Statistical Laws of Choice

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

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

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

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

The Practical Argument for Free Will

Richard Chappell discusses a practical argument for free will:

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

He remarks in the comments:

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

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

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

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

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

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

We can see this with the following thought experiment:

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

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

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

Little Things

Chapter 39 of Josemaria Escriva’s book The Way concerns the topic of “little things.” The whole chapter, and really the whole book, is worth reading. The text is composed in the form of a set of aphorisms, much like Francis Bacon’s work. I will quote two passages in particular from the chapter in question:

823. Have you seen how that imposing building was built? One brick upon another. Thousands. But, one by one. And bags of cement, one by one. And blocks of stone, each of them insignificant compared with the massive whole. And beams of steel. And men working, the same hours, day after day…

Have you seen how that imposing building was built?… By dint of little things!

826. Everything in which we poor men have a part — even holiness — is a fabric of small trifles which, depending upon one’s intention, can form a magnificent tapestry of heroism or of degradation, of virtues or of sins.

The epic legends always relate extraordinary adventures, but never fail to mix them with homely details about the hero. — May you always attach great importance to the little things. This is the way!

The second passage asserts that anything great in human life is essentially composed of “small trifles.” The first passage explains why this is so. The world is an ordered place, and one of the orders found in it is the order of material causality. Since the whole is greater than the part, it follows that great wholes are ultimately composed of little parts, or in other words, “small trifles.”

We often tend not to notice this in relation to human life, because we think of life as a kind of story, and it is normal for stories to leave out all sorts of detail, in order to concentrate on the overall picture. But all of that detail is always present: every day is made up of 24 hours, and everything we do ultimately is made up of individual immediate actions.

Thus Escriva says that we should “always attach great importance to the little things,” because there is no other way to accomplish anything. For example, someone might be assigned a paper in school, and find himself unable to write the paper, because he is constantly thinking of the need to “write a paper.” But “writing a paper” is not an action that can be chosen; it is just not a thing that can be done immediately. And unless it is first broken down into “little things,” it will never be done at all. This is one of the main causes of procrastination in people’s lives, namely failing to see that the larger goals that they wish to accomplish must be accomplished by means of little things, through individual actions. Thus someone might say, “I don’t know why, but I never feel like writing the paper.” But in fact he does not feel like writing it, because he has not yet presented himself with any option that can ever be chosen.

 

True and False Religion

What does it mean to say that a religion is true, or that it is false? The question is not as easy as it appears at first sight. Bertrand Russell, in Why I Am Not a Christianruns up against this difficulty. In order to explain why he is not a Christian, he has to know what it means to be a Christian in the first place:

As your Chairman has told you, the subject about which I am going to speak to you tonight is “Why I Am Not a Christian.” Perhaps it would be as well, first of all, to try to make out what one means by the word Christian. It is used these days in a very loose sense by a great many people. Some people mean no more by it than a person who attempts to live a good life. In that sense I suppose there would be Christians in all sects and creeds; but I do not think that that is the proper sense of the word, if only because it would imply that all the people who are not Christians — all the Buddhists, Confucians, Mohammedans, and so on — are not trying to live a good life. I do not mean by a Christian any person who tries to live decently according to his lights. I think that you must have a certain amount of definite belief before you have a right to call yourself a Christian. The word does not have quite such a full-blooded meaning now as it had in the times of St. Augustine and St. Thomas Aquinas. In those days, if a man said that he was a Christian it was known what he meant. You accepted a whole collection of creeds which were set out with great precision, and every single syllable of those creeds you believed with the whole strength of your convictions.

Nowadays it is not quite that. We have to be a little more vague in our meaning of Christianity. I think, however, that there are two different items which are quite essential to anybody calling himself a Christian. The first is one of a dogmatic nature — namely, that you must believe in God and immortality. If you do not believe in those two things, I do not think that you can properly call yourself a Christian. Then, further than that, as the name implies, you must have some kind of belief about Christ. The Mohammedans, for instance, also believe in God and in immortality, and yet they would not call themselves Christians. I think you must have at the very lowest the belief that Christ was, if not divine, at least the best and wisest of men. If you are not going to believe that much about Christ, I do not think you have any right to call yourself a Christian.

Thus Russell reduces being a Christian to believing in God, in the immortality of the soul, and that Christ was at least the best and wisest of men. Of course there are people who call themselves Christians who do not believe one or more of these things, and do not accept that you cannot call yourself a Christian without them. And other people might well give a different list. Thus for example St. Paul has his own requirements:

Now if Christ is proclaimed as raised from the dead, how can some of you say there is no resurrection of the dead? If there is no resurrection of the dead, then Christ has not been raised; and if Christ has not been raised, then our proclamation has been in vain and your faith has been in vain. We are even found to be misrepresenting God, because we testified of God that he raised Christ—whom he did not raise if it is true that the dead are not raised. For if the dead are not raised, then Christ has not been raised. If Christ has not been raised, your faith is futile and you are still in your sins. Then those also who have died in Christ have perished. If for this life only we have hoped in Christ, we are of all people most to be pitied.

Thus St. Paul says that belief in the resurrection of Christ, and therefore in a general resurrection, is required. Otherwise “your faith has been in vain,” which would certainly seem to say that your religion is not true.

Of course, St. Paul is polemically exaggerating the consequences of the position of his opponents. In the first place someone could believe in the resurrection of Christ without believing in a general resurrection. Likewise, even if Christ did not rise from the dead, it does not follow of necessity that anyone’s faith would be entirely vain, but that it would be vain in some respect, since he would still profit from it in various ways, such as by belonging to a Christian community. Similarly, even if Christians have a false belief in the immortality of the soul, there would still be more pitiable people in the world.

We can learn from these two examples. Russell says that you cannot “properly call yourself a Christian,” if you do not accept his list of three beliefs, while St. Paul says that “your faith is in vain” if you do not believe that Christ is risen. There is something common to the two. Some basic belief or beliefs are proposed, such that without these beliefs, it is not worthwhile to count yourself as a believer at all. For St. Paul, this has the form of saying that you should not bother to put your faith in Christ, while for Russell, this has the form of saying that you should not call yourself a Christian.

The basic difficulty is caused by the fact that being a Christian, considered in itself, is not a belief, but membership in a Christian community. Thus saying that “Christianity is true,” or that “Christianity is false,” ought to mean “belonging to a Christian community is true,” or that “belonging to a Christian community is false,” both of which are evidently absurd, since belonging to a community is not the kind of thing which is true or false. But since a Christian community happens to be a community of believers, we identify Christianity as a belief by saying that it is what that community believes.

But the problem is not resolved by this identification, for “what the Christian community believes” is somewhat indeterminate, since Christians believe different things. Russell and St. Paul resolve the issue in similar ways. Russell does so by saying that you cannot “properly call yourself a Christian,” unless you believe certain things, presumably because it is wrong to deceive people about your beliefs. St. Paul does so by saying that your faith is in vain if you think that Christ did not rise from the dead, presumably meaning that it is pointless for you to belong to a Christian community.

Thus both of them are saying that unless you think that such and such is true, it is a bad idea to be a Christian, that is, to belong to a Christian community.

With this analysis we can say in general what it means to say that a certain religion is true, or that it is false. If I say that Mormonism is true, I mean that there are certain true things usually believed by Mormons, which make it worthwhile to belong to a Mormon community, given that I accept those things. Likewise, if I say that Mormonism is false, I mean that there are things believed by Mormons that would make it worthwhile to be a Mormon, if they were true, but in fact those things are false, and consequently it is not worthwhile to be a Mormon. Or more directly, I mean that there are certain things normally believed by Mormons which happen to be false, and the fact that Mormons normally believe these false things, makes it not worthwhile for me to be a Mormon.

Someone might object that this leads to relativism, since according to this analysis, it seems that a religion might be true for one person, but false for another. For example, in an interview conducted by Sergiu Hart, Robert Aumann, the author of the agreement theorem we discussed earlier, explains, among other things, why he accepts Judaism:

H [Sergiu Hart]: So that’s the Center for Rationality. I know this doesn’t belong, but I’ll ask it here. You are a deeply religious man. How does it fit in with a rational view of the world? How do you fit together science and religion?

A [Robert Aumann]: As you say, it really doesn’t belong here, but I’ll respond anyway. Before responding directly, let me say that the scientific view of the world is really just in our minds. When you look at it carefully, it is not something that is out there in the real world. For example, take the statement “the earth is round.” It sounds like a very simple statement that is either true or false. Either the earth is round or it isn’t; maybe it is square, or elliptical, or whatever. But when you come to think of it, it is a very complex statement. What does roundness mean? Roundness means that there is a point, the “center” of the earth, such that any point on the surface of the earth is at the same distance from that center as any other point on the surface of the earth. Now that already sounds a little complex. But the complexity only begins there. What exactly do we mean by equal distance? For that you need the concept of a distance between two points. The concept of distance between two points is something that is fairly complex even if we are talking about a ball that we can hold in our hands; it involves taking a ruler and measuring the distance between two points. But when we are talking about the earth, it is even more complex, because there is no way that we are going to measure the distance between the center of the earth and the surface of the earth with a ruler. One problem is that we canít get to the center. Even if we could find it we wouldn’t be able to get there. We certainly wouldn’t be able to find a ruler that is big enough. So we have to use some kind of complex theory in order to give that a practical meaning. Even when we have four points and we say the distance from A to B is the same as the distance from C to D, that is fairly complex already. Maybe the ruler changes. We are using a whole big theory, a whole big collection of ideas, in order to give meaning to this very, very simple statement that the earth is round.

Don’t get me wrong. We all agree that the earth is round. What I am saying is that the roundness of the earth is a concept that is in our minds. It’s a product of a very complex set of ideas, and ideas are in people’s minds. So the way I think of science, and even of fairly simple things, is as being in our minds; all the more so for things like gravitation, the energy that is emitted by a star, or even the concept of a “species.” Yes, we are both members of the species homo sapiens. What does that mean? Obviously we are different. My beard is much longer than yours. What exactly does species mean? What exactly does it even mean to say “Bob Aumann” is sitting here? Is it the same Bob Aumann as five minutes ago? These are very complex ideas. Identity, all those things that we think of trivially on a day-to-day basis, are really complex ideas that are in our minds; they are not really out there. Science is built to satisfy certain needs in our minds. It describes us. It does have a relationship with the real world, but this relationship is very, very complex.

Having said that, I’ll get to your question. Religion is very different from science. The main part of religion is not about the way that we model the real world. I am purposely using the word “model.” Religion is an experience, mainly an emotional and aesthetic one. It is not about whether the earth is 5,765 years old. When you play the piano, when you climb a mountain, does this contradict your scientific endeavors? Obviously not. The two things are almost, though not quite, orthogonal. Hiking, skiing, dancing, bringing up your children; you do all kinds of things that are almost orthogonal to your scientific endeavor. That’s the case with religion also. It doesn’t contradict; it is orthogonal. Belief is an important part of religion, certainly; but in science we have certain ways of thinking about the world, and in religion we have different ways of thinking about the world. Those two things coexist side by side without conflict.

Well, it is your way of putting it. Let me enlarge on it. The observance of the Sabbath is extremely beautiful, and is impossible without being religious. It is not even a question of improving society; it is about improving one’s own quality of life. For example, let’s say I’m taking a trip a couple of hours after the Sabbath. Any other person would spend the day packing, going to the office, making final arrangements, final phone calls, this and that. For me it’s out of the question. I do it on Friday. The Sabbath is there. The world stops.

In short, you can be a moral person, but morals are often equivocal. In the eighties, copying software was considered moral by many people. The point I am making is that religion, at least my religion, is a sort of force, a way of making a commitment to conduct yourself in a certain way, which is good for the individual and good for society.

In the first part, Aumann is basically saying that science gives an idealized and approximate description of the world, rather than an exact description. In the second part he attempts to explain why he accepts Judaism, and he seems to be saying that it has little to do with the way the world is, and more to do with what is good for people. In other words, to explain it in the way we analyzed the truth of a religion, “Judaism is true” for Aumann because he believes that it is true that it is good and beautiful to observe the Sabbath, true that it is good to refrain from breaking copyright laws, and so on. And since these things are true it is worthwhile for him to be a member of a Jewish religious community.

You may or may not agree that the Sabbath is beautiful, and you may or may not agree that it is good to refrain from breaking copyright laws. But even if you do agree with these things, you probably don’t conclude that it is worthwhile for you to convert to Judaism. At the same time, you may realize that these things might well make it worthwhile for Robert Aumann to remain a Jew.

Thus our explanation seems to lead to relativism, because Judaism can be true for Aumann, but false for other people. However, there are several problems with calling this result relativism.

First of all, there was some remaining ambiguity in the way we defined the truth or falsity of a religion. Jews might normally believe certain true things, and given that Robert Aumann accepts those things, it might be worthwhile for him to remain a Jew. But it is possible that Jews also normally believe certain false things, such that if Aumann knew they were false, it would no longer be worthwhile for him to remain a Jew. Thus, for example, a Christian would argue that Jews falsely believe that Christ is not the Messiah, and that if Aumann knew that this was false, it would no longer be worthwhile for him to remain a Jew, but to convert to Christianity.

Thus we could make our definition more precise by saying that a religion is true if it is worthwhile to belong to that religion even after you know the truth or falsity of all the beliefs that the members of the religion usually hold, and that it is worthwhile by reason of some of the true things that they hold.

However, this does not sufficiently answer the charge of relativism, because it would still be possible that one religion would be true for one person, and not true for another person.

For example, suppose that theism is true, but that no divine revelation has been given. If Aumann realizes this, he might reasonably believe that it is worthwhile for him to remain a Jew, and unreasonable to convert to Islam, even after knowing the truth or falsity of every concrete belief held by Jews and Muslims. Likewise, a Muslim, knowing the same things, might reasonably believe that it is worthwhile for him to remain a Muslim, and unreasonable to convert to Judaism, even after knowing the truth or falsity of every concrete belief held by Muslims and Jews.

The answer in this case is that the situation simply does not imply relativism, because Aumann and the Muslim do not disagree about anything. Aumann may say, “Judaism is true,” and the Muslim may say, “Islam is true,” but when they explain what they mean and why they say it, they do not disagree with each other about any objective fact. This is no more relativism than it is relativism to admit that one person may prefer vanilla ice cream, and another person chocolate.

Thus, it is possible to mean something reasonable when saying that some religion is true, or that some religion is false. But in the end perhaps it would be better to avoid all the confusion in the first place, by following Robert Aumann’s example and simply distinguishing the question, “What is the world like?” from the question, “Is it, or would it be, good for me to belong to this community of believers?” Of course the answers to these questions are going to be related in various ways, but they are different questions.

Know Thyself

At the end of the last post I more or less challenged readers to consider their motives for their beliefs. This would be especially questionable if I was not willing to accept my own challenge, so here I will mention a few of the potential influences on my own opinions.

I want to be honest with people. This is a natural consequence of the love of truth, and it might seem surprising to mention this as one influence that can run against the truth, but it can do this. For wanting to be honest involves not only wanting to speak the truth, but to say what you think. And as Katja Grace says, “Imagine your friend said, ‘I promise that anything you tell me I will repeat to anyone who asks’. How honest would you be with that friend? If you say to yourself that you will report your thoughts to others, why wouldn’t the same effect apply?” In other words, this motive can influence me to avoid thinking things that I would not like to say to others, for whatever reasons.

I would like other people to be more concerned about the truth. This again is a somewhat natural consequence of the love of truth, but again it can be a misleading influence. For it can be a motive to avoid saying things which may tend to make people seek the truth less, even if those things are true. And in combination with the desire for honesty, it can be a motive to avoid thinking those things, even if they are true. This motive is currently telling me not to write this post, since theoretically people could use it as a reason to be concerned less about the truth.

I want to be respected by people. This can lead to saying and thinking things I expect to be respected by those I care about, whether or not those things are true.

I want to say interesting and important things. This makes it more likely that I will believe something interesting as opposed to something uninteresting, even if it is equally likely, and the same applies to things that seem important as opposed to unimportant. It also makes it more likely that I will exaggerate true statements somewhat so that they will seem interesting and important.

I want to be consistent, and to defend things that I have already said. In conjunction with the above fact about exaggeration, this makes it more likely that I will come to believe an exaggerated view of various things, even accidentally, since this type of exaggeration often happens in a somewhat thoughtless manner.

Although different people will have somewhat different concerns, none of these things are particularly strange. And in principle there is nothing wrong with wanting such things, just as there is nothing wrong with wanting to eat food that tastes good, rather than being concerned about health alone in one’s choices relative to food. But if you want to be healthy, it is pretty important to notice that your desire for ice cream is not exactly the desire for health, and to moderate this desire. And likewise if you want to know the truth, it is important to notice the nature of the other influences on your opinions, and to moderate these influences.

Belief and Probability

As was argued in an earlier post, any belief, or at any rate almost any belief, is voluntary insofar as we choose to think, act, and speak as though it were true, and in theory it is always in our power to choose to behave in the opposite way. In practice of course we would not do this unless we had some motive to do it, just as the fact that it is in someone’s power to commit suicide does not make him do so before he has a motive for this.

Such a belief, since it involves affirmation or denial, has a basically binary character — thus I say either that the sun will rise tomorrow, or that it will not. This binary character can of course be somewhat modified by the explicit addition of various qualifiers, as when I say that “I will probably be alive five years from now”, or that “there is a 75% chance that Mike will come to visit next week” or the like. Nonetheless, even these statements have a binary character even if at one remove from the original statement. Thus I can say “Mike will come to visit,” or “Mike will not come to visit”, but also “there is a 75% chance etc” or “there is not a 75% chance etc”.

The interior apprehension of the mind, however, does not have the same binary character, but is more a matter of degree. Thus for example someone may argue that increasing the restrictions on gun ownership in the United States would be a good idea. “More gun control would be good,” he says. This is the affirmation of one side of a contradiction. Then suppose he is involved in a conversation on the matter, with another person arguing against his position. As the conversation goes on, he may continue to assert the same side of the contradiction, but he may grow somewhat doubtful inside. As he walks away from the conversation, he still believes that more gun control would be good. He still chooses to speak, think, and act in that way. But he is less convinced than he was at first. In this sense his interior apprehension has degrees in a way in which the belief considered as an affirmation or denial does not.

Probability theory is a mathematical formalization of such degrees of belief as interior apprehension, and the laws of probability are rules which must be followed in order to maintain logical consistency when working with such degrees. In another post we looked at Hume’s claim about the impossibility of induction. It is likely that one cause of his error was the fact that the formal theory of probability was less developed at the time; in particular, Bayes’ theorem, which we used against Hume, was proved 20 years after Hume’s treatise was written.

Thus, in our speech and behavior, beliefs are basically binary, but we possess various degrees of certainty about our beliefs. And such a degree is reasonably considered to be something like the probability, as far as we are concerned, that our belief is true.

Voluntary Beliefs

Belief is a confusing mixture of the voluntary and the non-voluntary. St. Thomas tries to explain this by saying that the knowledge of first principles and of conclusions drawn from them are not voluntary, while other beliefs are voluntary:

Faith implies assent of the intellect to that which is believed. Now the intellect assents to a thing in two ways. First, through being moved to assent by its very object, which is known either by itself (as in the case of first principles, which are held by the habit of understanding), or through something else already known (as in the case of conclusions which are held by the habit of science). Secondly the intellect assents to something, not through being sufficiently moved to this assent by its proper object, but through an act of choice, whereby it turns voluntarily to one side rather than to the other: and if this be accompanied by doubt or fear of the opposite side, there will be opinion, while, if there be certainty and no fear of the other side, there will be faith. (ST. II-II Q. 1, a. 4, corp.

However, in reality it is highly questionable whether the intellect ever assents to anything of necessity in such a way that it is impossible to doubt it. For example, if a skilled mathematician shows you a proof of some new conclusion using premises which are well known to you, you may assent to the conclusion without any doubt. But if he then says, “There is a flaw in this proof,” you are unlikely to respond, “I cannot accept that claim, as I have seen beyond any possibility of doubt that this conclusion is true.” Or if you do respond in this way, suppose he says, “In that case, I will offer to bet you $1 against $100 that there is a flaw in the proof and that I can show it to you. Since you claim that you cannot be wrong, you are bound to win the bet and gain a dollar.” Hopefully in this situation you will come to your senses and doubt the proof, rather than continuing to assert your own infallibility, an act of insane overconfidence which will surely cost you $100.

St. Thomas does point out that the act of making a statement, whether to oneself or to others, is always a voluntary act. However, he does not seem to take note of the fact that this implies that the contrary act is also possible, even if it would violate first principles or conclusions drawn from them. For example, just as I can say or write “2 + 2 = 4” voluntarily, I can equally well say or write “2 + 2 = 5”, should I so choose, and I can say this not only to others but also to myself.

Someone will respond to this that if I do say this, whether to myself or to others, I am lying. Indeed. But how is this lying detected? The main way that we would determine that someone was lying in such a case is that he would refuse to act on this claim. As an obvious example, I might say that I want to change two twenty dollar bills for a fifty (when he has one), and I would expect him to refuse. This would actually be more obvious with statements like “it is raining.” If someone believes it is raining, he will probably carry an umbrella or something of the sort. The problem with the mathematical statement is that it is so basic that it is hardly clear what it would mean to act as though two and two made five. But given that we can determine how a person believing something would act, we can find evidence that someone is lying by showing that he refuses to act in conformity with his claim, at least in certain contexts.

This suggests that there is a sense in which any belief will be entirely voluntary: just as I can voluntarily choose to make any claim, I can voluntarily decide to conform the whole of my life to the claim. In this way I am deciding to act in every way as though the claim were true, both interior and exterior, insofar as these things are in my power.

Choosing to believe, in this sense, would be rather like choosing to love someone. Just as I choose to conform my life to love, I can choose to conform my life to belief. However, there is one significant difference. There is reason to believe that one who chooses to conform his life to love is disposing himself as fully as possible toward love, such that it will always be true that he does indeed love. But there may be reason to think that, at least in some cases, it is different with belief. For example, suppose that someone were to say, “I choose to believe that I can walk out of a fifth story window without getting hurt.” If he does choose this in the manner under discussion, he will be willing to put it into practice. But even if he does actually carry it out, it is possible that he is doing this to prove that he believes, while in fact still not truly giving intellectual assent. In other words, it may be that part of the disposition to believe is in the intellect itself, and that such a disposition must be present there in advance in order for the choice to believe to be efficacious.

If this is the case, we could say that someone who “chooses to believe” when his intellect entirely lacks the appropriate disposition is rather pretending to believe, in a sense, rather than truly believing. However, this is not completely clear and consequently it remains at least possible that such a choice to believe is always efficacious.