Thursday, September 20, 2007

Ecclesial Morphogenesis

The last post discussed the theme of natural development with the emphasis on "evolution not revolution": that discontunity is unnatural and severs identity. Now we examine the same principle from the opposite perspective: continuity through change.

Vladimir Soloviov, a Russian Orthodox Christian who came into communion with Rome, wrote vigorously in defense of the Papacy. Here's a beautiful excerpt that compares the historical growth of the Church to the dvelopment of a tree.

Though the transformation of a stone into a mountain is only a symbol, the transformation of a simple, almost impreceptible seed into an infinitely larger and more complicated organism is an actual fact. And it is by just this fact that the New Testament foretells and illustrates the development of the Church, as of a great tree which began in an impreceptible grain of seed and today gives ample shelter to the beasts of the field and the fowls of the air.

Now, even among Catholics we meet with ultradogmatic spirits who, while justly admiring the vast oak which covers them with its shade, absolutely refuse to admit that all this abundance of organic forms has grown from a structure as simple and rudimentary as that of an ordinary acorn. According to them, though the oak tree arose out of the acorn, the acorn must have contained in a distinct and discernible form, if not every leaf, at least every branch of the great tree, and must have been not only idenitical in substance with the latter but similar to it in every detail [like the old homonculus theory].

Whereupon ultracritical spirits of the opposite school set to work to examine the wretched acorn minutely from every angle. Naturally, they discover in it no resemblance whatever to the entwining roots, the stout trunk, the leafy branches, or the tough, corrugated foliage of the great tree. "What humbug," they exclaim. "The acorn is simply an acorn and can never be anything else; it is only too obvious where the great oak and all its characteristics came from. The Jesuits invented it at the [First] Vatican Council; we saw it with our own eyes—in the book of Janus [a dissenting account of the Council]."

At the risk of appearing a freethinker to the extreme dogmatists and of being at the same time labeled a Jesuit in disguise by the critics, I must affirm the unquestionable truth that the acorn actually has quite a simple and rudimentary structure, and that though not all the component parts of a great oak can be discovered in it, the oak has actually grown out of the acorn without any artificial stimulus or infringement of the laws of nature, but by its own right, nay, even by divine right. Since God, who is not bound by the limitations of space and time and of the mechanism of the material world, sees concealed in the actual seeds of things all their future potentialities, so in the little acorn he must not only have seen but ordained and blssed the mighty oak which was to grow from it. In the grain of mustard seed of Peter's faith he discerned and foretold the vast tree of the Catholic Church which was to cover the earth with its brances.

Though Jesus Christ entrusted Peter with that universal sovereign authority which was to endure and develop within the Church throughout its existence upon earth, he did not personally exercise this authority except in a measure and in a form suited to the primitive condition of the apostolic Church. The action of the prince of the apostles had as little resemblance to modern papal administration as the acorn has to the oak; but this does not prevent the papacy from being the natural, logical, and legitimate development of the primacy of Peter.

The growth of an organism ties back to Aristotle's discussion of the meaning of natural:

The form indeed is 'nature' rather than the matter; for a thing is more properly said to be what it is when it has attained to fulfillment than when it exists potentially. (Physics II.1.193b7-8)

Thus an oak tree is more natural than the acorn from which it grew, since it more fully expresses its nature. So human societies, like the family or a larger community, are more natural than the individuals from which they grow and who bind together to form them. Humanity fully expresses its nature in community (contrary to the Enlightenment philosophers' postulation that the State of Nature is solitary).

Similarly, the Catholic Christian Church is a more perfect expression of the Body of Christ than individual, particular Churches, but it also more fully expresses the nature of that universal Communion in its mature state than in it did at birth.

Vladmiri Soloviev (Solovyov), The Russian Church and the Papacy, trans. Herbert Rees, ed. Ray Ryland (San Diego, California: Catholic Answers, 2001), 149-150.

Personal note: I will be travelling for the next couple weeks, so posts if any will be intermittent.

Thursday, September 13, 2007

Return from the Wasteland

Tomorrow on the Feast of the Exaltation of the Holy Cross Pope Benedict XVI's Motu Proprio Summorum Pontificum officially takes effect and makes explicit the right that all Catholic priests have say the traditional "use" of the Roman Rite (i.e., the traditional Latin Mass that traces its lineage back to the original Apostolic Mass).

Many people date the liturgical reform to the Second Vatican Council's Dec. 4, 1963 promulgation of Sacrosanctum Concilium (Constitution on the Sacred Liturgy). But the changes actually implemented had the vaguest connection with the Council's decrees (as you can see from the actual document) or even unstated intentions (according, for example, to the recollections of someone who was actually there).1

Pope Paul VI actually promulgated the "new Mass" with his Apostolic Constitution Missale Romanum on April 3, 1969. This means the current Holy Father is correcting a misunderstanding of nearly forty years.

The Israelites spent forty years in the desert before entering the Promised Land. I don't think that it is an accident that we've spent nearly forty years in the liturgical wasteland. While I certainly wouldn't have willed this period of desolation, but our Lord is able to draw good out of our worst failures. It is clear in retrospect that it was part of God's Providence: among other benefits it allows us to better appreciate the traditional Mass (we never seem to know what we've got until we lose it), as well as our utter inability to draw life from any source except that our Lord gave us through his Apostles—the Liturgy grows by evolution, not revolution.

Now I need to say that I don't believe the return of the old Mass will bring the Church to some sort of idyllic state of perfection. First, as we all know perfection is impossible this side of heaven. Second, even the Israelites after returning had to fight to take possession of their heritage.

The difference the Motu Proprio makes is that tomorrow, we can stop wandering and begin to fight. Deo Gratias!


1. Really the concrete form of the reform Archbishop Annibale Bugnini was realized according to Archbishop Annibale Bugnini, a man who was exiled in July 1975, not long after his liturgical vision was promulgated to an unwary Church. (I understand that he was exiled after convincing evidence surfaced that he was a Freemason—an avowed enemy of the Church.)

Alfons Cardinal Stickler, "Recollections of a Vatican II Peritus," The Latin Mass Winter 1999.

The Pope's Letter Accompanying the Motu Proprio

Summorum Pontificum, English translation from the Latin original.

Here's a whole blog devoted to the Motu Proprio, its consequences, and surrounding issues: Summorum Pontificum.

An entertaining and somewhat insightful take on the old rite from a convert: What I think about the "Tridentine" Mass by David Palmer.

Tuesday, September 11, 2007

Moralism without Morals

In a recent National Review article on the office of Surgeon General, Yuval Levin makes an insightful remark about the new American way of being moralistic but without a reference to any sort of objective morality:

The tone of surgeon-general reports makes for a telling case study in the way health has usurped the place of virtue in America's public vocabulary. Public health is the only remaining language in which to speak of vice -- an old-fashioned word that once would have been the obvious way to refer to, say, smoking and drinking. The self-righteousness that colors the crusade against obesity, smoking, and other modern sins is as near as the Left gets to religion, and the surgeon general fills the role of oracle.

Mencken once memorably said, "Puritanism: The haunting fear that someone, somewhere, may be happy." The American elite are no longer be truly religious in attitude, but they are still Puritanical.

Yuval Levin "A Doctor, But Whose? Diagnosing the Disorder in the Surgeon General's Office," National Review LIX:15 (August 27, 2007).

Saturday, September 08, 2007

More on the Infinite

As I mentioned before, I'm reading A.W. Moore's The Infinite. (I found out about it through the webpage of a member of the Syndey School of Mathematics.) The book is much clearer than the Zellini book I commented on previously. Whereas Zellini makes a single distinction between the actual infinite and the potential infinite (which are synonymous with "true" and "false" infinites), Moore adds an additional distinction between true and false versions of the actual and potential infinites. The true versions of these he calls metaphysical and mathematical infinites.

Part of Moore's clarity comes from starting off (in the introduction) discussing the paradoxes of the infinite and defining terms.

[O]ne of the central issues concerning the infinite is whether it can be defined. Many have felt that it cannot; for if we try to define the infinite as that which is thus ans so, we fall foul of the fact that being thus and so is already a way of being limited or conditioned. (It is as if the infinite cannot, by definition, be defined....)1

Two clusters of concepts nevertheless dominate, and much of the dialectic in the history of the topic has taken the form of oscillation between them. Within the first cluster we find: boundlessness; endlessness; unlimitedness; immeasurability; eternity; that which is such that, given any determinate part of it, there is always more to come; that which is greater than any assignable quantity. Within the second cluster we find: completeness; wholeness; unity; universality; absoluteness; perfection; self-sufficiency; autonomy. The concepts in the first cluster are more negative and convey a sense of potentiality. They are the concepts that might be expected to inform a more mathematical or logical discussion of the infinite. The concepts in the second cluster are more positive and convey a sense of actuality. They are concepts that might be expected to inform a more metaphysical or theological discussion of the infinite. Let us label the concepts 'mathematical' and 'metaphysical' respectively. (1-2)

The book is divided into two parts. The first part is an overview of the historical of thought on the infinite, and the second part is an assessment of the various strains of thought. Aristotle has a foundational role in both. Moore points out that Aristotle wasn't saying that the (mathematical) infinite was false, but that it only exists potentially, not actually:

I said at the beginning of §2 that Aristotle appeared to abhor the mathematical infinite. We can now see how profoundly false such an appearance was. What he abhorred was the metaphysically infinite, and (relatedly) the actual infinite—a kind of incoherent compromise between the metaphysical and the mathematical, whereby endlessness was supposed to be wholly and completely present all at once. It was the mathematically infinite that he was urging us to take seriously. Properly understood, the mathematically infinite and the potentially infinite were, for Aristotle, one and the same. Far from abhorring the mathematically infinite, he was the first philosopher who seriously championed it. In so doing he recoiled from earlier thinking in such a way that he set the scene for nearly all subsequent discussion of this topic. (44)

According to Moore, the pre-Socratics had given voice to what was essentially the metaphysical infinite, but Plotinus first articulated it clearly and distinctly:

He called it self-sufficient, perfect, and omnipotent, a complete and pure unity, utterly beyond our finite experience. He also said that it was 'supremely adequate, autonomous, all-transcending, most utterly without need.' Sometimes he spoke of it in a Parmenidean way, implying that it had internal limits. 'Its manner of being is settled for it,' he said, 'by itself alone.' But elsewhere he emphasized its lack of limits, either exeternal or internal. Indeed, in line with this, he insisted that all our attempts to talk about it or derfine it were strictly speaking, and inevitably, inadeqaute. This, in truth, it even transcended such descriptions of it as 'The Good' or 'God'. Its ineffability meant that we had to be content with mystical insight into it. He nevertheless tried to convey as much as possible with words. And in so doing he supplied one of the first explicit identifications of the infinite with God. (46)

Moore very clearly explains the categorematic/syncategorematic distinction originated by Peter of Spain and taken up by Jean Buridan and Gregory of Rimini:

Roughly: to use 'infinite' categorematically is to say that there is something [an actual whole] which has a property that surpasses any finite measure; to use it syncategorematically is to say that, give any finite measure, there is something [another individual] which has a property that surpasses it. (51)

This distinction carlifies an important point about uses of infinite, and furthermore subsumes Aristotle's actual/potential distinction.

By way of illustration, consider the following application of the new distinction in a temporal context, noted by Gregory [of Rimini]. If I say, 'An infinity of men will be dead,' and use 'infinity' categorematically, then I mean that there will come a time when infinitely many men are dead; there will then be an actual infinity of dead men. If I say the same thing, and use 'infinity' sycategorematically, then I mean that there is no end to the number of men who will, each in his own time, be dead; there is a potential infinity of dead men. This explains, I think, why so many philosophers have thought that there was something deeper and more abstract underlying straight-forward temporal accounts of the actual/potential distinction. It seems they were right. There is something—something grammatical [cf. later invocation of Wittgenstein]. (Working with this new distinction also has the advantage that one can avoid the false implication in Aristotle's terminology, noted by Aristotle himself, that what is potentially infinite must be capable of being actually infinite.) (52)

Moore includes some provocative reactions of contemporaries to Cantor's transfinite mathematics:

[French mathematician Henri Poincaré] challenged Cantor's claim to have proved that R [the set of real numbers] was bigger than N [the set of natural numbers]. Cantor's proof could just as well be taken to establish merely that we could not devise a way of pairing off the natural numbers with the real numbers, or indeed that R was not a genuine set at all—presumably because the real numbers were somehow too unwieldy to be grouped together into one determinate totality.

This, incidentally, was something urged by the American philosopher and mathematician C.S. Peirce (1938-1914). He had independently discovered that there was no way of pairing off the natural numbers with the real numbers, but he concluded that R did not exist as a completed whole. At most it existed as something potentially infinite. However many reals had been actualized, there were always more waiting to be. A continuum, he felt, was precisely not just a set of points. It was something absolute, consisting of unactualized possibilities, cenmented together in a way that defied description but of which we were aware in experience.

I'm not sure how much credence to give these ideas, but they do seem to lead us back to Aristotle's notion of the continuum not being composed of points.

I'm still re-reading and digesting the book. Moore's advocacy of Kant and Wittgenstein's positions on the subject sound reasonable to me (from what he says), but I'm not entirely certain how kosher they are (especially Kant) and I need to examine them more closely because they have a big part to play in the second half of the book. Being a good Englishman, Moore ends (as I read him) with the empiricist (or more-or-less Aristotelian) position of denying the reality of the metaphysical infinite and affirming that while we can see things about the mathematical infinite, we cannot really say anything about it as actual.


1. Not sure this is the right way to note the ellipsis.

A.W. Moore, The Infinite (New York: Routledge, 1991). All emphases in original.

Paolo Zellini, A Brief History of Infinity, trans. David Marsh (New York: Penguin Books, 2004).

Sunday, September 02, 2007

Beach-blanket Natural Philosophy

At a yard sale recently, I bought an old copy of Hubbard's Battlefield Earth for twenty cents. "Beach" reading, perfect for summer. The characters are superficial, the plot movement often contrived, and some of the language confusing, but Hubbard does a good job building that momentum that gets you to turn to the next chapter (or part).

One of the main "science" premises of this science fiction novel is the mysterious workings of the antagonists' teleportation system:

Prior to this [discovery], it was thought that teleportation consisted of converting energy and matter to space and then reconverting it in another place so it would assume its natural form. But this had never been proven. En [the discoverer] had apparently found that space could exist entirely independently of time, energy, or mass and that all these things were actually separate items. Only when combined did they make up a universe.

Space was dependent only upon three coordinates. When one dictated [!] a set of space coordinates one shifted space itself. Any energy or mass contained in that space thereupon shifted with that space shift.

In the matter of a motor such as this freighter had, it was just an enclosed housing in which space coordinates could be changed. As the coordinates changed, the housing was forced to go along, and this gave the motor power.... A series of coordinates were progressively fed to the main motor and it self went forward or backward as the housed space occupied each set of coordinates in turn.

Teleportation over vast distances worked the same way. Matter and energy were pinned to the space, and when it was exchanged with another space, they simply changed too. Thus matter and energy would seem to disappear in one place and appear in another. They didn't actually change. Only the space did.

There are so many things wrong with this description that it is hard to know where to begin. Now of course, no one takes the "science" mumbo-jumbo in science fiction novels seriously (I mean most of these things technically don't even qualify as novels1), but for entertainment purposes, let's look at it more closely.

In the first place, this idea of absolute space (apart from an absolute time) was conjured up by Newton to facilitate his mechanics, which was based on Descartes's analytic geometry. It's took us centuries to get over this naive starting point, but as we all know, the consequences of Einstein's notions of space and time continua forming a unified space-time continuum were experimentally confirmed by the time Hubbard wrote his novel in 1982. In his special theory of relativity, Einstein showed how the dilation of time intervals and the correlative contraction of spatial dimensions at speeds approaching the speed of light explain many phenomena, most notably the constancy of the speed of light for all observers, however they are moving. So not only are space and time interdependent, but also there can be no absolute coordinate system---what would define the origin?

Further, in his general theory of relativity, Einstein showed that the geometrical structure of this spacetime depends on nearby masses. So space exists relative to mass-energy as well as time.

But the dubiousness of the idea goes deeper than physics. Coincidentally, I've also been reading A.W. Moore's The Infinite. Of course one of the puzzles of infinity is whether a magnitude or continuous quantity can be composed of discrete, infinitesimal points. Cantor's transfinite mathematics notwithstanding2, it is pretty clear that elements with length zero can never add up to a finite length. Philosophically speaking, using a teleporter to move through a continuum requires more sophistication (infinitely more!) than teleporting across the universe. That means that the teleportation motor that Hubbard describes cannot move continuously, but has to move itself through discrete points. Perhaps the resulting vibration is the reason the engines make such noise when "dictating" themselves through space. Of course, if space exists independent of the rest of the universe, then one has to wonder what sort of forces would allow one to shift it.

Hubbard's novel is interesting also for how it speaks about his personal philosophy, a philosophy that undoubtedly colors the doctrine of the Church of Scientology, which he founded. It shows a naive trust in human nature so characteristic of the 20th century. But in addition, Hubbard also displays a distrust of government and a simple faith in the abilities. More interestingly, Hubbard has at least a rudimentary respect for nature: his villains, a race of aliens called the Psychlos, have been altered at birth to suit arbitrary societal demands (working hard, preserving technological secrets) that also make them sadists.

Wikipedia says that Punch (April 4, 1984) sarcastically commended Hubbard's "excellent understanding of evil impulses, particularly deviousness, which helps with the plot, and [he] is well-enough aware of his weaknesses not to dwell upon frailties like love, generosity, compassion." I might add that Hubbard's detachment from humanity is reflected in his naive, purely quantitative conception of greatness. Beyond the 1000-page length of the book, the Psychlos are much bigger than humans (10-ft tall and weighing 1000 lbs each) and the greatness of their empire is reflected the vastness of the numbers that define it. As Hubbard writes,


The homeplanet of two hundred thousand worlds.

The center of an empire that had ruled and ruined sixteen universes over the period of three hundred and two thousand years.3

Wanna spice up your novel with more awe-inspiring bad-guys? Just add zeros!


1. A novel in the usual understanding centers around the development of a character. The cover of my copy of the present work is a painting in bold primary colors of a blond, bearded bare-chested man (physique of a body builder) firing two futuristic guns, in the background angular spacecraft zooming around (see the book homepage: In this case it seems you can judge a book by its cover. Tragic little of science fiction explores characters with any depth, though later writers have sought to overcome this shortcoming by introducing sex scenes, as if meaningless couplings add human depth! At least Hubbard refrains from the latter.

2. Cantor showed that there are (infinitely) more irrational numbers between any two rationals than there are rationals on the real number line. But his failure to show that the continuum is the next infinity bigger than the rationals leaves an indefiniteness to the place of the continuum in Cantor's hierarchy of transfinite numbers. More on this later.

3. P. 899. Somehow their tremendous evil does nothing to destablize their society.

4. Looks like Battlefield Earth is Presidential candidate Mitt Romney's favorite novel! Just the thing to read while you're having your hair blow-dried.

L. Ron Hubbard, Battlefield Earth: A Saga [!] of the Year 3000 (Los Angeles: Bridge Publications, 1984), 187-8.

A.W. Moore, The Infinite (Routledge, 1989).