.
    However–the theory is damn interesting all the same–it implies that the universe somehow involves consciousness. I find this hard to believe–but I could be wrong.

  22. Posted June 27, 2013 at 1:20 pm | Permalink

    “I assume that some of my actions are not given by predetermined functions of the past history of the universe.”

    An assumption is not a proof.

    • Kevin Henderson
      Posted June 27, 2013 at 3:39 pm | Permalink


      And one of his central tenets: “if indeed we humans have free will, then [so do] elementary particles.” is really off the mark.

      Start with particles and then humans. It is much easier to show that particles and fields may not be classically deterministic: i.e., statistical interactions are non-deterministic (chaotic).

  23. moarscienceplz
    Posted June 27, 2013 at 1:23 pm | Permalink

    “My friend Simon Kochen taught me one thing about quantum mechanics which I understood, and I find that many physicists don’t understand that one thing”

    At that point, I lost interest in anything else he had to say. I think it’s axiomatic that any argument that begins with “I am not an X-ist, but I know something that almost no professionals in the field of X knows/understands” is probably a steaming pile of horse-hockey.

    • Kevin Henderson
      Posted June 28, 2013 at 9:04 am | Permalink

      Well said. Few physicists today contend that they know quantum mechanics better than their colleagues. Some will argue that they can place limits to macroscopic entanglement, or decoherence, or Bell inequalities, but they do so in papers. Peripheral outsiders suggest they have greater conceptual understanding physicists, but they rarely if ever quantify their understanding.

    • Posted June 30, 2013 at 1:58 pm | Permalink

      What an amazing method of evaluation of arguments! Neglecting the obvious counterargument that Kochen has made important contributions to QM, perhaps I may take the liberty of pointing out that it might be more relevant to actually read the statement of the theorem and Conway’s statements in the interview (which happen to be exactly the opposite of what the headline of the post above would have us believe)?

  24. Posted June 27, 2013 at 1:33 pm | Permalink

    “Not determined” most emphatically does not imply free will.

    Free will requires determinism in the sense that the ghost in your machine must be the determining agent.

    Total indeterminacy (randomness) would have you observing yourself, perhaps in horror, as you did things possibly against whatever will you might have.

    Free will cannot come from indeterminacy.

    • Posted June 27, 2013 at 1:36 pm | Permalink

      And now I see eric already made this point in a reply to H.H.

    • DV
      Posted June 27, 2013 at 2:58 pm | Permalink

      Free Will requires determinism in another important sense. In a non-deterministic world, how can one “will” something at all? There must be a reasonably reliable mechanism for intention to turn into intended outcome, in order for outcome-pursuing agents to evolve at all. Imagine an animal intending to go somewhere and just randomly indeterministically end up anywhere. It’s an impossible environment for will, let alone free will.

      So whatever “Free Will” is free from, it cannot be determinism, because determinism it it’s prerequisite. The only sensible thing to be free from is the coercion of other willing agents.

      • darrelle
        Posted June 28, 2013 at 6:06 am | Permalink

        And in the christian tradition the coercer you are free from is the god you are a slave to. You can do what you want, but if it is the wrong thing your god will punish you. You have just enough rope to hang yourself. You are free to choose, a) obey your god, or b) burn.

        • DV
          Posted June 28, 2013 at 6:44 am | Permalink

          Since God doesn’t exist, it turns out the people are just slaves of their fears.

          • darrelle
            Posted June 28, 2013 at 7:59 am | Permalink

            Or desires?

    • Kevin Henderson
      Posted June 27, 2013 at 3:41 pm | Permalink

      But freewill can come from unpredictability independent of whether the world is deterministic or not.

      • Posted June 27, 2013 at 5:27 pm | Permalink

        You’re correct that determinism and unpredictability aren’t at odds (isn’t that what chaos theory is all about?), but, as with non-determined events, unpredictability doesn’t imply free will, either.

        The game “Plinko” on The Price is Right is deterministic but we can’t predict where the Plinko chip will end up. Does that mean the Plinko chip has free will?

        • Kevin Henderson
          Posted June 28, 2013 at 10:29 am | Permalink

          The Plinko chip does not have free will. Nor do we, in the sense that we can control our destiny with a force outside of nature (will, soul, magic, etc.).

          The Plinko chip, however does not care about free will…humans do (at least some of them). And a necessary condition for there to be no free will is the ability to predict and care about the prediction. Humans cannot predict the dynamics of the Plinko chip, and they care about that knowledge. Such a situation is indistinguishable from having free will.

          • Posted June 28, 2013 at 10:41 am | Permalink

            “And a necessary condition for there to be no free will is the ability to predict and care about the prediction.”

            Why is this a necessary condition?

          • Posted June 28, 2013 at 8:26 pm | Permalink

            In addition to what Jamie’s asked, let me ask what you mean by “ability to predict”. Predict everything? Or just some things? If the latter, what things?

            Is the point of the claim Jamie singled out that in the absence of free will we should gain the ability to predict everything? That doesn’t follow – again, let me bring up chaos theory.

            I’d think a perfect knowledge of every particle in the universe and what it’s doing (a la Laplace’s Demon) would be a more appropriate requirement for absolute predictability, if that’s what you mean.

  25. Posted June 27, 2013 at 2:04 pm | Permalink

    You might enjoy “The Nonsense of Free Will” by Oerton. His short sharp point is that the concept itself is paradoxical. A point also remarked on on this site by the estimable B&.

    Oerton elaborates that free will requires an uncaused cause that is wielded by “the character” of an agent. Therefore, causation runs right through the uncaused cause to the “character” of the one wielding it.

    As to quantum indeterminacy, I believe the majority of practicing physicists as well as philosophers of physics by now have come to accept the Many Worlds Interpretation as most likely right. In that understanding, determinism is fully restored to the universe by the removal of counter-factual definiteness in favor of multiplicity of outcomes to a single measurement. This understanding also eliminates non-locality and all the other violations of the known laws of physics required by the wave collapse or hidden variable interpretations.


  26. Torbjörn Larsson, OM
    Posted June 27, 2013 at 2:10 pm | Permalink

    Conway has a long history of overstating the results of his results, that are strained into irrelevancy (IMHO). He has a certain flair for that.

    • peterr
      Posted June 27, 2013 at 6:45 pm | Permalink

      I’d be interested in an explicit reference or two of that overstating.

      Conway can certainly be flippant. He also certainly does have a huge influence on young people. I have seen that day after day, at a time in the past. (Penrose also did at Oxford, but in a very different way—he is certainly far from flippant.)

      But I fail to understand this whole thread.
      Read the interview. You’ll find:

      1) Conway says he believes in human free will, but says nothing at all about what he means by the term.

      2) Conway definitely does not say that he has a theorem that proves the existence of human free will. The theorem referred to seems to do exactly the opposite, assuming human free will, but I have made no effort to understand that theorem’s statement in detail or its proof. As a theorem of mathematics, it will certainly contain precise definitions of all its assumptions and its conclusion, and there is no question in my mind that it is a correct theorem of pure mathematics (based on the reputations of him and of Kochen). Whether interpretations put on it by them or anybody else (in physics or psychology) are correct is an entirely different matter.

      So I have no idea why Jerry’s article here has the title he’s given it.

  27. nomad
    Posted June 27, 2013 at 2:46 pm | Permalink

    I think I might imagine a pathway of discrete energy born at the instant of the big bang which, pinball fashion, interacted with the myriad other forces within the the expanding fabric of the cosmos for billions of years. Eventually this pathway joins in and contributes to the cumulative momentum of infinite solution and dissolution of matter and energy resulting in the stars and elements and determines the behavior of quantum entities, etc, etc. Among all existence we see today, some specific and apparent outcomes of this sequence of causality are the evolution of the planet earth, the evolution of conscious life forms, the invention of mathematics and paper, and Dr. Conway. Had that discrete force ‘chosen” a slightly different path or not existed at all, perhaps this interview would be different as well.

    Just a liberal arts dude. Not keen on maths.

  28. chemicalscum
    Posted June 27, 2013 at 4:39 pm | Permalink

    It is somewhat ironic that Dennett has used Conway’s Game of Life as an example of how a simple deterministic algorithm can be used as a model to support his compatibilist position on free will.

    Conway writes in the ASMS paper:
    “Some believe that the alternative to determinism is randomness, and go on to say that “allowing randomness into the world does not really help in understanding free will.” However, this objection does not apply to the free responses of the particles that we have described. It may well be true that classically stochastic processes such as tossing a (true) coin do not help in explaining free will, but, as we show in the Appendix and in §10.1 of [1], adding randomness also does not explain the quantum mechanical effects described in our
    theorem. It is precisely the “semi-free” nature of twinned particles, and more generally of entanglement, that shows that something very different from classical stochasticism is at play here.”

    An Everettian (Many-Worlds) treatment removes the problem, as all of the permitted quantum outcomes exist in Hilbert space. A measurement tells us our location in Hilbert space 1.e. which branch of the wavefunction we are on. The weird “semi free” result becomes deterministic in the ensemble.

    Conway goes on in the Appendix to prove that there can be no mechanism for wavefunction collapse, no surprise as there is no wavefunction collapse only decoherence. The vast open future that quantum indeterminism plus deterministic chaos provides, in conjunction with the deterministic algorithms of our neural systems, gives us the basis for a rational compatibilist model of free will.

  29. Thanny
    Posted June 27, 2013 at 5:01 pm | Permalink

    There’s a stark difference between our inability to create a deterministic model of the universe and establishing that the universe is not deterministic.

  30. Posted June 27, 2013 at 5:28 pm | Permalink

    Thanny, see Bell’s Inequality in wikipedia. We can prove that there are no local hidden variables underlying nature.

    Interestingly. there are some suggestions in the physics literature that the distasteful reality implied by violation of Bell’s Inequality could be avoided if there were no such thing as free will. Non-locality can only be proved by assuming that the experimenter could have measured other things than he or she actually did measure. But this is a tough subject, with lots of wrinkles that are as deep as anything in physics.

  31. Peter Ozzie Jones
    Posted June 27, 2013 at 6:54 pm | Permalink

    If I understand what Richard Feynman says in these videos of his talks on QED (quantum electrodynamics) at the University of Auckland in 1979, available here:

    light explores all paths and then always takes the path of least time.

    It seems to me that photons do not exhibit “free will”.

  32. Jimbo
    Posted June 27, 2013 at 7:12 pm | Permalink

    Simple question. Science has determined that will (free or not), intent, reason, rationality occur in the prefrontal cortex, no? Then how is it that other animals with the same brain tissue, the same quantum indeterminacy, the same subatomic randomness, and all the other appeals to strange femtoscopic physics don’t have free will? (I freely admit that other primates and likely many mammals have elements of a “will”). But isn’t the distinction of a large prefrontal cortex and brain size the distinguishing human anatomical feature responsible for everything that makes us human? Isn’t this the same meat as found in a free-will-less shark? How could the extra human brain tissue possibly grant us access to new quantum physical effects not available to other brains? Admittedly, mathematical proofs are not my strong suit.

  33. Posted June 27, 2013 at 7:13 pm | Permalink

    There is a very good interpretation about the issue of determinism or not, going back to Laplace, in Stephen Hawking official blog, it is explained in an easy language. It is a lecture titled, DOES GOD PLAY DICE?

  34. David Duffy
    Posted June 27, 2013 at 7:39 pm | Permalink

    To intelligibly interpret a scientific experiment, you need to assume that the experimenter can choose freely. Otherwise, any inferences made about causality are suspect. The choice mechanism merely has to be uncorrelated with the outcome, so randomization is one way to will this kind of freedom.

    Colbeck and Renner are discussing this in

    with respect to quantum mechanical experiments (Bell type inequalities).

    But one doesn’t need traditional libertarian free will for this, just the freedom to be truly random, as per earlier comments.

  35. Rasmus Holm
    Posted June 27, 2013 at 8:54 pm | Permalink

    We all have our pet peeves. Jerry has several words he doesn’t like. One of my peeves is the phrase humans and animals as in ” the slippery slope toward humans marrying animals”. Should be “the slippery slope toward humans marrying other animals”

  36. Gavin
    Posted June 27, 2013 at 10:34 pm | Permalink

    The Free Will Theorem does not add anything significantly new to the broader discussion of free will. If you are operating on the assumption that quantum mechanics is correct, then the Free Will Theorem doesn’t impact you. You might want to learn more about quantum mechanics, perhaps from the excellent notes by John Preskill on quantum information (, but don’t waste any time with the Free Will Theorem.

    If you are holding on to the hope that maybe something less weird than quantum mechanics might be right, you are in trouble. Large classes of less-weird theories (hidden variables, certain sorts of randomness, etc.) cannot possibly match the experiments. This Free Will Theorem is just another example of why you are not going to be able to avoid facing quantum mechanics. I don’t think it is entirely new reason, since it appears to just be Bell’s Theorem again, but with a slightly experimental set-up.

    I have not followed the technical details of attempts to replace quantum mechanics. The Free Will Theorem seems to be a very technical point about what sorts of assumptions and observations are sufficient to defeat these attempts. Making free will one of the assumptions is a rather unusual approach, but the result is simply that quantum mechanics is unlikely to go away, as we’ve know for a long time.

  37. Shwell Thanksh
    Posted June 27, 2013 at 11:27 pm | Permalink

    One thing that might help explain the persistence of the illusion of libertarian free will is that each of us is, for the most part, really, really astonishingly good at predicting what we are about to do next. Almost effortlessly, even.

  38. Prof.Pedant
    Posted June 28, 2013 at 12:26 am | Permalink

    I haven’t chewed through all of the quotes yet, but my skimming of them has me saying “No, there is no such thing as free will, everything is probabilistically recently-determined, even though in the most technical sense everything does sort of go back to the big bang.”

  39. agentwhim
    Posted June 28, 2013 at 1:49 am | Permalink

    So does this mean we have free will in the same way that, say, a brick does?

    Also, is it not possible that QM’s apparent randomness is really just our lack of understanding of an underlying mechanism? If so, maybe determinism is completely true once you understand this – as yet unknown – mechanism.

  40. Thaddeus Aid
    Posted June 28, 2013 at 6:47 am | Permalink

    I am of two minds in the matter.

    I don’t fully accept determinism and I think that the universe is a set of probabilities. But we as humans don’t control these probabilities and that we are controlled by probabilities. This runs in line with my understanding of quantum theory and neuroscience. Given my understanding there is no free will as we are acted upon by physical and biological forces and we are forced into responses by them.

    My alternate idea is that all life has the ability to change the probabilities of outcome as Dennett suggests and so all life has compatible free will. But this isn’t special to humans, my dog can choose to take a nap or to play with her squeaky toy.

    So either there is no free will or there is free will and humans aren’t special in that regard. I do outright reject the idea that only humans are capable of free choice.

  41. Posted June 28, 2013 at 6:48 am | Permalink

    All of this smells disturbingly like a “free will of the gaps” argument.

  42. The Rose
    Posted June 28, 2013 at 12:17 pm | Permalink

    I’ve only just recently found out about this “free will” stuff, and I am fascinated by it. I’m trying to find out as much, and comprehend as much as I can about it, but it seems really hard for me and I’m still very confused. However, I asked myself this, “Would it be possible for all that we see around us to have occured, without the ability to, but only the illusion that we do, make any choices at all?”
    I thought that was a very easy “yes”.

    Thanks for the info, and thanks for all your excellent work!

  43. Posted June 28, 2013 at 5:30 pm | Permalink

    I’ve tried to read a few of the shorter papers about this theorem, and the only thing I can come up with is that either:
    a. this is nothing more than an abductive argument (and pointed out by another commenter), or
    b. this theorem has nothing to do with *human free will* but rather seeks to explain some wonky aspects of QM in light of some wonky human characteristic (free will).

  44. peterr
    Posted June 28, 2013 at 6:26 pm | Permalink

    “..this theorem has

    (1) nothing to do with *human free will*

    but rather seeks to explain
    some wonky aspects of QM in light of some wonky

    (2) human characteristic (free will).”

    Is this not self-contradictory?

    • Posted June 28, 2013 at 6:36 pm | Permalink

      Sorry, I miswrote myself.
      Item (b) might better read:
      “…some wonky human characteristic (that they call free will).”

      I suspect one could contrive a thought experiment where some non-human agent did the choosing that Conway & Kochen attribute to the human experimenters, thereby moving the free will away from the humans.

      • peterr
        Posted June 28, 2013 at 7:00 pm | Permalink

        To respond re the “non-human..”, here is one thing from the paper itself:

        “The humans who choose x, y, z, and w may of course be replaced by a computer program con- taining a pseudo-random number generator. If we dismiss as ridiculous the idea that the particles might be privy to this program, our proof would remain valid. However, as we remark in [1], free will would still be needed to choose the random number generator, since a determined determinist could maintain that this choice was fixed from the dawn of time.”
        [1] J. Conway and S. Kochen, The Free Will Theorem, Found. Phys. 36 (2006), 1441–1473….

        which is their original, weaker version.

        So it would seem to ultimately reduce to humans, they would seem to say.

        • Posted June 28, 2013 at 7:51 pm | Permalink

          I tend to give myself headaches when I try to solve these kinds of problems, so I’ll just take one quick stab at it.
          If we write code, then we still have to choose a RNG.
          If we provide a huge library of RNGs, and let the computer choose which one to apply, we are still choosing to have the computer do the job albeit in more abstract terms.
          So how about a program that decides (in some suitably pseudo-random way – or even by measuring some random physical process – whether to use a RNG at all. Essentially, we’re letting the computer decide whether to do the experiment or not.

  45. Posted June 29, 2013 at 8:32 am | Permalink

    First of all it is not possible to formally prove anything (for certain) about the real world, there lies room for future falsification. Basic empiricism here. So Conway cannot prove anything about humans only assert an hypothesis to be tested by experiment.

    Second, in quantum mechanics a particles behavior is not deterministic as Coyne and Conway rightly say. How they behave rests upon the particles wavefunction which gives a superposition of finite possibilities of how the particle will move. Once the particle is measured the wavefunction collapses meaning only one of the collection of possibilities is true.

    Particles do not have free will, they are restrained by the wavefunction which is a probabilistic function. One must not mix up probability with free will.

    Within free will lies the assumption that the agent can determine itself, which in physics does not happen. Systems obey statistics or classical determinism (macroscopicallly).

  46. Posted June 30, 2013 at 2:16 pm | Permalink

    Even if the theorem is true it does not prove free will exists, only that indeterminism exists. Philosopher Derk Pereboom argues that indeterminism also poses a threat to free will.

    See here for a discussion of why this is so.

  47. collin237
    Posted February 11, 2014 at 7:30 pm | Permalink

    Free will is an article of faith. It cannot be proven.

    I’ve read the so-called “Free Will Theorem”. I’m not even sure what it proves, because it’s mostly handwaving. In what little math there is, it defines a particle’s spin as a sphere-to-Boolean function, and shows that it cannot lead deterministically to the distribution in which entangled spins are known to appear at observation.

    The huge problem with this is that there’s nothing in physics that bears the slightest resemblance to a sphere-to-Boolean function!

  48. Jarod Benowitz
    Posted June 11, 2014 at 5:27 pm | Permalink

    The universe is fundamentally stochastic. “Free-Will” has no consistent definition and is rather thought of in a paradoxical manner. E.g. I can “choose” not to have free-will is a contradictory statement.

    There is an analogous genetic information uncertainty principle see

    One can extrapolate a fundamental proof that human behavior is not deterministic from both the above and the stochastic phenomenon of neurons from random collisions in the extracellular and intracellular solutions. In this manner “Precisely how we choose to do the things we do live in an impregnable black box”

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