Saturday, October 20, 2012

Education vs. Indulgence

An interesting passage from Whewell (Of a Liberal Education in General, p. 7):

The term Education especially implies, by its etymology, that character in the studies of the rising generation which I have attempted to describe: namely, that these studies draw forth and unfold a portion of our common human nature. They educe the elements of the Humanity which we have within us. The studies and occupations of the young are not properly called Education, merely because they draw out something, without considering whether it is an attribute of the race, or an accident of the individual. Young persons may be so employed and so treated, that their caprice, their self-will, their individual tastes and propensities, are educed and developed; but this is not Education. It is not the Education of a Man; for what is educed is not that which belongs to man as man, and connects man with man. It is not the Education of a man's Humanity, but the Indulgence of his Individuality.

He notes in a footnote that the actual etymological history is somewhat obscure; but, of course, he is only using it as a way of building a vocabulary for making his point. One interesting thing about it is that there are a lot of educational philosophies which would not count as educational in Whewell's sense.

Okelo and Irwa

Today in many places is the memorial for Bl. Daudi Okelo and Bl. Jildo Irwa, an interesting pair of Ugandan saints from the beginning of the twentieth century. (Okelo and Irwa were their pre-confirmation names; Daudi and Jildo were the names they took at confirmation.) Shortly after he had been confirmed, Daudi enrolled to be a catechist. When the catechist of Paimol had died, Daudi volunteered to take his place. There was some reluctance to send the young man, since it was a long road through bad country, but a catechist was definitely needed and Daudi insisted that he could do it, so it was decided that they would go (although with an escort in case of raiders). Jildo, an intelligent young man with a merry temperament, went with him as his assistant.

Every morning Daudi would beat the drum to call people to prayer, and would teach them the Words of the Morning, the next part of the catechism they were to learn, often turning the question and answer into a sort of sing-song call and response. Jildo would gather together the children and play games with them. Later in the day, Daudi would visit villages in the area and Jildo would often serve as secretary the village chief.

Things took a turn for the worse; relations between the Ugandans and the British were sometimes quite tense, and as Christianity was seen as a British religion, when the British would handle things too heavily retaliation was often taken out on the more easily reached Ugandan Christians. So it happened, and after the British District Commissioner made an unpopular decision, a group of people got together and set out to kill Daudi. A village elder who got wind of it tried to stop them, insisting that they were guests, but Daudi, afraid that the elder might be hurt, begged him not to involve himself. The group pushed their way inside the place Daudi and Jildo were staying and demanded that they give up catechizing, and when they refused, they were seized and dragged outside, where they were killed with spears.

Daudi of Payira was seventeen or eighteen years old, and young Jildo was about fourteen. It is said that the place where they died was given the name Wi Polo, 'in heaven', because those were the words of the Lord's Prayer that Daudi had been teaching on at the time.

Friday, October 19, 2012

The Sunshine of Kind Looks

by William Cullen Bryant

Ay, thou art welcome, heaven's delicious breath,
When woods begin to wear the crimson leaf,
And suns grow meek, and the meek suns grow brief.
And the year smiles as it draws near its death.
Wind of the sunny south! oh still delay
In the gay woods and in the golden air,
Like to a good old age released from care,
Journeying, in long serenity, away.
In such a bright, late quiet, would that
Might wear out life like thee, mid bowers and brooks,
And, dearer yet, the sunshine of kind looks,
And music of kind voices ever nigh;
And when my last sand twinkled in the glass,
Pass silently from men, as thou dost pass.

Bryant is best known for his poem, "Thanatopsis".

Thursday, October 18, 2012

Whales, Books, and Chapters

Apparently today is the anniversary of Herman Melville's Moby Dick. So I thought I'd put up a brief selection from my favorite chapter in the book, Chapter 32.

First: According to magnitude I divide the whales into three primary BOOKS (subdivisible into CHAPTERS), and these shall comprehend them all, both small and large.


As the type of the FOLIO I present the SPERM WHALE; of the OCTAVO, the GRAMPUS; of the DUODECIMO, the PORPOISE.

FOLIOS. Among these I here include the following chapters:—I. The SPERM WHALE; II. the RIGHT WHALE; III. the FIN-BACK WHALE; IV. the HUMP-BACKED WHALE; V. the RAZOR-BACK WHALE; VI. the SULPHUR-BOTTOM WHALE.

Yes, Chapter 32 really is my favorite chapter in the book.

Music on My Mind

Acquire A Capella, "Safe & Sound".

Enchantress of Numbers

It was recently Ada Lovelace Day. Ada Lovelace, who was the daughter of Lord Byron, is most famous for her collaboration with Charles Babbage and Luigi Menabrea, which in a sense makes her the author of the first English textbook on computers -- she translated Menebrea's account of Babbage's Analytical Engine and added in cooperation extensive notes of her own, including what are clearly things like computer programs. She thus sometimes gets the label 'the first computer programmer', which, like almost all such designations, is a bit questionable. However, there has recently arisen a sort of reaction to this which goes to an equally extreme length in the other direction, claiming that she was a mathematical incompetent. The arguments for this are somewhat varied. For instance, on one argument, Menebrea's text had a typo in which, instead of 'le cas' it had 'le cos', and the Countess Lovelace simply carried over the 'cos' despite the fact that it didn't make any mathematical sense in context. This is not a very strong argument, since the work seems to have been reviewed by Babbage, whom nobody thinks was a mathematical incompetent, and he didn't catch the error, either. And we get statements like this recent one from Julian Sanchez:

Dorothy Stein, the first of Lovelace’s biographers with sufficient training to seriously assess Ada’s frequent proclamations of her own extraordinary mathematical genius, concludes that Lovelace was scarcely the prodigy she imagined herself to be, and struggled to grasp concepts that would be standard fare in a modern high school course in AP calculus.

To which one is inclined to say, Well, obviously; a modern high school course in AP calculus presupposes lots and lots of ideas that were only just being developed by and diffused among the mathematical geniuses of Lovelace's day. Let's look at the dates of two extraordinarily important people in the development of the modern calculus and compare them with Ada Lovelace's dates:

Lovelace (1815-1852)
Cauchy (1789-1857)
Weierstrass (1815-1897)

Notice that there's just a bit of an overlap there; and it should be noted that Weierstrass only became known relatively late: the works that the mathematical community first started taking serious notice of were published after Lovelace's death. But it is Weierstrass who is usually credited with putting the calculus (including the limit concept, that bane of the high school AP student) on a rigorous basis. In Lovelace's day, people were still using a lot of guesswork; even well after her day you could still find competent British mathematicians (who, while often managing to do their own good work, were also often playing catch-up in using methods that had developed on the continent) trying to solve problems by methods that would be considered shockingly informal and wrongheaded today.

But behind Sanchez's hyperbole is Stein's argument that Lovelace, in her correspondence course with De Morgan, occasionally has difficulties with problems that would be fairly easy today. A serious examination of the matter, however, requires not looking at what we can do today, when notation has stabilized and there are lots of people are given extensive teaching in a formal setting, but at what could be done in Lovelace's day, in which notation for the calculus had not yet stabilized, many British mathematicians of undoubted competence were still uncomfortable with the continental ways of doing analysis, and someone like Lovelace was for all practical purposes studying the subject on her own with occasional help from people like DeMorgan (they met every few weeks and exchanged correspondence here and there between). We don't actually know why Lovelace had the difficulties she did; it could be that she was just not comfortable with the notation yet, or that she was making some silly mistake which she later corrected, or that it just hadn't clicked yet, or that De Morgan had explained something badly at some point, or that she wasn't really all that great at mathematics, or any number of other things. Even getting simple things wrong is not a sign of incompetence, especially when starting out; there isn't a mathematician in creation that would survive to remain in the competence box if the criterion were never making a mistake that someone else could easily avoid -- and this, it should be pointed out, is especially if the someone else lives a century and a half later. It is of a piece with people who claim that Lovelace's 'programs', as they are often called, are merely 'student exercises' without also pointing out that what we have of Babbage's 'programs' are often not any more sophisticated. I don't think the kind of study that is required for this sort of assessment has actually been done, and it's possible we simply lack the evidence to do so. It's entirely plausible to think that Babbage, who called her "the Enchantress of Numbers" was just excited to find someone so enthusiastic about his Analytical Engine and so willing to flatter him over it; and it is true that Lovelace liked to talk of her own intellectual abilities in overinflated rhetoric; but Babbage was not the only mathematician of note to comment on her high level of mathematical ability.

The debate, in short, is not yet played out, and it is premature to be dogmatic about the outcome.

But, of course, this is in some sense moot: people don't recognize Ada Lovelace day in order to celebrate the Countess of Lovelace; they recognize Ada Lovelace day in order to celebrate women in mathematics and science. Lovelace is the occasion.

Wednesday, October 17, 2012

Chesterton on Sincerity

What convinces mankind of a man's sincerity is this: that every now and then he should go with his principle and against his feelings. Sincerity can be shown in surrender, if it is self-surrender. For instance, a despotist is not necessarily honest because he praises the King; but he probably is honest if he blames the King--and obeys him. He shows that it is for his theory he cares, and not for himself. Or, again, a man is not necessarily democratic because he can call up the people to support him. But he is democratic if he calls up the people to oppose him. A man who gives votes to a class that will probably vote against him certainly believes in popular government. A vegetarian who hates meat is not so serious as a vegetarian who loves meat.

Illustrated London News, 12 October 1907.

Tuesday, October 16, 2012

Links of Note

* Jonathan Dresner on Marco Polo

* Richard Brown discusses Aristotle on pleasure

* Mikhail Emilianov on how to fake your way through Spinoza

* A website collecting earliest uses of common mathematical symbols. Unsurprisingly, a large portion of our current logical symbolisms comes from Peano. But it's always interesting to see how relatively recent some of these symbolisms are.

* John Fabian Witt clears up a common confusion about the history of the status of corporations as persons at "Balkinization".

* Sarah Avery discusses an Introduction to Mythology class that she once taught, which turned out quite well and which she will probably never be allowed to teach again:
The Once and Probably Not Future Mythology Class
Hazards of Teaching Cool Stuff You Love in a Classroom

* Michael Pakaluk has an excellent discussion of formal cooperation.

I am grading, grading, grading, grading, and grading, so things will be fairly sparse this week.

Monday, October 15, 2012

Watering the Garden

Today is the feast-day of St. Teresa of Avila, Doctor of the Church. From her Life, which is one of the pre-eminent spiritual autobiographies:

A beginner must look upon himself as making a garden, wherein our Lord may take His delight, but in a soil unfruitful, and abounding in weeds. His Majesty roots up the weeds, and has to plant good herbs. Let us, then, take for granted that this is already done when a soul is determined to give itself to prayer, and has begun the practice of it. We have, then, as good gardeners, by the help of God, to see that the plants grow, to water them carefully, that they may not die, but produce blossoms, which shall send forth much fragrance, refreshing to our Lord, so that He may come often for His pleasure into this garden, and delight Himself in the midst of these virtues.

Let us now see how this garden is to be watered, that we may understand what we have to do: how much trouble it will cost us, whether the gain be greater than the trouble, or how long a time it will take us. It seems to me that the garden may be watered in four ways: by water taken out of a well, which is very laborious; or with water raised by means of an engine and buckets, drawn by a windlass--I have drawn it this way sometimes--it is a less troublesome way than the first, and gives more water; or by a stream or brook, whereby the garden is watered in a much better way--for the soil is more thoroughly saturated, and there is no necessity to water it so often, and the labour of the gardener is much less; or by showers of rain, when our Lord Himself waters it, without labour on our part--and this way is incomparably better than all the others of which I have spoken.

Sunday, October 14, 2012

A Brief Introduction to Natural Law Theory II

Part I

Natural law theory is, as noted in the previous part, a theory of practical reason; but what gives its name is that it is a theory of practical reason that is also a theory of law, a theory of practical reason qua law. Thus an adequate discussion of natural law theory requires a discussion of the account of law it gives, and to this we now turn.

II. Law

While he is certainly not the first to say something that might be construed as suggesting the idea of natural law, a fairly reasonable starting point for the history of natural law theory in Western civilization is Cicero. In De Re Publica he gives what clearly has all the elements of a natural law theory, which is to say, an account of human practical reason based on principles natural to it that is also an account of law. It forms one of the key elements of Cicero's theory of a republic or commonwealth. Cicero notes that human beings are in some sense at a disadvantage in the world at large -- in his notable phrase, Nature has treated us more like a stepmother than like a mother; if it were not for one thing, we would be outmatched by our environment, and that one thing is understanding or reason. By this we are able to write and study the stars, and to develop philosophy and thus civilization, that is, civil society. While we are not thrown into civil society, it is in some sense natural for us to build such civil societies. And as civil societies are constituted by justice and laws, any discussion of civil society must consider what justice and laws are. In the course of the dialogue, one of Cicero's characters, Laelius, argues that expediency is not the foundation of justice or law, and thus not the foundation of a genuine republic or commonwealth. Rather, there is a more fundamental foundation for both that, transcending any utility one might gain from either, still has purchase on us, because it is based on that very reason or understanding that makes civilized life possible in the first place. This is a true law, which is the same as right reason and is in accordance with our nature. Unlike human law it is universal and immutable, and (as it is that law which enjoins upon us morality itself) there is no field of genuinely human action that is outside its jurisdiction. No senate and no popular will can override it, for any attempted dispensation is unjust and unreasonable; it stands above human action in the sense that all human action is judged by it. It is promulgated by the God, and anyone who disobeys it does violence to his own nature. Laelius's account is applauded and supported by Scipio, another major character in the dialogue; and the agreement of the two is a clear sign of Cicero's own good favor toward this account. Much of this comes from the Stoics, but we see it come together here in a shape that will be quite familiar through the centuries. St. Ambrose and St. Augustine both show the clear influence of it, but, of course, the most famous exposition of this view is that of St. Thomas Aquinas.

In the first question of the Treatise on Law in the Summa Theologiae, which is question 90 of the First Part of the Second Part, Aquinas gives a general definition of law: Law is "nothing other than a certain promulgated ordering of reason to common good by one who has the care for what is common" or, as it is often translated, "nothing else than an ordinance of reason for the common good, made by him who has care of the community, and promulgated". There are four basic elements of this definition.

Law has to do with reason. Law regulates and measures human action in such a way that action is encouraged or restrained. This is a rational function: all genuinely human action is measured and regulated on the basis of reason, so that reason can in some way be said to be its source; thus law has to do with reason, either immediately or derivatively.

Law is an ordering to common good. Reason organizes and regulates action according to means and ends, as we noted in the discussion of practical reason. The most general end with which reason deals is the totality of good in a good life, and this does not exclude (and, indeed, requires) that reason consider what is good for everyone. Law clearly has to do with human beings in society, and therefore must consider precisely this: what is good for everyone in common. Thus law is an ordering to common good. It is worth pointing out, I think, that this common good is not, as Aquinas understands it, an overarching collective good separate from all individual good. It is instead the kind of good people share, literally good in common, by virtue of their living in society. It is also worth being wary of assumptions that tend to get imported by the translation "the common good". There is no one common good; there are many common goods, as many common goods as there are communities. Some common goods are more inclusive than others, but it is impossible to talk about any common good without having established what society or community one is considering.

Law is from one to whom it belongs to care for what is common. Ordering to common good typically depends on a whole community working as a whole: it is the whole community working together that has natural and primary responsibility to order itself to the relevant common good. However, practically speaking (and with law we are always speaking practically) it is often not feasible for the community to work as a unitary authority. To get around this problem, assuming there is no natural caretaker for the whole community, the whole community chooses someone to act for the whole community. Since law is an ordering to common good, its source has to be someone who is in some way caretaker of what is common to everyone.

Law is promulgated. Laws exist in order to regulate and measure human action, but they must be applied to action in order for this to happen. Since human action has its source in reason, the way in which laws are applied to human action must accordingly be rational. That is, law must be communicated in a rational way to the people to whom it applies, so that their reason can take it into account. This can happen in many different ways, but it must happen.

If any of these four is lacking, we may have something that looks a lot like a law but is not actually a law, and has no force as a law; a point which will be of some importance. There are, however, many different kinds of laws.

One of these kinds of law is natural law, which is the law constituted by the basic principles of practical reason. Obviously these principles are rational. They concern how things are ordered to good as such, which means that they are concerned with both private good and common good; insofar as they concern common good, they fit that part of the definition of law. They are also clearly promulgated, that is, our reason is notified of them, because they are intrinsic to reason, and without them we cannot reason practically at all. Therefore that leaves simply the source to whom it belongs to care for what is common.

This gets into an interesting issue. Aquinas himself is quite clear that the source of natural law is God, on whom human beings depends; and because the whole human community depends on God, God is the natural caretaker of what is common to the whole human community. As he puts it, natural law is the human participation of the eternal law of God by which God providentially orders the whole universe; it is, so to speak, a parceling out of eternal law in human form specifically for human beings. However, the language of participation is much more intimate in its suggestion than merely God imposing a law on us. Aquinas is equally clear that human beings don't just have their specifically human parcel of the eternal law of divine providence; divine providence itself is parceled out to us, again in a specifically human form specifically concerned with human life. Each human being, as rational, is in a sense part of divine providence itself. We all have a share in divine providence so that we, as rational creatures, are in Aquinas's phrase, "provident for ourselves and others". Only creatures with reason and understanding can have this subordinate providentiality, this active participation in the very providence of God. Thus there is a definite sense -- a derivative sense, but still a definite sense -- in which each and every human being, as a rational person, is caretaker for what is common to all human beings.

The participatory authority of each human being accounts for a feature of natural law theory that often confuses people, namely, the fact that sometimes natural law theorists talk as if natural law theory crucially depended on recognizing the existence of God's eternal law and thus the existence of divine providence, but that sometimes natural law theorists talk as if natural law does not depend on any specific belief about God, even the belief that God exists, so that one can recognize the precepts of natural law as such even if one does not believe God exists. In actuality, both can be true. Any natural law theory that is genuinely Ciceronian, or Augustinian, or Thomistic in inspiration cannot be complete without taking into account the fact that natural law is a sharing of the eternal law. However, precisely because this is not a mere imposition but a participation, we can recognize that the precepts of natural law are laws simply from the naturally provident character of reason itself. Full understanding of this providential character, and the corresponding force of law, requires placing natural law in the context of God's providence, because human beings are secondary and not primary caretakers of human good; but human beings are each themselves, by virtue of their own reason, caretakers of human common good. Aquinas does not develop this point at great length, so it is difficult to say exactly how much emphasis should be placed on this; some Thomistically inspired natural law theorists prefer to emphasize the importance of putting natural law in the context of eternal law, while others prefer to emphasize the intrinsically legal character of the principles of practical reason. Both have foundation in Aquinas. It is also important to understand that from a strictly Thomistic perspective this is a purely epistemological question of whether one can recognize natural law as law if one does not believe in divine providence; Aquinas affirms principles that imply that one can, and this has some confirmation in actual human behavior. But even if it weren't so, principles of practical reason have the force of law, because God exists and is caretaker of human common good, indeed all common good; and, likewise, even though it is so, any complete explanation of why the principles of practical reason can have the force of law will ultimately trace back to the fact that divine providence has the force of law, or to put the same matter in different terms, that human beings are subordinate caretakers of human common good sharing in the primary caretaking of God. This parallels the way Aquinas understands God's causal activity generally, and the parallel is not accidental.

This gives us the general understanding of what natural law is, but we need to look at features that are specific natural law, and then look at how natural law relates to another important kind of law, human or positive law.

Part IIIa

Fortnightly Book, 14 October

I will be quite busy this week, and possibly also the next, so it was pretty clear that the next fortnightly book needed to be a re-read or quite short, preferably the former, since it is sometimes the case that reading short books properly is much more time-consuming than reading long books properly -- a verse novella may well take as long to read as a prose tome with ten times its word count. And as I was thinking this, my eye fell on a book I haven't read for several years, although I had read it many times before and liked it. So the fortnightly book is Till We Have Faces: A Myth Retold, by C. S. Lewis.

The original Cupid and Psyche story comes from Lucius Apuleius's The Golden Ass, which is, for lack of a better term, an ancient novel, that is, an extended prose narrative following the adventures of a single hero. Its actual name is the Metamorphoses, which hints at Ovid in the background, but it is often called The Golden Ass, or Asinus Aureus, because it was the name given to it by St. Augustine, who knew it quite well; the name comes from the fact that the main character manages to get himself turned into an ass for a considerable portion of the narrative. Much of the story is extraordinarily lewd, with all sorts of sexual shenanigans, but it occasionally slips into the philosophical, using physical transformation as a symbol of moral transformation; and throughout the story there are digressions in which people tell other stories each of which still touches on the underlying theme of transformation. This format, which may or may not have originated with Apuleius himself, influence much of later storytelling, of course. Of these secondary stories, the tale of Cupid and Psyche stands out because it is so radically different from the rest of the work -- whereas other secondary stories, and, indeed, much of the rest of the novel revels in sexual buffoonery and farce, here the theme of transformation takes on a different tone entirely. It's not that the sexual element is missing: Cupid is, after all, the god of erotic love, and there is sexual humor of a somewhat subtler sort (e.g., Cupid goes on strike, and everyone starts complaining about how boring things have become), and the daughter of Cupid and Psyche is Voluptas, who is the goddess of sexual pleasure. But the story itself is strikingly high-toned and lacking in buffoonery, with the allegorical overtones carried by this sort of myth (psyche is, after all, the Greek word for 'soul', what makes you a living thing; and eros, desire, has a long philosophical history, as anyone knows who has read Plato's Symposium). What is more, this is almost certainly deliberate: the story occurs right in the middle of The Golden Ass, and in a sense anticipates the religious character of the final book, in which the protagonist, Lucius, begins to be inititated into the rites of the goddess Isis.

Lewis had long been toying with the idea of a version of the Cupid and Psyche tale told through the eyes of Psyche's elder sister; she is in some ways the villain of the story, since she pesters Psyche to do things she shouldn't do, and which result in a great deal of suffering. He could very well have gotten the idea in part from William Morris's telling of the story in The Earthly Paradise; and the young Jack Lewis shows an interest elsewhere in retelling myths from the perspective of the villains and monsters, the sort connected with Promethean Romanticism. He dabbled in some poetic attempts, but not much came of it until he actually started working on a prose story in the 1950s, which he titled Bareface. He could not convince the publishers that this was a good title for a book (they said it sounded like it was a Western!), and eventually went instead with Till We Have Faces, from the single most important line in the book, which Orual says of the gods: "How can we meet them face to face till we have faces?" The book explores the theme of love, of course, both pure love and love that has become sick and devouring; and it explores the intersection of reason, cool and clear and bright as water, and imagination, warm and dark and earthy as blood; and it explores the agonies of religion, with its blood and dark places and terrible events that the gods rule but for which they never answer; and it is about self-knowledge and the lies, and truths, of reason and imagination alike, that is, it is about human faces; and it is about betrayal and death and reconciliation.

One of the things that has always intrigued me is Lewis's epitaph for the work: Love is too young to know what conscience is. It comes from Shakespeare's Sonnet 151:

Love is too young to know what conscience is,
Yet who knows not conscience is born of love?
Then, gentle cheater, urge not my amiss,
Lest guilty of my faults thy sweet self prove.
For, thou betraying me, I do betray
My nobler part to my gross body's treason;
My soul doth tell my body that he may
Triumph in love; flesh stays no farther reason,
But rising at thy name doth point out thee
As his triumphant prize; proud of this pride,
He is contented thy poor drudge to be,
To stand in thy affairs, fall by thy side.
No want of conscience hold it that I call
Her ‘love’ for whose dear love I rise and fall.

It, like the original Cupid and Psyche story, is a poem that can be read in a bawdy or non-bawdy way, as you please. But I suspect the connection here is chiefly that posited between conscience and love in the first two lines: love must find fruition in conscience, but conscience cannot be had unless we first love.