Thursday, May 04, 2006

Viva México, Viva Juárez

I'll be gone this weekend, and don't know if I'll have the time to post anything tomorrow, so I thought I'd put up my Cinco de Mayo post a day early.

Cinco de Mayo celebrates the battle of Puebla on May 5, 1862, in which Mexican soldiers, facing a much larger French army, achieved victory. (It is not to be confused with Mexico's Independence Day, which is September 16; Mexican independence from Spain was achieved almost fifty years before the battle of Puebla.) During the administration of Mexican president Benito Juarez, an impressive political hero who deserves wider renown, Napoleon III had sent an army, under the pretext of debt collection, to establish French rule in Mexico under the viceroy Maximilian. It was a bold plan, but the odds dramatically favored Napoleon III: the French army was one of the finest in the world at that time, and the United States who would certainly have opposed the French incursion and assisted the Mexicans (and did indeed do so when they had a chance) was embroiled in the Civil War. The French smashed through the initial Mexican defenses.

Operating under the assumption that the Mexicans would capitulate if their capital were to fall, the French set out to attack Mexico City. The Mexican army, under the leadership of Texas-born Ignacio Zaragoza (Texas, of course, was at the time of his birth still part of Mexico; Zaragoza was born in Goliad and moved with his family to Mexico after Texas independence), retreated to the fortified city of Puebla. When the French arrived, they sent their cavalry out to the French flanks; the French army made the mistake of sending its own cavalry to chase them. The Mexican cavalry was easily able to take tie up the French cavalry, thus forcing the French infantry to charge the Mexican infantry unassisted. The ground was muddy from rain, making it difficult to maneuver. It is also sometimes said that the Mexicans stampeded large herds of cattle against the French; which, if true, would have no doubt been a bit disconcerting. In any case, the French were eventually forced to retreat from Puebla. The Mexicans won the battle.

But lost the war. The French brought in reinforcements and seized control of Mexico. Juarez was sent into hiding, where he organized the resistance. Maximilian ruled until 1867, when he was executed by troops loyal to Juarez.

Cinco do Mayo is celebrated in Mexico, but except for perhaps Puebla and the surrounding areas, it is not as popular as it appears to be in the U.S., where it is perhaps second only to St. Patrick's Day as the most widely celebrated ethnic holiday. And deservedly so, I think; it's a cool victory to celebrate, and serves as a useful occasion for remembering all facets of Mexican culture and legacy. (It doesn't hurt that in the person of Zaragoza it has a connection to U.S. soil.)

Physics and Philosophy

I found this interesting: R. F. Streater's Lost Causes in Theoretical Physics (HT: Reality Conditions). The primary purpose of this list is, as Streater says at the beginning, is to note topics of various degrees of popularity that, due to difficulty, obsolescence, or lack of promise, are probably not topics suitable for students. I don't have the expertise to comment intelligently on the more physics-related issues, but while some of the topics listed would fairly narrowly be of interest only to physicists, the list is also useful in giving sets of topics to be wary of if you are not a physicist, particularly if you are in a field (like philosophy) that will at least occasionally touch on physics-relevant issues. The most obvious case, because the most popular, is the many worlds interpretation, which secretly carries all the most serious dangers for the philosophically minded: it's different enough from ordinary assumptions that it gives an intoxicating feeling of liberation, its basic idea is accessible enough that it quickly gives you the misleading impression that you understand it, it has a long series of sci-fi associations that give the misleading impression of old familiarity, and it looks vague enough that you can think about it at will without bumping too often into pesky things like facts or needing to conform your inferences too often to rigorous mathematical equations. It's a breeding ground for bad reasoning. There are others among the topics listed by Streater that, although less popular, can get philosophers into similar dangerous territory. Even if some of these ideas eventually pan out in one way or another, or are eventually re-thought enough that they become useful, physicists at present simply haven't worked them out enough for others, and especially philosophers, to do anything with them (beyond writing fictional stories).

On a complete tangent, I liked the following passage in the discussion of the many worlds interpretation:

Science is not the collection of impressions got by watching Nature unfurl. In the most useful phrase from the book by Durr, Goldstein and Zanghi, Bohmian Mechanics and Quantum Theory, "we do not come to the Navier-Stokes equations by admiring water waves". We find the laws of Nature by reproducible experiments. The theory needs a cut, between the observer and the system, and the details of the apparatus should not appear in the theory of the system. The heat capacity of a crystal should not depend on the shape of the calorimeter used to measure it. The result of an experiment should not depend how it is performed (contrary to the claim of Durr et al. q. v. above, p 36, lines 1-2), but on what it is measuring.


It puts me in mind (on a tangent again) of the Romantic critique of Newtonianism in the nineteenth century. Contrary to what seems to be the common impression, the Romantics were not in general opposed to science; in fact, they usually regarded themselves as pro-science and their opponents as anti-scientific. Thus Goethe, for instance, criticizes Newton's theory of color not for being scientific but for not being scientific enough. But the Romantics had a quirky view of science, one that made science out to be very empiricist in its approach. So on the Goethean view of science science really does just collect impressions by watching nature unfurl; it eventually gets into the theoretical, but the theoretical is supposed just to grow out of the impressions, bit by bit. No fact is irrelevant, every fact -- including those pertaining to the observer -- has to be somehow taken into account in your theory, and idealization is not acceptable unless it is reached by carefully taking into account everything you experience in the phenomena. If that's your view of science, it's not surprising that you would have a problem with Newton's whole approach, doubting its status as scientific, since Newton makes all sorts of choices about which facts are most important for understanding the phenomena, and is willing to theorize about nature at large on the basis of a handful of carefully controlled experiments. I think one lingering problem of that dispute is that the Romantic view of science is fairly common in our culture: we have a tendency to overemphasize how empiricist its approach is, particularly with regard to physics. I once TA'd for a Science and Society course -- philosophy of science dealing largely with issues like pedagogy, popularization, and policy-making -- which was largely filled with engineering students. The course touched on the Romantics at a few points, and I was surprised at how much sympathy there was for this approach, despite the fact that most of the students had a science background; there was a tendency to regard Goethe as right about how physics in general should go, and Newton was allowed in as an exception. Try as I might, I couldn't convince most of them that it was odd to think of the success of Newtonian physics as a matter of Newton's just happening to luck out in diverging from good scientific practice. I don't know if some of this had to do with their being engineers, or if I had without realizing it oversold Goethe and the Romantics in explaining their view; but I'm fairly sure from some of their comments that a great deal of it had to do with pedagogy and popularization: one way or another they had had it so drilled into them that science was empiricist that they would sympathize with any critique that focused on neglect of empirical facts -- even if the neglect of facts were being done by Isaac Newton, in the midst of some paradigmatically good science, and the facts neglected weren't especially helpful for construction of theory, and the resulting idealization was wildly successful. In any case, the Romantic view still seems common; and it is worth reminding ourselves that science does not simply consist in gathering impressions from watching nature unfurl. That's what painting is for.

Notable Links

* The discussion of traversal of the infinite continues at "Alanyzer".

* Bonnie Kent, On the Track of Lust: Luxuria, Ockham, and the Scientists (PDF)

* The Dogs Playing Poker Code (HT: Another Think) All it needs to be complete are references to the Templars and the evil machinations of Opus Dei in trying to keep the Code secret. And Rolfes is just a little bit too sane to convey the fullness of what Umberto Eco fittingly called the psychosis of resemblances, the pathology at the root of it all.

* Monty Python's International Philosophy Match. The best part of all is when the Germans dispute the goal:

Hegel is arguing that the reality is merely an a priori adjunct of non-naturalistic ethics, Kant via the categorical imperative is holding that ontologically it exists only in the imagination, and Marx is claiming it was offside. But Confucius has answered them with the final whistle! It's all over! Germany, having trounced England's famous midfield trio of Bentham, Locke and Hobbes in the semi-final, have been beaten by the odd goal, and let's see it again.

(HT: prosthesis)

* "Earmarks in Early Modern Culture" has a post on the maternal connection account of heredity, which was very popular in the early modern period (and well into the nineteenth century, despite rejection by occasional greats like Nicholas Steno). I've posted on this briefly in connection with Malebranche.

* Rebecca has a nice post up on Eternality.

* Clark discusses volitional belief. The old discussion of the subject he links to is also worth re-reading.

* Oppressed, poor, facing economic collapse, the people of Zimbabwe find some strength in their sense of humor. (HT: Magic Statistics)

* La Bandera de las Estrellas: The 1919 Spanish edition of the U.S. national anthem. They did a surprisingly good job. The last stanza:

¡Oh asi sea siempre, en lealtad defendamos
Nuestra tierra natal contra el torpe invasor!
A Dios quien nos dio paz, la libertad, y honor,
Nos mantuvo nacion, con fervor bendigamos.
Nuestra causa es el bien, y por eso triumfamos,
Siempre fue nuestro lema: "¡En Dios confiamos!"
!Y desplegara asi su hermosura estrellada,
Sobre tierra de libres, la bandera sagrada!


It's interesting that it is much less cautious than the English original, which pulls some of its punches with conditionals (e.g., the Spanish version says, "Our cause is good, and because of this we triumph" whereas the English says "Then conquer we must, when our cause it is just," which is similar in meaning, but much less certain and more qualified, since it leaves open the possbility that our cause won't always be just. (HT: Rhine River)

* UPDATE: Anyone of my generation will appreciate the humor of this. (HT: Cnytr)

Wednesday, May 03, 2006

Traversal and an Infinite Past

A bit of blogging serendipity: I posted my recent thoughts on Bonaventure and Aquinas on the newness of the world because I was reading Benjamin Brown's defense of Bonaventure. Unbeknownst to me, there was a discussion going on at "Alanyzer" of the Kalam Argument, which is, essentially the same issue. In the comments Aquinas's response to the traversal argument came up. Aquinas's argument is this:

Traversal is always understood to be from term to term. But whatever past day is designated, from that (day) to this there are finite days that can be traversed. But the objection proceeds from this, that, positing the extremes, there are infinite terms in between. [ST 1.46.2 ad 6]


Alan in the comments replied to this:

Aquinas didn't come close to refuting the "traversal of the infinite" argument. On the contrary, the fact that traversal requires two termini supports the kalam argument. It's the absence of a beginning terminus given an infinitely old universe that creates the problems, exactly as the kalam arguer contends.


To which I replied:

I'm baffled by the claim that Aquinas doesn't refute the traversal argument. If every traversal requires a beginning and an end, and an infinite past has no beginning, this is a problem only if we already assume that traversal of an infinite past would require traversal of infinite days. But on the infinite past view, every day in the past is finitely distant from the present; it's just that for every finitely distant day there's a day that is more distant. Thus this is true: For every day in the past, traversal of the days from that day to today is traversal of a finite number of days. The fact that there are infinite such days doesn't change this. This is true just as much as it is true that the fact that every integer is a finite distant from 1 is not affected by the fact that there are infinite integers.


That's the background; Alan has a new post up in response to this that I'd like to comment on. But first I want to make some distinctions. With regard to this topic, we often make a distinction between a potential and an actual infinite. It is important that we tread carefully here, because 'actual infinite' does not mean the same as 'actually infinite'. Every actual infinite is actually infinite, but something can be actually infinite without being an actual infinite. If Aristotle's solution to the infinite divisibility problem is right, for instance, the potential divisions of a line segment are actually infinite. This is not the same as to to say that they constitute an actual infinite -- to constitute an actual infinite the line segment would have to be actually divided into infinite parts. Likewise, the set of integers is actually infinite; but it is not an actual infinite. The reason is that in one case -- 'actual infinite' -- the 'actual' means 'not of something potential'; in the other -- 'actually infinite' -- it means 'not merely apparently'. This is significant.

Alan's response to my objection is that it conflates potential and actual infinity. As he says:

(A) is clearly true when we're talking about a potential infinite. We start at the present and run through the time series in reverse, moving farther and farther into the past. Nevertheless, at any point we stop at, we're only a finite remove from the present. But if the distance from past event E to the present is actually finite, then we haven't yet captured the idea of an actually infinite past.

Similarly, the notion of ever larger integers being still a finite remove from 1 is that of a potential infinite, of a magnitude increasing without bound, not of an actual infinite.

(A) is the claim I made in bold above. This response, I think, conflates the actual infinite with the actually infinite. Alan is right that the integers are a potential infinite; it does not follow from this, however, that they are not actually infinite. And that's the key. If anything is actually infinite the integers are; but you cannot start from the premise "The integers are actually infinite" to "Some integer is infinitely distant from some other integer." In fact, the former is necessarily true and the latter is necessarily false: no integer is infinitely distant from any other integer, because every integer is, by its very nature, finitely distant from every other integer. Pick any integer you like, it is a finite distance from every other integer. Nonetheless, the integers are actually infinite, because there are infinitely many such finite distances. Alan is, I think, confusing 'indefinite finite' with 'potential infinite'.*

That is the point of Aquinas's response to the traversal argument. In claiming that the past is infinite the advocates of the eternity of the world are not committed to saying that any day is infinitely distant from any other day, only that there are infinitely many days finitely distant from each other. Thus the traversal argument fails because it assumes that the claim of an infinite past means that there is an infinite that is traversed; but this is false: necessarily, there is no infinite to be traversed, only infinitely many possible finite traversals of any size you choose. The case is, if we are considering only the infinity involved, exactly parallel to the case of the integers: within the set of integers, there is no actual infinite to be traversed from integer to integer because no integer is infinitely distant from any other; but the integers are actually infinite.

So, in other words, infinitely many traversals of finite distances is not the same as traversal of an infinite distance. The claim that there is no traversal of an infinite (as opposed to infinite traversals of finites) in the infinite past can't be shown wrong unless some other consideration is added that shows that the days of an infinite past must not only be actually infinite, but must constitute an actual infinite that has to be traversed.

---

* Added later: Perhaps a better way to put this is to say that Alan is confusing the syncategorematic/categorematic infinites distinction with the distinction between the finite indefinite and the actually infinite. A syncategorematic infinite is actually infinite: it is an infinite such that for any finite number there is a greater finite number. The categorematic infinite is an infinite such that it is greater than any finite number. Alan seems to be assuming that there are no merely syncategorematic infinites; but this would be denied by most defenders of an infinite past.

Tuesday, May 02, 2006

A New Poem Draft

Thalassa

Bent back, aching feet,
shoulders overladen,
endless march behind me,
in weariness I have journeyed,
seeking rest.

In this up-country climb,
endless driving days,
I have journeyed onward,
seeking the end.

But now the final hill,
swarded green and sandy,
falls back beneath my feet;
it opens endlessly out
to a never-ending roar.

It is morning here;
the march is done;
the strong light leaps,
somersaulting the sea.

---
UPDATE: With a sharp eye, Michael Gilleland recognizes the allusion.

Monday, May 01, 2006

Links and the Like

[There have been some updates.]

* "Islamicate" has a great series of posts on Islamic interpretation of the Qur'an:
(1) Interpretation
(2) Interpreting and Translating
(3) Translations and Secondary Sources
(HT: Dappled Things)

* The economist John Kenneth Galbraith recently died; you can read an interview with him online.

* The Online Philosophy Conference has begun. There's nothing especially interesting this week, although some readers might find Julia Driver's paper on Luck or Jessica Wilson's paper on non-reductive physicalism worth reading.

* In the modern Catholic calendar, today is the day of St. Joseph the Worker. In observance of the day, I direct you to Aquinas's discussion of the purposes of manual labor (they are: to obtain sustenance, to remove idleness, to submit the body to the higher faculties of reason and will, and to make almsgiving possible; these are the things that work contributes to a life of virtue and excellence). Also, the legend of the Miraculous Staircase of Loretto Chapel in Santa Fe. The so-called Miraculous Staircase, a beautifully balanced piece of master carpentry, has been attributed to a number of people throughout its 130 years; the most favored candidate at present appears to be Francois-Jean 'Frenchy' Rochas. Local legend, of course, attributes it to St. Joseph. Whoever built it, it does seem a fitting symbol of the builder of Nazareth, who is the patron saint of all those who work with their hands to make useful and beautiful things.

* "Mode for Caleb" has a Jazz Primer.

* Sharon Howard discusses and provides links about the self-archiving of academic publications, with a link to her own archive page.

* The History Carnival should be up at some point today. I'll link to it when it is. [UPDATE: And History Carnival #30 is now up. Of especial interest is the post on Margery Kempe at "Quod She". Margery Kempe is no Julian of Norwich, but she's actually not bad at all once one realizes that she's doing much the same thing as Julian (namely, reflecting on her experiences and filtering them through what she knows theologically) -- it's just that, unlike Julian, she doesn't go through such pains to tell us that this is what she's doing, and (admittedly) her theology is much less sophisticated. I've found in my own experience that Kempe grows on you considerably once you get used to her. Yes, she's sometimes a little much, but there's a lot to admire in her.] [UPDATE 2: In answer to a question I asked about where one could find something about marginalia on Kempe's book (which would give some indication of how she was read), Dr. Virago pointed to the introduction to the TEAMS edition; this introduction is online. Very cool stuff.]

* Scott Gilbreath discusses James the Less and James the Just at "Magic Statistics".

* UPDATE: The 29th Philosophers' Carnival is up at "Daylight Atheism." Particularly of interest are About Morality at "Obsidian Wings"; and Pride and Humility at "Goosing the Antithesis" (which is basically a crude cousin of a genuinely interesting Humean argument); and Richard's post The Actual World is not a Possible World at "Philosophy, etc."