Tuesday, December 06, 2005

A Brief Note on Miracles and Hume

The most recent God or Not carnival is up at "Evangelical Atheist"; the subject is miracles, and it's not surprising that Hume figures heavily in the discussion. Hume famously defined a miracle as "a transgression of a law of nature" or "a violation of the laws of nature" -- somewhat oddly, I've always thought, since he would have known at least two people whose understanding of miracle is quite opposed to formulating the definition this way (Malebranche & Butler). But there's perhaps reason to think that Hume's use of the terms 'violation' and 'transgression' are like his use of the term 'contradiction' elsewhere when talking about unifrom experience, i.e., the idea is simply that a miracle is something that is contrary to our uniform experience. (In the Essay on Miracles he is only considering knowledge of miracles by testimony, so the person being considered there hasn't experienced the miracle himself.) One of the chief difficulties with Hume's argument -- it has always been a contentious point -- is making it work without also condemning all of astrophysics and any other science that deals with phenomena outside our rather mundane uniform experience. Indeed, a common complaint is that Hume's argument, if taken seriously would push our ignorance even farther than that. One of the most fun formulations of such an argument is Richard Whately's 1819 Historic Doubts Relative to Napoleon Buonaparte. And, indeed, because Hume puts the same weight on uniform experience of human nature as he does on uniform experience of the physical world, Whately may have something of a point. In any case, it's a tricky issue; Hume doesn't appear to have recognized the problem, although possibly his ultimate qualification of his argument, that it simply disproves the possibility of proving a miracle from testimony "so as to be the foundation of a system of religion" might provide an escape hatch. But what exactly this means is hard to pin down; perhaps he means that young religions are missed by the historical evidence (which he does say), or that religious people are more likely to lie about marvels (which he does imply), but perhaps the point is that "it would be absurd to employ any prophecy as an argument for a divine mission or authority from heaven". This latter issue about divine mission was a major part of discussion of miracles at the time, so it may well be Hume's primary target. Or perhaps Hume intends the qualification only to apply to some of his later arguments in the essay (but which ones?) -- in which case it doesn't provide a way of dealing with the problem at all. We might well borrow a sentence from Hume in another context to characterize the argument: The whole is a riddle, an enigma, an inexplicable mystery.

Tolkien on Lewis

I've already said my piece on the Narnia criticisms. I did want to say something about this paragraph in a different Guardian review:

Tolkien hated Narnia: the two dons may have shared the same love of unquestioning feudal power, with worlds of obedient plebs and inferior folk eager to bend at the knee to any passing superior white persons - even children; both their fantasy worlds and their Christianity assumes that rigid hierarchy of power - lord of lords, king of kings, prince of peace to be worshipped and adored. But Tolkien disliked Lewis's bully-pulpit.

As I recall this was not Tolkien's reason for disliking it at all; what he didn't like is the carelessness of the creation. Tolkien took artistic creation (sub-creation, as he called it) very seriously, thinking that the author should craft a consistent, coherent world with its own inner logic. Lewis piled a whole lot of things together, from talking beavers with sewing machines to Fauns to Father Christmas. This sentence from The New Yorker is a bit better:

Tolkien hated the Narnia books, despite Lewis’s avid sponsorship of Tolkien’s own mythology, because he hated to see an imagination constrained by the allegorical impulse.

It is true that Tolkien had a distaste for the 'allegorical impulse', particularly the tendency to read every story as an allegory. But, again, I can't recall that this fits with anything Tolkien actually says about the Narnia books; and one could just as easily say that Tolkien's tendency to dislike allegorical reading would have led him to be irritated by those who insist on reading the Narnia books only as an allegory -- it isn't necessary, and many people don't, for the very good reason that the books are not properly allegories at all, except in the sense that any book making extensive use of certain kinds of imagery will have allegorical tones, which can as a matter of art be explicitly harnessed. In that sense Tolkien himself does the same thing, and admits it: his descriptions of Galadriel are influenced by the imagery of the Virgin Mary, etc. It doesn't follow from these things that The Lord of the Rings is an allegory. (Eliot's Middlemarch taps into the imagery of earth and vegitation; it doesn't follow that Middlemarch is an allegory for the earth. Pullman's His Dark Materials series makes rather extensive use of Miltonic imagery, as interpreted by Blake. It doesn't follow that it's an allegory for a Blakean worldview, just that the imagery is supposed to have Blakean-Miltonic tones in acting on the reader.) Lewis denied (quite rightly) that the Narnia works are allegories in any proper sense. He was trying to write books that will strike readers the way MacDonald's books struck him, namely, those that 'baptized his imagination' in giving him an imaginative sense of Something More; but his mode of writing wasn't particularly allegorical -- he started with a few striking pictures in his head and wrote about them. The allegorical associations just followed from that. Further, the above description of Tolkien's complaint is very implausible; Perelandra, which is a re-telling of Paradise Lost, is even more easily read as allegory than Narnia, and Tolkien loved it. Tolkien's complaint was not about the content, but about the art: he thought the works weren't serious enough.

(As a side note, I find interesting some of these secular criticisms of the Christian-like content of the Narnia books, because they often seem to echo things Lewis attributed to his own atheist years, e.g., an appreciation of certain sorts of myth, but a revulsion toward the same kind of myth when it was put in Christian form. At least, I very much doubt they would make similar criticisms of a book about the Corn King or Odin on Yggdrasil. And what is it with all these people who seem to think that the lion is not a traditional symbol of Christ? The funniest point in these criticisms, though, is found in the first review I linked to above; she calls the books 'Republican', which seems a teeny-weeny bit of a stretch!)

A Poem Draft

Angel on the Gallows

Ruthlessness of law establishes
one path, and one alone;
as proportionment itself requires,
each shall have its due.
Tho' he be as pure in every else
as snow on mountain summits,
for each jot we take a tittle,
and by little piled upon little,
from droplets an ocean forms.
No excuses will be accepted
(the balance must be right);
the penalty shall fall
without regard for plea or plight.
As others have now suffered,
the gallows will be made;
for treason to our customs
he is assigned his proper death.
And we sit in aureate judgment,
in the glow of well-deserved pride,
for our rightness has returned rightness,
and the criminal has died.

Cold comfort, O ye children,
who cannot see the grace
that shines in every heart's hearth
and glows in every face.
Tho' you be as right as compasses,
tho' you flatter yourselves with law,
a higher Judge is judging
who holds each soul in awe!

Again on Miscompassion

I've been meaning to say something more about the recent case of a single pregnant teacher being fired from a Catholic school, but on reflection I don't have much to say, since I basically agree with Jack Perry on this point. Just the following:

(1) There is not, and cannot be, anything morally problematic about being pregnant. It does not matter whether it occurs inside or outside marriage; whatever the ethics of extramarital sex, there is nothing morally problematic about extramarital pregnancy. Yet there is a shocking and shameful tendency to treat pregnancy as the problem. It has been asked about this case whether a man whose extramarital affair had come to light would also have been fired; and it is a serious question.

(2) But it is not the only question. For, more seriously, we need to ask what example the school is setting. Note that I emphasize the example of the school, which tends to be overlooked. An ostensible defense of the school's actions might go something like this: As a Catholic school, the school has certain responsibilities to guarantee that those in positions of authority over children should publically act in conformity with Catholic doctrine; McCusker has acted in a way that cannot be condoned by the school; so the firing was necessary. But this, I think, is a poor defense. For if the school is really in the business of teaching by example, it must consider what example it is setting by firing pregnant women. As a teacher, McCusker inevitably would have difficulty finding employment in the middle of the school year; effectively the school turned her and her baby out on the street -- not literally, perhaps, but they might as well have. What sort of charity is that? What sort of mercy?

I also must confess that I am rarely impressed by arguments from what would or would not be construed as condoning something. If Jesus could associate with prostitutes and publicans, I think it shouldn't be so very difficult for us to associate with more reputable people. Thus saith the Preacher: be not overly righteous. If you spend too much time trying not to condone sin, you will never have the time to be charitable to sinners. We should all try to act as if the old toast might come true: May you yourself be treated as mercifully and charitably in your failings as you treat others in theirs.


This post at "The Little Professor," on a discussion about Harold Bloom, started me thinking about the phrase "Judeo-Christian". On the one hand, I think it's admirable that people try to think in terms of the unity, or a unity; on the other, I think it's clear that most Christians who use it know so little about Judaism that it ends up meaning 'Christian with some verbal modifications we think might make it more palatable to Jews'. Then again, I think a great many people, while right to recognize a certain amount of kinship, really do think that Christianity and Judaism differ in only a few details -- important details, but just a few; and, of course, that makes it difficult to take properly into account that 1900 years or so of both traditions going their own way. (And, of course, it's sometimes the case that the reason for this is that the people using the term know almost nothing about Christianity as well.) I think it would work fine if people were to see it as what it is: primarily a regulative, not a constitutive, concept. That is, if it's seen as a platform for cooperation, not so much the identification of an actual fact. (It's used in this way by some Jewish supporters of a Judeo-Christian program, e.g., Toward Tradition.) The phrase really began coming into its own in the U.S. after WWII, as a way to unite Christians and Jews together against anti-Semitism as a common enemy. And it seems to have been useful in this regard, however clumsily it might have been used at times. If Christians think of themselves as in a sort of unity with Jews (which they should) they are less likely to find anti-Semitism tempting. The real remedy against abuse is to make sure people are better informed about Judaism.

Saturday, December 03, 2005


* Carnivalesque XI (ancient/medieval edition) is up at Blogenspiel. It's quite good. (I really like the brief discussion of the Song of Roland.)

* The Nine Ways of Prayer of Saint Dominic: a lovely little work of 13th century Dominican spirituality. (HT: Magic Statistics)

* A very thoughtful and thought-provoking post by Myers on teaching intro bio.

* Timothy Sandefur has an interesting, if unnecessarily abusive, post on Alexander Hamilton. I'm not a Hamilton expert, and I haven't read Chernow's biography; but if Chernow's biography tends hagiographical, the truth almost certainly falls somewhere between that biography and Sandefur's post. Not being a great admirer of Jefferson, beyond a few of his ideas, I'm not inclined to regard Jefferson's characterization of Hamilton as trustworthy -- on the contrary, I'm more inclined to regard Hamilton's characterization of Jefferson as right: too partial an idea of his own powers, expecting to have a greater share in things than he did, and inclined to ill humor when not getting his own way. I say 'more inclined' because on considered judgment I think it very likely that both were partly right about the other, and only partly right; for the other part, they were confused in labeling their opponents with their own flaws (a common confusion in politics). I think Sandefur's characterization of Hamilton's actions in the 1800 election is a bit extreme; there is an entirely reasonable interpretation under which Hamilton's actions are just ordinary politics. It is certainly true that Hamilton seems to have a long history of taking things too personally; although given how much he was vilified by his opponents, it's a bit tricky to estimate exactly where the line should have been. I think Madison is right that Hamilton had a tendency to think that the government should be 'administrationed' into something new; and the common opinion of him at the time that he was strong in ambition and weak in discretion is unfortunately true. I've never actually seen a good argument for Hamilton's corruption, so I'll have to defer to Sandefur on that point. I'm not sure I follow Sandefur's reasoning about the duel, which seems just to be a vague analogy. Of course, for full disclosure: it's no secret that I like Hamilton; I have no distaste for flawed heroes, and despite my rather non-Hamiltonian political tendencies, I find Hamilton more likable than most of our other flawed Founding Fathers.

On Criticisms of Narnia

I found this article at Guardian Unlimited occasionally a little puzzling. Particularly this:

Lewis, however, had a preference for what used to be called "muscular Christianity", which recommended a strong and even militant faith, and the portrayal of Christ as athletic and super-masculine. This may have been responsible for his choice of a beautiful but terrifying lion the size of a small elephant as his allegorical figure of Jesus, rather than something nearer to the traditional innocent, meek and mild Lamb of God.

Or what may have been responsible for the choice of beautiful but terrifying lion is that it's quite as traditional as the "traditional innocent, meek and mild Lamb of God." Indeed, the two go very closely together, as in this well-known passage from Revelation:

I saw in the right hand of Him Who sat on the throne a book written inside and on the back, sealed up with seven seals.

And I saw a strong angel proclaiming with a loud voice, "Who is worthy to open the book and to break its seals?"

And no one in Heaven or on the Earth or under the Earth was able to open the book or to look into it.

Then I began to weep greatly because no one was found worthy to open the book or to look into it; and one of the elders said to me, "Stop weeping; behold, the Lion that is from the Tribe of Judah, the Root of David, has overcome so as to open the book and its seven seals."

And I saw between the throne (with the four living creatures) and the elders a Lamb standing, as if slain, having seven horns and seven eyes, which are the seven Spirits of God, sent out into all the Earth.

And He came and took the book out of the right hand of Him who sat on the throne.

And notice, by the way, that the Lamb is in this passage not 'mild' but a terrible and powerful being with seven horns and seven eyes.

There are basically three major fields of criticism that come up in criticism of the Narnia books.

The charge, attributed (I hope with some exaggeration) to Pullman, that Narnia is religious propaganda is as silly as some people's condemnation of His Dark Materials as anti-Christian propaganda. I think the label 'propaganda' is very difficult to pin on any children's story. Is The Cat Who Went to Heaven Buddhist propaganda? (It's an exquisite little story, by the way. If you haven't read it, go to the children's section of your local library and look it up.) Are the works of Isaac Bashevis Singer Jewish propaganda? Is Arni's The Mahabharata: A Child's View Hindu propaganda? One might as well call The Dark Is Rising series Manichaean propaganda. It's difficult to see that there is any meaning in using the term this way. Anyone who talks in this way is somehow failing to be mature enough to be able to read children's books.

I am much more sympathetic to the other two criticisms, which pertain to race and gender.

I'm not sure, though, what is meant by the 'serious political repercussions' of a The Horse and His Boy movie. I do think people's worries about the Calormenes are a serious issue; but putting it in terms of 'political repercussions' misses the real point of the worry, which is that The Horse and His Boy, read a certain way, reads a little too much like one of those old dark continent adventure tales, and thus has to face the same sorts of questions. Plus, putting it in terms of 'political repercussions' just propagates a bad way of looking at the matter: there's always a danger that, sometimes, comes too near the top, of the Western critic advocating that (say) we treat Muslims well, but adding in support of this, or in explanation of this, some argument or statement that paints Muslims in ominous tones as people who go around taking frightful vengeance on people who stir up their wrath -- as if Muslims weren't by and large decent and reasonable people just trying to get along with their lives in a world that keeps trying to paint them in ominous tones. I hope there's no hint of that here; but I don't know what else there would be.

It is certainly true that Lewis tends to write boy stories, and is uneven in his characterization of girls; I always liked Polly, Aravis, and Lucy, but not so much Jill and Susan. I think a protest of what happened to Susan is entirely reasonable; although the problem is not, as Lurie suggests, one of bad writing. We are, after all, talking about a good portion of a lifetime, one that includes adolescence and young adulthood, so there's time and opportunity enough for Susan to change; and I'm not sure the later off-stage Susan is entirely unrepresented in the earlier Susan, despite the turn for the worse. Susan was always a little wavery and indecisive, and, despite Lurie's suggestion otherwise, it's actually the sort of failure she would find dangerous. Likewise, the problem is not unfairness, since unfairness is really not a significant criticism of point of plot -- whenever was a fictional plot fair? It could have been handled better, though; it's too easy to read in a problematic way. It should be noted, incidentally, that Lurie is speaking nonsense in saying that Susan is 'shut out of paradise forever' -- this is a massive eisegesis. We don't actually know what happens to Susan, at all. We don't even have any indication that she died with everyone else, so we don't ever hear the end of Susan's story. In fact, there have been occasional rumors -- how creidble I do not know -- that Lewis toyed with writing a story about Susan's redemption after having inherited Diggory's house, but never did it. It's difficult to know what to make of such rumors, since fans have been aching for some closure about Susan ever since the beginning. The Problem of Susan a common topic in the underground world of Narnia fan fiction (underground because C.S. Lewis Pte., the C. S. Lewis estate, has a reputation for being ruthlessly defensive of its copyrights -- cracking down hard on fan tributes of any kind has been one of the many bad mistakes of the estate, which has earned them much anger among C. S. Lewis fans).

I think it's entirely possible to have an ethical critique of fiction without falling into a sort of literary puritanism in which we go about wagging our finger at artifacts of our own flawed manner of reading. I think such an ethical critique needs to focus on ways of writing and reading. We can with great fruitfulness pinpoint weaknesses, incompletenesses, distortions etc., involved in reading a work a certain way, as well as tendencies in the work to be read a certain way, without thereby suggesting that there's something vaguely evil about people who like to read that work, particularly if they read it a different way. A well-considered critique can have the beneficial result of improving the way we read every work. We learn from the lapses as well as from the excellences, and are enriched in the learning. But it's difficult to do; the key to it is a judiciousness most of us lack.

Pentarchs and Patriarchs

Or: A trip throught Wikipedia lists (always the best part of Wikipedia), wherein I mention a lot of important people that you have never heard of, and that neither your nor I ever hear about. The traditional list of the Patriarchs of Constantinople, going back to Andrew. Wikipedia is a good source for the traditional list of the Patriarchs of Rome, going back to Peter. It also is a good source for the traditional list of the Patriarchs of Alexandria up to Chalcedon, which begins with Mark, and the continuing lists after the Miaphysite split betweem the conciliar (Chalcedonian) Patriarchs of Alexandria and the nonconciliar Coptic Popes. You should also see the traditional list for the Patriarchs of Antioch, also tracing back to Peter, and the split list after 518 between the Patriarchs of Antioch and the Syriac Patriarchs of Antioch. The final element in the Pentarchy is Jerusalem. Its traditional list traces back to James; and you can find the lists of Patriarchs of Jerusalem The current bishops in these seats are, of course: Benedict XVI (Rome), Bartholomew I (New Rome), Theodore II (Alexandria), Shenouda III (Coptic Alexandria), Ignatius IV (Antioch), Ignatius Zakka I (Syriac Antioch), and Theophilus III (Jerusalem). There are also, of course, Latin Patriarchates in the Eastern branches of the Catholic Church, which are responsible to the Pope in matters of faith and morals but are autonomous in everything else: Jerusalem (currently Michael Sabbah), Coptic Catholic Alexandria (currently Stephanos II), Syrian Catholic Antioch (currently Ignace Pierre VIII), Melkite Catholic Antioch (currently Gregory III), Maronite Antioch (currently Nasrallah Sfeir), Chaldaean Babylon (currently Emmanuel III Delly), and Armenian Catholic (currently Nerses Bedros XIX).

The Chaldaean Patriarchs of Babylon are not to be confused with the Assyrian Patriarchs of Babylon, who derive from Nestorius (but whose current Christology, laid out by Babai the Great in the sixth century, while still not the standard Orthodox picture, is closer to the Orthodox Christology than Nestorius's -- it avoids Nestorius's dualism, although it denies theopaschism, i.e., the claim that God suffered on the cross). The current Assyrian Patriarch of Babylon is Addai II; its traditional list goes back to Thomas.

Of course, I haven't discussed the Oriental Orthodoxy, except in passing. They differ from the above in tending Monophysite -- I say 'tending' because strictly speaking they are usually officially Miaphysite, which is a more vague position, and can be interpreted either as strictly Monophysite or as much closer to Chalcedon. I've already mentioned Coptic Alexandria and Syriac Antioch, which are both examples of Oriental Orthodoxy. The current Catholicos of Armenia (the traditional list of which traces back to Thaddeus and Bartholomew) is Karekin II. The largest Oriential Orthodox Church is the Ethiopian, often called the Tewahedo Church (Tewahedo='being made one', a reference to their Christology), which (of course) traditionally traces itself back as a Church, although not as a patriarchate, to Philip, and is currently headed by (depending on whom you talk to, since there's a split over it) Merkorios or Paulos. The closely related Eritrean Orthodox Church is currently led by its third Patriarch, Antonios. The Malankara Orthodox Church, in India, traditionally traces itself as a church back to Thomas, although not as a patriarchate; its present Catholicos is Thoma Didymos I. (As an autonomous church, it is not to be confused with the older Malankara Syriac Orthodox Church, which is entirely under the authority of the Syriac Orthodox Church of Antioch, and is headed by Catholicos Thomas I, and with which it is still in communion.)

Friday, December 02, 2005

Catching Up

I've been busy, and so most of the things I've been posting have been things that were already in the works in one form or another. Some catching up.

December 1st was Blog Against Racism Day; people are still trying to collate all the different participants (see milkriverblog and the trackback list at Creek Running North for a sample) -- in excess of 200, it seems, and since a few are posting belatedly, it can only increase. Naturally it will take a while to run through even a fraction of them. Amanda Marcotte's post on stereotypes at "Pandagon" seems to be a particular favorite for reflection. Strictly speaking I didn't do any blogging on the day, but I had a relevant post the day before, in which I linked to various discussions of racism in the context of modern philosophy (Hume and Kant in particular).

Speaking of which, Chris of Mixing Memory has, after a long absence returned to blogging with some posts for the occasion. Glad he's back.

I missed that "Ralph the Sacred River" had its blog-birthday on Wednesday. Congratulations on that!

I've promised a further post on the issue of miscompassion; that will be coming along in the next few days, although I don't know precisely when.

Clark has put up one of my favorite stories about a saint. It gives a slightly different perspective on the jolly old fellow.

And if you haven't done it yet, you should still stop by History Carnival XXI. I submitted a post at Houyhnhnm Land on Lady Mary Shepherd.

Hume on Geometrical Equality

One of the more interesting and overlooked passages in Hume's Treatise is the discussion of equality in geometry (1.2.4). In context, Hume is arguing against geometrical arguments for infinite divisibility; he takes a very strong stance against them:

But I go farther, and maintain, that none of these demonstrations can have sufficient weight to establish such a principle, as this of infinite divisibility; and that because with regard to such minute objects, they are not properly demonstrations, being built on ideas, which are not exact, and maxims, which are not precisely true. When geometry decides antyhing concerning the proportions of quantity, we ought not to look for the utmost precision and exactness. None of its proofs extend so far. It takes the dimensions and proportions of figures justly; but roughly, and with some liberty. Its errors are never considerable; nor wou'd it err at all, did it not aspire to such an absolute perfection. (

Despite the qualification in the last sentence, this is a strong position to take: that geometry is inexact, imprecise, and merely approximate in its conclusions is not a claim that is usually made. Part of Hume's argument for this interesting conclusion is an argument about the standard of equality in geometry.

If we were to think of geometric lines as composed of points, we could (in principle) simply identify geometric and arithmetic equality: Line A would be equal to Line B iff the number of points on Line A is equal to the number of points on Line B. Even setting aside the qualms we might have with treating points in this way, Hume notes that this would be "entirely useless"; no one actually identifies two lines as equal by counting their indivisible points.

Another argument, which Hume found in the mathematician Isaac Barrows, was to define geometric equality by appeal to congruity: Figure A is equal to Figure B iff, by placing the one on the other, every part in Figure A contacts every part in Figure B. Hume argues, however, that this is just an elaborate way of conflating arithmetic with geometric equality: ultimately, the congruity position reduces to the claim that for every point on Figure A there must be a corresponding point on Figure B.

Hume's own view is that "the only useful notion of equality...is deriv'd from the whole united appearance and the comparison of particular objects" ( In effect, the only standard of equality in geometry is the one you use when you eyeball it.

In effect. When we look at the details, it ends up being more complicated. The general appearance can be put into doubt. When it is, "we frequently correct our first opinion by a review and reflection"; this correction may be corrected with another correction, and so forth. We use instruments of measurement that are of varying degrees of precision. At different times we exercise more or less care in the determination. Our idea of equality, therefore, is not exact. On the contrary: we form "a mix'd notion of equality deriv'd both from the looser and stricter methods of comparison" (

However, we don't stick with this. Having become accustomed to making these judgments and corrections, we get into the habit of doing so, and led on by a sort of mental momentum, we suppose an exact standard of equality. Knowing that there are bodies more minute than those that appear to the senses, we falsely suppose that there are things infinitely more minute than those that appear to the senses; and in light of that we recognize that we don't have any instrument or means of measurement that will secure us from error and uncertainty in such a context: the difference of a single mathematical point could be crucial. Because of this we suppose the corrections in our "mix'd notion" of equality to converge on the existence of a perfect but "plainly imaginary" standard of equality. What makes this "plainly imaginary," Hume thinks, is that our idea of equality is just the "mix'd notion," i.e., the appearance plus the corrections used by applying a common measure, juxtaposition, or instrument. The supposition that there is a standard of equality far beyond what we can actually measure is "a mere fiction of the mind." It's a natural fiction, since it is a result of this mental impulse or momentum whereby the mind keeps going even when it has ceased to be in touch with the facts. It is, however, a fiction.

Hume notes that this point, if true, is perfectly general: it applies not only to geometrical equality, but to equality in any sort of measurement: whether in time, or physics, or music, or art (e.g., hue). In all such cases we are led by the impulse of the mind to something far beyond the judgments of the senses. Our real notion of equality is "loose and uncertain": the exact standard of equality is more than we could possible know to be the case.

The problem this poses for the geometer is this. Either (a) equality in geometry is imprecise; or (b) it is precise. If (b), then geometrical equality is useless in practice (we can never know that a case exists) and depends on the controversial notion that lines are really and actually composed of infinitely divisible points, which Hume (and most of the geometers he would have known) thinks simply absurd. The standard they actually use, Hume thinks, is the imprecise one; but if we accept this view, many of the inferences made b geometers are ill-founded, since they assume a precision far beyond what the imagination and senses can yield. Thus, says, Hume, this shows that a geometrical demonstration of the infinite divisibility of a line is impossible.

One of the reasons I find this an interesting discussion is that in 1.4.2 he appeals to the same mechanism by which he explains how we come up with an exact standard of equality to explain how we come up with an idea of body continuing independently of our perceiving it. I presented a paper before the Hume Society a few years ago on this topic; my views have changed a bit, but I still think it's a key issue in understanding what Hume's theory of the external world really is.

History Carnival XXI

The Twenty-first History Carnival is up at CLEWS: The Historical Crime Blog. Enjoy!

Invisible Ideal Reasons

An interesting passage from Aquinas's Commentary on Hebrews(PDF) (par. 565). Aquinas is commenting on Hebrews 11:3 ("By faith we understand that the world was created by the word of God, so that what is seen was made out of things which do not appear").

He continues, that from invisible things visible things might be made. But because the common notion among the ancients was that the soul was produced from nothing (2 Physics), when they saw a new work, they said that it was made from invisible things. Hence, they either supposed that everything was in everything else, as Empedocles and Anaxagoras, of whom we shall say nothing at present; or thought that forms were in hiding, as Anaxagoras. Still others supposed that they were formed from ideas, as Plato; and others from a mind, as Avicenna. Hence, according to all these philosophers, visible things were made from invisible ideal reasons. But we say, according to the aforesaid manner, that visible things were produced from invisible ideal reasons in the Word of God, by Whom all things were made. These reasons, even thought they are the same reality, differ in aspect by diverse relations connoted in respect to the creature. Hence, man was created by one reason, and a horse by another reason, as Augustine says in the Book of 83 Questions. Thus, therefore, the world was framed by the word of God, that from invisible ideal reasons in the World of God, visible things, i.e., every creature, might be made.