Whewell and Found Poetry

Found poetry, of course, is language that was not intended to be poetry but nonetheless bears the marks of it. William Whewell, whom I talk about quite a bit here, is actually the source of one of the most famous examples of it. In his 1819 work An Elementary Treatise of Mechanics, he wrote the following sentence (on p. 44, in the middle of a discussion of the equilibrium of forces on a point): "Hence no force however great can stretch a cord however fine into an horizontal line which is accurately straight: there will always be a bending downwards." Adam Sedgwick, the famous geologist, with a sharp eye recognized what happens if you rearrange it, like this:

No force however great
can stretch a cord however fine
into an horizontal line
which is accurately straight.

Apparently he quoted it when giving a speech at a dinner. I don't know what Whewell's immediate reaction was. The sentence doesn't appear in later editions, but he reworked the whole chapter in which it was found, so that perhaps had nothing to do with the sentence itself. However, if Whewell was embarrassed by it, it was too late. John Radford Young's The Elements of Mechanics (1834) quotes it in a similar discussion; it was given out to the public in magazines like Notes and Queries and Van Nostrand's Eclectic Engineering Magazine; everyone talking about involuntary versification from then on out has used it as an example; and, to take the cake, the Church of Christ, Scientist will be reading it for all time, because Mary Baker Eddy quotes it in Science and Health (attributing it to a "humorous poet" and using it as a metaphor for the relation between matter and spirit).* Whewell wrote serious poetry -- he has several volumes of it, including translations of German poetry, at which he was actually quite good -- but the poem people most associate with him is this one. People are tickled at the idea of a dignified philosopher, discussing a problem in physics, suddenly bursting out, quite by accident, in doggerel verse.

* ADDED LATER: Actually I find that I need to qualify this. Eddy did quote Whewell in Science and Health (Chapter 10), but the book went through many revisions between the first edition in 1875 and Eddy's death in 1910, and the lines don't seem to have lasted past the edition of 1889. But the metaphor, which originally was based on Whewell's sentence, still remains.

Newton's First and Second

As we usually learn it, Newton's second law of motion is:

F=ma

If we try to interpret Newton's first law of motion in terms of algebraic equations, it's very natural to take it as simply describing the case where the acceleration, and thus the resultant force, is zero. The first law then becomes a special case of the second law; and you will find that many physics textbooks state this.

This is quite right and reasonable if we mean by Newton's first and second laws what most physics textbooks mean. But it's worth noting that if we take the laws as actually stated in the Principia, this conclusion is impossible: the first law can't be a special case of the second law, if we take them in Newton's own formulation. Newton's own second law, of course, is not the equation F=ma.

It is easy enough to prove, however, that if we use the right combination of units, the first law, the second law, and the definition of quantity of motion (definition II), then F=ma for cases where mass is constant. To do it you use the method of construction The first law, as Newton states it, is:

Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

The second law is:

The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

(1) Posit an alteration of motion.
(2) Use Law I to conclude that there is a force impressed upon the object whose motion is altered.
(3) Since Law II tells you how the change of motion is related to this impressed force, you can use Law II along with the definition of quantity of motion (Definition II) to infer F=ma. So F=ma follows from the second law plus some basic assumptions.

Definition II tells us that quantity of motion is the measure of motion from velocity and quantity of matter (mass). Therefore suppose we start at time t_i with a body of mass m_i whose motion is measured at a velocity v_i. And suppose it changes, so that at t_f we have m_f at v_f. Then (m_fv_f - m_iv_i)/(t_i-t_f) is our change of motion for those times. According to Law I, there is a force F for this; according to Law II, the change of motion is proportional to F. Let us assume that mass doesn't arbitrarily (or even non-arbitrarily) change: m_f=m_i, so both can just be called m, and m can be factored out to get the claim that m(v_f-v_i)/(t_f-t_i) is proportional to F. That's mass times change of velocity over change of time; change of velocity over change of time is acceleration, which gives ma, which is proportional to F. That should look familiar.

Newton's first law can't be a special case of his second because they aren't in the same category. What Law I in effect does is tell us that an alteration of motion requires a particular kind of cause, namely, an impressed force, or a combination of impressed forces; and (depending on how it is read) it tells us that we do not need to look for such a cause unless the motion is altered. Law II extends this by telling us how, precisely, the alteration of motion is related to the impressed force causing it, assuming that there is both an alteration of motion and an impressed force. One of Newton's major projects in the Principia is to develop a method for properly accounting for the difference between true and apparent motions and the causes underlying that difference; he needs Law I to do this properly. But if we interpret them in this light, Law I is not a special case of Law II; it simply tells us when a certain sort of cause exists, while Law II tells us how the effect is related to that cause when it does exist. These are two completely distinct things, and you have to use both of them to get the usual equations. If we took Law I simply to say that when force is zero, acceleration is zero, it would be a special case of F=ma; but Law I as Newton formulates it doesn't say that. It tells us when we must appeal to forces and when we don't need to do so. We need to know this before equations about forces are even possible. This is something I think even physicists sometimes forget: equations are never fundamental. We don't start with equations; we start with rules of inference and means of measurement, then use those to get equations.

It's interesting in this light to look at William Whewell's interpretation of Newton's laws of motion, because Whewell is very sensitive to the fact that we start with rules of inference. Whewell argues in his Philosophy of the Inductive Sciences and in his 1834 essay, "On the Nature and Truth of the Laws of Motion," that the laws of motions are actually general causal principles to which we add certain experimental facts to obtain more restricted causal principles suitable for discussing physical motion. Thus Newton's First Law is, on his view, nothing other than the claim Every change is produced by a cause, given that we have experimentally ruled out certain things as causes for motion (time is the major one that needs to be ruled out; but location, which Whewell considers but takes to be ruled out by the fact that we are considering no external forces, and the object's own mass, which Whewell does not, also need to be ruled out). That is, Law I is just "Velocity does not change without a cause" plus "The time for which a body has already been in motion is not a cause of change of velocity." With the specific causal inferences provided by Newton's three laws, we can then produce the whole of Newtonian dynamics (add rules governing how we reason about equilibrium and you have statics as well).

In any case, the case of Newton's laws of motion shows one way in which science changes by drifting: because of the usefulness of F=ma, over time it has come to be treated as indistinguishable from Law II, even though they are logically distinct.

Modality and the Third Way III

Perhaps the way to think of the modality in the Third Way is to think of it not as 'able' or 'possible' but as 'can'. What I mean is this: we can ask of a given thing, given what we know about its duration, "Can it have come to be and can it come to fail to be?" I will only focus on the "Can it have come to be?" (i.e., can it have been generated?) since the Aristotelian position is that anything that can come to be can come to fail to be, i.e., anything generable is corruptible. Also, it will have to be kept in mind that when I say, "come to be" I mean "come to be in the sense that is in view in Aristotle's account of generation". Then we have the following cases:

(1) Something that always exists.
Can it have come to be? No: Since it has always been, there is no point at which it could come to be (be generated). This is necessity in the relevant sense: it cannot be generated or corrupted given that it always is.

(2) Something that never exists.
Can it have come to be? No: Since it never existed, there is no point at which it could come to be (be generated). This is impossibility in the relevant sense: it cannot be generated or corrupted given that it never is.

(3) Something that exists but does not always eixst.
Can it have come to be? Yes: It was not, then it was, there was a point when it could come to be (be generated). It is possible-to-be-and-not-to-be.

Then the basic line of thought in the Third Way would be:

(1) Some things can have come to be (be generated).
: We know this because there are things that came to be.

(2) What can have come to be, at some point was not.
: That is, things that can have come to be cannot always have existed.
: Because if they always existed, there was never a point at which they could come to be.

(3) If the whole world (i.e., everything, taken collectively) can have come to be, at some point nothing existed.
: From (2)

(4) What does not exist can only exist if it is caused by something that exists.

(5) If the whole world (taken all together) can have come to be, nothing exists now.
: From (3) and (4)

(6) Something exists now.
: Look around you.

(7) It is not the case that the whole world (taken all together) can have come to be.
: From (3), (5), (6).

(8) Something or other must have always been.
: Or, to be more precise, something or other exists that has not been generated (=something ingenerable exists).

From this point, of course, we have an ordinary causal argument, on the principle that something that has always been could have always been either because its own nature is such that if it exists it must always be, or because it was caused always to exist by something that has always been.

Incidentally, you'll notice that I keep taking "all beings" and "everything" collectively to mean "the whole world". In this context, I think that is the most natural interpretation: the roots of the Third Way are in Aristotle's De Caelo, and Aquinas very clearly (and plausibly) reads De Caelo as a work of natural philosophy discussing the universe as a whole. Aquinas identifies three subjects of the De Caelo:

(1) the entire corporeal universe, considered as prior to its parts;
(2) simple bodies, considered as prior to mixed bodies;
(3) the first simple body (i.e., the heavens), considered as prior to other simple bodies

If we were to read the first part of the Third Way with purely Aristotelian eyes, it looks like an argument for heavenly body; that is, the part of Aristotelian cosmology it looks most like is Aristotle's argument that the heavenly body is neither generable nor corruptible. Aristotle, as Aquinas interprets him, holds that every form has a power to exist: and everything exists for the extent of time this power to exist covers. The heavenly body, having the most perfect corporeal form, can have no privation of form (it is only capable of privation, and therefore change, of place), and thus always is. Aquinas, of course, doesn't think the heavens have actually existed always; but, as he says, the Catholic view is not that the heavens were generated in the proper Aristotelian sense but that they were caused to exist by the first principle at some point in time. On Aquinas's view, the ingenerable heavens were caused to exist; 'ingenerability' like 'generability' in this context presupposes existence. Given that the heavens exist they cannot have been generated. But although there is no cause of their coming to exist, there still can be a cause of their existence.

However, you will notice a conspicuous lack of any of this in the actual Third Way: the heavens or heavenly body finds no mention at all. This fits with a noticeable pattern throughout the Five Ways: all of them take Aristotelian principles but treat them in a more generalized way than Aristotle himself does. This may have something to do with the fact that they are summaries; it makes sense to put them in the more general form, to avoid potential disputes over details that won't change the main point. In the Third Way it's very likely that Aquinas doesn't want to focus on the heavens alone: another kind of ingenerable is the incorporeal ingenerable (separate substances -- angels, planetary intelligences), and there's no good reason to leave them out in this context. Some have suggested that he's also thinking of matter itself. But strictly, Aquinas doesn't need the specifics: all he needs is that there is something ingenerable because it always exists. This gets him to the point at which he can ask about the reason for its ingenerability; then rejection of infinite regress brings us to a first ingenerable that causes other ingenerables to exist always.

Gaberbocchus -- Oh! Frabiusce Dies!

Gaberbocchus
by Hassard Dodgson

Hora aderat briligi. Nunc et Slythreia Tova
Plurima gyrabant gymbolitare vabo ;
Et Borogovorum mimzebant undique formae,
Momiferique omnes exgrabuere Rathi.

"Cave, Gaberbocchum moneo tibi, nate cavendum
(Unguibus ille rapit. Dentibus ille necat.)
Et fuge Jubbubbum, quo non infestior ales,
Et Bandersnatcham, quae fremit usque, cave."

Ille autem gladium vorpalem cepit, et hostem
Manxonium longa sedulitate petit;
Turn sub tumtummi requiescens arboris umbra
Stabat tranquillus, multa animo meditans.

Dum requiescebat meditans uffishia, monstrum
Praesens ecce ! oculis cui fera flamma micat,
Ipse Gaberbocchus dumeta per horrida sifflans
Ibat, et horrendum burbuliabat iens !

Ter, quater, atque iterum cito vorpalissimus ensis
Snicsnaccans penitus viscera dissecuit.
Exanimum corpus linquens caput abstulit heros
Quocum galumphat multa, domumque redit.

" Tune Gaberbocchum potuisti, nate, necare ?
Bemiscens puer ! ad brachia nostra veni.
Oh! frabiusce dies ! iterumque caloque calaque
Laetus eo" ut chortlet chortla superba senex.

Hora aderat briligi. Nunc et Slythseia Tova
Plurima gyrabant gymbolitare vabo ;
Et Borogovorum mimzebant undique formae,
Momiferique omnes exgrabuere Rathi.

A Latinate rendering of a more famous Anglo-nonsense poem, by the uncle of the man who wrote the latter.

The Strangest Whim Has Seized Me

A Ballade of Suicide
by G. K. Chesterton

The gallows in my garden, people say,
Is new and neat and adequately tall;
I tie the noose on in a knowing way
As one that knots his necktie for a ball;
But just as all the neighbours--on the wall--
Are drawing a long breath to shout "Hurray!"
The strangest whim has seized me. . . . After all
I think I will not hang myself to-day.

To-morrow is the time I get my pay--

My uncle's sword is hanging in the hall--
I see a little cloud all pink and grey--
Perhaps the rector's mother will not call--
I fancy that I heard from Mr. Gall
That mushrooms could be cooked another way--
I never read the works of Juvenal--

I think I will not hang myself to-day.

The world will have another washing-day;
The decadents decay; the pedants pall;
And H.G. Wells has found that children play,
And Bernard Shaw discovered that they squall,
Rationalists are growing rational--
And through thick woods one finds a stream astray
So secret that the very sky seems small--

I think I will not hang myself to-day.

ENVOI

Prince, I can hear the trumpet of Germinal,
The tumbrils toiling up the terrible way;
Even to-day your royal head may fall,
I think I will not hang myself to-day.

Always good for an academic to remember during this busy time of year!

Of course, it's a bit optimistic to think that rationalists are growing rational, but there's hope.

Bowels of Compassion

A salutary warning from St. Gregory the Great, whose feast day it is:

These are wishes peculiar to the haughty, to pray that the lives of those who are suffering may be more severely examined, because the more just they are in their own eyes, the more hardened are they in others’ sufferings. For they know not how to take to them the feeling of the other’s infirmity, and to feel pity for their neighbour’s weakness, as they do for their own. For since they think highly of themselves, they do not at all condescend to the humble. Eliu believed that blessed Job had been smitten for his sin, and therefore believed that no bowels of compassion were to be shewn to him, even in the midst of so many sorrows. But when men, who are truly holy, behold any one smitten, even for his faults, though they reprove some of his inordinate doings, yet they sympathize with some of his sufferings; and they are so skilled in keeping down swellings, as yet to know how to relieve wounds, in order that when their hardnesses are softened, their infirmities may be strengthened. But because, on the other hand, haughty men have no bowels of love, they not only do not sympathize with the righteous when suffering, but moreover afflict them, under pretence of proper reproof, and they either exaggerate trifling faults, if there are any in them, or pervert by wrong construction those points which are really good.

Moralia in Job, Part V, Book XXVI, Section 6. It sounds so straightforward; and yet it's extraordinarily difficult to practice.

IPod Random Fifteen

1. Screamin' Jay Hawkins, I Put a Spell on You
2. Mediaeval Baebes, The Snake
3. The Charlie Daniels Band, The Devil Went Down to Georgia
4. Nena, Leuchtturm
5. Epica, Every Time It Rains
6. Metallica, Nothing Else Matters
7. Ellis Paul, God's Promise
8. Leonard Cohen, Hallelujah
9. Linda Ronstadt, Long Long Time
10. Rosanne Cash, Seven Year Ache
11. Jann Arden, Never Mind
12. Katie Melua, Nine Million Bicycles
13. Cerena, Quelque Part C'est Ici
14. Kareem Salama, Aristotle and Averroes
15. Matisyahu, King Without a Crown

"The Snake" can be found performed live by the Mediaeval Baebes here; and while the sound quality is not great, it captures the catchiness of the song. It's a version -- Catalan, if I recall correctly -- of a kind of poem that's fairly common, in which someone (in this case, a farmer) discovers a half-frozen snake, takes it in and nurtures it back to health, then crosses it at some point, leading the snake to respond as snakes do (in this case, the snake has grown to very great size and so it hisses and wraps itself around the farmer to kill him). You can find another, more swinging variation on the theme in Al Wilson's The Snake. The moral of the story should be obvious.

Links and Notes

* John Farrell has an article on Pius XII and Humani Generis at the WSJ. He discusses it further in a post here.

* My favorite logical positivist, Otto Neurath, at the SEP.

* William Bristow has an article at the SEP on the Enlightenment. I don't think it's a bad article, but I find it odd to read, because in virtually every choice one has to make in writing an article on this topic, Bristow chose the opposite of what I would have done. Unlike Eric Schliesser, I can see the point of saying that the Enlightenment only became self-reflective in its later German form, although it is potentially misleading and skews the discussion. (It's like saying that rationalists and empiricists only became self-aware of themselves as such toward the end of the early modern period; there's a legitimate sense in which this is so, but putting this way is potentially misleading as to the actual disputes between rationalists and empiricists.) I think it was a mistake to speak in terms of general tendencies of the 'the Enlightenment'; the local expressions (the French Enlightenment, the German Enlightenment, the Scottish Enlightenment, etc.) are indeed nodes in a general communication network concerned with intellectual development, but they do not all have the same general tenor, nor are their favored projects the same. To do justice to anything in the Enlightenment, one really must focus on the hubs, both the activity within the hub and between hubs. One reason for this is infrastructure: the French Enlightenment, for instance, is radically different from the Scottish Enlightenment, and much of the reason is the different role both educational institutions and churches play in each. A further issue is the abstraction from chronology and historical events; many of the things we associate with the Enlightenment period arise fairly late due to, e.g., educational reforms following from interest in Rousseau; the American and French Revolutions are historical events that leave their mark very clearly on the history of the period; much Enlightenment thought spreads due to specific actions by governments; and so forth. All of this is important.

* The BBC has an interview from its archives with J. R. R. Tolkien.

* There is a European region whose dominant religion is Tibetan Buddhism. The Head of Kalmykia, Kirsan Nikolayevich Ilyumzhinov, is apparently one odd politician, who is obsessed with chess (making it a compulsory subject in school) and believes he was abducted by aliens once.

* Roger Pearse has a good post on the cliche, often uncritically bandied about, that extraordinary claims require extraordinary evidence. I've criticized it myself before and said that it is gibberish that has the function of furthering intellectual laziness: when you try unpack the meaning of both 'extraordinary claims' and 'extraordinary evidence' you find that the only plausible ways of doing so leave you with principles that are either obviously false or only true given highly controversial assumptions. Its plausibility is entirely a matter of its rhetorical parallelism -- there is literally no substance to it beyond that.

* AS Byatt says, in response to a question about religious belief, "I think Wallace Stevens is my religion," which is about as pretentious as I would have expected her response to be: her abiding sin, in which her books are steeped, lies in a capacity for expression that is too clever by half and too clumsy by far. But she actually says some interesting things in the interview, especially when she starts getting excited as to possible future avenues for novels.

* A good post on homology and analogy by John Wilkins. Some of the commenters note some weaknesses with the abstract algebra, but since we in philosophy have a Manifest Destiny to mangle as we please, and I think the primary interest in the post is not in the finer details but the overall approach, I regard this as a minor matter. This is the sort of thing that needs to be done; that it's still at draft stage doesn't change that. Mathematicians only reach dianoia on the Divided Line, anyway. (^_~)

* Speaking of which last, I think Japanese-style emoticons (both kao-moji proper and the more general 'anime' emoticons derived from them) should be more common; they are so much more expressive than Western-style emoticons.

* Isaac Bonewits, the founder of the Ár nDraíocht Féin, one of the major Neo-Druid organizations, died recently; the ADF has some interesting YouTube videos excerpting eulogies from the memorial service.

* JavOICe: this is a quite interesting Java applet in which you can draw sounds.

* Daniel Fincke has the 113th Philosopher's Carnival at "Camels with Hammers". I think this carnival is one of the more interesting collections of posts in recent times; Daniel is to be congratulated on the work of putting it together.

* Kenny Pearce has been blogging on various points that arise in reading Sobel's Logic and Theism, which I've recommended before as probably the best discussion of theistic arguments from an atheistic perspective that is currently available. So far the posts are:
Sobel's Logic and Theism
Divine Freedom and Worship
Normative Skepticism and the Existence of God
The Dialectical Appropriateness of Ontological Arguments
Sobel's Argument Against Believing in the Possibility of a Perfect Being
A Genuine Dialectical Problem for Ontological Arguments

* Enbrethiliel has a post on theology of the body, at least as commonly understood; fairly harsh and not very wrong, I think.

* Ed Feser discusses Thelonius Monk.

* The beauty of Google: A very long time ago, in elementary school, I remember reading a short story about unicorns. I don't remember the story itself, but I remember very vividly that a character in it was thinking about what to call a group of unicorns -- a word like 'herd' not really doing justice to them -- and settled on 'surprise': a surprise of unicorns. That has always stuck with me, since it's just exactly right, but I hadn't the faintest idea where it comes from. So I googled the phrase "surprise of unicorns" and it came up: "The Boy Who Drew Unicorns" by Jane Yolen, in The Unicorn Treasury.

Eartha Makes It Sound So Nice

I always start my ethics course with the question "Why be moral rather than not?", having the students read selections from Plato's Republic. My class this term didn't manage a very enthusiastic or exciting answer to that question, so I told them today that this was their theme song, and the song that would come to my mind every time I thought of them.

I Mine Own Prison

The Thread of Life
by Christina Rossetti

I

The irresponsive silence of the land,
The irresponsive sounding of the sea,
Speak both one message of one sense to me: —
Aloof, aloof, we stand aloof, so stand
Thou too aloof bound with the flawless band
Of inner solitude; we bind not thee;
But who from thy self-chain shall set thee free?
What heart shall touch thy heart? what hand thy hand? —
And I am sometimes proud and sometimes meek,
And sometimes I remember days of old
When fellowship seemed not so far to seek
And all the world and I seemed much less cold,
And at the rainbow's foot lay surely gold,
And hope felt strong and life itself not weak.

II

Thus am I mine own prison. Everything
Around me free and sunny and at ease:
Or if in shadow, in a shade of trees
Which the sun kisses, where the gay birds sing
And where all winds make various murmuring;
Where bees are found, with honey for the bees;
Where sounds are music, and where silences
Are music of an unlike fashioning.
Then gaze I at the merrymaking crew,
And smile a moment and a moment sigh
Thinking: Why can I not rejoice with you?
But soon I put the foolish fancy by:
I am not what I have nor what I do;
But what I was I am, I am even I.

III

Therefore myself is that one only thing
I hold to use or waste, to keep or give;
My sole possession every day I live,
And still mine own despite Time's winnowing.
Ever mine own, while moons and seasons bring
From crudeness ripeness mellow and sanitive;
Ever mine own, till Death shall ply his sieve;
And still mine own, when saints break grave and sing.
And this myself as king unto my King
I give, to Him Who gave Himself for me;
Who gives Himself to me, and bids me sing
A sweet new song of His redeemed set free;
he bids me sing: O death, where is thy sting?
And sing: O grave, where is thy victory?