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.

---

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.

---

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.

---

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.

---

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.

Nature, Science and Wisdom

This year's American Maritain Association conference is on the subject of

"Nature, Science and Wisdom:
The Role of the Philosophy of Nature"

It will be held Thursday, November 2- Sunday, November 5 in Nashville.

The line-up of speakers reads like a "who's who" of realists in the philosophy of science and philosophy of nature, and includes William Wallace, Stanley Jaki, Anthony Rizzi, Chris Morrissey, Mark Ryland, Ralph McInerny, Jude Dougherty, and Jean DeGroot. (I've omitted many others of merit, I am sure, simply out of my own ignorance.)

Definitely worth taking time out to attend. I hope to see you there!

Papal Controversy: Faith and Reason

I wrote most of this last week, but didn't get a chance to post it.

With all the controversy, how many people do you think have actually read the offending text? So that you can be one, here it is:

Pope's controversial German speech on reason and religion

The irony has undoubtedly been observed before that some Muslims would protest a statement that Islam is evil by murdering innocents. Almost as if they're trying to prove the charge true.

This weekend I viewed Islam: Empire of Faith, a feature very positive on Islam produced by PBS. According to this documentary, Islam calls for a totalizing unity of life, which would seem to be consistent with the claim I've previously heard that Islam leaves no room for reason—that faith subsumes reason. Certainly Islam has had much more reasonable periods in its history, but was this a true manifestation of Islam? It is clear the Muslim commentators on Aristotle seem to have been good philosophers to the extent that they ignored their faith; perhaps the same is true of their peaceful relations with non-Muslims. I'd really appreciate seeing a full discussion of the issues.

The main thrust of the Pope's talk is not the (alleged) fideism of Islam, but the manifest division of faith and reason in modern Western culture and how this opens the way for violence as arbiter. The Pope traces this division to the gradual dehellenization of Christian thought.

He recounts how the Christian Faith was born from an encounter of Judaism with Greek thought (for example, the Septuagint translation of the Hebrew Scriptures), which allowed formulation of belief in Christ as Logos, Divine Reason. By severing itself from the Hellenic spring of its existence, Christianity has become not only untrue to itself, but has retreated to the subjective world and abandoned the objective world of reason to the amorality and ultimate meaninglessness of modern empiricism.

This gives rise to two principles which are crucial for the issue we have raised. First, only the kind of certainty resulting from the interplay of mathematical and empirical elements can be considered scientific. Anything that would claim to be science must be measured against this criterion. Hence the human sciences, such as history, psychology, sociology and philosophy, attempt to conform themselves to this canon of scientificity.

A second point, which is important for our reflections, is that by its very nature this method excludes the question of God, making it appear an unscientific or pre-scientific question. Consequently, we are faced with a reduction of the radius of science and reason, one which needs to be questioned.

I will return to this problem later. In the meantime, it must be observed that from this standpoint any attempt to maintain theology's claim to be "scientific" would end up reducing Christianity to a mere fragment of its former self.

But we must say more: if science as a whole is this and this alone, then it is man himself who ends up being reduced, for the specifically human questions about our origin and destiny, the questions raised by religion and ethics, then have no place within the purview of collective reason as defined by "science", so understood, and must thus be relegated to the realm of the subjective. The subject then decides, on the basis of his experiences, what he considers tenable in matters of religion, and the subjective "conscience" becomes the sole arbiter of what is ethical.

In this way, though, ethics and religion lose their power to create a community and become a completely personal matter. This is a dangerous state of affairs for humanity, as we see from the disturbing pathologies of religion and reason which necessarily erupt when reason is so reduced that questions of religion and ethics no longer concern it. Attempts to construct an ethic from the rules of evolution or from psychology and sociology, end up being simply inadequate.

Faith needs a vital connection to reason. Without it, man loses direction in his life, and the assertion of individual power becomes the sole rule of conduct.

Purpose and Order in Nature

According to conventional wisdom, the dawn of modern science dispelled the gloom of moth-bitten superstition, and banished purposes from nature. But such Enlightenment propaganda leaves out the tradition the modern world inherited from its predecessors. At the heart of the modern scientific conception of the world is the idea that nature is a knowable order. Without this belief, Galileo would never have troubled himself to roll balls down inclined planes. Exploring chemical reactions would be pointless. Geneticists would have no reason to take pains sequencing nucleic acid base pairs. What modern scientists take for granted was established by reason in the ancient world—by philosophy. In Book II of the Physics, Aristotle argues that nature’s obvious regularities—its tendency to act in a given way under given circumstances—reveal an ordering to specific ends:

For teeth and all other natural things either invariably or normally come about in a given way; but of not one of the results of chance or spontaneity is this true. We do not ascribe to chance or mere coincidence the frequency of rain in winter, but frequent rain in summer we do; nor heat in the dog-days, but only if we have it in winter. If then, it is agreed that things are either the result of coincidence or for an end, and these cannot be the result of coincidence or spontaneity, it follows that they must be for an end; and that such things are all due to nature even the champions of the theory which is before us would agree. Therefore action for an end is present in things which come to be and are by nature.¹

In other words, although “chance” events often obtain, the natural world is inherently teleological. Scientific laws, modern and ancient, physical, chemical, and biological, disclose nature’s regularities and testify to teleology. That baking soda and vinegar react expansively, and that confetti is almost always attracted to the static electric charge on a balloon show the order and purpose of nature. Far from being opposed to modern science, teleology is its sine qua non.

The ascendance of the Darwinian narrative leaves the situation unchanged. Darwin’s Theory of Natural Selection encompasses two pieces, chance variation and natural selection: (1) genetic novelty originates in chance, and (2) novel forms less suited to existence tend to fail in passing their genes to posterity. While the latter point may well be a valuable contribution to the scientific understanding of the world, the former point simply puts a name (and a deceptive one) on an unknown. As Aristotle’s classic definition observes, chance is the intersection of two otherwise unrelated lines of causality. Chance itself is not a cause; to invoke chance is not to explain, but to label an unknown. To the extent that any theory relies on chance, that theory is not science, but rather ignorance.²

The champions of chance argue that teleology is an intellectual opiate and kills the quest for the acatual mechanism of change. On the contrary, teleology does not eliminate the need for an efficient causal explanation: just because one appreciates the sublime order of the parts of a horse does not negate the molecular forces that maintain its form. Teleology compliments other modes of explanation.

The source of the many prejudices people hold against teleology is that an order in nature apparently points to

1. an Orderer, and
2. a natural moral law (order).

And these are both true. The source of people's fear is the misconception that God somehow imposes the moral order on the world from the outside. Nothing could be further from the truth. Whom would you most trust to write the instruction manual for your lawnmower? Obviously the person who designed and built it. My take is that in the same fashion, revealed moral laws (i.e., the Ten Commandments) are simply God giving us certainty about how to find happiness through the regularities we observe in nature on our own.

The natural moral law is inscribed within creation—it is an integral part of its workings. The "law" we learn simply makes note of regularities in human existence (and in the universe at large) and enjoins us to work with them for our ultimate happiness.

Forget about crime. Forget about sin. Forget about "right and wrong." Disobeying the moral law is worse than a crime: it's a mistake.³ In the same way as one knows better than to spit into the wind, a healthy society doesn't (in my view) encourage certain practices, for example, the taking of any innocent human life, rape, extramarital sexual relations, divorce, contraception, and so many other things that have become accepted in our society. The West is dying because we won't listen to God—yes—but also because we are too full of ourselves and seeking our immediate gratification even to hear nature.

No matter what one thinks about the content of the natural moral law, anyone who values science in the least has to agree that there are regularities in nature. We can argue about what these regularities indicate, but there should be no disagreement that learning these regularities and working with them is the way to find happiness in this world.

---

Notes

1. Physics, Book II, chapter 2, 198b34–199, Hardie and Gaye translation.

2. See also: Providence and Chance and Intelligence Transcends Science.

3. A variation on Talleyrand. "Stupid" might be more accurate.

---

Classes began last week, so I've been busy laying a solid foundation for the semester. This piece is partially something I've been working on for something else.