A humble science

Mathematics is the lowest and humblest of all the sciences. It makes slow but steady progress, and it says little to nothing about the questions dearest to the hearts of human beings, but what it says is absolutely certain. What gives it such certainty? It is content to study objects which are wholly abstract, so that the relations between them are absolute, eternal, and necessary. The word abstract implies that they are drawn away from reality. In this way they are lifeless. Rather than exploring strange new worlds with their own vibrant existence, the mathematician is content to study lifeless forms which are absolutely transparent to the mind. Let the brave adventurers go off to study living creatures, the cosmos, and that most mysterious object of all, human pyschology. The mathematician will humbly work at understanding that which is already closer to home than anything can be--that is, close to the mind.

It would be a fatal mistake, then, to view mathematics as a lofty venture, towering over all the other sciences, for that is the opposite of the truth. Mathematics, like anyone who wishes to be great in God's kingdom, must be the servant of all. We happily live in a world which follows certain patterns, often not at all obvious, and the objects we encounter, though they have in some sense a life of their own, can be seen to follow abstract rules which can be studied at the level of theory. In this way the applications of mathematics are abundant, starting with the simplest of all objects (physics) and working our way up even to the most complex and spontaneous (biology, economics).

But it is a slippery slope from application to assimilation. The problem with much modern thought is the way it treats all objects as abstract, lifeless forms. What mathematics so useful and reliable is that it studies objects which have no independent existence and no context. To study living things--and particularly the human mind--in such a way would be (and often is) disastrous. Psychologists have noticed, for example, that searching for universal principles governing human thought by observing only Western, educated, industrialized, rich, democratic people is a flawed idea. Yet in observing that our methods do not lead to what we are searching for, rarely do we ask whether the search itself is misguided.

Why does modern thought push relentlessly toward that which is universal? I suspect the reason is as much moral as scientific. On the one hand, science seeks that which is universal because it gives us a deeper understanding of life as a whole, and that allows us to do the greatest amount of good. On the other hand, we would also find it unfair if our particular context really mattered. The universe should be, above all, fair, even if that implies it is meaningless. History must be random, because otherwise that would imply something special about the way things happen to be. We have concluded, after thoroughly deconstructing the moral pretentions of past generations, that there can be nothing special about our heritage, culture, or anything else passed down to us.

As an aside, I highly suspect this attitude explains why physicists have come up with the idea of a multiverse. If there really is one universe, with exactly one history, that means a practically infinite number of possibilities are shut off forever from all reality. That would mean all of reality is dependent on a particular context--it is no longer held captive by abstract concepts. Such a conclusion is intolerable in our intellectual climate.

The modern reaction against the Judeo-Christian tradition can be explained in these terms. If there is a God, its existence should be explicable in rational, abstract terms that do not depend on context--that is, mathematically. There is a long tradition of such proofs in Western tradition. But that is not what we find in the Bible. What we find there is a God who, though he is supposed to be the creator of all things, has attached himself to a particular people in the Middle East. "I Am Who I Am," God says, affirming his utterly transcendent identity, and then adds soon after, "the God of Abraham, Isaac, and Jacob." How can all of reality find its source in a God so particular? How could one petty group of people out in the middle of nowhere happened to have stumbled onto the source of life and hope for all humanity, and indeed all the universe?

As much as it offends our sensibilities, we ought to be able to understand this. Life is a serious of decisions and commitments, each of which cuts off others which were at one time possible. Once you say a word, it will be forever true that you said it. Once you are married, it will be forever true that you decided to marry. Once you go to your grave, whatever you have done with your life is all that you have done. There is no going back. Indeed, we might perhaps better understand this than our ancestors, since because of the Internet, nearly everything we say in public will be forever recorded somewhere in this vast ocean of data.

Is it really so impossible to believe that God himself would make such commitments, and that those commitments would be the basis of all reality? In fact I myself find it very hard. If at one time in human development it was natural to anthropomorphize God, today it seems difficult to think of God as anything other than an abstract concept.

Theology isn't the only thing at stake. It is not just the living God whom we try to kill with our abstract thinking. It is anything living. We moderns are increasingly detached from our own history, living in the dream that we can transcend history, which was random and arbitrary up to exactly our generation, and then build the future on abstract principles from here on. Naturally, we refuse to believe that this dream came from anywhere other than our own reason.

To be sure, looking at the abstract principles behind living realities is a good thing. It helps us to simplify problems and find solutions agreeable to everyone. It can even help us know better what we observe, so that we can appreciate it all the more. (I find this especially true of music, and I suspect it is true of art. For me, music theory makes great works come to life even more than they already do.)

The problem comes when we confuse abstract principles with true or ultimate reality. That is the path to self-destructive rationalism--it empties the world of all meaning, it jettisons history as a source of knowledge, and it risks degrading civilization itself, which is built on living traditions. No, reality is not a set of equations. It is a living, spontaneous, external universe which imposes its particularity on us. I say this not to denigrate my own field, but merely to put it in its rightful place as a loving servant of the real.

Hayek on reason and tradition

Today's quote from F. A. Hayek is from The Fatal Conceit, chapter 1, page 21:

Learning how to behave is more the source than the result of insight, reason, and understanding. Man is not born wise, rational and good, but has to be taught to become so. It is not our intellect that created our morals; rather, human interactions governed by our morals make possible the growth of reason and those capabilities associated with it. Man became intelligent because there was tradition--that which lies between instinct and reason--for him to learn. This tradition, in turn, originated not from a capacity rationally to interpret observed facts but from habits of responding. It told man primarily what he ought or ought not to do under certain conditions rather than what he must expect to happen.

(Note: the emphasis is all Hayek's.)

This view is the result of Hayek's own studies and reflections on history and anthropology, and it provides a foundation for his anti-rationalist epistemology. I find myself lately rather hooked on this principle, as I see that it has far-reaching consequences. In education, for instance, I think we often see two schools of thought: one assumes that children are naturally gifted with the ability to think for themselves, and the other assumes that all knowledge must be handed down in the form of tradition. Hayek's principle is a little more favorable to the latter view, but even this will not suit: it is not merely knowledge which gets passed down through tradition, but a habit of thought enabling the mind to process things in an orderly fashion, for instance by the rules of deductive or inductive reasoning.

In terms of moral philosophy, I think this principle also leads us away from being (too) consequentialist in our reasoning. While it is often the case that our morals can be justified based on the general sort of consequence which we wish to avoid, there is in fact no way we can ever predict all the particular consequences of the various choices we make and the innumerable ways we make them. At bottom, we just have to accept that there are certain things you can't do, because, well, you just can't--even if you have some reason to suspect that it would be better in the long run if you did.

What goes mostly unstated in Hayek's moral philosophy is the underlying humanism implicit in his argument. Our morals have evolved to allow human beings to flourish to the greatest possible extent, given a world with ever-changing and unpredictable circumstances. This, for Hayek, is enough to place the benefit of the doubt on the morals we have inherited from tradition. On the other hand, it also justifies for him a great deal of skepticism about moral knowledge: "reluctant as we may be to accept this, no universally valid system of ethics can ever be known to us." One might call this the Incompleteness Principle of ethics, mirroring the Incompleteness Theorems of mathematical logic.

As a result, it is always possible to correct previous moral assumptions, either by showing some of our morals to be mutually incompatible or by showing empirically that some of our morals tend to do more harm than good. Such corrections can be continued ad infinitum, since no step in the process can ever produce the complete system of ethics we might strive for. What we absolutely cannot do is throw out traditional morality altogether and replace it with a plan by which we seek to deliberately conquer all obstacles to human flourishing. The dream of accomplishing this is exactly what Hayek names the fatal conceit. Not only will it not work, but it will backfire in devastating ways.

Hayek's moral philosophy is the right place to start if you want to understand the principles of a liberal social order of the "Hayekian" tradition, which, he would argue, goes at least back to the Scottish philosophers of the Enlightenment. But I think it's significant that, for a man known mostly for his thoughts on economics and politics, he had pretty brilliant insight into the complex and subtle relationship between reason, instinct, morals, and tradition.

Newcomb's Paradox

From Wikipedia:

A person is playing a game operated by the Predictor, an entity somehow presented as being exceptionally skilled at predicting people's actions. The exact nature of the Predictor varies between retellings of the paradox. Some assume that the character always has a reputation for being completely infallible and incapable of error; others assume that the predictor has a very low error rate. The Predictor can be presented as a psychic, as a superintelligent alien, as a deity, as a brain-scanning computer, etc. ...

The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000.

By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.

So which do you choose?

The paradox is that there are two lines of reasoning which both appear to be "rational," yet produce opposite conclusions. The first is this: since the Predictor has already placed the money in the boxes, my decision has no effect on whether or not B has $1,000,000. I should choose both boxes, since that will give me more money than if I only chose one. The second line of reasoning is this: the Predictor is never (or almost never) wrong, so I should choose just box B, because if I choose box B then it will be $1,000,000.

A couple of interesting observations. First, it seems to me to make all the difference in the world whether or not you're the one actually making the choice. If I were observing someone else make the choice, I would think, "Gosh, I hope for his sake that he's the type to take just box B, because then surely he will make more money." But if I'm the one who has to choose, well, it's hard to make such a statement about myself.

There's an interesting discussion about the paradox here, although it's a bit long. The perspective taken there is an appealing one, in my view: rationality ought to win. It's no excuse for the rationalist to say, "I choose both because this is the most logical answer; I cannot help the fact that I am rational and therefore wasn't given the option of making $1,000,000." If that's what it means to be rational to you, then rationality isn't going to get you very far.

Another interesting question: what if the Predictor tells you the money is for charity? Does that change the rationalist's reasoning? Logically speaking, it shouldn't.

I'm adding this to my list of lovable paradoxes, because yet again we have an example demonstrating how reason is insufficient for making decisions. Sometimes logic is an obstacle to being rational.

Origen on the planets and the stars

Origen's rationalism is just painful in this passage from De Principiis:

But to arrive at a clearer understanding on these matters, we ought first to inquire after this point, whether it is allowable to suppose that they are living and rational beings; then, in the next place, whether their souls came into existence at the same time with their bodies, or seem to be anterior to them; and also whether, after the end of the world, we are to understand that they are to be released from their bodies; and whether, as we cease to live, so they also will cease from illuminating the world. Although this inquiry may seem to be somewhat bold, yet, as we are incited by the desire of ascertaining the truth as far as possible, there seems no absurdity in attempting an investigation of the subject agreeably to the grace of the Holy Spirit.

We think, then, that they may be designated as living beings, for this reason, that they are said to receive commandments from God, which is ordinarily the case only with rational beings. “I have given a commandment to all the stars,” says the Lord. What, now, are these commandments? Those, namely, that each star, in its order and course, should bestow upon the world the amount of splendour which has been entrusted to it. For those which are called “planets” move in orbits of one kind, and those which are termed ἀπλανεῖς are different. Now it manifestly follows from this, that neither can the movement of that body take place without a soul, nor can living things be at any time without motion. And seeing that the stars move with such order and regularity, that their movements never appear to be at any time subject to derangement, would it not be the height of folly to say that so orderly an observance of method and plan could be carried out or accomplished by irrational beings? In the writings of Jeremiah, indeed, the moon is called the queen of heaven. Yet if the stars are living and rational beings, there will undoubtedly appear among them both an advance and a falling back. For the language of Job, “the stars are not clean in His sight,” seems to me to convey some such idea.

When one is absolutely convinced that order cannot come into being without reason, one will even ascribe souls to the sun and the moon.

The beauty of abstract simplicity

Gary Davis over at Republic of Mathematics has an interesting hypothesis about how less able mathematics students are making problem solving unnecessarily complicated. He uses some good illustrations to show how an astute mathematics student will take the time to formulate the simplest method of approach. He hypothesizes that a less able student will even choose more complicated examples in studying a particular idea (see his example of multivariable functions).

Excelling in mathematics, or in any theoretical field, requires an ability to make things simpler. It seems to me that what holds people back is that they erroneously equate "abstract" with "complicated," when in fact it's just the other way around. We create abstractions precisely to make simple the things that are complicated.

The use of the mind in society

Friedrich Hayek is primarily known for his contributions to economics and political philosophy. Yet one of his best contributions to both of these fields is an underlying theory of social learning. As an economist, he was interested in how it is that civilizations make use of information which is distributed among many individual minds (see, for instance, Hayek's essay, "The Use of Knowledge in Society"). As a political philosopher, he was interested in how institutions come to be, and how these institutions benefit individuals and allow society to progress. In both cases, Hayek finds that people engaged in free exchanges with one another unwittingly contribute to a process of social learning of which they themselves are mostly unaware.

Hayek Against Rationalism

All political theories assume, of course, that most individuals are very ignorant. Those who plead for liberty differ from the rest in that they include among the ignorant themselves as well as the wisest. Compared with the totality of knowledge which is continually utilized in the evolution of a dynamic civilization, the difference between the knowledge that the wisest and that which the most ignorant individual can deliberately employ is comparatively insignificant.

F. A. Hayek
The Constitution of Liberty

Perhaps the single most attractive part of Hayek's philosophy is, in my view, his epistemology. This is not something that the majority of people are likely to care about. Yet whether most people care about them or not, questions about what we know and how we know it are intensely important to the intellectuals who are often most influential in shaping society. The argument for a free society must have, as part of its foundation, an argument for the right kind of answers to these questions.

Voting Paradox

Key quote from this video: "While it's entirely rational not to vote...maybe that's not how people decide whether or not to vote."

Concerning philosophy and one year olds

rationalism -noun
1. the principle or habit of accepting reason as the supreme authority in matters of opinion, belief, or conduct.

The life of a graduate student, in my experience, is typically spent around peers, around professors, or in solitude. Marriage is common enough in graduate school, but I would venture to guess that the majority of us aren't married. Parents make up a much smaller percentage of graduate students. In this environment it is taken as a truism that having children hinders progress in our studies. (I have heard stunning exceptions to this. One student in religious studies once told me that his advisor recommends having children as a graduate student--then suddenly you will be unable to waste time.)

Well, you'll get no argument from me on the practical implications of having children--they take a lot of work. What I'm interested in is the effect of simply not being around children, of being immersed in a world of professionals. Of course we could go on all day about how this affects our priorities, what it does to our personal development, and so on. But I'm really interested in the intellectual side of it. How does being absent from children all the time affect the way we think, about ourselves and about our beliefs?

Concrete vs. Abstract Society

Not that you should necessarily watch the whole thing (you would if you were a nerd like me) but here's an interview with Friedrich Hayek from 1985:

F.A. Hayek Interviewed By John O'Sullivan from FEE on Vimeo.

Here's a key idea. As humans move from small, homogeneous societies to large, pluralist societies, they also have to move from "concrete" to "abstract." In a small society, you know the people you work for, both your employers and your customers. In a large, pluralist society, you don't know whom you work for. In a complex society designed to sustain the number of people who now exist in the world it is impossible to see how it all fits together.

This has crucial implications, Hayek says, for how we view serving one another. In a small, concrete society, you know what it means to serve others: you address their needs directly. In a large, abstract society, this is impossible. The best way to serve others, he argues, is to maximize profit, i.e. be as efficient as possible. Efficient markets ensure that resources will shift to where they are needed the most.

The problem is that it's impossible to actually see those resources shifting the way you hope they will. We see in our common experience that a lot of people make money out of sheer luck, others by hard work. Some professions which seem more worthy of higher salaries don't pay as well as we think they should. How can we possibly trust that in the end, resources are going where they need to?

Well, partly these problems stem from the fact that our markets aren't entirely free. (For instance, I could go on about how the teaching profession is dominated by a monopoly created by bad government policies. This, I am convinced, is the reason why the salary for a teacher isn't as high as it should be.) But to be fair, results that seem grating to a person's intuition are bound to happen in a free market system.

Hayek suggests we ought to overcome that intuition. He even suggests that for exactly this reason, human beings may not be ready for a free market system. We are simply not ready to overcome our desire to see the system as a whole achieve a predetermined outcome. We do not like spontaneous growth. We prefer systematic, planned growth.

Perhaps what appeals to me about Hayek's argument is its critique of rationalism, i.e. the belief that human reason can obtain all the means necessary for progress. Moreover, Hayek's preference for spontaneous over planned growth suggests that he cherishes life over machines. Life is spontaneous and beautiful; machines are cold and rational, and they don't have the same self-sustaining qualities that life does.

But in times of economic turmoil, it seems most likely that people will turn to rationalistic attempts to fix the economy, disregarding the possibly disastrous side effects such a route could have. I guess that just proves there's nothing "natural" about the free market. Only a principled society can sustain it.