Structure of Explanation

When we explain a thing, we give a cause; we assign the thing an origin that explains it.

We can go into a little more detail here. When we ask “why” something is the case, there is always an implication of possible alternatives. At the very least, the question implies, “Why is this the case rather than not being the case?” Thus “being the case” and “not being the case” are two possible alternatives.

The alternatives can be seen as possibilities in the sense explained in an earlier post. There may or may not be any actual matter involved, but again, the idea is that reality (or more specifically some part of reality) seems like something that would be open to being formed in one way or another, and we are asking why it is formed in one particular way rather than the other way. “Why is it raining?” In principle, the sky is open to being clear, or being filled with clouds and a thunderstorm, and to many other possibilities.

A successful explanation will be a complete explanation when it says “once you take the origin into account, the apparent alternatives were only apparent, and not really possible.” It will be a partial explanation when it says, “once you take the origin into account, the other alternatives were less sensible (i.e. made less sense as possibilities) than the actual thing.”

Let’s consider some examples in the form of “why” questions and answers.

Q1. Why do rocks fall? (e.g. instead of the alternatives of hovering in the air, going upwards, or anything else.)

A1. Gravity pulls things downwards, and rocks are heavier than air.

The answer gives an efficient cause, and once this cause is taken into account, it can be seen that hovering in the air or going upwards were not possibilities relative to that cause.

Obviously there is not meant to be a deep explanation here; the point here is to discuss the structure of explanation. The given answer is in fact basically Newton’s answer (although he provided more mathematical detail), while with general relativity Einstein provided a better explanation.

The explanation is incomplete in several ways. It is not a first cause; someone can now ask, “Why does gravity pull things downwards, instead of upwards or to the side?” Similarly, while it is in fact the cause of falling rocks, someone can still ask, “Why didn’t anything else prevent gravity from making the rocks fall?” This is a different question, and would require a different answer, but it seems to reopen the possibility of the rocks hovering or moving upwards, from a more general point of view. David Hume was in part appealing to the possibility of such additional questions when he said that we can see no necessary connection between cause and effect.

Q2. Why is 7 prime? (i.e. instead of the alternative of not being prime.)

A2. 7/2 = 3.5, so 7 is not divisible by 2. 7/3 = 2.333…, so 7 is not divisible by 3. In a similar way, it is not divisible by 4, 5, or 6. Thus in general it is not divisible by any number except 1 and itself, which is what it means to be prime.

If we assumed that the questioner did not know what being prime means, we could have given a purely formal response simply by noting that it is not divisible by numbers between 1 and itself, and explaining that this is what it is to be prime. As it is, the response gives a sufficient material disposition. Relative to this explanation, “not being prime,” was never a real possibility for 7 in the first place. The explanation is complete in that it completely excludes the apparent alternative.

Q3. Why did Peter go to the store? (e.g. instead of going to the park or the museum, or instead of staying home.)

A3. He went to the store in order to buy groceries.

The answer gives a final cause. In view of this cause the alternatives were merely apparent. Going to the park or the museum, or even staying home, were not possible since there were no groceries there.

As in the case of the rock, the explanation is partial in several ways. Someone can still ask, “Why did he want groceries?” And again someone can ask why he didn’t go to some other store, or why something didn’t hinder him, and so on. Such questions seem to reopen various possibilities, and thus the explanation is not an ultimately complete one.

Suppose, however, that someone brings up the possibility that instead of going to the store, he could have gone to his neighbor and offered money for groceries in his neighbor’s refrigerator. This possibility is not excluded simply by the purpose of buying groceries. Nonetheless, the possibility seems less sensible than getting them from the store, for multiple reasons. Again, the implication is that our explanation is only partial: it does not completely exclude alternatives, but it makes them less sensible.

Let’s consider a weirder question: Why is there something rather than nothing?

Now the alternatives are explicit, namely there being something, and there being nothing.

It can be seen that in one sense, as I said in the linked post, the question cannot have an answer, since there cannot be a cause or origin for “there is something” which would itself not be something. Nonetheless, if we consider the idea of possible alternatives, it is possible to see that the question does not need an answer; one of the alternatives was only an apparent alternative all along.

In other words, the sky can be open to being clear or cloudy. But there cannot be something which is open both to “there is something” and “there is nothing”, since any possibility of that kind would be “something which is open…”, which would already be something rather than nothing. The “nothing” alternative was merely apparent. Nothing was ever open to there being nothing.

Let’s consider another weird question. Suppose we throw a ball, and in the middle of the path we ask, Why is the ball in the middle of the path instead of at the end of the path?

We could respond in terms of a sufficient material disposition: it is in the middle of the path because you are asking your question at the middle, instead of waiting until the end.

Suppose the questioner responds: Look, I asked my question at the middle of the path. But that was just chance. I could have asked at any moment, including at the end. So I want to know why it was in the middle without considering when I am asking the question.

If we look at the question in this way, it can be seen in one way that no cause or origin can be given. Asked in this way, being at the end cannot be excluded, since they could have asked their question at the end. But like the question about something rather than nothing, the question does not need an answer. In this case, this is not because the alternatives were merely apparent in the sense that one was possible and the other not. But they were merely apparent in the sense that they were not alternatives. The ball goes both goes through the middle, and reaches the end. With the stipulation that we not consider the time of the question, the two possibilities are not mutually exclusive.

Additional Considerations

The above considerations about the nature of “explanation” lead to various conclusions, but also to various new questions. For example, one commenter suggested that “explanation” is merely subjective. Now as I said there, all experience is subjective experience (what would “objective experience” even mean, except that someone truly had a subjective experience?), including the experience of having an explanation. Nonetheless, the thing experienced is not subjective: the origins that we call explanations objectively exclude the apparent possibilities, or objectively make them less intelligible. The explanation of explanation here, however, provides an answer to what was perhaps the implicit question. Namely, why are we so interested in explanations in the first place, so that the experience of understanding something becomes a particularly special type of experience? Why, as Aristotle puts it, do “all men desire to know,” and why is that desire particularly satisfied by explanations?

In one sense it is sufficient simply to say that understanding is good in itself. Nonetheless, there is something particular about the structure of a human being that makes knowledge good for us, and which makes explanation a particularly desirable form of knowledge. In my employer and employee model of human psychology, I said that “the whole company is functioning well overall when the CEO’s goal of accurate prediction is regularly being achieved.” This very obviously requires knowledge, and explanation is especially beneficial because it excludes alternatives, which reduces uncertainty and therefore tends to make prediction more accurate.

However, my account also raises new questions. If explanation eliminates alternatives, what would happen if everything was explained? We could respond that “explaining everything” is not possible in the first place, but this is probably an inadequate response, because (from the linked argument) we only know that we cannot explain everything all at once, the way the person in the room cannot draw everything at once; we do not know that there is any particular thing that cannot be explained, just as there is no particular aspect of the room that cannot be drawn. So there can still be a question about what would happen if every particular thing in fact has an explanation, even if we cannot know all the explanations at once. In particular, since explanation eliminates alternatives, does the existence of explanations imply that there are not really any alternatives? This would suggest something like Leibniz’s argument that the actual world is the best possible world. It is easy to see that such an idea implies that there was only one “possibility” in the first place: Leibniz’s “best possible world” would be rather “the only possible world,” since the apparent alternatives, given that they would have been worse, were not real alternatives in the first place.

On the other hand, if we suppose that this is not the case, and there are ultimately many possibilities, does this imply the existence of “brute facts,” things that could have been otherwise, but which simply have no explanation? Or at least things that have no complete explanation?

Let the reader understand. I have already implicitly answered these questions. However, I will not link here to the implicit answers because if one finds it unclear when and where this was done, one would probably also find those answers unclear and inconclusive. Of course it is also possible that the reader does see when this was done, but still believes those responses inadequate. In any case, it is possible to provide the answers in a form which is much clearer and more conclusive, but this will likely not be a short or simple project.

Words, Meaning, and Formal Copies

There is quick way to respond to the implicit questions at the end of the last post. I noted in an earlier discussion of form that form is not only copied into the mind; it is also copied into language itself. Any time you describe something in words, you are to some degree copying its form into your description.

This implies that Aristotle’s objection that a mind using an organ would not be able to know all things could equally be made against the possibility of describing all things in words. There simply are not enough combinations of words to relate them to all possible combinations of things; thus, just as a black and white image cannot imitate every aspect of a colored scene, so words cannot possibly describe every aspect of reality.

Two things are evident from this comparison:

First, the objection fails overall. There is nothing that cannot be described in words because words are flexible. If we don’t have a word for something, then we can make up a name. Similarly, the meaning of a single word depends on context.  The word “this” can refer to pretty much anything, depending on the context in which it is used. Likewise meaning can be affected by the particular situation of the person using the word, or by broader cultural contexts, and so on.

Second, there is some truth in the objection. It is indeed impossible to describe every aspect of reality at the same time and in complete detail, and the objection gives a very good reason for this: there are simply not enough linguistic combinations to represent all possible combinations of things. The fact that language is not prime matter does mean that language cannot express every detail of reality at once: the determination that is already there does exclude this possibility. But the flexibility of language prevents there from being any particular aspect of things that cannot be described.

My claim about the mind is the same. There is nothing that cannot be understood by the mind, despite the fact that the mind uses the brain, because the relationship between the brain, mind, and world is a flexible one. Just as the word “this” can refer to pretty much anything, so also the corresponding thought. But on the other hand, the limitations of the brain do mean that a perfectly detailed knowledge of everything is excluded.

Our Interlocutor Insists

In a sense, the above account is sufficient to respond to the objection. There does not seem to be a reason to hold Aristotle’s account of the immateriality of the mind, unless there is also a reason to hold that language cannot be used to describe some things, and this does not seem like a reasonable position. Nonetheless, this response will give rise to a new and more detailed objection.

A black and white scene, it will be said, really and truly copies some aspects of a colored scene, and fails to copy others. Thus right angles in the black and white scene may be identical to right angles in the colored scene. The angles are really copied, and the angles are not. But language seems different: since it is conventional, it does not really copy anything. We just pretend, as it were, that we are copying the thing. “Let the word ‘cat’ stand for a cat,” we say, but there is nothing catlike about the word in reality. The form of the cat is not really copied into the word, or so it will be argued. And since we are not really copying anything, this is why language has the flexibility to be able to describe all things. The meaning of thoughts, however, is presumably not conventional. So it seems that we need to copy things in a real way into the mind, the way we copy aspects of a colored scene into a black and white image. And thus, meaning in the mind should not be flexible in this way, and a particular material medium (such as the brain) would still impede knowing all things, the way the black and white image excludes color.

Formal Copies

The above objection is similar to Hilary Lawson’s argument that words cannot really refer to things. In the post linked above on form and reality, we quoted his argument that cause and effect do not have anything in common. I will reproduce that argument here; for the purpose of the following discussion it might be useful to the reader to refer to the remainder of that post.

For a system of closure to provide a means of intervention in openness and thus to function as a closure machine, it requires a means of converting the flux of openness into an array of particularities. This initial layer of closure will be identified as ‘preliminary closure’. As with closure generally, preliminary closure consists in the realisation of particularity as a consequence of holding that which is different as the same. This is achieved through the realisation of material in response to openness. The most minimal example of a system of closure consists of a single preliminary closure. Such a system requires two discrete states, or at least states that can be held as if they were discrete. It is not difficult to provide mechanical examples of such systems which allow for a single preliminary closure. A mousetrap for example, can be regarded as having two discrete states: it is either set, it is ready, or it has sprung, it has gone off. Many different causes may have led to it being in one state or another: it may have been sprung by a mouse, but it could also have been knocked by someone or something, or someone could have deliberately set it off. In the context of the mechanism all of these variations are of no consequence, it is either set or it has sprung. The diversity of the immediate environment is thereby reduced to single state and its absence: it is either set or it is not set. Any mechanical arrangement that enables a system to alternate between two or more discrete states is thereby capable of providing the basis for preliminary closure. For example, a bell or a gate could function as the basis for preliminary closure. The bell can either ring or not ring, the gate can be closed or not closed. The bell may ring as the result of the wind, or a person or animal shaking it, but the cause of the response is in the context of system of no consequence. The bell either rings or it doesn’t. Similarly, the gate may be in one state or another because it has been deliberately moved, or because something or someone has dislodged it accidentally, but these variations are not relevant in the context of the state of system, which in this case is the position of the gate. In either case the cause of the bell ringing or the gate closing is infinitely varied, but in the context of the system the variety of inputs is not accessible to the system and thus of no consequence.

Lawson’s basic argument is that any particular effect could result from any of an infinite number of different causes, and the cause and effect might be entirely different: the effect might be ringing of a bell, but the cause was not bell-like at all, and did not have a ringing sound. So the effect, he says, tells you nothing at all about the cause. In a similar way, he claims, our thoughts cause our words, but our words and our thoughts have nothing in common, and thus our words tell us nothing about our thoughts; and in that sense they do not refer to anything, not even to our thoughts. Likewise, he says, the world causes our thoughts, but since the cause and effect have nothing in common, our thoughts tell us nothing about the world, and do not even refer to it.

As I responded at the time, this account is mistaken from the very first step. Cause and effect always have something in common, namely the cause-effect relationship, although they each have different ends of that relationship. They will also have other things in common depending on the particular nature of the cause and effect in question. Similarly, the causes that are supposedly utterly diverse, in Lawson’s account, have something in common themselves: every situation that rings the bell has “aptness to ring the bell” in common. And when the bell is rung, it “refers” to these situations by the implication that we are in a situation that has aptness to ring the bell, rather than in one of the other situations.

It is not accidental here that “refer” and “relate” are taken from forms of the same verb. Lawson’s claim that words do not “refer” to things is basically the same as the claim that they are not really related to things. And the real problem is that he is looking at matter (in this case the bell) without considering form (in this case the bell’s relationship with the world.)

In a similar way, to say that the word “cat” is not catlike is to look at the sound or at the text as matter, without considering its form, namely the relationship it has with the surrounding context which causes that word to be used. But that relationship is real; the fact that the word is conventional does not prevent it from being true that human experience of cats is the cause of thoughts of cats, and that thoughts of cats are concretely the cause of the usage of the word “cat,” even if they could in some other situation have caused some other word to be used.

I argued in the post on the nature of form (following the one with the discussion of Lawson) that form is a network of relationships apt to make something one. Insofar as an effect really receives form from a cause in the above way, words really receive meaning from the context that gives rise to their use. And in this way, it is not true that form in language is unlike form in a black and white scene, such that one could say that form in the scene is “real” and form in language is not. Both are real.

Thus the objection fails. Nonetheless, it is true that it is easier to see why it is possible to describe anything in words, than it is to see why anything can be known. And this happens simply because “anything is describable in words” precisely because “anything can be known.” So the fact that anything can be known is the more remote cause, and thus harder to know.

 

And Fire by Fire

Superstitious Nonsense asks about the last post:

So the answer here is that -some- of the form is present in the mind, but always an insufficient amount or accuracy that the knowledge will not be “physical”? You seem to be implying the part of the form that involves us in the self-reference paradox is precisely the part of the form that gives objects their separate, “physical” character. Is this fair? Certainly, knowing progressively more about an object does not imply the mental copy is becoming closer and closer to having a discrete physicality.

I’m not sure this is the best way to think about it. The self-reference paradox arises because we are trying to copy ourselves into ourselves, and thus we are adding something into ourselves, making the copy incomplete. The problem is not that there is some particular “part of the form” that we cannot copy, but that it is in principle impossible to copy it perfectly. This is different from saying that there is some specific “part” that cannot be copied.

Consider what happens when we make “non-physical” copies of something without involving a mind. Consider the image of a gold coin. There are certain relationships common to the image and to a gold coin in the physical world. So you could say we have a physical gold coin, and a non-physical one.

But wait. If the image of the coin is on paper, isn’t that a physical object? Or if the image is on your computer screen, isn’t your screen a physical object? And the image is just the colors on the screen, which are apparently just as “physical” (or non-physical) as the color of the actual coin. So why we would say that “this is not a physical coin?”

Again, as in the last post, the obvious answer is that the image is not made out of gold, while the physical coin is. But why not? Is it that the image is not accurate enough? If we made it more accurate, would it be made out of gold, or become closer to being made out of gold? Obviously not. This is like noting that a mental copy does not become closer and closer to being a physical one.

In a sense it is true that the reason the image of the coin is not physical is that it is not accurate enough. But that is because it cannot be accurate enough: the fact that it is an image positively excludes the copying of certain relationships. Some aspects can be copied, but others cannot be copied at all, as long as it is an image. On the other hand, you can look at this from the opposite direction: if you did copy those aspects, the image would no longer be an image, but a physical coin.

As a similar example, consider the copying of a colored scene into black and white. We can copy some aspects of the scene by using various shades of gray, but we cannot copy every aspect of the scene. There are simply not enough differences in a black and white image to reflect every aspect of a colored scene. The black and white image, as you make it more accurate, does not become closer to being colored, but this is simply because there are aspects of the colored scene that you never copy. If you do insist on copying those aspects, you will indeed make the black and white image into a colored image, and thus it will no longer be black and white.

The situation becomes significantly more complicated when we talk about a mind. In one way, there is an important similarity. When we say that the copy in the mind is “not physical,” that simply means that it is a copy in the mind, just as when we say that the image of the coin is not physical, it means that it is an image, made out of the stuff that images are made of. But just as the image is physical anyway, in another sense, so it is perfectly possible that the mind is physical in a similar sense. However, this is where things begin to become confusing.

Elsewhere, I discussed Aristotle’s argument that the mind is immaterial. Considering the cases above, we could put his argument in this way: the human brain is a limited physical object. So as long as the brain remains a brain, there are simply not enough potential differences in it to model all possible differences in the world, just as you cannot completely model a colored scene using black and white. But anything at all can be understood. Therefore we cannot be understanding by using the brain.

I have claimed myself that anything that can be, can be understood. But this needs to be understood generically, rather than as claiming that it is possible to understand reality in every detail simultaneously. The self-reference paradox shows that it is impossible in principle for a knower that copies forms into itself to understand itself in every aspect at once. But even apart from this, it is very obvious that we as human beings cannot understand every aspect of reality at once. This does not even need to be argued: you cannot even keep everything in mind at once, let alone understand every detail of everything. This directly suggests a problem with Aristotle’s argument: if being able to know all things suggests that the mind is immaterial, the obvious fact that we cannot know all things suggests that it is not.

Nonetheless, let us see what happens if we advance the argument on Aristotle’s behalf. Admittedly, we cannot understand everything at once. But in the case of the colored scene, there are aspects that cannot be copied at all into the black and white copy. And in the case of the physical coin, there are aspects that cannot be copied at all into the image. So if we are copying things into the brain, doesn’t that mean that there should be aspects of reality that cannot be copied at all into the mind? But this is false, since it would not only mean that we can’t understand everything, but it would also mean that there would be things that we cannot think about at all, and if it is so, then it is not so, because in that case we are right now talking about things that we supposedly cannot talk about.

Copying into the mind is certainly different from copying into a black and white scene or copying into a picture, and this does get at one of the differences. But the difference here is that the method of copying in the case of the mind is flexible, while the method of copying in the case of the pictures is rigid. In other words, we have a pre-defined method of copying in the case of the pictures that, from the beginning, only allows certain aspects to be copied. In the case of the mind, we determine the method differently from case to case, depending on our particular situation and the thing being copied. The result is that there is no particular aspect of things that cannot be copied, but you cannot copy every aspect at once.

In answer to the original question, then, the reason that the “mental copy” always remains mental is that you never violate the constraints of the mind, just as a black and white copy never violates the constraints of being black and white. But if you did violate the constraints of the black and white copy by copying every aspect of the scene, the image would become colored. And similarly, if you did violate the constraints of the mind in order to copy every aspect of reality, your mind would cease to be, and it would instead become the thing itself. But there is no particular aspect of “physicality” that you fail to copy: rather, you just ensure that one way or another you do not violate the constraints of the mind that you have.

Unfortunately, the explanation here for why the mind can copy any particular aspect of reality, although not every aspect at once, is rather vague. Perhaps a clearer explanation is possible? In fact, someone could use the vagueness to argue for Aristotle’s position and against mine. Perhaps my account is vague because it is wrong, and there is actually no way for a physical object to receive copied forms in this way.

Employer and Employee Model: Happiness

We discussed Aristotle’s definition of happiness as activity according to virtue here, followed by a response to an objection.

There is another objection, however, which Aristotle raises himself in Book I, chapter 8 of the Nicomachean Ethics:

Yet evidently, as we said, it needs the external goods as well; for it is impossible, or not easy, to do noble acts without the proper equipment. In many actions we use friends and riches and political power as instruments; and there are some things the lack of which takes the lustre from happiness, as good birth, goodly children, beauty; for the man who is very ugly in appearance or ill-born or solitary and childless is not very likely to be happy, and perhaps a man would be still less likely if he had thoroughly bad children or friends or had lost good children or friends by death. As we said, then, happiness seems to need this sort of prosperity in addition; for which reason some identify happiness with good fortune, though others identify it with virtue.

Aristotle is responding to the implicit objection by saying that it is “impossible, or not easy” to act according to virtue when one is doing badly in other ways. Yet probably most of us know some people who are virtuous while suffering various misfortunes, and it seems pretty unreasonable, as well as uncharitable, to assert that the reason that they are somewhat unhappy with their circumstances is that the lack of “proper equipment” leads to a lack of virtuous activity. Or at any rate, even if this contributes to the matter, it does not seem to be a full explanation. The book of Job, for example, is based almost entirely on the possibility of being both virtuous and miserable, and Job would very likely respond to Aristotle, “How then will you comfort me with empty nothings? There is nothing left of your answers but falsehood.”

Aristotle brings up a similar issue at the beginning of Book VIII:

After what we have said, a discussion of friendship would naturally follow, since it is a virtue or implies virtue, and is besides most necessary with a view to living. For without friends no one would choose to live, though he had all other goods; even rich men and those in possession of office and of dominating power are thought to need friends most of all; for what is the use of such prosperity without the opportunity of beneficence, which is exercised chiefly and in its most laudable form towards friends? Or how can prosperity be guarded and preserved without friends? The greater it is, the more exposed is it to risk. And in poverty and in other misfortunes men think friends are the only refuge. It helps the young, too, to keep from error; it aids older people by ministering to their needs and supplementing the activities that are failing from weakness; those in the prime of life it stimulates to noble actions-‘two going together’-for with friends men are more able both to think and to act. Again, parent seems by nature to feel it for offspring and offspring for parent, not only among men but among birds and among most animals; it is felt mutually by members of the same race, and especially by men, whence we praise lovers of their fellowmen. We may even in our travels how near and dear every man is to every other. Friendship seems too to hold states together, and lawgivers to care more for it than for justice; for unanimity seems to be something like friendship, and this they aim at most of all, and expel faction as their worst enemy; and when men are friends they have no need of justice, while when they are just they need friendship as well, and the truest form of justice is thought to be a friendly quality.

But it is not only necessary but also noble; for we praise those who love their friends, and it is thought to be a fine thing to have many friends; and again we think it is the same people that are good men and are friends.

There is a similar issue here: lack of friends may make someone unhappy, but lack of friends is not lack of virtue. Again Aristotle is in part responding by pointing out that the activity of some virtues depends on the presence of friends, just as he said that temporal goods were necessary as instruments. Once again, however, even if there is some truth in it, the answer does not seem adequate, especially since Aristotle believes that the highest form of happiness is found in contemplation, which seems to depend much less on friends than other types of activity.

Consider again Aristotle’s argument for happiness as virtue, presented in the earlier post. It depends on the idea of a “function”:

Presumably, however, to say that happiness is the chief good seems a platitude, and a clearer account of what it is still desired. This might perhaps be given, if we could first ascertain the function of man. For just as for a flute-player, a sculptor, or an artist, and, in general, for all things that have a function or activity, the good and the ‘well’ is thought to reside in the function, so would it seem to be for man, if he has a function. Have the carpenter, then, and the tanner certain functions or activities, and has man none? Is he born without a function? Or as eye, hand, foot, and in general each of the parts evidently has a function, may one lay it down that man similarly has a function apart from all these? What then can this be? Life seems to be common even to plants, but we are seeking what is peculiar to man. Let us exclude, therefore, the life of nutrition and growth. Next there would be a life of perception, but it also seems to be common even to the horse, the ox, and every animal. There remains, then, an active life of the element that has a rational principle; of this, one part has such a principle in the sense of being obedient to one, the other in the sense of possessing one and exercising thought. And, as ‘life of the rational element’ also has two meanings, we must state that life in the sense of activity is what we mean; for this seems to be the more proper sense of the term. Now if the function of man is an activity of soul which follows or implies a rational principle, and if we say ‘so-and-so-and ‘a good so-and-so’ have a function which is the same in kind, e.g. a lyre, and a good lyre-player, and so without qualification in all cases, eminence in respect of goodness being added to the name of the function (for the function of a lyre-player is to play the lyre, and that of a good lyre-player is to do so well): if this is the case, and we state the function of man to be a certain kind of life, and this to be an activity or actions of the soul implying a rational principle, and the function of a good man to be the good and noble performance of these, and if any action is well performed when it is performed in accordance with the appropriate excellence: if this is the case, human good turns out to be activity of soul in accordance with virtue, and if there are more than one virtue, in accordance with the best and most complete.

Aristotle took what was most specifically human and identified happiness with performing well in that most specifically human way. This is reasonable, but it leads to the above issues, because a human being is not only what is most specifically human, but also possesses the aspects that Aristotle dismissed here as common to other things. Consequently, activity according to virtue would be the most important aspect of functioning well as a human being, and in this sense Aristotle’s account is reasonable, but there are other aspects as well.

Using our model, we can present a more unified account of happiness which includes these other aspects without the seemingly arbitrary way in which Aristotle noted the need for temporal goods and friendship for happiness. The specifically rational character belongs mainly to the Employee, and thus when Aristotle identifies happiness with virtuous action, he is mainly identifying happiness with the activity of the Employee. And this is surely its most important aspect. But since the actual human being is the whole company, it is more complete to identify happiness with the good functioning of the whole company. And the whole company is functioning well overall when the CEO’s goal of accurate prediction is regularly being achieved.

Consider two ways in which someone might respond to the question, “How are you doing?” If someone isn’t doing very well, they might say, “Well, I’ve been having a pretty rough time,” while if they are better off, they might say, “Things are going pretty smoothly.” Of course people might use other words, but notice the contrast in my examples: a life that is going well is often said to be going “smoothly”, while the opposite is described as “rough.” And the difference here between smooth and rough is precisely the difference between predictive accuracy and inaccuracy. We might see this more easily by considering some restricted examples:

First, suppose two people are jogging. One is keeping an even pace, keeping their balance, rounding corners smoothly, and keeping to the middle of the path. The other is becoming tired, slowing down a bit and speeding up a bit. They are constantly off balance and suffering disturbing jolts when they hit unexpected bumps in the path, perhaps narrowly avoiding tripping. If we compare what is happening here with the general idea of predictive processing, it seems that the difference between the two is that first person is predicting accurately, while the second is predicting inaccurately. The second person is not rationing their energy and breath correctly, they suffer jolts or near trips when they did not correctly expect the lay of the land, and so on.

Suppose someone is playing a video game. The one who plays it well is the one who is very prepared for every eventuality. They correctly predict what is going to happen in the game both with regard to what happens “by itself,” and what will happen as a result of their in-game actions. They play the game “smoothly.”

Suppose I am writing this blog post and feel myself in a state of “flow,” and I consequently am enjoying the activity. This can only happen as long as the process is fairly “smooth.” If I stop for long periods in complete uncertainty of what to write next, the state will go away. In other words, the condition depends on having at each moment a fairly good idea of what is coming next; it depends on accurate prediction.

The reader might understand the point in relation to these limited examples, but how does this apply to life in general, and especially to virtue and vice, which are according to Aristotle the main elements of happiness and unhappiness?

In a basic way virtuous activity is reasonable activity, and vicious activity is unreasonable activity. The problem with vice, in this account, is that it immediately sets up a serious interior conflict. The Employee is a rational being and is constantly being affected by reasons to do things. Vice, in one way or another, persuades them to do unreasonable things, and the reasons for not doing those things will be constantly pulling in the opposite direction. When St. Paul complains that he wills something different from what he does, he is speaking of this kind of conflict. But conflicting tendencies leads to uncertain results, and so our CEO is unhappy with this situation.

Now you might object: if a vicious man is unhappy because of conflicting tendencies, what if they are so wicked that they have no conflict, but simply and contentedly do what is evil?

The response to this would be somewhat along the lines of the answer we gave to the objection that moral obligation should not depend on desiring some particular end. First, it is probably impossible for a human being to become so corrupted that they cannot see, at least to some degree, that bad things are bad. Second, consider the wicked men according to Job’s description:

Why do the wicked live on,
reach old age, and grow mighty in power?
Their children are established in their presence,
and their offspring before their eyes.
Their houses are safe from fear,
and no rod of God is upon them.
Their bull breeds without fail;
their cow calves and never miscarries.
They send out their little ones like a flock,
and their children dance around.
They sing to the tambourine and the lyre,
and rejoice to the sound of the pipe.
They spend their days in prosperity,
and in peace they go down to Sheol.

Just as we said that if you assume that someone is entirely corrupt, the idea of “obligation” may well become irrelevant to them, without that implying anything wrong with the general idea of moral obligation, in a similar way, it would be metaphorical to speak of such a person as “unhappy”; you could say this with the intention of saying that they exist in an objectively bad situation, but not in the ordinary sense of the term, in which it includes subjective discontent.

We could explain a great deal more with this account of happiness: not only the virtuous life in general, but also a great deal of the spiritual, psychological, and other practical advice which is typically given. But this is all perhaps for another time.

Violations of Bell’s Inequality: Drawing Conclusions

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

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:

  1. It looks like situation B except also that it looks like we took the first path
  2. It looks like situation B except also that it looks like we took the second path
  3. 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.

Open Future

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.”