Degrees of Abstraction

I doubt I'll be able to post anythign substantial next week, as I'll be in Nashville at the American Maritain Association convention on "Nature, Science and Widsom." In preparation, I've been reading Jacques Maritain. His Science and Wisdom is a wonderfully brief and lucid explanation of many things I've been trying to convey here. I highly recommend it. His Degrees of Knowledge is longer but includes more complete explanations.

Below is a very helpful selection from Degrees of Knowledge on the three degrees of abstraction. The diagram is my contribution. The a axis parametrizes displines by whether their objects can exist without matter, while the b axis parametrizes disciplines by whether their objects can be conceived without matter. (Maritain's diagram from Degrees of Knowledge is here [new window]; it is more detailed, but for that somewhat less clear on the main point of this post.)

The mind can consider objects abstracted from, and purified of, matter but only to the extent that matter is the basis of diversity amongst individuals within a species.... In this way, the object remains; and remains to the very extent that it has been presented to the intellect, impregnated with all the notes coming from matter, and abstracts only from the contingent and strictly individual peculiarities, which science overlooks. The mind thus considers bodies in their mobile and sensible reality, bodies garbed in their empirically ascertainable qualities and properties. Such an object can neither exist without matter and the qualities bound up with it, nor can it be conceived without matter. It is this great realm that the ancients called Physica, knowledge of sensible nature [i.e., natural philosophy and modern science], the first degree of abstraction.

Secondly, the mind can consider objects abstracted from, and purified of, matter insofar as matter is the general basis for the active and passive sensible properties of bodies. In this case, it considers nothing more than a certain property which it isolates within bodies—a property that remains when everything sensible is left aside—quantity, number or the extended taken in itself. This is an object of thought which cannot exist without sensible matter, but which can be conceived without it. For, nothing sensible or experimental enters into the definition of the ellipse or of the square root. This is the great field of Mathematica, knowledge of Quantity as such according to the relations of order and measure proper to it—the second degree of abstraction.

Finally, the mind can consider objects abstracted from, and purified of, all matter. In this case it considers in things only the very being with which they are saturated, being as such and its laws. These objects of thought which not only can be conceived without matter, but which can even exist without it, whether they never exist in matter, as in the case of God and pure spirits, or whether they exist in material as well as in immaterial things, for example, substance, quality, act and potency, beauty, goodness, etc. This is the wide domain of Metaphysica, knowledge of that which is beyond sensible nature, or of being as being—the third degree of abstraction.

Maritain further explains in Science and Wisdom how the degrees of abstraction are inhomogeneous in degree:

The way in which things are organised in the thought of Aristotle is well known. The theory of the three degrees or the three orders of abstraction became classic in the schools.

In the first degree of this process, the mind knows an object which it disengages from the singular and contingent moment of sense perception, but whose very intelligibility implies a reference to the sensible. This first and lowest degree of scientific abstraction is precisely the degree of physics and of the philosophy of nature. It defines the field of sensible reality. Above it comes the degree of mathematical abstraction, in which the mind knows an object whose intelligibility no longer implies an intrinsic reference to the sensible, but to the imaginable. This is the domain of the mathematical praeter-real. And finally, in the highest degree of intelletual vision, the metaphysical degree, the intelligibility of the object is free from any intrinsic reference to the senses or to imagination. This is the field of the trans-sensible reality.

Thus Aristotle did not only lay the foundations of physics. At the same time he threw light on the difference which distinguishes physics from metaphysics—a matter of capital importance. The division of the three orders of abstraction is an analogical division. The three orders are not part of the same genus: they constitute fundamentally different genera. They are not set at stages one above the other in the same generical line: there is a true noetic heterogeneity between them.

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Jacques Maritain, "The Philosophy of Nature," Science and Wisdom, trans. Bernard Wall (New York: Charles Scribner's Sons, 1954), 37-39.

Jacques Maritain, The Degrees of Knowledge, trans. Gerald B. Phelan (New York: Charles Scribner's Sons, 1959), 35-36 (diagram, 39).

Equality's Discontents

I'm still working on a lengthier, substantial post, but in the meantime, I just re-read a great story by Kurt Vonnegut and thought you might enjoy it as well:

Harrison Bergeron.

Ignore the gratuitous initial editorialization by the person who so kindly posted the story. There has always been a tension between those two virtues of the French Revolution, liberty and equality. Hopefully our current leaning toward the latter won't eventuate in the dystopic future Vonnegut imagines.

The Virtue of Vanity

Now you might be inclined to think that an essay claiming to upholding vanity as a positive good is akin to Erasmus' "In Praise of Folly," but you would be mistaken. I mean seriously to point out the oft-neglected good side to what is often called vanity.

(This essay takes its inspiration in part from Alan Ehrenhalt's essay "Hypocrisy Has Its Virtues" from the waning days of the Clinton-Lewinsky scandal; the piece explained how hypocrisy really is the tribute vice pays to virtue.¹)

We Americans pride ourselves on being practical, results-oriented people. We don't go in for the foppery that preoccupies other cultures (what Tocqueville called "forms"). We don't care as much for how a thing looks as for what it does. Ceremony should be minimized Furnishings and clothing should be functional, not fancy.

There is of course a great amount of goodness in this view, which is one thing that makes this a great country. However, there are two sides to everything. o as usual, I'm assuming the devil's advocate role, first of all to point out that any behavior taken to an extreme is no longer a virtue, but a vice. As Aristotle observed, true virtue is the medium between two extremes, and it must be admitted that we Americans, as with any other people in this fallen world, sometimes take our virtues beyond their proper limits.

The truth is that often what we call vanity is just being thoughtful of others. This realization first dawned on me when I noticed the dress of one of my fellow grad students, whom I'll call "Joe." He always wore "comfortable" clothes: birkenstocks, shorts and a t-shirt. I probably dressed only marginally better myself at the time, but whereas I didn't have to look at myself much, I did have to look at him: his hairy legs, long hair, and poorly shaven face were an eyesore. On reflection, I realized that "dressing up" was really a form of consideration for the people around us.

Women are often accused of being vain and the charge is not always just, but a reflection of their being much more "relational" creatures who take joy in pleasing others. As a current colleague of mine says, whereas men define themselves by what they do, women define themselves by their relationships. Of course, pleasing others can become self-serving—the vicious side of the virtue. Women just as easily as men use others, and usually by manipulation.² Our "vanity" or consciousness of the importance of others' perceptions is the glue that holds society together and keeps us from fragmenting into cultural solipsists.

Last time I saw Joe, he had become engaged and his mode of self-presentation had shaped up substantially. He'd clipped his hair, and wore much more respectable clothing. His fiancee had obviously inspired him with some of her feminine "vanity." And the world is a better place for it.

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Notes

1. The only quality immoral moderns like Bill Clinton regard as a virtue is consistency. "At least I'm not a hypocrite," they say in an effort to excuse themselves. But really they indict themselves of being "little minds"—ala Ralph Waldo Emerson.

2. Karol Wojtyla writes very well about the reciprocal unfortunate way each sex often uses the other in Love and Responsibility.

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Alan Ehrenhalt, "Hypocrisy Has Its Virtues," The New York Times[!], February 6, 2001.

The Future of Physics

Last time I visited New York was this summer and I had the pleasure of lunch with my old advisor. He thinks that string theory is a dead end, and I have to agree with him. Physics is entering a new era. My advisor would cringe at the company his opinion keeps, but Robert Laughlin A Different Universe (which I discussed here) agrees. Laughlin sees the the future of physics in emergence (as opposed to the reductionism of which string theory is a grand culmination).

A couple of items have surfaced that similarly question the future path of physics. First, John Horgan, in his review of Lee Smolin's book The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, writes about how the great promise string theory showed in 1990's has been achieved only frustration:

Physics at the end of its string?

Smolin pleads with his colleagues to explore alternative theories of everything, including twistor space theory, an invention of British physicist Roger Penrose; doubly special relativity, proposed by Portuguese theorist Joäo Magueijo; and loop quantum gravity theory, to which Smolin has contributed. Acknowledging that "no idea yet has that absolute ring of truth," Smolin also calls for "a radical rethinking of our basic ideas about space, time and the quantum world."

Horgan disagrees with Smolin and thinks that money, not a new mindset, is the key to the future of physics:

Although I admire the authority and passion of Smolin's diagnosis, I disagree with his prescription. What physics desperately needs is not new ideas but hard experimental data that can test ideas or inspire new ones. But these data are costly. [etc. etc.]

Secondly, Burton Richter, former director of SLAC, writes the "Reference Frame" piece in the current Physics Today:

Theory in particle physics: Theological speculation versus practical knowledge.

Richter bemoans string theory as more akin to theology than science (and he uses theology in the most pejorative sense). He especially laments Leonard Susskind's "Cosmic Landscape" of unlimited universes that sample the parameter space of all cosmic constants (review forthcoming). Richter, like Horgan, sees experiment as the ultimate way to salvation.

My prognosis for today's physics is even more dire: we are due for a larger shift than Smolin hopes for, an even more radical break than Laughlin heralds: reductionism has played itself out, but it's not emergence per se that will rule. Instead physics will have to go back to its conceptual roots to a rediscover nature as an organizing principle, of matter as possessing inherent purposes. As I've written before, teleology compliments other modes of explanation.

The shift in mindset with be tectonic. The reigning paradigm has made progress by ignoring purpose in nature, thereby blinding itself to the major component of the natural order that it seeks to describe. The program has been a great success: we've certainly managed to circumscribe the physical world of ordinary experience... and much beyond ordinary experience. But the overwhelming mathematicization of this description keeps it from being hinged on the ordinary human experience that forms the basis of human meaning.

The new physics will open man's second eye and discover a whole new dimension to the world. Experiment will necessarily play a role, but the new mindset will lead in new, more quotidian directions (directions that will be much less costly than multi-billion-dollar particle accelerators). We might actually have to open our eyes to the world around us.

The revolution will not happen overnight. The programs of renewal for which Horgan, Smolin, and Richter hope may first come and go. It may be decades before the new physics can stand on its own.

But it is coming.

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John Horgan, "Physics at the end of its string?," The Globe and Mail, (October 4, 2006), A2.

Burton Richter, "Theory in particle physics: Theological speculation versus practical knowledge," Physics Today (October 2006), 8.