Predictive Processing and Free Will

Our model of the mind as an embodied predictive engine explains why people have a sense of free will, and what is necessary for a mind in general in order to have this sense.

Consider the mind in the bunker. At first, it is not attempting to change the world, since it does not know that it can do this. It is just trying to guess what is going to happen. At a certain point, it discovers that it is a part of the world, and that making specific predictions can also cause things to happen in the world. Some predictions can be self-fulfilling. I described this situation earlier by saying that at this point the mind “can get any outcome it ‘wants.'”

The scare quotes were intentional, because up to this point the mind’s only particular interest was guessing what was going to happen. So once it notices that it is in control of something, how does it decide what to do? At this point the mind will have to say to itself, “This aspect of reality is under my control. What should I do with it?” This situation, when it is noticed by a sufficiently intelligent and reflective agent, will be the feeling of free will.

Occasionally I have suggested that even something like a chess computer, if it were sufficiently intelligent, could have a sense of free will, insofar as it knows that it has many options and can choose any of them, “as far as it knows.” There is some truth in this illustration but in the end it is probably not true that there could be a sense of free will in this situation. A chess computer, however intelligent, will be disembodied, and will therefore have no real power to affect its world, that is, the world of chess. In other words, in order for the sense of free will to develop, the agent needs sufficient access to the world that it can learn about itself and its own effects on the world. It cannot develop in a situation of limited access to reality, as for example to a game board, regardless of how good it is at the game.

In any case, the question remains: how does a mind decide what to do, when up until now it had no particular goal in mind? This question often causes concrete problems for people in real life. Many people complain that their life does not feel meaningful, that is, that they have little idea what goal they should be seeking.

Let us step back for a moment. Before discovering its possession of “free will,” the mind is simply trying to guess what is going to happen. So theoretically this should continue to happen even after the mind discovers that it has some power over reality. The mind isn’t especially interested in power; it just wants to know what is going to happen. But now it knows that what is going to happen depends on what it itself is going to do. So in order to know what is going to happen, it needs to answer the question, “What am I going to do?”

The question now seems impossible to answer. It is going to do whatever it ends up deciding to do. But it seems to have no goal in mind, and therefore no way to decide what to do, and therefore no way to know what it is going to do.

Nonetheless, the mind has no choice. It is going to do something or other, since things will continue to happen, and it must guess what will happen. When it reflects on itself, there will be at least two ways for it to try to understand what it is going to do.

First, it can consider its actions as the effect of some (presumably somewhat unknown) efficient causes, and ask, “Given these efficient causes, what am I likely to do?” In practice it will acquire an answer in this way through induction. “On past occasions, when offered the choice between chocolate and vanilla, I almost always chose vanilla. So I am likely to choose vanilla this time too.” This way of thinking will most naturally result in acting in accord with pre-existing habits.

Second, it can consider its actions as the effect of some (presumably somewhat known) final causes, and ask, “Given these final causes, what am I likely to do?” This will result in behavior that is more easily understood as goal-seeking. “Looking at my past choices of food, it looks like I was choosing them for the sake of the pleasant taste. But vanilla seems to have a more pleasant taste than chocolate. So it is likely that I will take the vanilla.”

Notice what we have in the second case. In principle, the mind is just doing what it always does: trying to guess what will happen. But in practice it is now seeking pleasant tastes, precisely because that seems like a reasonable way to guess what it will do.

This explains why people feel a need for meaning, that is, for understanding their purpose in life, and why they prefer to think of their life according to a narrative. These two things are distinct, but they are related, and both are ways of making our own actions more intelligible. In this way the mind’s task is easier: that is, we need purpose and narrative in order to know what we are going to do. We can also see why it seems to be possible to “choose” our purpose, even though choosing a final goal should be impossible. There is a “choice” about this insofar as our actions are not perfectly coherent, and it would be possible to understand them in relation to one end or another, at least in a concrete way, even if in any case we will always understand them in a general sense as being for the sake of happiness. In this sense, Stuart Armstrong’s recent argument that there is no such thing as the “true values” of human beings, although perhaps presented as an obstacle to be overcome, actually has some truth in it.

The human need for meaning, in fact, is so strong that occasionally people will commit suicide because they feel that their lives are not meaningful. We can think of these cases as being, more or less, actual cases of the darkened room. Otherwise we could simply ask, “So your life is meaningless. So what? Why does that mean you should kill yourself rather than doing some other random thing?” Killing yourself, in fact, shows that you still have a purpose, namely the mind’s fundamental purpose. The mind wants to know what it is going to do, and the best way to know this is to consider its actions as ordered to a determinate purpose. If no such purpose can be found, there is (in this unfortunate way of thinking) an alternative: if I go kill myself, I will know what I will do for the rest of my life.

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Self-Fulfilling Prophecy

We can formulate a number of objections to the thesis argued in the previous post.

First, if a belief that one is going to do something is the same as the decision to do it, another person’s belief that I am going to do something should mean that the other person is making a decision for me. But this is absurd.

Second, suppose that I know that I am going to be hit on the head and suffer from amnesia, thus forgetting all about these considerations. I may believe that I will eat breakfast tomorrow, but this is surely not a decision to do so.

Third, suppose someone wants to give up smoking. He may firmly hold the opinion that whatever he does, he will sometimes smoke within the next six months, not because he wants to do so, but because he does not believe it possible that he do otherwise. We would not want to say that he decided not to give up smoking.

Fourth, decisions are appropriate objects of praise and blame. We seem at least somewhat more reluctant to praise and blame beliefs, even if it is sometimes done.

Fifth, suppose someone believes, “I will kill Peter tomorrow at 4:30 PM.” We will wish to blame him for deciding to kill Peter. But if he does kill Peter tomorrow at 4:30, he held a true belief. Even if beliefs can be praised or blamed, it seems implausible that a true belief should be blamed.

The objections are helpful. With their aid we can see that there is indeed a flaw in the original proposal, but that it is nonetheless somewhat on the right track. A more accurate proposal would be this: a decision is a voluntary self-fulfilling prophecy as understood by the decision maker. I will explain as we consider the above arguments in more detail.

In the first argument, in the case of one person making a decision for another, the problem is that a mere belief that someone else is going to do something is not self-fulfilling. If I hold a belief that I myself will do something, the belief will tend to cause its own truth, just as suggested in the previous post. But believing that someone else will do something will not in general cause that person to do anything. Consider the following situation: a father says to his children as he departs for the day, “I am quite sure that the house will be clean when I get home.” If the children clean the house during his absence, suddenly it is much less obvious that we should deny that this was the father’s decision. In fact, the only reason this is not truly the father’s decision, without any qualification at all, is that it does not sufficiently possess the characteristics of a self-fulfilling prophecy. First, in the example it does not seem to matter whether the father believes what he says, but only whether he says it. Second, since it is in the power of the children to fail to clean the house in any case, there seems to be a lack of sufficient causal connection between the statement and the cleaning of the house. Suppose belief did matter, namely suppose that the children will know whether he believes what he says or not. And suppose additionally that his belief had an infallible power to make his children clean the house. In that case it would be quite reasonable to say, without any qualification, “He decided that his children would clean the house during his absence.” Likewise, even if the father falsely believes that he has such an infallible power, in a sense we could rightly describe him as trying to make that decision, just as we might say, “I decided to open the door,” even if it turns out that my belief that the door could be opened turns out to be false when I try it; the door may be locked. This is why I included the clause “as understood by the decision maker” in the above proposal. This is a typical character of moral analysis; human action must be understood from the perspective of the one who acts.

In the amnesia case, there is a similar problem: due to the amnesia, the person’s current beliefs do not have a causal connection with his later actions. In addition, if we consider such things as “eating breakfast,” there might be a certain lack of causal connection in any case; the person would likely eat breakfast whether or not he formulates any opinion about what he will do. And to this degree we might feel it implausible to say that his belief that he will eat breakfast is a decision, even without the amnesia. It is not understood by the subject as a self-fulfilling prophecy.

In the case of giving up smoking, there are several problems. In this case, the subject does not believe that there is any causal connection between his beliefs and his actions. Regardless of what he believes, he thinks, he is going to smoke in fact. Thus, in his opinion, if he believes that he will stop smoking completely, he will simply hold a false belief without getting any benefit from it; he will still smoke, and his belief will just be false. So since the belief is false, and without benefit, at least as he understands it, there is no reason for him to hold this belief. Consequently, he holds the opposite belief. But this is not a decision, since he does not understand it as causing his smoking, which is something that is expected to happen whether or not he believes it will.

In such cases in real life, we are in fact sometimes tempted to say that the person is choosing not to give up smoking. And we are tempted to this to the extent that it seems to us that his belief should have the causal power that he denies it has: his denial seems to stem from the desire to smoke. If he wanted to give up smoking, we think, he could just accept that he would be able to believe this, and in such a way that it would come true. He does not, we think, because he wants to smoke, and so does not want to give up smoking. In reality this is a question of degree, and this analysis can have some truth. Consider the following from St. Augustine’s Confessions (Book VIII, Ch. 7-8):

Finally, in the very fever of my indecision, I made many motions with my body; like men do when they will to act but cannot, either because they do not have the limbs or because their limbs are bound or weakened by disease, or incapacitated in some other way. Thus if I tore my hair, struck my forehead, or, entwining my fingers, clasped my knee, these I did because I willed it. But I might have willed it and still not have done it, if the nerves had not obeyed my will. Many things then I did, in which the will and power to do were not the same. Yet I did not do that one thing which seemed to me infinitely more desirable, which before long I should have power to will because shortly when I willed, I would will with a single will. For in this, the power of willing is the power of doing; and as yet I could not do it. Thus my body more readily obeyed the slightest wish of the soul in moving its limbs at the order of my mind than my soul obeyed itself to accomplish in the will alone its great resolve.

How can there be such a strange anomaly? And why is it? Let thy mercy shine on me, that I may inquire and find an answer, amid the dark labyrinth of human punishment and in the darkest contritions of the sons of Adam. Whence such an anomaly? And why should it be? The mind commands the body, and the body obeys. The mind commands itself and is resisted. The mind commands the hand to be moved and there is such readiness that the command is scarcely distinguished from the obedience in act. Yet the mind is mind, and the hand is body. The mind commands the mind to will, and yet though it be itself it does not obey itself. Whence this strange anomaly and why should it be? I repeat: The will commands itself to will, and could not give the command unless it wills; yet what is commanded is not done. But actually the will does not will entirely; therefore it does not command entirely. For as far as it wills, it commands. And as far as it does not will, the thing commanded is not done. For the will commands that there be an act of will–not another, but itself. But it does not command entirely. Therefore, what is commanded does not happen; for if the will were whole and entire, it would not even command it to be, because it would already be. It is, therefore, no strange anomaly partly to will and partly to be unwilling. This is actually an infirmity of mind, which cannot wholly rise, while pressed down by habit, even though it is supported by the truth. And so there are two wills, because one of them is not whole, and what is present in this one is lacking in the other.

St. Augustine analyzes this in the sense that he did not “will entirely” or “command entirely.” If we analyze it in our terms, he does not expect in fact to carry out his intention, because he does not want to, and he knows that people do not do things they do not want to do. In a similar way, in some cases the smoker does not fully want to give up smoking, and therefore believes himself incapable of simply deciding to give up smoking, because if he made that decision, it would happen, and he would not want it to happen.

In the previous post, I mentioned an “obvious objection” at several points. This was that the account as presented there leaves out the role of desire. Suppose someone believes that he will go to Vienna in fact, but does not wish to go there. Then when the time comes to buy a ticket, it is very plausible that he will not buy one. Yes, this will mean that he will stop believing that he will go to Vienna. But this is different from the case where a person has “decided” to go and then changes his mind. The person who does not want to go, is not changing his mind at all, except about the factual question. It seems absurd (and it is) to characterize a decision without any reference to what the person wants.

This is why we have characterized a decision here as “voluntary”, “self-fulfilling,” and “as understood by the decision maker.” It is indeed the case that the person holds a belief, but he holds it because he wants to, and because he expects it to cause its own fulfillment, and he desires that fulfillment.

Consider the analysis in the previous post of the road to point C. Why is it reasonable for anyone, whether the subject or a third party, to conclude that the person will take road A? This is because we know that the subject wishes to get to point C. It is his desire to get to point C that will cause him to take road A, once he understands that A is the only way to get there.

Someone might respond that in this case we could characterize the decision as just a desire: the desire to get to point C. The problem is that the example is overly simplified compared to real life. Ordinarily there is not simply a single way to reach our goals. And the desire to reach the goal may not determine which particular way we take, so something else must determine it. This is precisely why we need to make decisions at all. We could in fact avoid almost anything that feels like a decision, waiting until something else determined the matter, but if we did, we would live very badly indeed.

When we make a complicated plan, there are two interrelated factors explaining why we believe it to be factually true that we will carry out the plan. We know that we desire the goal, and we expect this desire for the goal to move us along the path towards the goal. But since we also have other desires, and there are various paths towards the goal, some better than others, there are many ways that we could go astray before reaching the goal, either by taking a path to some other goal, or by taking a path less suited to the goal. So we also expect the details of our plan to keep us on the particular course that we have planned, which we suppose to be the best, or at least the best path considering our situation as a whole. If we did not keep those details in mind, we would not likely remain on this precise path. As an example, I might plan to stop at a grocery store on my way home from work, out of the desire to possess a sufficient stock of groceries, but if I do not keep the plan in mind, my desire to get home may cause me to go past the store without stopping. Again, this is why our explanation of belief is that it is a self-fulfilling prophecy, and one explicitly understood by the subject as such; by saying “I will use A, B, and C, to get to goal Z,” we expect that keeping these details in mind, together with our desire for Z, we will be moved along this precise path, and we wish to follow this path, for the sake of Z.

There is a lot more that could be said about this. For example, it is not difficult to see here an explanation for the fact that such complicated plans rarely work out precisely in practice, even in the absence of external impediments. We expect our desire for the goal to keep us on track, but in fact we have other desires, and there are an indefinite number of possibilities for those other desires to make something else happen. Likewise, even if the plan was the best we could work out in advance, there will be numberless details in which there were better options that we did not notice while planning, and we will notice some of these as we proceed along the path. So both the desire for the goal, and the desire for other things, will likely derail the plan. And, of course, most plans will be derailed by external things as well.

A combination of the above factors has the result that I will leave the consideration of the fourth and fifth arguments to another post, even though this was not my original intention, and was not my belief about what would happen.

Statistical Laws of Choice

I noted in an earlier post the necessity of statistical laws of nature. This will necessarily apply to human actions as a particular case, as I implied there in mentioning the amount of food humans eat in a year.

Someone might object. It was said in the earlier post that this will happen unless there is a deliberate attempt to evade this result. But since we are speaking of human beings, there might well be such an attempt. So for example if we ask someone to choose to raise their right hand or their left hand, this might converge to an average, such as 50% each, or perhaps the right hand 60% of the time, or something of this kind. But presumably someone who starts out with the deliberate intention of avoiding such an average will be able to do so.

Unfortunately, such an attempt may succeed in the short run, but will necessarily fail in the long run, because although it is possible in principle, it would require an infinite knowing power, which humans do not have. As I pointed out in the earlier discussion, attempting to prevent convergence requires longer and longer strings on one side or the other. But if you need to raise your right hand a few trillion times before switching again to your left, you will surely lose track of your situation. Nor can you remedy this by writing things down, or by other technical aids: you may succeed in doing things trillions of times with this method, but if you do it forever, the numbers will also become too large to write down. Naturally, at this point we are only making a theoretical point, but it is nonetheless an important one, as we shall see later.

In any case, in practice people do not tend even to make such attempts, and consequently it is far easier to predict their actions in a roughly statistical manner. Thus for example it would not be hard to discover the frequency with which an individual chooses chocolate ice cream over vanilla.

The Practical Argument for Free Will

Richard Chappell discusses a practical argument for free will:

1) If I don’t have free will, then I can’t choose what to believe.
2) If I can choose what to believe, then I have free will [from 1]
3) If I have free will, then I ought to believe it.
4) If I can choose what to believe, then I ought to believe that I have free will. [from 2,3]
5) I ought, if I can, to choose to believe that I have free will. [restatement of 4]

He remarks in the comments:

I’m taking it as analytic (true by definition) that choice requires free will. If we’re not free, then we can’t choose, can we? We might “reach a conclusion”, much like a computer program does, but we couldn’t choose it.

I understand the word “choice” a bit differently, in that I would say that we are obviously choosing in the ordinary sense of the term, if we consider two options which are possible to us as far as we know, and then make up our minds to do one of them, even if it turned out in some metaphysical sense that we were already guaranteed in advance to do that one. Or in other words, Chappell is discussing determinism vs libertarian free will, apparently ruling out compatibilist free will on linguistic grounds. I don’t merely disagree in the sense that I use language differently, but in the sense that I don’t agree that his usage correspond to the normal English usage. [N.B. I misunderstood Richard here. He explains in the comments.] Since people can easily be led astray by such linguistic confusions, given the relationships between thought and language, I prefer to reformulate the argument:

  1. If I don’t have libertarian free will, then I can’t make an ultimate difference in what I believe that was not determined by some initial conditions.
  2. If I can make an ultimate difference in what I believe that was not determined by some initial conditions, then I have libertarian free will [from 1].
  3. If I have libertarian free will, then it is good to believe that I have it.
  4. If I can make an ultimate difference in my beliefs undetermined by initial conditions, then it is good to believe that I have libertarian free will. [from 2, 3]
  5. It is good, if I can, to make a difference in my beliefs undetermined by initial conditions, such that I believe that I have libertarian free will.

We would have to add that the means that can make such a difference, if any means can, would be choosing to believe that I have libertarian free will.

I have reformulated (3) to speak of what is good, rather than of what one ought to believe, for several reasons. First, in order to avoid confusion about the meaning of “ought”. Second, because the resolution of the argument lies here.

The argument is in fact a good argument as far as it goes. It does give a practical reason to hold the voluntary belief that one has libertarian free will. The problem is that it does not establish that it is better overall to hold this belief, because various factors can contribute to whether an action or belief is a good thing.

We can see this with the following thought experiment:

Either people have libertarian free will or they do not. This is unknown. But God has decreed that people who believe that they have libertarian free will go to hell for eternity, while people who believe that they do not, will go to heaven for eternity.

This is basically like the story of the Alien Implant. Having libertarian free will is like the situation where the black box is predicting your choice, and not having it is like the case where the box is causing your choice. The better thing here is to believe that you do not have libertarian free will, and this is true despite whatever theoretical sense you might have that you are “not responsible” for this belief if it is true, just as it is better not to smoke even if you think that your choice is being caused.

But note that if a person believes that he has libertarian free will, and it turns out to be true, he has some benefit from this, namely the truth. But the evil of going to hell presumably outweighs this benefit. And this reveals the fundamental problem with the argument, namely that we need to weigh the consequences overall. We made the consequences heaven and hell for dramatic effect, but even in the original situation, believing that you have libertarian free will when you do not, has an evil effect, namely believing something false, and potentially many evil effects, namely whatever else follows from this falsehood. This means that in order to determine what is better to believe here, it is necessary to consider the consequences of being mistaken, just as it is in general when one formulates beliefs.

Chastek on Determinism

On a number of occasions, James Chastek has referred to the impossibility of a detailed prediction of the future as an argument for libertarian free will. This is a misunderstanding. It is impossible to predict the future in detail for the reasons given in the linked post, and this has nothing to do with libertarian free will or even any kind of free will at all.

The most recent discussions of this issue at Chastek’s blog are found here and here. The latter post:

Hypothesis: A Laplacian demon, i.e. a being who can correctly predict all future actions, contradicts our actual experience of following instructions with some failure rate.

Set up: You are in a room with two buttons, A and B. This is the same set-up Soon’s free-will experiment, but the instructions are different.

Instructions: You are told that you will have to push a button every 30 seconds, and that you will have fifty trials. The clock will start when a sheet of paper comes out of a slit in the wall that says A or B. Your instructions are to push the opposite of whatever letter comes out.

The Apparatus: the first set of fifty trials is with a random letter generator. The second set of trials is with letters generated by a Laplacian demon who knows the wave function of the universe and so knows in advance what button will be pushed and so prints out the letter.

The Results: In the first set of trials, which we can confirm with actual experience, the success rate is close to 100%, but, the world being what it is, there is a 2% mistake rate in the responses. In the second set of trials the success rate is necessarily 0%. In the first set of trials, subject report feelings of boredom, mild indifference, continual daydreaming, etc. The feelings expressed in the second trial might be any or all of the following: some say they suddenly developed a pathological desire to subvert the commands of the experiment, others express feelings of being alienated from their bodies, trying to press one button and having their hand fly in the other direction, others insist that they did follow instructions and consider you completely crazy for suggesting otherwise, even though you can point to video evidence of them failing to follow the rules of the experiment, etc.

The Third Trial: Run the trial a third time, this time giving the randomly generated letter to the subject and giving the Laplacian letter to the experimenter. Observe all the trials where the two generate the same number, and interate the experiment until one has fifty trials. Our actual experience tells us that the subject will have a 98% success rate, but our theoretical Laplacian demon tells us that the success rate should be necessarily 0%. Since asserting that the random-number generator and the demon will never have the same response would make the error-rate necessarily disappear and cannot explain our actual experience of failures, the theoretical postulation of a Laplacian demon contradicts our actual experience. Q.E.D.

The post is phrased as a proof that Laplacian demons cannot exist, but in fact Chastek intends it to establish the existence of libertarian free will, which is a quite separate thesis; no one would be surprised if Laplacian demons cannot exist in the real world, but many people would be surprised if people turn out to have libertarian free will.

I explain in the comments there the problem with this argument:

Here is what happens when you set up the experiment. You approach the Laplacian demon and ask him to write the letter that the person is going to choose for the second set of 50 trials.

The demon will respond, “That is impossible. I know the wave function of the universe, and I know that there is no possible set of As and Bs such that, if that is the set written, it will be the set chosen by the person. Of course, I know what will actually be written, and I know what the person will do. But I also know that those do not and cannot match.”

In other words, you are right that the experiment is impossible, but this is not reason to believe that Laplacian demons are impossible; it is a reason to believe that it is impossible for anything to write what the person is going to do.

E.g. if your argument works, it proves either that God does not exist, or that he does not know the future. Nor can one object that God’s knowledge is eternal rather than of the future, since it is enough if God can write down what is going to happen, as he is thought to have done e.g. in the text, “A virgin will conceive etc.”

If you answer, as you should, that God cannot write what the person will do, but he can know it, the same applies to the Laplacian demon.

As another reality check here, according to St. Thomas a dog is “determinate to one” such that in the same circumstances it will do the same thing. But we can easily train a dog in such a way that no one can possibly write down the levers it will choose, since it will be trained to choose the opposite ones.

And still another: a relatively simple robot, programmed in the same way. We don’t need a Laplacian demon, since we can predict ourselves in every circumstance what it will do. But we cannot write that down, since then we would predict the opposite of what we wrote. And it is absolutely irrelevant that the robot is an “instrument,” since the argument does not have any premise saying that human beings are not instruments.

As for the third set, if I understood it correctly you are indeed cherry picking — you are simply selecting the trials where the human made a mistake, and saying, “why did he consistently make a mistake in these cases?” There is no reason; you simply selected those cases.

Chastek responds to this comment in a fairly detailed way. Rather than responding directly to the comment there, I ask him to comment on several scenarios. The first scenario:

If I drop a ball on a table, and I ask you to predict where it is going to first hit the table, and say, “Please predict where it is going to first hit the table, and let me know your prediction by covering the spot with your hand and keeping it there until the trial is over,” is it clear to you that:

a) it will be impossible for you to predict where it is going to first hit in this way, since if you cover a spot it cannot hit there

and

b) this has nothing whatsoever to do with determinism or indeterminism of anything.

The second scenario:

Let’s make up a deterministic universe. It has no human beings, no rocks, nothing but numbers. The wave function of the universe is this: f(x)=x+1, where x is the initial condition and x+1 is the second condition.

We are personally Laplacian demons compared to this universe. We know what the second condition will be for any original condition.

Now give us the option of setting the original condition, and say:

Predict the second condition, and set that as the initial condition. This should lead to a result like (1,1) or (2,2), which contradicts our experience that the result is always higher than the original condition. So the hypothesis that we know the output given the input must be false.

The answer: No. It is not false that we know the output given the input. We know that these do not and cannot match, not because of anything indeterminate, but because the universe is based on the completely deterministic rule that f(x)=x+1, not f(x)=x.

Is it clear:

a) why a Laplacian demon cannot set the original condition to the resulting condition
b) this has nothing to do with anything being indeterminate
c) there is no absurdity in a Laplacian demon for a universe like this

The reason why I presented these questions instead of responding directly to his comments is that his comments are confused, and an understanding of these situations would clear up that confusion. For unclear reasons, Chastek failed to respond to these questions. Nonetheless, I will respond to his detailed comments in the light of the above explanations. Chastek begins:

Here are my responses:

That is impossible… I know what will actually be written, and I know what the person will do. But I also know that those do not and cannot match

But “what will actually be written” is, together with a snapshot of the rest of the universe, an initial condition and “what the person will do” is an outcome. Saying these “can never match” means the demon is saying “the laws of nature do not suffice to go from some this initial condition to one of its outcomes” which is to deny Laplacian demons altogether.

The demon is not saying that the laws of nature do not suffice to go from an initial condition to an outcome. It is saying that “what will actually be written” is part of the initial conditions, and that it is an initial condition that is a determining factor that prevents itself from matching the outcome. In the case of the dropping ball above, covering the spot with your hand is an initial condition, and it absolutely prevents the outcome being that the ball first hits there. In the case of f(x), x is an initial condition, and it prevents the outcome from being x, since it will always be x+1. In the same way, in Chastek’s experiment, what is written is an initial condition which prevents the outcome from being that thing which was written.

If you answer, as you should, that God cannot write what the person will do, but he can know it, the same applies to the Laplacian demon.

When God announces what will happen he can be speaking about what he intends to do, while a LD cannot. I’m also very impressed by John of St. Thomas’s arguments that the world is not only notionally present to God but even physically present within him, which makes for a dimension of his speaking of the future that could never be said of an LD. This is in keeping with the Biblical idea that God not only looks at the world but responds and interacts with it. The character of prophesy is also very different from the thought experiment we’re trying to do with an LD: LD’s are all about what we can predict in advance, but Biblical prophesies do not seem to be overly concerned with what can be predicted in advance, as should be shown from the long history of failed attempts to turn the NT into a predictive tool.

If God says, “the outcome will be A,” and then consistently causes the person to choose A even when the person has hostile intentions, this will be contrary to our experience in the same way that the Laplacian demon would violate our experience if it always got the outcome right. You can respond, “ok, but that’s fine, because we’re admitting that God is a cause, but the Laplacian demon is not supposed to be affecting the outcome.” The problem with the response is that God is supposed to be the cause all of the time, not merely some of the time; so why should he not also say what is going to happen, since he is causing it anyway?

I agree that prophecy in the real world never tells us much detail about the future in fact, and this is verified in all biblical prophecies and in all historical cases such as the statements about the future made by the Fatima visionaries. I also say that even in principle God could not consistently predict in advance a person’s actions, and show him those predictions, without violating his experience of choice, but I say that this is for the reasons given here.

But the point of my objection was not about how prophecy works in the real world. The point was that Catholic doctrine seems to imply that God could, if he wanted, announce what the daily weather is going to be for the next year. It would not bother me personally if this turns out to be completely impossible; but is Chastek prepared to say the same? The real issues with the Laplacian demon are the same: knowing exactly what is going to happen, and to what degree it can announce what it knows.

we can easily train a dog in such a way that no one can possibly write down the levers it will choose, since it will be trained to choose the opposite ones.

Such an animal would follow instructions with some errors, and so would be a fine test subject for my experiment. This is exactly what my subject does in trial #1. I say the same for your robot example.

(ADDED LATER) I’m thankful for this point and developed for reasons given above on the thread.

This seems to indicate the source of the confusion, relative to my examples of covering the place where the ball hits, and the case of the function f(x) = x+1. There is no error rate in these situations: the ball never hits the spot you cover, and f(x) never equals x.

But this is really quite irrelevant. The reason the Laplacian demon says that the experiment is impossible has nothing to do with the error rate, but with the anti-correlation between what is written and the outcome. Consider: suppose in fact you never make a mistake. There is no error rate. Nonetheless, the demon still cannot say what you are going to do, because you always do the opposite of what it says. Likewise, even if the dog never fails to do what it was trained to do, it is impossible for the Laplacian demon to say what it is going to do, since it always does the opposite. The same is true for the robot. In other words, my examples show the reason why the experiment is impossible, without implying that a Laplacian demon is impossible.

We can easily reconstruct my examples to contain an error rate, and nonetheless prediction will be impossible for the same reasons, without implying that anything is indeterminate. For example:

Suppose that the world is such that every tenth time you try to cover a spot, your hand slips off and stops blocking it. I specify every tenth time to show that determinism has nothing to do with this: the setup is completely determinate. In this situation, you are able to indicate the spot where the ball will hit every tenth time, but no more often than that.

Likewise suppose we have f(x) = x+1, with one exception such that f(5) = 5. If we then ask the Laplacian demon (namely ourselves) to provide five x such that the output equals the input, we will not be able to do it in five cases, but we will be able to do it in one. Since this universe (the functional universe) is utterly deterministic, the fact that we cannot present five such cases does not indicate something indeterminate. It just indicates a determinate fact about how the function universe works.

As for the third set, if I understood it correctly you are indeed cherry picking — you are simply selecting the trials where the human made a mistake,

LD’s can’t be mistaken. If they foresee outcome O from initial conditions C, then no mistake can fail to make O come about. But this isn’t my main point, which is simply to repeat what I said to David: cherry picking requires disregarding evidence that goes against your conclusion, but the times when the random number generator and the LD disagree provide no evidence whether LD’s are consistent with our experience of following instructions with some errors.

I said “if I understood it correctly” because the situation was not clearly laid out. I understood the setup to be this: the Laplacian demon writes out fifty letters, A or B, being the letters it sees that I am going to write. It does not show me this series of letters. Instead, a random process outputs a series of letters, A or B, and each time I try to select the opposite letter.

Given this setup, what the Laplacian demon writes always matches what I select. And most of the time, both are the opposite of what was output by the random process. But occasionally I make a mistake, that is, I fail to select the opposite letter, and choose the same letter that the random process chose. In these cases, since the Laplacian demon still knew what was going to happen, the demon’s letter also matches the random process letter, and my letter.

Now, Chastek says, consider only the cases where the demon’s letter is the same as the random process letter. It will turn out that over those cases, I have a 100% failure rate: that is, in every such case I selected the same letter as the random process. According to him, we should consider this surprising, since we would not normally have a 100% failure rate. This is not cherry picking, he says, because “the times when the random number generator and the LD disagree provide no evidence whether LD’s are consistent with our experience of following instructions with some errors.”

The problem with this should be obvious. Let us consider demon #2: he looks at what the person writes, and then writes down the same thing. Is this demon possible? There will be some cases where demon #2 writes down the opposite of what the random process output: those will be the cases where the person did not make a mistake. But there will be other cases where the person makes a mistake. In those cases, what the person writes, and what demon #2 writes, will match the output of the random process. Consider only those cases. The person has a 100% failure rate in those cases. The cases where the random process and demon #2 disagree provide no evidence whether demon #2 is consistent with our experience, so this is not cherry picking. Now it is contrary to our experience to have a 100% failure rate. So demon #2 is impossible.

This result is of course absurd – demon#2 is obviously entirely possible, since otherwise making copies of things would be impossible. This is sufficient to establish that Chastek’s response is mistaken. He is indeed cherry picking: he simply selected the cases where the human made a mistake, and noted that there was a 100% failure rate in those cases.

In other words, we do not need a formal answer to Chastek’s objection to see that there is something very wrong with it; but the formal answer is that the cases where the demon disagrees with the random process do indeed provide some evidence. They question is whether the existence of the demon is consistent with “our experience of following instructions with some errors.” But we cannot have this experience without sometimes following the instructions correctly; being right is part of this experience, just like being wrong. And the cases where the demon disagrees with the random process are cases where we follow the instructions correctly, and such cases provide evidence that the demon is possible.

Chastek provides an additional comment about the case of the dog:

Just a note, one point I am thankful to EU for is the idea that a trained dog might be a good test subject too. If this is right, then the recursive loop might not be from intelligence as such but the intrinsic indeterminism of nature, which we find in one way through (what Aristotle called) matter being present in the initial conditions and the working of the laws and in another through intelligence. But space is opened for one with the allowing of the other, since on either account nature has to allow for teleology.

I was pointing to St. Thomas in my response with the hope that St. Thomas’s position would at least be seen as reasonable; and there is no question that St. Thomas believes that there is no indeterminism whatsoever in the behavior of a dog. If a dog is in the same situation, he believes, it will do exactly the same thing. In any case, Chastek does not address this, so I will not try at this time to establish the fact of St. Thomas’s position.

The main point is that, as we have already shown, the reason it is impossible to predict what the dog will do has nothing to do with indeterminism, since such prediction is impossible even if the dog is infallible, and remains impossible even if the dog has a deterministic error rate.

The comment, “But space is opened for one with the allowing of the other, since on either account nature has to allow for teleology,” may indicate why Chastek is so insistent in his error: in his opinion, if nature is deterministic, teleology is impossible. This is a mistake much like Robin Hanson’s mistake explained in the previous post. But again I will leave this for later consideration.

I will address one last comment:

I agree the physical determinist’s equation can’t be satisfied for all values, and that what makes it possible is the presence of a sort of recursion. But in the context of the experiment this means that the letter on a sheet of paper together with a snapshot of the rest of the universe can never be an initial condition, but I see no reason why this would be the case. Even if I granted their claim that there was some recursive contradiction, it does not arise merely because the letter is given in advance, since the LD could print out the letter in advance just fine if the initial conditions were, say, a test particle flying though empty space toward button A with enough force to push it.

It is true that the contradiction does not arise just because the Laplacian demon writes down the letter. There is no contradiction even in the human case, if the demon does not show it to the human. Nor does anything contrary to our experience happen in such a case. The case which is contrary to our experience is when the demon shows the letter to the person; and this is indeed impossible on account of a recursive contradiction, not because the demon is impossible.

Consider the case of the test particle flying towards button A: it is not a problem for the demon to write down the outcome precisely because what is written has no particular influence, in this case, on the outcome.

But if “writing the letter” means covering the button, as in our example of covering the spot where the ball will hit, then the demon will not be able to write the outcome in advance. And obviously this will not mean there is any indeterminism.

The contradiction comes about because covering the button prevents the button from being pushed. And the contradiction comes about in the human case in exactly the same way: writing a letter causes, via the human’s intention to follow the instructions, the opposite outcome. Again indeterminism has nothing to do with this: the same thing will happen if the human is infallible, or if the human has an error rate which has deterministic causes.

“This means that the letter on a sheet of paper together with a snapshot of the rest of the universe can never be an initial condition.” No, it means that in some of the cases, namely those where the human will be successful in following instructions, the letter with the rest of the universe cannot be an initial condition where the outcome is the same as what is written. While there should be no need to repeat the reasons for this at this point, the reason is that “what is written” is a cause of the opposite outcome, and whether that causality is deterministic or indeterministic has nothing to do with the impossibility. The letter can indeed be an initial condition: but it is an initial condition where the outcome is the opposite of the letter, and the demon knows all this.

The Good I Do Not Want

St. Paul says in the letter to the Romans, “I can will what is right, but I cannot do it. For I do not do the good I want, but the evil I do not want is what I do.”

This happens because the person is divided. Simply speaking I may believe that the thing that I want to do is right; but in another way, I perceive or suppose that “the evil I do not want” is good.

This sort of division can happen in the opposite way as well, so that a person wills the evil that he takes to be good, but cannot do it, because another part of him perceives that it is evil and to be avoided.

Procrastination can work as an example of both cases. Without a doubt procrastinating is often failing to do the good that one wills; but it is also often refusing to do something that would be mostly pointless, and in this sense, it is refusing to do something bad, and thus one could say that “I do not the evil I want, but the good I do not want is what I do.”

 

Composing Elements

Suppose we have two elements, as for example water and earth (not that these are really elements.) How do we make something out of the elements? We can consider two different possible ways that this could happen.

Suppose that when we combine one part water and one part earth, we get mud, and when we combine one part water and two parts earth, we get clay. Thus clay and mud are two different composite bodies that can be made from our elements.

How do we expect clay and mud to behave? We saw earlier that the nature of the physical world more or less requires the existence of mathematical laws of nature. Now we could say, “Clay and mud are made of earth and water, and we know the laws governing earth and water. So we can figure out the behavior of clay and mud using the laws governing earth and water.”

But we could also say, “Although clay and mud are made of earth and water, they are also something new. Consequently we can work out the laws governing them by experience, but we cannot expect to work them out just from the laws governing earth and water.”

These two claims are basically opposed to one another, and we should not expect that both would be true, at least in any particular instance. It might be that one is true in some cases and the other is true in some cases, or it might be that one side is always true. But in any case one will be true and not the other, in each particular situation.

Someone might argue that the first claim must be always true in principle. If water behaves one way by itself, and another way when it is combined with earth, then you haven’t sufficiently specified the behavior of water without including how it behaves when it is beside earth, or mixed with earth, or combined in whatever way. So once you have completely specified the behavior of water, you have specified how it behaves when combined with other things.

But this way of thinking is artificial. If water follows an inverse square law of gravity by itself, but an entirely different mathematical law when it is combined with earth, rather than saying that the entirely different law is a special case governing water, we should just admit that the different law is a law governing clay and mud, but not water. On the other hand, it is not unreasonable to include various potential interactions in your laws governing water, rather than only considering how water behaves in perfect isolation. Thus for example one would want to say that water suffers gravitational effects from all other bodies, rather than simply saying that water attracts itself. Nonetheless, even if the distinction is somewhat rough, there is a meaningful distinction between situations where the laws governing the elements also govern the composites, and situations where we need new laws for the composites.

In one way, the second claim is always true. It is always the case that something is true of the composite which is not true of the elements in themselves, since the composite is a whole composed of elements, while the elements in themselves are not. This is true even in artificial compositions; the parts of a bicycle are not a bicycle, but the whole is. And I can ride a bicycle, but  I cannot ride the individual pieces of metal that form it. Likewise, it is evidently true of living things, which are alive, and in some cases have conscious experience, even though the individual elements do not.

In a second way, the second claim is almost always true. If we consider our laws as practical methods for predicting the behavior of a physical system, in practice we will almost always need special laws to predict the behavior of a complex composite, if only because it would be too complex and time consuming to predict the behavior of the composite using laws governing only the parts. Thus people who wish to predict the weather use generalizations based on the experience of weather, rather than trying to predict the weather simply by considering more general laws of physics, despite believing that the weather is in fact a consequence of such general laws.

In a third way, the first claim is true at least frequently, and possibly always. If we consider the behavior of a bicycle or a computer, not with respect to general questions such as “can I ride it?” or “can it calculate the square root of two?”, but with respect to the physical movement of the parts, there are good reasons to think that the behavior of the whole can be determined from the behavior of the parts of which it is composed. For these are human inventions, and although experience is involved in such inventions, people make guesses about new behavior largely from their understanding of how the parts behave which they plan to put together. So if the whole behaved in ways which are significantly unpredictable from the behavior of the parts, we would not expect such inventions to work. Likewise, as said above, there is little reason to doubt that the weather results from general principles of physics that apply to earth, air, water, and so on.

I say “possibly always” above, because there is no case where the second claim is known to be true in this sense, and many instances, as noted, where the first is known or reasonably believed to be the case. Additionally, one can give reasons in principle for expecting the first claim to be true in this way, although this is a matter for later consideration.

An important objection to this possibility is that the fact that the second claim is always true in the first way mentioned above, seems to imply that the first claim cannot be true even in the third way, at least in some cases. In particular, the conscious behavior of living things, and especially human free will, might seem inconsistent with the idea that the physical behavior of living things is in principle predictable from laws governing their elements.