A Poem Draft

Vine

You ask, and I wonder,
but I know my mind;
here in the garden the columbine
spirals and curls, begging for rain,
and your words like thunder
echo from clouds;
I know your pain, but I am proud,
and here in the garden the rosy thorn
mocks me with a fitting scorn.
You ask, but the iris will pay you no mind
as the wind starts to hum
through the harp and the vine.

Out to the Horizon

This short story draft is a revision of one that was posted here a few years ago.

She stood on the beach, looking out to the horizon, her hair flowing back as if blown by the wind; but she was as still as stone. I wept at her feet.

The sand was cold, the sea was cold, the wind was cold. It rushed past us into the forest of palms some distance from the strand. I had met her in that forest one day as she went to bathe in the stream. As soon as I saw her smile I knew I loved her; and she loved me as swiftly.

She was a priestess of our people, newly consecrated. She served in the village beside the great rocks just south of where the jungle grows dense, where the pineapples, springing up like noxious weeds, render the forest impassable. Once a month she would walk to the base of the Unforgiving Mountain to offer a sacrifice of grains and flowers. Once, long ago, the mountain had destroyed almost everything for miles around; even now the mountain-gods growl and shake the earth to remind us all of their power. I do not know why the gods act this way; we need no reminder beyond the Mountain itself. Wherever you are on this island, whether it be the beach or the forest or the village, you can see the Mountain if you can see the sky. Its unimpassioned face glowers at everything that stands or moves.

A priestess of the Unforgiving Mountain is sworn to take no lovers. The Mountain is jealous, they say; it demands total devotion. She had given it that before she met me. Afer we met, such oaths and devotions seemed a small thing.

We would sneak away some mornings to sit on the seashore. She loved the waves, and named them as they came, treating each one as if it came bearing the treasures of the world. I loved her love of them. We would stare at them for long hours, looking out to their apparent source in the cloudy horizon. Sometimes we would discuss our plans and dreams. More often we would simply sit together in silence and feel how near the other was.

Not far from the beach, at the edge of the forest, I had long ago built a hut. It was not long until she began visiting me there at night, stealing away from the watchful vigils of the elder priestesses. I cannot clearly recall how long we did this. We should have known, and, indeed, we did know, that too much self-indulgence in this would awaken suspicions. We hardly cared. We could not stay apart.

One night, a full moon night, I lay awake in the darkness, trying to think of some plan to take her away, away from the forest, away from the village, away from the grim coldness of the Unforgiving Mountain. Outside there was no sound but the waves; inside there were only the sounds of her sleep as she turned into me and softly sighed upon my shoulder.

My thoughts were broken by a rumbling: the Mountain was restless. I rose and paced the room. Back and forth I went, trying to recollect my thoughts. The door burst open violently and I saw, in silhouette against the brightness of the moon, the figure of one of the elder priestesses. She saw my beloved and hissed. The mountain continued to rumble in the background. Pointing a finger at us she spoke a curse, and my beloved woke with a small scream. The mountain rumbled louder, then suddenly stopped; just as suddenly the priestess at the door was gone.

After a few more shudders of the earth, the Unforgiving Mountain subsided again. It had happened quickly but, as when the lightning strikes the tree, marring it forever, the damage had been done.

She could not return to the village; that would be death. Nor could we remain where we were. All those hours in which we had dreamed up plans of escape flashed through my mind, and in the harsh atmosphere of recent events, all those plans dissipated like clouds. They were nothing but the idle dreams of prisoners in an inescapable prison. Half the island was impenetrable jungle, where spiny plants grew so thickly that they could shred the flesh of the unwary. All of it was surrounded by vast, rolling hills of sea-surf; over everything, a tireless sentinel, the Unforgiving Mountain held vigil. Wherever one looked the gods of the Mountain held sway; wherever we could go they could pursue us with their vengeance, unresting, unrelenting, and no remission of sin or guilt was possible to us. We both knew this, and with knowledge came the sapping of hope.

I tried to set these thoughts aside. Whatever happened, I knew I must do whatever was needed to distract her from despair, to make some space, however small and slight, for a genuine hope. Perhaps also, still not understanding the brutality of the mountain-gods, I hoped, in giving her hope, to find some hope myself.

I seized her hand, holding it to my heart, whispering encouragements in her ear, sealing each encouragement with a small kiss. It was all in vain, for as I held her hand the gods of the Unforgiving Mountain began to take their most terrible vengeance. The hand I held grew cold; her body grew still. I pulled away and froze in fear. From head to foot where my beloved had been was solid stone, as if some demonic hand had perfectly carved her form into a stone from the Mountain.

The moment passed, and her flesh quickened again, but we both knew it would not last. She burst into tears; I pulled her close to me, fighting tears myself. Every so often she would become stone again, and the time she spent as stone grew longer and longer. In desperation we tried to do what seemed our only option: we held each other closely, in order to spend the last moments awake, catching every heartbeat of the other. But the mountain-gods were not so kind. As we lay trembling in fear they sent forth an atmosphere of heat and humidity so great that it dragged us both to sleep. We fought, but to no avail. The gods having determined that we would lose even our last moments together, we fell asleep.

When I awoke, she was no longer there. With a cry of trepidation I rushed out of the hut, and saw, with a terrible chill up and down my spine, what I had most feared. I flew forward and fell at her feet, which were washed by the careless waves. She stood looking out to the sea, her hair flowing back as if blown by the wind. It was not the wind that blew it, however, for she was stone, through and through, and with the coldness of stone she stood unacknowledging as I wept. So she stood, and so she stands forever, cold and immutable, looking out to the horizon.

One wonders...

...what goes through students' heads. I'm grading logic quizzes now, as I said, and one of the questions is, "Name two logicians whose work we've discussed." I had a student who put down as one of the logicians we'd studied --

Barbara Syllogism.

The work of Ms. Syllogism does indeed seem to be popular; we encounter her work everywhere.

I also had a student who, when asked to explain the difference between a proposition that is categorical and a proposition that is not categorical, wrote down that the latter comes from a hooker. I'm pretty sure that one was a deliberate joke. I'm not at all sure that the Barbara one was.

Existence and Causal Explanation

As I mentioned before, Jason Zarri has an interesting post entitled, How Free is God's Will? in which he makes the argument that God's existence can only be an explanation if God's will is not completely free. In effect, the argument goes like this:

(1a) Suppose that God's existence is compatible with possible worlds which are disordered and hostile to life.
(1b) Then the existence of God cannot explain the order and life-friendliness of the universe because those characteristics are no more likely if God exists than if He doesn’t.
(2a) Suppose that God's existence is incompatible with possible worlds which are disordered and hostile to life.
(2b) Then there are significant constraints on what God can will, for then God cannot actualize just any possible world.

From which it follows that either God is completely free, in which case God's existence does not explain order and life-friendliness in the universe, or God's existence does explain order and life-friendliness in the universe, in which case God is not completely free.

I think the argument is falling victim to an ambiguity about what is meant when we say, "Y is explained by X's existence." On the one hand, we could mean that Y is explained by the bare fact of X's existence: from the proposition "X exists" we can directly infer (either defeasibly or indefeasibly) "Y exists (or occurs)." However, if we think about how we talk about causal explanation, we virtually never talk about causal explanations in such a way as to mean this. If I say, "The trash is gone because there is a trash collector," I am not saying that from "This person that is the trash collector exists" I can infer "The trash is gone." I am saying instead that "The trash is gone" can be explained given that there is a trash collector who takes away the trash; the one explains the other because from "The trash is gone" I can reasonably conclude "The trash collector did the sort of thing that makes it to be the case that the trash be gone." What explains here is not mere fact of existence but the fact that the existent thing is engaging in a particular kind of action; in other words, what explains is not simply that something exists but that it exists in a particular causal role.

Likewise here. When someone says, "The existence of order in the universe can be explained by God's existence," they aren't saying that you can infer anything from God's existence, but that you can explain the explanandum if there is something that exists in the right kind of explaining role, e.g., God. Thus the advocate of the teleological argument is saying that the order and life-friendliness of the universe can be explained if something, namely God, does a particular sort of thing, which requires, of course, that God exist, not that the order and life-friendliness of the universe can be explained simply by an appeal to God's existence.

Jason is exactly right that if the advocate of the teleological argument tries to explain the order and life-friendliness of the universe purely in terms of God's existence, and not in terms of God's being the only sort of thing that can plausibly fill the sort of causal role that is required for explanation, that he is committed to saying that God is not completely free. In fact, the only way that will work is if the effects of order and life-friendliness follow necessarily from the mere fact of God's existence; only when we can assume that effects are related to their causes deterministically can we infer (indefeasibly) the effects from the mere existence of their causes. This is an entirely general point. Suppose a detective is trying to solve a case and suddenly realizes that the facts can only be explained if Moriarty exists. The only way he can take the mere existence of Moriarty to explain the facts is if he thinks that the facts follow merely from Moriarty's existence, without any free choices by Moriarty intervening. And things remain much the same if we are talking about defeasible inferences: for the mere existence of Moriarty to explain the facts, the mere existence of Moriarty has to rule out possibilities relevant to the facts, and thus the very existence of Moriarty implies limits on Moriarty's freedom.

But usually we would expect the detective to mean that the facts can only be explained if a certain causal role is filled (if certain things have been done) and that Moriarty is the only plausible candidate for fulfilling that role (and thus must exist in order to fufill it). Thus, while Jason is right that God cannot be completely free if effects like 'order' and 'life-friendliness' follow from God's existence with either probability or certainty, nonetheless this does not generalize, because most causal explanations are not explanations by appeals to mere existence but by appeals to causal roles that imply (defeasibly or indefeasibly) the explananda if something exists to serve in that role. When people say that God's existence is necessary to explain certain facts, they are saying that the facts can only obtain if certain things are done that only God can do; since the facts obtain, those things must be done, and thus God must do them; and in order to do them God must exist. Thus the explananda are not explained in terms of the possibilities available to their cause, but entirely in terms of the necessary conditions of the explananda themselves. There might be no possible world, even a hostile world, incompatible with God's existence; what matters for the explanation, however, is that the existence of an orderly and life-friendly world is incompatible with the non-fulfillment of a causal role only God can fulfill. That's a rather different sort of incompatibility. And mutatis mutandis if we weaken the connections here so that we are dealing with probabilities rather than necessities.

Links for Thinking, Notes for Noting

* Philosophers' Carnival CV is up at "Kenny Pearce". I found especially interesting Jason Zarri's post on divine freedom and teleological arguments (which, however, I think trades on an ambiguity; perhaps I'll write a post on it at some point) and Richard Chappell's post on hypothetical imperatives.

* John Wilkins has a very nice post on thermodynamics and the evolution of replicators. The post is the first in a series.

* Incidentally, I've just finished reading his book, Species: A History of the Idea, which is quite good. More books should be written like this one: clearly it is one that sums up in a clear way an immense amount of scholarly time and effort. Too much Great Chain of Being, though; much as I like Lovejoy, if the phrase means anything, it identifies positions that clearly combine a law of plenitude with a law of continuity, and such positions are relatively rare -- plenitude requires a very robust rationalism, which is why you only find clear statements of it in very rationalistic systems. When people are talking about scala naturae or using the metaphor of a chain, they are usually doing no more than indicating a general sense of hierarchy or order. We see this especially clearly in someone like Berkeley, whose Siris is based entirely on the metaphor of the chain (hence the title of the work, which is an anglicization of sereis, the Greek word for chain, and based on a passage in the Iliad involving a chain linked to Zeus's throne), but who has no commitment either to plenitude or to continuity. Likewise, medieval 'chains' usually just mean that reason is superior to sense and intellect to reason, which is a pretty minimal sense. Hierarchical order and continuity are common enough; plenitude turns out to be very difficult to find, and is usually explicitly rejected as inconsistent with the distinction between creature and Creator. (Lovejoy argued for it in Aquinas, but it is clear enough that this was an error, as Pegis argued.) Thus I am very skeptical of the view that Albertus Magnus, for instance, reflects any sort of "Great Chain consensus of the period" (p. 43), in part because there is no such consensus -- at least, what 'Great Chain' here would have to mean in order to be applicable is a weaker and different position than what is elsewhere called 'Great Chain' -- they should not be lumped under the same term. But that's a small thing, and perhaps a controvertible one; I recommend the book highly and, as I said, philosophy would be healthier if more books were like it.

* Since I'm talking about books by bloggers I've recently read, I've also recently finished David Corfield's The Philosophy of Real Mathematics,
which I also recommend highly. I liked the early parts of the book best; they discuss the roles of conjecture, induction, and analogy in actual mathematical reasoning. Since I am very anti-Bayesian in epistemological matters I was not expecting to like the Bayesian middle part of the book, but I was pleasantly proven wrong. And the latter parts of the book were good, too; especially the chapter on higher-dimensional algebra, which I am going to have to read more closely. I had been trying to get a hold of Corfield's book for almost a year now, but it was always checked out of the library -- which I suppose is a good thing. But having a little more month in my book budget this room, I went ahead and bought a copy, and am glad I did.

* David has an interesting recent article (PDF, can load slowly) in the Newsletter of the European Mathematical Society on nominalism versus realism in mathematics

* Along the lines of LOLCat, there's a common game of taking various pictures and captioning them with a claim plus "Your argument is invalid." My favorite is: Hello, my name is Inigo Montoya. Your argument is invalid. Prepare to die. I should put this at the top of my next logic quiz; I'm grading logic quizzes right now, and it sums up the mood in which I sometimes find myself.

* Gondor and Byzantium.

* This website, which week by week explains the joke in the xkcd comic, is hilariously funny. Much funnier than most xkcd comics, in fact.

* Lucas and Sheeran, Asperger's Syndrome and the Eccentricity and Genius of Jeremy Bentham (PDF). The authors consider whether Bentham can be seen as having a form of the syndrome. Bentham had a notorious inability to sympathize with others; almost everyone who knew him mentions it at some point or another.

* Jon Haidt has argued that moral reasoning is built on five basic conceptual distinctions (loyalty/disloyalty, deference/nondeference, purity/impurity, fairness/unfairness, harm/care). He's adopted an interesting idea for testing this: hold a contest for the best ideas for additional distinctions or for reconceiving how the original five relate to each other. A very nice idea.

* Barro, McCleary, McQuoid, Economics of Saint-Making (A Preliminary Investigation) (PDF). A problem with the paper is that canonization isn't saint-making or sanctification but entry of a person into a canonical liturgical calendar -- usually the universal or catholic calendar of Rome.

* Obviously French TV producers have never taken basic psychology. (ht) But it is very difficult to imagine that the people involved weren't just thinking, "It's a TV show, so there's obviously some trick."

* An interesting post on St. Patrick and the snakes at "The Wild Hunt", from a pagan perspective.

A Poem Re-Draft and a New Poem Draft

The Isles

Your reason is a snowdrift-reason,
icy in and out of season,
cold and sharded frost with flakes
in which no grace or fervor wakes --
but what of reason's South Sea isles,
flush and warm with native smiles?
Golden-hearted breeze-winds sway
to charge the night and warm the day
as, by the currents warm and clear,
the joys go dancing without fear
and, on the beach-sand wet and fair,
a sunrise gilds the scented air.

Stone

Farther shores I know than this,
visions vivid like the morrow;
holy heaven, everlightened,
sends a mercy, master's sorrow.
I wish anew on falling stars;
those leaping lights in dance display
a dream of powers pouring down
like righteous ruin of the day.
Rue no more the pastward lesson,
harbor here in love alone;
that castle-keep and quiet eyrie
stands blessed beside a saving stone.

Shepherd, Locke, and Fricandeau

An interesting anecdote about Lady Mary Shepherd, in a letter (November 19, 1829) from Joseph Jekyll to Lady Gertrude Sloane Stanley:

Joseph dined yesterday with that crazy metaphysician Lady Mary Sheppard, who swore to me that she read and mastered Mr. Locke's profound treatise at eight years old. The best of it is that Joseph will not admit that she is insane, as she gives him fricandeau.

About Joseph Jekyll I have been able to find very little. He was a barrister who went up to Parliament; he was one of several candidates preferred by Lord Lansdowne. Jeremy Bentham, the utilitarian, was so furious at not having been chosen that he wrote Lansdowne a letter consisting of an extended rant seventy pages long. In the course of it, he says that Jekyll in Parliament was a burlesque on the very idea of Parliament. Be that as it may, Jekyll seems to have acquitted himself well enough as a member of the Whig party; he was in Parliament for over three decades during which, he says in one of his letters, "I gave hopeless votes for Reform, Catholics, Dissenters, and black men," but the 'hopeless' part came to an end with the government of Earl Grey, which passed the Reform Act of 1832 and abolished slavery throughout the Empire. The Joseph mentioned in the letter is his son; the younger Jekyll was a friend of Washington Irving. In November of 1829 Lady Mary would have been approaching sixty years old. Fricandeau is a way of cooking veal by larding and braising it; I've never had it, but it is supposed to be quite the delicacy: famously it is so tender that it is supposed to be carved with a spoon, never a knife.

In any case, the interesting comment is his claim that Lady Mary "swore...that she read and mastered Mr. Locke's profound treatise at eight years old."

UPDATE: Apparently Joseph Jekyll wrote a biographical essay on Ignatius Sancho

Newton Against the Trinity (Re-post)

This is a somewhat revised version of a post that was first posted in 2006.

Isaac Newton's place in the history of science is generally known. What it is less known is his place in the history of the doctrine of the Trinity. Newton devoted considerably attention to the Trinity, which (as an Arian) he opposed, even using the General Scholium to the Principia Mathematica as a forum to take a subtle swipe or two at the doctrine. I want to look briefly at this attack on the Trinity, which is actually quite clever; but a bit of background might be useful at first.

In one of Newton's manuscripts (Yahuda Ms. 1.4) we find a discussion of the Arian controversy in the context of an exegesis of a vision in the book of Revelation, with which he had a bit of a fascination. On Newton's view, the primary purpose of Revelation was "to describe & obviate the great Apostacy," which "was to begin by corrupting the truth about the relation of the Son to the Father in putting them equal." For this reason, on Newton's view, the vision in Revelation 5, in which a figure is seen upon a throne and gives to the Lamb a scroll, is not a mere set of images but a doctrinal system put in imagistic form. In particular, it is a prophecy showing the true relation between Father and Son: "the Son's subordination, & that by an essentiall character, his having the knowledge of futurities only so far as the father communicates it to him." The scroll is originally sealed; Newton points to this as evidence that the Son's receiving of knowledge from the Father is not eternal. This knowledge "was not given to the Lamb at his first generation but since his resurrection; he meriting it by his obedience to death." The obvious orthodox response to this, of course, would be to say that Newton is confusing the Word in Himself with the Word Incarnate. Newton, however, is no fool, and anticipates the response, which he thinks the vision also guards against "by a threefold insinuation."

First, the vision begins with the one on the throne holding the book in his hand, and is closely followed by the declaration, in the entire company of heaven, that only the Lamb is worthy of it. Thus the vision shows God and the Lamb as the most worthy in this assembly; and the Lamb is shown originally without the book. On Newton's view, this suggests that the distinction between the Word as God and the Word as Incarnate is sophistical: if the Word had known these matters beforehand, the Lamb would have been as much in possession of the book as the one on the throne. This argument depends crucially on his assumption that the scroll is some sort of divine knowledge. The usual interpretation, developed in light of imagery used elsewhere in the book of Revelation, is that the scroll has to do not with knowledge but with salvation and judgment. Newton's interpretation relates the vision to the claim in the Gospels that only the Father, and not even the Son, knows the day and hour of judgment.

Second, Newton notes that the Lamb in this vision is the object of worship, both alone and together with the one on the throne. This might at first seem to cause a problem for Newton's own view, but he has a clever response, on which will be relevant to his jab at Trinitarianism in the General Scholium:

Now this worship was given to the Lamb as he was a God without all doubt, Divinity & worship being relative terms, & yet it was given to him as he was worthy to take & open the Book for at the falling down of the four Beasts & 24 Elders before him to worship him, the very act of their worship was to celebrate him for his worthines to take & open the book. The Lamb therefore as he was a God was worshipped for his worthines to take & open the book & therefore took & opened the Book as he was the object of worship, that is a God. But to make all this plainer you may compare it with Philip: 2.9 where tis expresly said, that for his obedience to death God gave him a name above every name that at the name of Iesus every knee should bow &c. that is that all the creation should worship him which is as much as to say that he should be ισα θεω as a God over the creation: for Deity & worship are relative terms & infer one another.

In other words: 'God' is not an absolute term; it doesn't identify anything ontological. The reason we call something a 'God' has nothing to do with what it is in itself. Rather, we call a thing 'God' if it has the sort of dominion or authority that calls for worship. Thus Newton has no problem with calling the Lamb 'God', because the Lamb is given divine authority (which he previously did not have) by the Supreme God (the one on the throne).

Third, Newton identifies a difference in how God and the Lamb are treated by the vision as objects of worship. (1) The Lamb does not sit on the Throne but stands by it; whereas the one on the throne (and who is therefore King over all who are not on the throne, including the Lamb) represents God. (2) In Newton's view, the doxologies that follow the investiture of the Lamb show a gradation, with God being given a "higher degree of worship" than the Lamb, a pattern that he thinks is repeated in Revelation 7.

Thus Revelation 5 on Newton's interpretation is:

a system of the Christian religion, showing the relation of the ffather & Son, & how they are to be worshipped in a general Assembly of the Church & of the whole creation. The ffather the supreme King upon the Throne, the fountain of prescience & of all perfections. The Lamb the next in dignity, the only being worthy to receive full communications at the hand of the ffather. No Holy Ghost, no Angels, no Saints worshipped here: none worshipped but God & the Lamb, & these worshipped by all the rest. None but God upon the Throne worshipped with the supreme worship; none with any other degree of worship but the Lamb; & he worshipped not on the account of what he had by nature, but as he was slain, as he became thereby worthy to be exalted & indowed with perfections by the father. This was the religion to be corrupted by the Apostacy. This therefore was very pertinently shaddowed out in the exordium to the Prophesy of that Apostacy.

This is Newton's Arianism in a nutshell; somewhat strained but quite striking, and much more creative and original than most forms of subordinationism.

On to the Principia. In the General Scholium, which was added to the Mathematical Principles in 1713, after having stated that a system as beautiful as the solar system must be "under the dominion of One," goes on to consider the nature of this being:

This Being governs all things, not as the soul of the world, but as Lord over all: And on account of his dominion he is wont to be called Lord God Pantokrator, or Universal Ruler. For God is a relative word, and has a respect to servants; and Deity is the dominion of God, not over his own body, as those imagine who fancy God to be the soul of the world, but over servants. The supreme God is a Being eternal, infinite, absolutely perfect; but a being, however perfect, without dominion, cannot be said to be Lord God; for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords; but we do not say, my Eternal, your Eternal, the Eternal of Israel, the Eternal of Gods; we do not say, my Infinite, or my Perfect: These are titles which have no respect to servants. The word God usually a signifies Lord; but every lord is not a God. It is the dominion of a spiritual being which constitutes a God; a true, supreme, or imaginary dominion makes a true, supreme, or imaginary God.

It can be seen easily enough that this is the same argument that we saw above. There it was used to interpret the prophecy of Revelation in a non-Trinitarian way. Notice the claim that "a being, however perfect, without dominion, cannot be said to be Lord God". (As we saw above, Newton interprets claims that the Son was given dominion quite strictly with regard to the person of the Son.) Notice also the distinction between 'true', 'supreme', and 'imaginary' Gods. (As we saw above, according to this distinction the Word is a true God, but not the Supreme God.) By relativizing the term 'God' in this way, Newton can break up the apparent unity that seems to be attributed to Father and Son in Scripture. Of course, by relativizing the term 'God' in this way, Newton seems to be committing himself to polytheism. He does, however, make some effort to alleviate this by pointing out occasional uses in Hebrew and the like where the relevant term for 'God' is applied to people who aren't God, which is certainly fair enough. But Newton's Arianism does still require that there be many gods.