Perception of free will is a result of Gödel’s incompleteness theorem

Gödel’s second incompleteness theorem states that any sufficiently strong consistent system cannot prove its own consistency. Basically, there’s always some part of a system left that’s not provable or disprovable. For example, if you write a paragraph about itself, there’ll always be one sentence left that has to talk about itself or some codependency between sentences. Because of this, it cannot fully describe itself. Or, if you wish to measure everything in the universe, you’re left with a measuring device that must measure itself. It’s impossible for a complex system to be self-consistent. Even science is based on a few arbitrary statements that cannot be proven or disproven called the philosophy of science.

When an individual observes the universe, he can observe and conclude about nearly any part of it. However, the incompleteness theorem prevents him from making consistent conclusions about his own conclusion-making device, his brain, in the same way that a ruler can measure anything but itself.

Let’s assume the ruler can be manipulated by the environment in the same way our brain can. If it’s stretched or contracted through whatever interaction, it can’t tell. As far as it knows, it’s still 12 inches long. Instead, it would perceive every other object in the universe as changing in length.

Just like the ruler can’t perceive its changing length because it’s using itself to measure, we cannot perceive our own decision-making process because we’re using that subsystem to come to conclusions about itself.

This is how we perceive the sensation of free will. The environment modifies our brain in a clearly deterministic manner, altering our neural network in ways we are totally unable to perceive. We go out to remeasure the world around us and see that everything has changed. What’s going on? How can I stay constant while everything else changes radically?

This is exactly the mechanism at work when we misunderstand chaos. We think of the Butterfly Effect as giving us this incredible power over the universe¹. We think we can choose to move our hand and cause a tornado on another continent. We forget about the causality that shaped our brain and caused us to move our hand in that way. We no more caused the tornado by moving our hand than the formation of the earth caused it.

Because of the incompleteness theorem, our brains and the hypothetical ruler cannot perceive how they themselves are manipulated by the environment, but perceive radical change in the environment. We’re left with a hole in our understanding. Why does causality seem to apply to a billiard table yet not ourselves? Let’s bring the ruler back to simplify things once more. We concluded above that the ruler cannot detect when it’s stretched or shortened. However, it does see that everything else gets proportionally larger and smaller. It therefore reasonably concludes that it can manipulate the universe to change the length of objects.

Analogously, the halting of causality we perceive in ourselves is resolved by the creation of an odd sensation that we can freely manipulate the environment independent of its effect on us.

¹Sensitive dependence on initial conditions (the Butterfly Effect) is an element of deterministic chaos. Chaos is simply a tendency of deterministic systems to diverge much sooner than would be expected even with greater precision. It is not a magical, unpredictable randomness that comes from the netherworld.

24 thoughts on “Perception of free will is a result of Gödel’s incompleteness theorem

  1. So what you’re saying is…….. ???

    A.) We don’t actually have free will?
    B.) We can’t think about our own thought processes with any clarity?
    C.) We actually think we can create tornados by waving our hands?

  2. A) Accepting that we don’t have free will is a prerequisite of the essay. This is just to explain why it feels like we do.

    B+C) Yeup.

  3. I don’t buy into the premise that we don’t have free will. I also happen to think that we can think about our own thought processes with some level of clarity. How many people actually think they can create tornados by waving their hands?

  4. Maybe billiard tables do think we have free will!😉

    The fundamental difference between human beings and animals is our ability to choose our response to a stimulus.

  5. That sounds like a cool thing to say, but what causes a brain to have some magical ability to escape causality that a billiard table doesn’t have?

  6. That’s a very good question, but I think that’s what my old friends the Catholics call “the mystery of life.”

    I don’t think this is something that can be proven or disproven as a premise to another argument. It’s like starting from the existence or non-existence of God to build to a further point. Who cares, since we don’t know if the premise is true?

    Truth be told, I don’t know why we have the ability to escape pure causality. But my experience tells me that we do.

  7. I think you’re drawing conclusions from Incompleteness that aren’t there to be drawn. Just because no formal system can prove something (nontrivial) about all formal systems doesn’t mean a formal system can’t come to the right answer. The theorem allows for reasonable performance via heuristics. It’s far from a consequence of Gödel’s theorem that we can’t understand our thought process. All the basic version tells us is that there is some conclusion which we cannot reach, but which has a truth value. For instance, you cannot consistently assert “lucent cannot consistently assert this sentence,” but I can. The expanded version tells us that any formal system which includes us is either inconsistent or incomplete.

    (I actually think the human mind is inconsistent as well as incomplete, but the reasoning implementation doesn’t usually go through the needed steps to bring us to “P and not P.”)

  8. …you cannot consistently assert “lucent cannot consistently assert this sentence,” but I can.

    That’s why I used first person pronouns in the second paragraph. I make no assertion that the mind itself can’t be understood in general using the scientific method.

    You’re right, we can make some conclusions about how we think and understand ourselves to a limited degree because, to bring up my trite analogy, we have many rulers.

    However, what I’m arguing is that this sensation of free will is a result of incompleteness and because we cannot think about our thinking, it’s literally impossible to fully grasp and feel that we’re just another deterministic component of the universe. We can’t wrap our own mind around itself because of incompleteness.

    Just curious: would you agree that the ruler was a reasonable extrapolation of the incompleteness?

  9. What makes you think that other animals can’t choose their response to a stimulus? My cat doesn’t always react the same way to the same stimuli.

  10. Cats don’t sit and ponder their reaction to a stimulus. They just react. It may not be the same reaction every time, but then again I doubt the stimulus or their previous experience is the same every time.

  11. Have you ever watched a cat look at something novel? When he isn’t sure what it is or what to do with it, he’ll ponder it, stare at it, maybe sniff or bat at it. I have 3 kittens and they do that kind of thing all the time. Unless you’re a cat, you have no way to know what they’re thinking.

  12. The idea that the universe is deterministic is several hundred years old, and is no longer a useful concept in describing the world.

    Quantum Mechanics has shown us that at the most fundamental level, our world is unpredictable. To say that we can’t predict the motion of every particle is misleading; from a scientific standpoint if you can’t ever predict it, then you can’t say that it exists and it’s unknowable–rather, you must say, it does not exist, it has not been determined.

    Mathematical Chaos Theory has shown us that even when we do have determinism at the microscopic level (which we don’t–it is random), the events at a large scale can remain unpredictable. So, from a practical standpoint, large systems can exhibit a large degree of randomness even if they are made out of deterministic components (such as large bodies acting under gravitational attraction–these can and do behave chaotically, even though they are so large that the laws describing their motion are essentially deterministic).

    So…the world is random. What other causal agent is acting on them? It is the agent of constraint! Of all the possible paths that could play out in a system, according to the randomness, many of them are more feasible than others because of the large-scale constraints acting on the system. The constraints of a system can be of many types–it could be the boundaries of the system, certain laws of physics that constrain it, or it could be complex feedback mechanisms within the system itself.

    A random world with constraint determining large-scale behaviour is scarcely deterministic! It becomes a world which is largely unpredictable, but in which greater purposes and patterns emerge, not out of determinism, but out of feedback loops and external constraints. This is the world we live in!!!

    Now…thinking about this world, what is free will? It seems like a much more valid concept in this type of world!

  13. Yeah, there’s probably true randomness at the subatomic level. It doesn’t really affect things as large as neurons, though.

    Free will is an invalid concept at any scale with any amount of randomness. It’s this totally preposterous belief that something happens in our brains and nowhere else that allows it to make choices independent of its input.

    Similarly, if I make a computer with a true random number generator and have it insert one every few million cycles, would you argue that the computer program has some sort of freedom to select its output?

    You didn’t address the theme of the essay.

  14. You have evoked “Godel’s incompleteness” as a generic catchall for a whole bunch of terms. What your really talking about is closer to relativity and frames of reference. Godel doesn’t state that you can’t measure yourself, in fact, its taken as a given by all formal mathematics that there exist axiomatic facts that cannot be disproven. Rather, what Godel is saying is that GIVEN these axiomatic facts, we cannot generate a system that is both complete and consistent. We could quite easily postulate a universe in which a 12″ ruler is axiomatic.

    Quantum theory does nothing to debunk determinism. At the very base level, Quantum IS deterministic to the best of our knowledge, its merely the measurement of quantum effects which is constrained by Heisenburg. However, even if it were random, it still wouldn’t be free will although it wouldn’t be strictly determinism. Instead of billiard balls telling us what to do, instead we have a cosmic dice roller.

    My personal take on the free will issue is that I believe in empiricism. Given the fact that whether we have free will or not cannot be detected by everyday empirical experience, it is as much “true” to say we have free will as to say that we do not. Thus, we should take the most useful definition which is that we do have free will. Even if objectively, we do not.

    Thats my take on the issue anyhow.

  15. Individual quantum events appear to be totally random to the best of our knowledge, even disregarding HUP. While you brush up on quantum theory, I’ll brush up on incompleteness.

    Notice the person above your reply and my reply to him, “Yeah, there’s probably true randomness at the subatomic level. It doesn’t really affect things as large as neurons, though. Free will is an invalid concept at any scale with any amount of randomness.”

    You’re looking at the concept of free will in a fundamentally different way than me. My entire argument is that free will is a feeling to be explained as any other feeling. Love is a result of oxytocin, free will is a result of frame of reference or whatever you like to call my explanation. It is not an algorithm or a proof or a philosophical question. I’m using analogy to explain why we experience this feeling.

    Without a definition of free will, your empiricism is on dangerous grounds. I’m not sure what you define useful to be. Encouraging? You could make the same argument about god. If god doesn’t touch the universe, take the most “useful” definition and say he’s there. If empiricism allows these kinds of jumps, I want nothing to do with it.

  16. Hmm… to the best of my knowledge, Schrodinger’s equations describe completely deterministic progressions of a probability density function. Maybe I’m wrong, its irrelevant to the position anyhow.

    As I said in a later entry, sure, you could try to use science to explain it away (and possibly even find what amounts to a free will gene although I can’t imagine what turning it off would do), but its of little use except in the academic, philosophical sense.

    A modified pascal’s wager if you will:

    If you believe in determinism and the world is deterministic, you had no choice in the matter.

    If you believe in determinism and the world is free, you live a pretty shitty life.

    If you believe in free will and the world is deterministic, then you also had no choice in the matter.

    If you believe in free will and the world is free, you were pretty much correct.

    Thus, the only tenable position is to belive in free will.

    As regards to empiricism, sure, you could believe in a god. But this god would have ne evidence of miracles or any influence on the world. According to our best observations, he might as well not exist. If you wan’t to believe in such a god, a watered down deist god, then by all means go ahead. I don’t see exactly how such a thing comforts you.

  17. You’re still treating determinism/free will like a philosophical concept to be believed in. I treat it like an emotion, like love, for example. Both motivate us. We can understand them, but there’s no reason we should want the understanding to override their intuitive sensation. It’s certainly not beneficial to override either.

    However, knowledge of determinism seems to be driving current trends in science and even justice. The insanity plea, for example, is kind of an acknowledgment of determinism and is certainly a good step in the direction of just justice. Why people have the same religion as their children, why the abused become abusers, and the entire field of evolutionary psychology. Science as a whole is definitely moving toward an implicit acceptance of determinism.

  18. Exactly.

    It’s a feeling, like love or greed. We shouldn’t treat it as a philosophical concept or a magical force or whatnot. It’s just a sensation. Asking what free will is and hoping for a scientific answer is like asking what love is and hoping to hear it’s a magical force that can be detected that draws people of similar attractiveness, socioeconomic status, etc. together.

  19. yes, but if you cant define ‘free will’, then the question “does free will exist?” is meaningless.
    Its like asking “does spon exist?”
    – Steeeve

  20. I agree completely. The question is clearly meaningless, and I’d be a fool to bother to address it. This made no comment on the philosophical idea of free will.

    However, when you go about daily life, you do have a sensation that you can make any number of choices or do things spontaneously. This is unrelated to any philosophy or physics. It’s just psychology.

    You could make the same complaint about love. If I wrote an essay saying love was an adaptation to force people to stay together even if better partners were all around them, you could say that there’s no physical force flowing through the universe that attaches people in this way, and so my essay was null.

    At some point in history, people probably did think love was some magical, unseen physical force. Hell, some people today probably do. But we’ve mostly figured out that it’s just another bunch of neurotransmitters and circuits. That’s why no one would demand a mechanism from an article that explained love. We’re having the same problem now with free will. It’s just another feeling, but many are confused and think it’s either some physical property of the universe or doesn’t exist at all.

  21. Godel proves that no system can perfectly know itself. If you need perfect self-knowing you must believe that Godel doesn’t apply to humans. But do you need Perfect self-minitoring?

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