“Moral” Responsibility

December 24, 2018December 24, 2018 entirelyuseless Ethics, Uncategorized Choice, Determinism, Evil, Good, Jerry Coyne, Moral Object, Moral Responsibility, Necessity, Punishment, Reward, Will

In a passage quoted here, Jerry Coyne objected to the “moral” in “moral responsibility”:

To me, that means that the concept of “moral responsibility” is meaningless, for that implies an ability to choose freely. Nevertheless, we should still retain the concept of responsibility, meaning “an identifiable person did this or that good or bad action”. And, of course, we can sanction or praise people who were responsible in this sense, for such blame and praise can not only reinforce good behavior but is salubrious for society.

Suppose someone completely insane happens to kill another person, under the mistaken belief that they are doing something completely different. In such a case, “an identifiable person did this or that good or bad action,” and yet we do not say they are responsible, much less blame such a person; rather we may subject them to physical restraints, but we no more blame them than we blame the weather for the deaths that it occasionally inflicts on people. In other words, Coyne’s definition does not even work for “responsibility,” let alone moral responsibility.

Moral action has a specific meaning: something that is done, and not merely an action in itself, but in comparison with the good proposed by human reason. Consequently we have moral action only when we have something voluntarily done by a human being for a reason, or (if without a reason) with the voluntary omission of the consideration of reasons. In exactly the same situations we have moral responsibility: namely, someone voluntarily did something good, or someone voluntarily did something bad.

Praise and blame are added precisely because people are acting for reasons, and given that people tend to like praise and dislike blame, these elements, if rightly applied, will make good things better, and thus more likely to be pursued, and bad things worse, and thus more likely to be avoided. As an aside, this also suggests occasions when it is a bad idea to blame someone for something bad; namely, when blame is not likely to reduce the bad activity, or by very little, since in this case you are simply making things worse, period.

Stop, Coyne and others will say. Even if we agree with the point about praise and blame, we do not agree about moral responsibility, unless determinism is false. And nothing in the above paragraphs even refers to determinism or its opposite, and thus the above cannot be a full account of moral responsibility.

The above is, in fact, a basically complete account of moral responsibility. Although determinism is false, as was said in the linked post, its falsity has nothing to do with the matter one way or another.

The confusion about this results from a confusion between an action as a being in itself, and an action as moral, namely as considered by reason. This distinction was discussed here while considering what it means to say that some kinds of actions are always wrong. It is quite true that considered as a moral action, it would be wrong to blame someone if they did not have any other option. But that situation would be a situation where no reasonable person would act otherwise. And you do not blame someone for doing something that all reasonable people would do. You blame them in a situation where reasonable people would do otherwise: there are reasons for doing something different, but they did not act on those reasons.

But it is not the case that blame or moral responsibility depends on whether or not there is a physically possible alternative, because to consider physical alternatives is simply to speak of the action as a being in itself, and not as a moral act at all.

Quantum Mechanics and Libertarian Free Will

December 21, 2018 entirelyuseless Ethics, Metaphysics, Probability, Science, Uncategorized Artifacts, Causes, Computers, Determinism, Free Will, Jerry Coyne, Moral Responsibility, Quantum Mechanics, Randomness, St. Thomas

In a passage quoted in the last post, Jerry Coyne claims that quantum indeterminacy is irrelevant to free will: “Even the pure indeterminism of quantum mechanics can’t give us free will, because that’s simple randomness, and not a result of our own ‘will.'”

Coyne seems to be thinking that since quantum indeterminism has fixed probabilities in any specific situation, the result for human behavior would necessarily be like our second imaginary situation in the last post. There might be a 20% chance that you would randomly do X, and an 80% chance that you would randomly do Y, and nothing can affect these probabilities. Consequently you cannot be morally responsible for doing X or for doing Y, nor should you be praised or blamed for them.

Wait, you might say. Coyne explicitly favors praise and blame in general. But why? If you would not praise or blame someone doing something randomly, why should you praise or blame someone doing something in a deterministic manner? As explained in the last post, the question is whether reasons have any influence on your behavior. Coyne is assuming that if your behavior is deterministic, it can still be influenced by reasons, but if it is indeterministic, it cannot be. But there is no reason for this to be case. Your behavior can be influenced by reasons whether it is deterministic or not.

St. Thomas argues for libertarian free will on the grounds that there can be reasons for opposite actions:

Man does not choose of necessity. And this is because that which is possible not to be, is not of necessity. Now the reason why it is possible not to choose, or to choose, may be gathered from a twofold power in man. For man can will and not will, act and not act; again, he can will this or that, and do this or that. The reason of this is seated in the very power of the reason. For the will can tend to whatever the reason can apprehend as good. Now the reason can apprehend as good, not only this, viz. “to will” or “to act,” but also this, viz. “not to will” or “not to act.” Again, in all particular goods, the reason can consider an aspect of some good, and the lack of some good, which has the aspect of evil: and in this respect, it can apprehend any single one of such goods as to be chosen or to be avoided. The perfect good alone, which is Happiness, cannot be apprehended by the reason as an evil, or as lacking in any way. Consequently man wills Happiness of necessity, nor can he will not to be happy, or to be unhappy. Now since choice is not of the end, but of the means, as stated above (Article 3); it is not of the perfect good, which is Happiness, but of other particular goods. Therefore man chooses not of necessity, but freely.

Someone might object that if both are possible, there cannot be a reason why someone chooses one rather than the other. This is basically the claim in the third objection:

Further, if two things are absolutely equal, man is not moved to one more than to the other; thus if a hungry man, as Plato says (Cf. De Coelo ii, 13), be confronted on either side with two portions of food equally appetizing and at an equal distance, he is not moved towards one more than to the other; and he finds the reason of this in the immobility of the earth in the middle of the world. Now, if that which is equally (eligible) with something else cannot be chosen, much less can that be chosen which appears as less (eligible). Therefore if two or more things are available, of which one appears to be more (eligible), it is impossible to choose any of the others. Therefore that which appears to hold the first place is chosen of necessity. But every act of choosing is in regard to something that seems in some way better. Therefore every choice is made necessarily.

St. Thomas responds to this that it is a question of what the person considers:

If two things be proposed as equal under one aspect, nothing hinders us from considering in one of them some particular point of superiority, so that the will has a bent towards that one rather than towards the other.

Thus for example, someone might decide to become a doctor because it pays well, or they might decide to become a truck driver because they enjoy driving. Whether they consider “what would I enjoy?” or “what would pay well?” will determine which choice they make.

The reader might notice a flaw, or at least a loose thread, in St. Thomas’s argument. In our example, what determines whether you think about what pays well or what you would enjoy? This could be yet another choice. I could create a spreadsheet of possible jobs and think, “What should I put on it? Should I put the pay? or should I put what I enjoy?” But obviously the question about necessity will simply be pushed back, in this case. Is this choice itself determinate or indeterminate? And what determines what choice I make in this case? Here we are discussing an actual temporal series of thoughts, and it absolutely must have a first, since human life has a beginning in time. Consequently there will have to be a point where, if there is the possibility of “doing A for reason B” and “doing C for reason D”, it cannot be any additional consideration which determines which one is done.

Now it is possible at this point that St. Thomas is mistaken. It might be that the hypothesis that both were “really” possible is mistaken, and something does determine one rather than the other with “necessity.” It is also possible that he is not mistaken. Either way, human reasons do not influence the determination, because reason B and/or reason D are the first reasons considered, by hypothesis (if they were not, we would simply push back the question.)

At this point someone might consider this lack of the influence of reasons to imply that people are not morally responsible for doing A or for doing C. The problem with this is that if you do something without a reason (and without potentially being influenced by a reason), then indeed you would not be morally responsible. But the person doing A or C is not uninfluenced by reasons. They are influenced by reason B, or by reason D. Consequently, they are responsible for their specific action, because they do it for a reason, despite the fact that there is some other general issue that they are not responsible for.

What influence could quantum indeterminacy have here? It might be responsible for deciding between “doing A for reason B” and “doing C for reason D.” And as Coyne says, this would be “simple randomness,” with fixed probabilities in any particular situation. But none of this would prevent this from being a situation that would include libertarian free will, since libertarian free will is precisely nothing but the situation where there are two real possibilities: you might do one thing for one reason, or another thing for another reason. And that is what we would have here.

Does quantum mechanics have this influence in fact, or is this just a theoretical possibility? It very likely does. Some argue that it probably doesn’t, on the grounds that quantum mechanics does not typically seem to imply much indeterminacy for macroscopic objects. The problem with this argument is that the only way of knowing that quantum indeterminacy rarely leads to large scale differences is by using humanly designed items like clocks or computers. And these are specifically designed to be determinate: whenever our artifact is not sufficiently determinate and predictable, we change the design until we get something predictable. If we look at something in nature uninfluenced by human design, like a waterfall, is details are highly unpredictable to us. Which drop of water will be the most distant from this particular point one hour from now? There is no way to know.

But how much real indeterminacy is in the waterfall, or in the human brain, due to quantum indeterminacy? Most likely nobody knows, but it is basically a question of timescales. Do you get a great deal of indeterminacy after one hour, or after several days? One way or another, with the passage of enough time, you will get a degree of real indeterminacy as high as you like. The same thing will be equally true of human behavior. We often notice, in fact, that at short timescales there is less indeterminacy than we subjectively feel. For example, if someone hesitates to accept an invitation, in many situations, others will know that the person is very likely to decline. But the person feels very uncertain, as though there were a 50/50 chance of accepting or declining. The real probabilities might be 90/10 or even more slanted. Nonetheless, the question is one of timescales and not of whether or not there is any indeterminacy. There is, this is basically settled, it will apply to human behavior, and there is little reason to doubt that it applies at relatively short timescales compared to the timescales at which it applies to clocks and computers or other things designed with predictability in mind.

In this sense, quantum indeterminacy strongly suggests that St. Thomas is basically correct about libertarian free will.

On the other hand, Coyne is also right about something here. While it is not true that such “randomness” removes moral responsibility, the fact that people do things for reasons, or that praise and blame is a fitting response to actions done for reasons, Coyne correctly notices that it does not add to the fact that someone is responsible. If there is no human reason for the fact that a person did A for reason B rather than C for reason D, this makes their actions less intelligible, and thus less subject to responsibility. In other words, the “libertarian” part of libertarian free will does not make the will more truly a will, but less truly. In this respect, Coyne is right. This however is unrelated to quantum mechanics or to any particular scientific account. The thoughtful person can understand this simply from general considerations about what it means to act for a reason.

Causality and Moral Responsibility

December 20, 2018December 20, 2018 entirelyuseless Ethics, Probability, Science, Uncategorized C.S. Lewis, Causes, Determinism, Evil, Free Will, Good, Jerry Coyne, Moral Responsibility, Murder, Punishment, Quantum Mechanics

Consider two imaginary situations:

(1) In the first situation, people are such that when someone sees a red light, they immediately go off and kill someone. Nothing can be done to prevent this, and no intention or desire to do otherwise makes any difference.

In this situation, killing someone after you have seen a red light is not blamed, since it cannot be avoided, but we blame people who show red lights to others. Such people are arrested and convicted as murderers.

(2) In the second situation, people are such that when someone sees a red light, there is a 5% chance they will go off and immediately kill someone, and a 95% chance they will behave normally. Nothing can change this probability: it does not matter whether the person is wicked or virtuous or what their previous attitude to killing was.

In this situation, again, we do not blame people who end up killing someone, but we call them unlucky. We do however blame people who show others red lights, and they are arrested and convicted of second degree murder, or in some cases manslaughter.

Some people would conclude from this that moral responsibility is incoherent: whether the world is deterministic or not, moral responsibility is impossible. Jerry Coyne defends this position in numerous places, as for example here:

We’ve taken a break from the many discussions on this site about free will, but, cognizant of the risks, I want to bring it up again. I think nearly all of us agree that there’s no dualism involved in our decisions: they’re determined completely by the laws of physics. Even the pure indeterminism of quantum mechanics can’t give us free will, because that’s simple randomness, and not a result of our own “will.”

Coyne would perhaps say that “free will” embodies a contradiction much in the way that “square circle” does. “Will” implies a cause, and thus something deterministic. “Free” implies indeterminism, and thus no cause.

In many places Coyne asserts that this implies that moral responsibility does not exist, as for example here:

This four-minute video on free will and responsibility, narrated by polymath Raoul Martinez, was posted by the Royal Society for the Encouragement of the Arts, Manufactures, and Commerce (RSA). Martinez’s point is one I’ve made here many times, and will surely get pushback from: determinism rules human behavior, and our “choices” are all predetermined by our genes and environment. To me, that means that the concept of “moral responsibility” is meaningless, for that implies an ability to choose freely. Nevertheless, we should still retain the concept of responsibility, meaning “an identifiable person did this or that good or bad action”. And, of course, we can sanction or praise people who were responsible in this sense, for such blame and praise can not only reinforce good behavior but is salubrious for society.

I think that Coyne is very wrong about the meaning of free will, somewhat wrong about responsibility, and likely wrong about the consequences of his views for society (e.g. he believes that his view will lead to more humane treatment of prisoners. There is no particular reason to expect this.)

The imaginary situations described in the initial paragraphs of this post do not imply that moral responsibility is impossible, but they do tell us something. In particular, they tell us that responsibility is not directly determined by determinism or its lack. And although Coyne says that “moral responsibility” implies indeterminism, surely even Coyne would not advocate blaming or punishing the person who had the 5% chance of going and killing someone. And the reason is clear: it would not “reinforce good behavior” or be “salubrious for society.” By the terms set out, it would make no difference, so blaming or punishing would be pointless.

Coyne is right that determinism does not imply that punishment is pointless. And he also recognizes that indeterminism does not of itself imply that anyone is responsible for anything. But he fails here to put two and two together: just as determinism does not imply punishment is pointless, nor that it is not, indeterminism likewise implies neither of the two. The conclusion he should draw is not that moral responsibility is meaningless, but that it is independent of both determinism and indeterminism; that is, that both deterministic compatibilism and libertarian free will allow for moral responsibility.

So what is required for praise and blame to have a point? Elsewhere we discussed C.S. Lewis’s claim that something can have a reason or a cause, but not both. In a sense, the initial dilemma in this post can be understood as a similar argument. Either our behavior has deterministic causes, or it has indeterministic causes; therefore it does not have reasons; therefore moral responsibility does not exist.

On the other hand, if people do have reasons for their behavior, there can be good reasons for blaming people who do bad things, and for punishing them. Namely, since those people are themselves acting for reasons, they will be less likely in the future to do those things, and likewise other people, fearing punishment and blame, will be less likely to do them.

As I said against Lewis, reasons do not exclude causes, but require them. Consequently what is necessary for moral responsibility are causes that are consistent with having reasons; one can easily imagine causes that are not consistent with having reasons, as in the imaginary situations described, and such causes would indeed exclude responsibility.

Violations of Bell’s Inequality: Drawing Conclusions

August 17, 2018 entirelyuseless Metaphysics, Science, Uncategorized Absolute Time, Action at a Distance, Albert Einstein, Aristotle, Bell Inequality, David Hume, Determinism, Erwin Schrödinger, Future, Hugh Everett, Induction, Intelligibility, Isaac Newton, John Bell, Many Worlds, Mark Alford, Marvin Edwards, Ptolemaic System, Quantum Mechanics, Relativity, Vagueness

In the post on violations of Bell’s inequality, represented there by Mark Alford’s twin analogy, I pointed out that things did not seem to go very well for Einstein’s hope for physics, I did not draw any specific conclusions. Here I will consider the likely consequences, first by looking at the relationship of the experiments to Einstein’s position on causality and determinism, and second on their relationship to Einstein’s position on locality and action at a distance.

Einstein on Determinism

Einstein hoped for “facts” instead of probabilities. Everything should be utterly fixed by the laws, much like the position recently argued by Marvin Edwards in the comments here.

On the face of it, violations of Bell’s inequality rule this out, represented by the argument that if the twins had pre-existing determinate plans, it would be impossible for them to give the same answer less than 1/3 of the time when they are asked different questions. Bell however pointed out that it is possible to formulate a deterministic theory which would give similar probabilities at the cost of positing action at a distance (quoted here):

Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That particular interpretation has indeed a grossly non-local structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions.

Nonetheless, I have set aside action at a distance to be discussed separately, and I would argue that we should accept the above surface appearance: the outcomes of quantum mechanical experiments are actually indeterministic. These probabilities represent something in the world, not merely something in our knowledge.

Why? In the first place, note that “reproduces exactly the quantum mechanical predictions” can be understood in two ways. A deterministic theory of that kind would say that because the details are unknown to us, we cannot know what is going to happen. But the details are there, and they in fact determine what is going to happen. There is still a difference on the object level between a world where the present fixes the future to a single possibility, and one in which the future is left open, as Aristotle supposed.

Of course there is no definitive proof here that we are actually in the situation with the open future, although the need for action at a distance in the alternative theory suggests that we are. Even apart from this, however, the general phenomena of quantum mechanics directly suggest that this is the situation. Even apart from violations of Bell’s inequality, quantum mechanics in general already looked exactly as we should have expected a world with an indeterminate future to look.

If this is the case, then Einstein was mistaken on this point, at least to this extent. But what about the deterministic aspect, which I mentioned at the end of this post, and which Schrödinger describes:

At all events it is an imagined entity that images the blurring of all variables at every moment just as clearly and faithfully as does the classical model its sharp numerical values. Its equation of motion too, the law of its time variation, so long as the system is left undisturbed, lags not one iota, in clarity and determinacy, behind the equations of motion of the classical model.

The answer is that this is deterministic not because the future, as we know it, is deterministic, but because it describes all of the possibilities at once. Thus in the case of the cat it includes both the cat living and the cat dying, which are two possible outcomes. It is “deterministic” only because once you have stated all of the alternatives, there is nothing left to say.

Why did Einstein want a deterministic theory? He openly admits that he does not have a convincing argument for it. It seems likely, however, that the fundamental motivation is the conviction that reality is intelligible. And an indeterministic world seems significantly less intelligible than a deterministic one. But this desire can in fact be satisfied by this second kind of “determinism”; thus Schrödinger calls it “one perfectly clear concept.”

In this respect, Einstein’s intuition was not mistaken. It is possible to give an intelligible account of the world, even a “deterministic” one, in this sense.

Einstein on Locality

Einstein also wanted to avoid “spooky action at a distance.” Admitting that the future is indeterminate, however, is not enough to avoid this conclusion. In Mark Alford’s twin analogy, it is not only pre-determined plans that fail, but also plans that involve randomness. Thus it first appears that the violations of Bell’s inequality absolutely require action at a distance.

If we follow my suggestion here, however, and consequently adopt Hugh Everett’s interpretation of quantum mechanics, then saying that there are multiple future possibilities implies the existence of multiple timelines. And if there are multiple timelines, violations of Bell’s inequality no longer necessarily imply action at a distance.

Why not? Consider the twin experiment with the assumption of indeterminacy and multiple timelines. Suppose that from the very beginning, there are two copies of each twin. The first copy of the first twin has the plan of responding to the three questions with “yes/yes/yes.” Likewise, the first copy of the second twin has the plan of responding to the three questions with, “yes/yes/yes.” In contrast, the second copy of each twin has the plan of responding with “no/no/no.”

Now we have four twins but the experimenter only sees two. So which ones does he see? There is nothing impossible about the following “rule”: if the twins are asked different questions, the experimenter sees the first copy of one of the twins, and the second copy of the other twin. Meanwhile, if the twins are asked the same question, the experimenter sees either the first copy of each twin, or the second copy of each twin. It is easy to see that if this is the case, the experimenter will see the twins agree, when they are asked the same question, and will see them disagree when they are asked different questions (thus agreeing less than 1/3 of the time in that situation.)

“Wait,” you will say. “If multiple timelines is just a way of describing a situation with indeterminism, and indeterminism is not enough to avoid action at a distance, how is it possible for multiple timelines to give a way out?”

From the beginning, the apparent “impossibility” of the outcome was a statistical impossibility, not a logical impossibility. Naturally this had to be the case, since if it were a logical impossibility, we could not have coherently described the actual outcomes. Thus we might imagine that David Hume would give this answer:

The twins are responding randomly to each question. By pure chance, they happened to agree the times they were asked the same question, and by pure chance they violated Bell’s inequality when they were asked different questions.

Since this was all a matter of pure chance, of course, if you do the experiment again tomorrow, it will turn out that all of the answers are random and they will agree and disagree 50% of the time on all questions.

And this answer is logically possible, but false. This account does not explain the correlation, but simply ignores it. In a similar way, the reason why indeterministic theories without action at a distance, but described as having a single timeline, cannot explain the results is that in order to explain the correlation, the outcomes of both sides need to be selected together, so to speak. But “without action at a distance” in this context simply means that they are not selected together. This makes the outcome statistically impossible.

In our multiple timelines version, in contrast, our “rule” above in effect selected the outcomes together. In other words, the guideline we gave regarding which pairs of twins the experimenter would meet, had the same effect as action at a distance.

How is all this an explanation? The point is that the particular way that timelines spread out when they come into contact with other things, in the version with multiple timelines, exactly corresponds to action at a distance, in the version without them. An indeterministic theory represented as having a single timeline and no action at a distance could be directly translated into a version with multiple timelines; but if we did that, this particular multiple timeline version would not have the rule that produces the correct outcomes. And on the other hand, if we start with the multiple timeline version that does have the rule, and translate it into a single timeline account, it will have action at a distance.

What does all this say about Einstein’s opinion about locality? Was he right, or was he wrong?

We might simply say that he was wrong, insofar as the actual situation can in fact be described as including action at a distance, even if it is not necessary to describe it in this way, since we can describe it with multiple timelines and without action at a distance. But to the degree that this suggests that Einstein made two mistakes, one about determinism and one about action at a distance, I think this is wrong. There was only one mistake, and it was the one about determinism. The fact is that as soon you speak of indeterminism at all, it becomes possible to speak of the world as having multiple timelines. So the question at that point is whether this is the “natural” description of the situation, where the natural description more or less means the best way to understand things, in which case the possibility of “action at a distance” is not an additional mistake on Einstein’s part, but rather it is an artifact of describing the situation as though there were only a single timeline.

You might say that there cannot be a better or worse way to understand things if two accounts are objectively equivalent. But this is wrong. Thus for example in general relativity it is probably possible to give an account where the earth has no daily rotation, and the universe is spinning around it every 24 hours. And this account is objectively equivalent to the usual account where the earth is spinning; exactly the same situation is being described, and nothing different is being asserted. And yet this account is weird in many ways, and makes it very hard to understand the universe. The far better and “natural” description is that the earth is spinning. Note, however, that this is an overall result; just looking out the window, you might have thought that saying that the universe is spinning is more natural. (Notice, however, that an even more natural account would be that neither the earth nor the universe is moving; it is only later in the day that you begin to figure out that one of them is moving.)

In a similar way, a single timeline account is originally more natural in the way a Ptolemaic account is more natural when you look out the window. But I would argue that in a similar way, the multiple timeline account, without action at a distance, is ultimately the more natural one. The basic reason for this is that there is no Newtonian Absolute Time. The consequence is that if we speak of “future possibilities,” they cannot be future possibilities for the entire universe at once. They will be fairly localized future possibilities: e.g. there might be more than one possible text for the ending to this blog post, which has not yet been written, and those possibilities are originally possibilities for what happens here in this room, not for the rest of the universe. These future alternatives will naturally result in future possibilities for other parts of the world, but this will happen “slowly,” so to speak (namely if one wishes to speak of the speed of light as slow!) This fits well with the idea of multiple timelines, since there will have to be some process where these multiple timelines come into contact with the rest of the world, much as with our “rule” in the twin experiment. On the other hand, it does not fit so well with a single timeline account of future possibilities, since one is forced (by the terms of the account) to imagine that when a choice among possibilities is made, it is made for the entire universe at once, which appears to require Newton’s Absolute Time.

This suggests that Einstein was basically right about action at a distance, and wrong about determinism. But the intuition that motivated him to embrace both positions, namely that the universe should be intelligible, was sound.

Open Past

August 15, 2018August 13, 2018 entirelyuseless Metaphysics, Science, Uncategorized Aristotle, Determinism, Double-Slit Experiment, Erwin Schrödinger, Future, Lucretius, Quantum Mechanics

Suppose that Aristotle was right, and the future is open. What would things be like in detail?

There are many ways things could go, so for concreteness let’s assume that (in some local area) there are approximately 100 possibilities for the next second, and approximately 100 x 100, or 10,000 possibilities for the next two seconds.

Then the question arises: do some of the two-second outcomes have overlapping paths? In other words, suppose we take the first option in the first second. Are all of the outcomes we can reach different from all of the outcomes we could reach if we took the second option in the first second?

It is at least plausible that some overlapping paths can exist. For example, something might swerve to the left in the first second, and then to the right in the second second, ending up just where it would have been if it had swerved to the right in the first second and to the left in the second. Let’s suppose it turns out this way. Thus we have situation A and time A, and situation B and time B, with a first and second path, both of which lead from situation A at time A, to situation B at time B.

When we get to situation B, what does the world look like? In particular, if someone is in situation B and says, “let’s look at the world and figure out what just happened,” what does it look like? Consider three different accounts:

It looks like situation B except also that it looks like we took the first path
It looks like situation B except also that it looks like we took the second path
It looks like situation B, and we can’t tell which path was taken

The problem is evident. These are three different situations. If things currently look different, the situation is different. So these cannot possibly all be descriptions of situation B. And in particular, only the third is a reasonable description of the situation we should expect. We have set up the situation so that there is no difference in our current situation, whether the first or second path was taken. So of course in situation B it will be impossible to know which path was taken.

But what does that look like, exactly? “We don’t know” is not a description of a situation, but a description of our state of knowledge. What is it about situation B that makes it impossible to tell which path was taken? What happens if you describe the situation as exactly as possible, and then explain why that “exact” description still does not determine which path was taken?

Consider again Schrödinger’s confusion about his cat. The reason why the notion of “bluriness” came up at all was not merely that the wave equation seems to describe something blurred, but also because the actual results of experiments suggest that something blurred took place. Thus for example in double-slit experiments, interference patterns suggest that something is going through both slits at once, while if detectors are added to determine what, if anything, is going through the slits, one seems to find that only one slit is used at a time, and the interference pattern goes away.

This fits the above description of situation A and situation B almost perfectly. In the double slit experiment, there are two paths that could be taken to arrive at the same outcome. But that “same outcome” is not one in which it looks like the first path was taken, nor one in which it looks like the second path was taken, but one in which the outcome’s relationship to the path appears to be confused. And on the other hand, if we can tell which path was taken, as we can when we add detectors, there is no such confusion, because the outcomes no longer overlap; the outcome where the first detector registers is not the same as an outcome where the second detector registers.

In this sense, quantum theory is simply the situation where Aristotle was right about the indeterminacy of the future, with the minor addition that it turned out to be possible to get to the same future by more than route.

Note, however, that this implies the worrisome outcome that I suggested in that post. Just as the future is indeterminate, so is the past. Just as the present has many possible future outcomes, there are many past paths that could have resulted in the present.

Schrödinger’s Cat

August 14, 2018August 13, 2018 entirelyuseless Metaphysics, Probability, Science, Uncategorized Determinism, Erwin Schrödinger, Hugh Everett, Many Worlds, Prediction, Quantum Mechanics, Reality, Schrödinger's Cat, Truth

Erwin Schrödinger describes the context for his thought experiment with a cat:

The other alternative consists of granting reality only to the momentarily sharp determining parts – or in more general terms to each variable a sort of realization just corresponding to the quantum mechanical statistics of this variable at the relevant moment.

That it is in fact not impossible to express the degree and kind of blurring of all variables in one perfectly clear concept follows at once from the fact that Q.M. as a matter of fact has and uses such an instrument, the so-called wave function or psi-function, also called system vector. Much more is to be said about it further on. That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message. At all events it is an imagined entity that images the blurring of all variables at every moment just as clearly and faithfully as does the classical model its sharp numerical values. Its equation of motion too, the law of its time variation, so long as the system is left undisturbed, lags not one iota, in clarity and determinacy, behind the equations of motion of the classical model. So the latter could be straight-forwardly replaced by the psi-function, so long as the blurring is confined to atomic scale, not open to direct control. In fact the function has provided quite intuitive and convenient ideas, for instance the “cloud of negative electricity” around the nucleus, etc. But serious misgivings arise if one notices that the uncertainty affects macroscopically tangible and visible things, for which the term “blurring” seems simply wrong. The state of a radioactive nucleus is presumably blurred in such a degree and fashion that neither the instant of decay nor the direction, in which the emitted alpha-particle leaves the nucleus, is well-established. Inside the nucleus, blurring doesn’t bother us. The emerging particle is described, if one wants to explain intuitively, as a spherical wave that continuously emanates in all directions and that impinges continuously on a surrounding luminescent screen over its full expanse. The screen however does not show a more or less constant uniform glow, but rather lights up at one instant at one spot – or, to honor the truth, it lights up now here, now there, for it is impossible to do the experiment with only a single radioactive atom. If in place of the luminescent screen one uses a spatially extended detector, perhaps a gas that is ionised by the alpha-particles, one finds the ion pairs arranged along rectilinear columns, that project backwards on to the bit of radioactive matter from which the alpha-radiation comes (C.T.R. Wilson’s cloud chamber tracks, made visible by drops of moisture condensed on the ions).

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

We see here the two elements described at the end of this earlier post. The psi-function is deterministic, but there seems to be an element of randomness when someone comes to check on the cat.

Hugh Everett amusingly describes a similar experiment performed on human beings (but without killing anyone):

Isolated somewhere out in space is a room containing an observer, A, who is about to perform a measurement upon a system S. After performing his measurement he will record the result in his notebook. We assume that he knows the state function of S (perhaps as a result of previous measurement), and that it is not an eigenstate of the measurement he is about to perform. A, being an orthodox quantum theorist, then believes that the outcome of his measurement is undetermined and that the process is correctly described by Process 1 [namely a random determination caused by measurement].

In the meantime, however, there is another observer, B, outside the room, who is in possession of the state function of the entire room, including S, the measuring apparatus, and A, just prior to the measurement. B is only interested in what will be found in the notebook one week hence, so he computes the state function of the room for one week in the future according to Process 2 [namely the deterministic wave function]. One week passes, and we find B still in possession of the state function of the room, which this equally orthodox quantum theorist believes to be a complete description of the room and its contents. If B’s state function calculation tells beforehand exactly what is going to be in the notebook, then A is incorrect in his belief about the indeterminacy of the outcome of his measurement. We therefore assume that B’s state function contains non-zero amplitudes over several of the notebook entries.

At this point, B opens the door to the room and looks at the notebook (performs his observation.) Having observed the notebook entry, he turns to A and informs him in a patronizing manner that since his (B’s) wave function just prior to his entry into the room, which he knows to have been a complete description of the room and its contents, had non-zero amplitude over other than the present result of the measurement, the result must have been decided only when B entered the room, so that A, his notebook entry, and his memory about what occurred one week ago had no independent objective existence until the intervention by B. In short, B implies that A owes his present objective existence to B’s generous nature which compelled him to intervene on his behalf. However, to B’s consternation, A does not react with anything like the respect and gratitude he should exhibit towards B, and at the end of a somewhat heated reply, in which A conveys in a colorful manner his opinion of B and his beliefs, he rudely punctures B’s ego by observing that if B’s view is correct, then he has no reason to feel complacent, since the whole present situation may have no objective existence, but may depend upon the future actions of yet another observer.

Schrödinger’s problem was that the wave equation seems to describe something “blurred,” but if we assume that is because something blurred exists, it seems to contradict our experience which is of something quite distinct: a live cat or a dead cat, but not something in between.

Everett proposes that his interpretation of quantum mechanics is able to resolve this difficulty. After presenting other interpretations, he proposes his own (“Alternative 5”):

Alternative 5: To assume the universal validity of the quantum description, by the complete abandonment of Process 1 [again, this was the apparently random measurement process]. The general validity of pure wave mechanics, without any statistical assertions, is assumed for all physical systems, including observers and measuring apparata. Observation processes are to be described completely by the state function of the composite system which includes the observer and his object-system, and which at all times obeys the wave equation (Process 2).

…

It is evident that Alternative 5 is a theory of many advantages. It has the virtue of logical simplicity and it is complete in the sense that it is applicable to the entire universe. All processes are considered equally (there are no “measurement processes” which play any preferred role), and the principle of psycho-physical parallelism is fully maintained. Since the universal validity of the state function is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the whole universe. In this sense this theory can be called the theory of the “universal wave function,” since all of physics is presumed to follow from this function alone. There remains, however, the question whether or not such a theory can be put into correspondence with our experience.

This present thesis is devoted to showing that this concept of a universal wave mechanics, together with the necessary correlation machinery for its interpretation, forms a logically self consistent description of a universe in which several observers are at work.

Ultimately, Everett’s response to Schrödinger is that the cat is indeed “blurred,” and that this never goes away. When someone checks on the cat, the person checking is also “blurred,” becoming a composite of someone seeing a dead cat and someone seeing a live cat. However, these are in effect two entirely separate worlds, one in which someone sees a live cat, and one in which someone sees a dead cat.

Everett mentions “the necessary correlation machinery for its interpretation,” because a mathematical theory of physics as such does not necessarily say that anyone should see anything in particular. So for example when Newton when says that there is a gravitational attraction between masses inversely proportional to the square of their distance, what exactly should we expect to see, given that? Obviously there is no way to answer this without adding something, and ultimately we need to add something non-mathematical, namely something about the way our experiences work.

I will not pretend to judge whether or not Everett does a good job defending his position. There is an interesting point here, whether or not his defense is ultimately a good one. “Orthodox” quantum mechanics, as Everett calls it, only gives statistical predictions about the future, and as long as nothing is added to the theory, it implies that deterministic predictions are impossible. It follows that if the position in our last post, on an open future, was correct, it must be possible to explain the results of quantum mechanics in terms of many worlds or multiple timelines. And I do not merely mean that we can give the same predictions with a one-world account or with a many world account. I mean that there must be a many-world account such that its contents are metaphysically identical to the contents of a one-world account with an open future.

This would nonetheless leave undetermined the question of what sort of account would be most useful to us in practice.

Open Future

August 13, 2018August 11, 2018 entirelyuseless Logic, Metaphysics, Science, Uncategorized Aristotle, Determinism, Eternalism, Future, Modal Realism, Necessity, Paradoxes, Presentism, Time, Time Travel

Let’s return for a moment to the question at the end of this post. I asked, “What happens if the future is indeterminate? Would not the eternalist position necessarily differ from the presentist one, in that case?”

Why necessarily different? The argument in that post was that eternalism and presentism are different descriptions of the same thing, and that we see the sameness by noting the sameness of relations between the elements of the description. But if the future is open, as Aristotle supposed, it is hard to see how we can maintain this. Aristotle says that the present is open to either having the sea battle tomorrow or not having it. With an eternalist view, the sea battle is “already there” or it is not. So in Aristotle’s view, the present has an open relationship to both possibilities. But the eternalist view seems to be truly open only to the possibility that will actually happen. We no longer have the same set of relationships.

Notice the problem. When I attempted to equate eternalism and presentism, I implicitly assumed that determinism is true. There were only three states of the universe, beginning, middle, and end. If determinism is false, things are different. There might be beginning, middle, and two potential ends. Perhaps there is a sea battle in one of the potential ends, and no sea battle in the other.

This suggests a solution to our conundrum, however. Even the presentist description in that post was inconsistent with an open future. If there is only one possible end, the future is not open, even if we insist that the unique possible end “currently doesn’t exist.” The problem then was not eternalism as such, but the fact that we started out with a determinist description of the universe. This strongly suggests that if my argument about eternalism and presentism was correct, we should be able to formulate eternalist and presentist descriptions of an open future which will be equivalent. But both will need to be different from the fixed “beginning-middle-end” described in that post.

We can simply take Aristotle’s account as the account of presentism with an open future. How can we give an eternalist account of the same thing? The basic requirement will be that the relationship between the present and the future needs to be the same in both accounts. Now in Aristotle’s account, the present has the same relationship to two different possibilities: both of them are equally possible. So to get a corresponding eternalist account, we need the present to be equally related to two futures that correspond to the two possiblities in the presentist account. I do not say “two possible futures,” but “two futures,” precisely because the account is eternalist.

The careful reader will already understand the account from the above, but let us be more explicit. The eternalist account that corresponds to the presentist account with an open future has multiple timelines, all of which “exist”, in the eternalist sense. The reader will no doubt be familiar with the idea of multiple timelines, at least from time travel fiction. In a similar way, the eternalist reworking of Aristotle’s position is that there is a timeline where the sea battle takes place, and another timeline where the sea battle does not take place. In this view, both of them “actually” happen. But even in this view, an observer in the middle location will have to say, “I do not, and cannot, know whether the sea battle will take place or not,” just as in Aristotle’s view. For the observer cannot traverse both timelines at once. From his point of view, he will take only one, but since his relationship to the two possibilities (or actualities) is the same, it is indeterminate which one it will be.

Even if one cannot prove my account of equivalence to be wrong, the reader may worry. Time travel fiction frequently seems incoherent, and this suggests that any view with multiple timelines may also be incoherent. But this potential incoherence supports the equivalence, rather than subtracting from it. For as we noted in the post on Aristotle, there is a definite appearance of incoherence in his position. It is not even clear how his view is logically possible. So it would not be surprising, but quite natural, if views which are intended to be equivalent to his position are also not clearly coherent. Nonetheless, the multiple timelines description does have some logical advantage over Aristotle’s position, in the sense that “the sea battle will take place in timeline A” does not even appear to contradict “the sea battle will not take place in timeline B.”

Spooky Action at a Distance

August 12, 2018August 10, 2018 entirelyuseless Mathematics, Science, Uncategorized Action at a Distance, Albert Einstein, Bell Inequality, Causes, Determinism, John Bell, Locality, Mark Alford, Max Born, Natural Laws, Quantum Mechanics, Realism, Space, Speed of Light

Albert Einstein objected to the usual interpretations of quantum mechanics because they seemed to him to imply “spooky action at a distance,” a phrase taken from a letter from Einstein to Max Born in 1947 (page 155 in this book):

I cannot make a case for my attitude in physics which you would consider at all reasonable. I admit, of course, that there is a considerable amount of validity in the statistical approach which you were the first to recognize clearly as necessary given the framework of the existing formalism. I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance. I am, however, not yet firmly convinced that it can really be achieved with a continuous field theory, although I have discovered a possible way of doing this which so far seems quite reasonable. The calculation difficulties are so great that I will be biting the dust long before I myself can be fully convinced of it. But I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts, as used to be taken for granted until quite recently. I cannot, however, base this conviction on logical reasons, but can only produce my little finger as witness, that is, I offer no authority which would be able to command any kind of respect outside of my own hand.

Einstein has two objections: the theory seems to be indeterministic, and it also seems to imply action at a distance. He finds both of these implausible. He thinks physics should be deterministic, “as used to be taken for granted until quite recently,” and that all interactions should be local: things directly affect only things which are close by, and affect distant things only indirectly.

In many ways, things do not appear to have gone well for Einstein’s intuitions. John Bell constructed a mathematical argument, now known as Bell’s Theorem, that the predictions of quantum mechanics cannot be reproduced by the kind of theory desired by Einstein. Bell summarizes his point:

The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts to show that even without such a separability or locality requirement no “hidden variable” interpretation of quantum mechanics is possible. These attempts have been examined elsewhere and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That particular interpretation has indeed a grossly non-local structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions.

“Causality and locality” in this description are exactly the two points where Einstein objected in the quoted letter: causality, as understood here, implies determinism, and locality implies no spooky action at a distance. Given this result, Einstein might have hoped that the predictions of quantum mechanics would turn out to fail, so that he could still have his desired physics. This did not happen. On the contrary, these predictions (precisely those inconsistent with such theories) have been verified time and time again.

Rather than putting the reader through Bell’s math and physics, we will explain his result with an analogy by Mark Alford. Alford makes this comparison:

Imagine that someone has told us that twins have special powers, including the ability to communicate with each other using telepathic influences that are “superluminal” (faster than light). We decide to test this by collecting many pairs of twins, separating each pair, and asking each twin one question to see if their answers agree.

To make things simple we will only have three possible questions, and they will be Yes/No questions. We will tell the twins in advance what the questions are.

The procedure is as follows.

A new pair of twins is brought in and told what the three possible questions are.

The twins travel far apart in space to separate questioning locations.

At each location there is a questioner who selects one of the three questions at random, and poses that question to the twin in front of her.

Spacelike separation. When the question is chosen and asked at one location, there is not enough time for any influence traveling at the speed of light to get from there to the other location in time to affect either what question is chosen there, or the answer given.

He now supposes the twins give the same responses when they are asked the same question, and discusses this situation:

Now, suppose we perform this experiment and we find same-question agreement: whenever a pair of spacelike-separated twins both happen to get asked the same question, their answers always agree. How could they do this? There are two possible explanations,

1. Each pair of twins uses superluminal telepathic communication to make sure both twins give the same answer.

2. Each pair of twins follows a plan. Before they were separated they agreed in advance what their answers to the three questions would be.

The same-question agreement that we observe does not prove that twins can communicate telepathically faster than light. If we believe that strong locality is a valid principle, then we can resort to the other explanation, that each pair of twins is following a plan. The crucial point is that this requires determinism. If there were any indeterministic evolution while the twins were spacelike separated, strong locality requires that the random component of one twin’s evolution would have to be uncorrelated with the other twin’s evolution. Such uncorrelated indeterminism would cause their recollections of the plan to diverge, and they would not always show same-question agreement.

The results are understandable if the twins agree on the answers Yes-Yes-Yes, or Yes-No-Yes, or any other determinate combination. But they are not understandable if they decide to flip coins if they are asked the second question, for example. If they did this, they would have to disagree 50% of the time on that question, unless one of the coin flips affected the other.

Alford goes on to discuss what happens when the twins are asked different questions:

In the thought experiment as described up to this point we only looked at the recorded answers in cases where each twin in a given pair was asked the same question. There are also recorded data on what happens when the two questioners happen to choose different questions. Bell noticed that this data can be used as a cross-check on our strong-locality-saving idea that the twins are following a pre-agreed plan that determines that their answers will always agree. The cross-check takes the form of an inequality:

Bell inequality for twins:

If a pair of twins is following a plan then, when each twin is asked a different randomly chosen question, their answers will be the same, on average, at least 1/3 of the time.

He derives this value:

For each pair of twins, there are four general types of pre-agreed plan they could adopt when they are arranging how they will both give the same answer to each of the three possible questions.

(a) a plan in which all three answers are Yes;

(b) a plan in which there are two Yes and one No;

(c) a plan in which there are two No and one Yes;

(d) a plan in which all three answers are No.

If, as strong locality and same-question agreement imply, both twins in a given pair follow a shared predefined plan, then when the random questioning leads to each of them being asked a different question from the set of three possible questions, how often will their answers happen to be the same (both Yes or both No)? If the plan is of type (a) or (d), both answers will always be the same. If the plan is of type (b) or (c), both answers will be the same 1/3 of the time. We conclude that no matter what type of plan each pair of twins may follow, the mere fact that they are following a plan implies that, when each of them is asked a different randomly chosen question, they will both give the same answer (which might be Yes or No) at least 1/3 of the time. It is important to appreciate that one needs data from many pairs of twins to see this effect, and that the inequality holds even if each pair of twins freely chooses any plan they like.

The “Bell inequality” is violated if we do the experimental test and the twins end up agreeing, when they are asked different questions, less than 1/3 of the time, despite consistently agreeing when they are asked the same question. If one saw such results in reality, one might be forgiven for concluding that the twins do have superluminal telepathic abilities. Unfortunately for Einstein, this is what we do get, consistently, when we test the analogous quantum mechanical version of the experiment.

Aristotle on Future Contingents

August 11, 2018August 10, 2018 entirelyuseless Logic, Metaphysics, Science, Uncategorized Aristotle, CPT Symmetry, Deliberation, Determinism, Excluded Middle, Free Will, Future, Necessity, Non-Contradiction, Past, Prediction, Propositions, Quantum Mechanics, Time, Truth

In Chapter 9 of On Interpretation, Aristotle argues that at least some statements about the future need to be exempted from the principle of Excluded Middle:

In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,’ one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.

When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.

Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.

Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word ‘fortuitous’ with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions. Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be, and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.

The argument here is that if it is already true, for example, that I will eat breakfast tomorrow, then I will necessarily eat breakfast tomorrow, and there is no option about this and no ability of anything to prevent it. Aristotle is here taking it for granted that some things about the future are uncertain, and is using this as a reductio against the position that such claims can be already true. He goes on to give additional reasons for the same thing:

Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend. In the first place, though facts should prove the one proposition false, the opposite would still be untrue. Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.

These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity. There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow. For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.

Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time. Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.

Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place. There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.

Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.

Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character.

This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated.

Basically, then, there are two arguments. First there is the argument that if statements about the future are already true, the future is necessary. If a sea battle will take place tomorrow, it will necessarily take place. Second, there is the argument that this excludes deliberation. If a sea battle will take place tomorrow, then it will necessarily take place, and no place remains for deliberation and decision about whether to fight the sea battle. Whether you decide to fight or not, it will necessarily take place.

Unfortunately for Aristotle, both arguments fail. Consider the first argument about necessity. Aristotle’s example is that “if it is true to say that a thing is white, it must necessarily be white.” But this is hypothetical necessity, not absolute necessity. A thing must be white if it is true that is white, but that does not mean that “it must be white, period.” Thus for example I have a handkerchief, and it happens to be white. If it is true that it is white, then it must be white. But it would be false to simply say, “My handkerchief is necessarily white.” Since I can dye it other colors, obviously it is not simply necessary for it to be white.

In a similar way, of course it is true that if a sea battle will take place, it will take place. It does not follow at all that “it will necessarily take place, period.”

Again, consider the second argument, that deliberation would be unnecessary. Aristotle makes the point that deliberation is causative with respect to the future. But gravity is also causative with respect to the future, as for example when gravity causes a cup to fall from a desk. It does not follow either that the cup must be able not to fall, nor that gravity is unnecessary. In a similar way, a sea battle takes place because certain people deliberated and decided to fight. If it was already true that it was going to take place, then it also already true that they were going to decide to fight. It does not follow that their decision was unnecessary.

Consider the application to gravity. It is already true that if the cup is knocked from the desk, it will fall. It does not follow that gravity will not cause the fall: in fact, it is true precisely because gravity will cause the fall. In a similar way, if it true that the battle will take place, it is true because the decision will be made.

This earlier discussion about determinism is relevant to this point. Asserting that there is a definite outcome that our deliberations will arrive at, in each case, goes against our experience in no way. The feeling of “free will,” in any case, has a different explanation, whether or not determinism is true.

On the other hand, there is also no proof that there is such a determinate outcome, even if in some cases there are things that would suggest it. What happens if in fact there is nothing ensuring one outcome rather than another?

Here we could make a third argument on Aristotle’s behalf, although he did not make it himself. If the present is truly open to alternative outcomes, then it seems that nothing exists that could make it be true that “a sea battle will take place,” and false that “a sea battle will not take place.” Presumably if a statement is true, there must be something in reality which is the cause of the statement’s truth. Now there does not seem to be anything in reality, in this scenario, which could be a cause of truth. Therefore it does not seem that either alternative could be true, and Aristotle would seem to be right.

I will not attempt to refute this argument at this point, but I will raise two difficulties. First of all, it is not clear that his claim is even coherent. Aristotle says that “either there will be a sea battle or there will not be,” is true, but that “there will be a sea battle” is not true, and “there will not be a sea battle” is not true. This does not seem to be logically consistent, and it is not clear that we can even understand what is being said. I will not push this objection too hard, however, lest I be accused of throwing stones from a glass house.

Second, the argument that there is nothing in reality that could cause the truth of a statement might apply to the past as well as to the future. There is a tree outside my window right now. What was in that place exactly 100 million years ago to this moment? It is not obvious that there is anything in the present world which could be the cause of the truth of any statement about this. One might object that the past is far more determinate than the future. There are plenty of things in the present world that might be the cause of the truth of the statement, “World War II actually happened.” It is hard to see how you could possibly have arrived at the present world without it, and this “necessity” of World War II in order to arrive at the present world could be the cause of truth. The problem is that there is still no proof that this is universal. Once things are far enough in past, like 100 million years, perhaps minor details become indeterminate. Will Aristotle really want to conclude that some statements about the past are neither true nor false?

I will more or less leave things here without resolving them in this post, although I will give a hint (without proof at this time) regarding the truth of the matter. It turns out that quantum mechanics can be interpreted in two ways. In one way, it is a deterministic theory, and in this way it is basically time reversible. The present fully determines the past, but it equally fully determines the future. Interpreted in another way, it is an indeterministic theory which leaves the future uncertain. But understood in this way, it also leaves the past uncertain.

Chastek on Determinism

February 26, 2017February 26, 2017 entirelyuseless Catholicism, Logic, Metaphysics, Science, Uncategorized Determinism, Final Causes, Freedom, Future, God, James Chastek, Prediction, Prophecy, Robin Hanson, Will

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.

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