Misunderstandings, Custom, and the Modern World's Mathematical Habit of Mind

Orientation #

He continues the account of the importance of the question whether nature acts for an end, having done ethics “last time” (prev. lecture): “after ethics” he now takes the arts that help nature, then theology. He recalls “I mentioned before last time” Max Planck, and the four kinds of causes and three corollaries already learned. The previous class set out the stakes of the question and Aristotle’s distinctions among causes; the next presents the arguments that nature acts for an end and the counterarguments.

The class, in order #

1. Importance for the arts that help nature (“help nature in what it’s already trying to do”) #

Point: the character of the arts that help nature depends on nature acting for an end.

• Distinction: arts that help nature (medicine) vs. arts that do not (carpentry). What separates them: helping nature “in what it’s already trying to do, even without the art.” Obstetrician helps the woman deliver, which nature after nine months is already pushing to do; the carpenter making a chair from the tree is not helping the tree, “the tree is not trying to make a chair.”
• Logic is like the medical art: men without logic already try to “give birth to thoughts”; hence Socrates could call himself an intellectual midwife.
• Caution on the wide sense: you can say all the servile arts help nature (a bed gives me a place to rest), but “we’re taking a more strict sense.”
• Examples of medical helping: styptic on a shaving cut, stitches on a big cut: they don’t complete the healing but pull the ends together so nature heals with less scar.
• Argument: (1) if nature acts for an end, these arts must begin by recognizing that end and how to help nature reach it (Hippocratic Oath forbade abortion, “because that’s not what nature’s intending”); (2) if nature does not act for an end, the medical art becomes arbitrary, with no parameters from nature; same for logic, whose rules “fit the natural procedure of reason.” Modern logicians in his office: rules of logic are like the rules of any game, Hoyle, Monopoly, arbitrarily invented. Conclusion: “the very kind of art they are” is destroyed by the denial.

2. Importance for theology; importance is not truth (“You can hardly say this is irrelevant”) #

• Theology: whoever says nature acts for an end will ask “doesn’t that require a mind?”, then “does nature have a mind, or is it directed by another?”, and if not its own, then a product of another mind: leading eventually to recognition of the divine mind.
• Caution: from the importance of the question for ethics, medicine, logic, theology “you can’t reason to what the truth or falsity is,” only to its enormous importance. Students may not care to understand nature, but they can’t avoid living a human life, seeing a doctor, or using their mind.
• Socrates in the Phaedo: philosophers are accused of talking about irrelevant things, yet on the day he dies he discusses whether the soul survives death; that question is relevant to how you live your whole life. “This whole life is just up for grabs.”

3. Three common misunderstandings (“misunderstanding the kind of cause that is the end”) #

Point: these lead some to deny that nature acts for an end, but are not arguments, only misunderstandings of what is meant; he ties them to the four causes and three corollaries.

1. Kind of cause the end is, bound up with the equivocation of “mover”/“motive” and more particular words, “attract,” “draw,” which serve for the fourth kind of cause as well as the third. Moving the eraser: I am a cause in the third sense. The prince climbing Rapunzel’s tower: her beauty “moved him,” but not in the third sense. Pulling the glass toward me vs. a performer at the Sun Room in Worcester “drawing in the crowds”: if he lassoed you it would be the third kind; he is “a big draw” in the fourth. Midsummer Night’s Dream: the pursuing girl compares the man to a magnet; a real magnet is a mover in the third sense, the young man a magnet metaphorically, in the fourth. The misunderstanding gives “a kind of pseudo-mystical” picture of the end reaching out and pulling you: “a fictitious understanding.”
2. The first corollary: they think the end is proposed in place of the more known causes, a false dichotomy. Why am I walking across campus toward the Dean? Nerve impulses and muscles, or to eat lunch? Forced to choose, people pick the muscles, “because that third kind of cause is more known.” (Sometimes, though, the end is easier to see than the mechanism of heart, eyes or lungs.)
3. The second corollary: is intercourse the cause of the baby, or the baby the cause of intercourse? Again a false dichotomy; it can be both, one as end, the other as [ed.: efficient cause; he says “that for the sake of which” for the second half, apparently a slip]. Faced with the dichotomy a person picks the more known cause.

• “I’m sure there are other misunderstandings”; these tie to what was already learned.

4. Custom stronger than argument (“which is stronger, for the most part, in our thinking”) #

Point: more important than the misunderstandings in leading men to deny final causes is custom.

• Apology: Socrates answers not only his accusers in court but his anonymous accusers, who over years have accustomed Athens to think him a bad man; he is more concerned with them. The contrast: force of custom vs. force of argument, and custom seems stronger. Something more universal than the trial: students asked “which is stronger” tend to say custom.
• Witness: Max Planck, uneasy about his own theory; new ideas win not by convincing older physicists but because they die off and the young accept them at the start. If this holds for scientists, “how much more so for men in general.”
• Day-and-night example: a student says the earth turns on its axis, not by proof but because parents and teachers said so. He argues the opposite by reason: a lump of earth let go falls straight down, does not circle or rotate; a ball spun on the desk soon stops and falls apart; so it “makes no sense” that the earth spins so regularly that we set clocks by it. The students can’t answer, “but do they agree with me? No.” So custom is stronger.
• Aristotle in “the second book of wisdom” [ed.: Metaphysics II] and Thomas at the beginning of the Summa Contra Gentiles speak of the influence of custom on what we think; what we’ve heard since young “seems to be naturally clear.”
• Warren Murray at Wisconsin: the English professor mocked the ancients as if it were obvious the earth goes round the sun; Murray: by Newtonian physics both go round a common center of gravity, like a man swinging a child in a circle, both rotating around a center nearer the man. So “it’s not so obvious as you think; in fact, it may not even be true.”
• C. S. Lewis’s reason for reading the ancients: not that they are wiser, but their mistakes are not ours, so seeing them say the opposite makes us examine our positions. Travel broadens, geographically and in time; living abroad, or marrying into another family, you see some things better there and some better at home; that weakens custom a bit.
• We too take things for granted: “all men are created equal” said in slave Athens or Rome would get you locked up.
• Custom of one’s discipline (Aristotle, same place): some want everything said mathematically, some want a poet quoted. Descartes wants mathematical clarity and certainty everywhere; Novalis, “the more poetic, the more true.” Committees of professors approach a problem each as their discipline is accustomed to. Aside: a video of a sociologist illustrating with a word count in Thomas: “what the hell would I be doing a word count in Thomas for?”

5. Sources of the modern world’s customs, first: the mercantile city (“the mercantile origin of the modern city”) #

Point: “at least three major sources” of the modern world and its customs; the first in time, not necessarily most important.

• Aside: Msgr. Knox: stupid of the modern world to stop believing in the devil, “when he’s the only explanation for it.”
• McNeill, The Rise of the West (perhaps the best secular world history): the Greek city grew from the landed aristocracy settling near the seat of government, an aristocratic stamp never wholly lost even in its most commercial cities; the modern city, founded in the late Middle Ages by merchants (“converted pirates,” a source of Western aggressiveness). Since civilization is tied to the city (civitas, civis), each stamp colors the whole civilization: ours is more commercial than any ever.
• Signs: economics as an independent discipline, with Nobel prizes, prestige above political science and sociology (maybe because mathematical). Adam Smith, in the history of ethics for Theory of Moral Sentiments, most famous for The Wealth of Nations; unthinkable as Plato’s or Aristotle’s major work. Smith a Scotsman: 18th-century Scotland’s “economic takeoff” from poverty to teaching England drew his mind to why nations grow rich. Marx: Das Kapital (dedicated to Darwin), Economic and Philosophic Manuscripts, everything explained by the economic mode of production. The President’s two standard addresses: State of the Union (last night) and the economic report; Coolidge, the business of America is business. Newspapers, TV, radio as advertising media; his memory of early Sunday-evening TV movies with half an hour of commercials. Contrast the Greek religious festivals that produced Sophocles, Euripides, Aeschylus; the Symposium at a dinner honoring Agathon’s prize; the Ion, the rhapsode reciting Homer: the elevation of Greek tragedy vs. movies made for the box office.

6. Second source: the mathematical union of natural and technical science (“the mathematical union of natural and technical science”) #

Point: this, from the 17th–18th centuries, is the source most important for our question.

• Thomas’s division of order in relation to reason (recalled): the order reason only considers (nature); the order reason makes in its own acts (logic), in acts of the will (ethics), in exterior matter (the mechanical or servile arts). Natural philosophy and the mechanical arts are “quite different,” yet in the 17th–18th centuries they fused: one history of science and technology, techniques enabling experiments, theories suggesting new techniques.
• Why mathematics made the marriage possible: it abstracts from the natural/artificial difference. Four legs of the chair by art, four legs of the cat by nature, the abstract four by neither, applicable to both.
• Heisenberg (Gifford lectures): it turned our attitude to nature from contemplation to “what can you do with it,” a pragmatic attitude; modern philosophers see the purpose of knowledge as power.
• Sign in the words: “physics” from the Greek for nature, “mechanics” from the mechanical arts; the oldest part of modern science (Galileo, Kepler, Newton) is the physics called mechanics.
• Newton, who united Galileo and Kepler, became the model: 20th-century physicists call 17th–19th-century physics “classical” or “Newtonian”; Cassirer’s Philosophy of the Enlightenment, everyone follows Newton; Locke “clearing the way for more Newtons”; the poet, God said Newton would be, and all was light. Descartes and Kant were physicists of this kind; Descartes developed a mathematics, Newton with Leibniz founded calculus; Kant’s Critique tries to understand this kind of knowledge, which becomes for them the whole knowledge of nature.
• Relation of first to second: the mercantile city “disposes” (not causes) toward using science to make and sell. The “industrial revolution” involves the two working together; support for science comes from business and government, for practical reasons (a chemist at Minnesota Mining: ideas belong to the company).
• Student: did Newton merit that grandeur? Answer: a great scientist, yes; but not a model for all human knowledge. Newton’s own image: a boy on the seashore playing with shells, the ocean of truth undiscovered. Aside: in later years Newton ran the Mint.

7. Third source: the democratic revolutions (“the social condition of equality”) #

• Many democratic revolutions, most striking the French (liberté, égalité, fraternité); the 19th century more democratic than the 18th even in England, the 20th more still. Equality vs. hereditary inequality of ancient societies.
• Tocqueville, Democracy in America: came for a pure case, France still having an aristocratic hangover. Vol. I, American institutions local to federal; vol. II, four books contrasting democratic with aristocratic customs: on the mind (literature, history, science), on morals and manners, on government.
• Historians: the democratic historian stresses mass movements, individuals as tools of them; the aristocratic sees great men changing things. Churchill: questionable whether England would have made a deal with Germany without him; Shakespeare’s Julius Caesar calls Brutus “the soul of Rome,” more apt of Churchill as the soul of Britain.
• Literature: aristocratic ages look to the past (Iliad, Aeneid set in a greater past), democratic to the future (1984, Brave New World, Star Wars). “I don’t know exactly why that is.”
• Religion: democratic customs suggest pantheism, visible in German philosophy and French literature; he cites it when discussing Einstein’s pantheistic mind, against Anaxagoras’s Mind altogether distinct from things; 19th-century Church corrections of German Catholic theologians, Rahner “a little bit,” his excommunicated compatriot more.
• World histories name the industrial and democratic revolutions as the major changes; the industrial involves sources one and two.

8. Why the second source matters most: no substance, sense quality, or purpose in mathematics (“there’s no substance, there’s no sense qualities, and there’s no purpose”) #

• Substance “persona non grata, or res non grata”: Berkeley denies material substance, Hume any substance, Russell: Mr. Smith’s accidents no more need a substance than the earth needs an elephant to rest on. Even the Creed: avoiding “consubstantial” for “same being.” Descartes replaces substance with extension, which is quantity, the second category.
• Sense qualities: modern philosophers and many scientists deny redness, hot, cold out there; naturally, since none are in a mathematical description. Schrödinger’s point: you read instruments (black mark, blue column) by sense qualities, yet the scientific picture has none: “kind of strange situation.”
• Purpose: his brother Mark: we never say the sphere is smooth so it can roll from danger, the pyramid pointed to protect itself like a porcupine; the triangle’s angles are two right angles not because better, “just the way it is.”
• Conclusion: the moderns see a world without sense qualities, substance, or purpose; that is the influence of custom.
• Student: is this the “anti-metaphysical stance” of Fides et Ratio? Answer: part of it, but more basic; it starts in the study of the natural world. Aside: a colleague converted to denying sense qualities, holding that to see them is a sign of irrationality.
• Accustomed only to this knowledge of nature, one finds talk of purpose “unscientific.”

9. Eddington’s net and Schrödinger’s stuffless atom (“your net is not designed to catch”) #

Point: the mathematical net’s failure to catch an end is no proof there is none.

• Eddington (who led the team confirming general relativity; Einstein: “I knew it would be”): a man netting fish year after year never catches one shorter than a certain size and concludes there are none; the ichthyologist: examine your net, it isn’t designed to catch smaller fish. Like saying “I’ve never heard color, so color doesn’t exist”: the ear isn’t designed to catch it. So: a mathematical net is not designed to catch an end, even if there’s one out there.
• Argument by parity: (1) if not appearing in the mathematical net proved non-existence, matter too would not exist; (2) Schrödinger, who perfected wave mechanics (and showed its equivalence to Heisenberg’s and Born’s quantum mechanics, one being sometimes more convenient), and so best knows the mathematical theory of matter, says the modern atom “consists of no stuff at all,” comparing it to Plato’s geometrical theory of earth, air, fire, water in the Timaeus; (3) nobody says there is no matter. Conclusion: likewise for the end. Aside: Moscow’s worry that matter was disappearing from science and so science wasn’t proving dialectical materialism.
• Custom stronger even among scientists: Bohr kept his atom paper locked in a desk nearly a year for fear of being laughed at; de Broglie’s wave mechanics was called “La Comédie Française” until Einstein said test it, and Bell Labs confirmed it. If he came to class in a toga he’d be laughed at.
• Closing: custom is more important than the arguments, and than the misunderstandings, in explaining why many deny that nature acts for an end; “but neither misunderstandings nor the custom are a reason for saying nature doesn’t act for an end.”

His words #

• arts that help nature: help nature “in what it’s already trying to do, even without the art” (medicine, logic), against carpentry
• intellectual midwife: Socrates’s name for himself, logic as helping art
• mover / motive, attract, draw: equivocal between the third kind of cause (agent) and the fourth (end)
• first corollary / second corollary: recalled from earlier; misunderstood as false dichotomies between end and the more known cause
• custom vs. argument: custom “for the most part” stronger, even among scientists
• second book of wisdom [ed.: Metaphysics II]: Aristotle on custom’s influence on thought
• order reason considers vs. order reason makes (in its own acts, in the will, in exterior matter): Thomas’s division; mechanical arts = servile arts
• technical science / union of science and technology: the second source of modern customs
• res non grata: his twist on persona non grata, for substance in the modern mind
• civitas, civis: civilization tied to the city
• mathematical net: Eddington’s image applied to end and to matter

Texts #

Read in class: none read verbatim. Mentioned: Plato, Apology (anonymous accusers); Phaedo (day of his death); Symposium (dinner for Agathon); Ion; Timaeus (geometrical theory of the elements); Aristotle, “second book of wisdom” [ed.: Metaphysics II]; Thomas, Summa Contra Gentiles, beginning; Thomas’s division of order (locus not stated); Hippocratic Oath; Shakespeare, A Midsummer Night’s Dream, Julius Caesar; McNeill, The Rise of the West; Adam Smith, Theory of Moral Sentiments, Wealth of Nations; Marx, Das Kapital, Economic and Philosophic Manuscripts; Heisenberg, Gifford lectures; Cassirer, Philosophy of the Enlightenment; Tocqueville, Democracy in America vol. II; Orwell 1984, Huxley Brave New World; Iliad, Aeneid; Eddington (a book, unnamed); Schrödinger (paper, unnamed); Fides et Ratio (student).

His questions #

• Is the obstetrician helping nature, and is the carpenter? The obstetrician helps nature do what it is already doing; the carpenter is not helping the tree make a chair.
• Did Rapunzel’s beauty move the prince in the third sense of cause? No; it moved him as an end, the fourth sense.
• Which is stronger in our thinking, custom or argument? Custom, for the most part, even among scientists.
• What is the cause of day and night? Students say the earth’s rotation from custom, cannot defend it against his arguments, and still do not agree with him.
• Is intercourse the cause of the baby, or the baby of intercourse? Both, in different senses; the dichotomy is false.
• Are the four legs of the chair, of the cat, and the number four by nature or by art? Chair by art, cat by nature, the abstract four by neither.
• Did Newton merit the grandeur given him? (student) A great scientist, but not a model for all human knowledge.
• Is this the anti-metaphysical stance of Fides et Ratio? (student) Part of it, but more basic: it begins in the study of nature.
• Is the fact that no end shows up in the mathematical net a reason to say there is none? No, any more than the absence of matter (Schrödinger’s stuffless atom) proves there is no matter.