Three Is Enough: The Number Three in Logic, Rhetoric, Music, Physics and Theology

Orientation #

He opens by recalling that “when you were reading ten, it seemed quite probable that there is just two things,” the two contraries, and that now there is reason to think there is a third; the class picks up at Aristotle’s closing sentence of that stretch, that the beginnings are “neither one nor more than two or three.” He ends by promising “to get to wisdom,” which “is about three things.” Verified sources place the class at Aquinas’s lectio 11 on Physics I, with readings from his handouts “Whether the beginnings are two, three or more” (p. 2) and “Foreword to Logic” (p. 8). The previous class worked through the arguments for a third underlying thing and Aristotle’s conclusion that three principles suffice; the next introduces readings twelve and thirteen on “becoming.”

The class, in order #

1. Two or three: the “rule of two or three” (“neither one nor more than two or three”) #

Point: Aristotle’s hesitation between two and three beginnings recalls his own “rule of two or three”: the same subject can often be sensibly divided both ways, and each division brings something out.

• Logic example (one name said of many things): divide into two: same meaning in all cases (univocal) vs. more than one meaning (equivocal); then subdivide equivocal into “equivocal by reason” (some connection among the meanings) and “equivocal by chance” (none). But Thomas sometimes divides at once into three: wholly the same meaning, wholly different, partly the same and partly different. Same three, reached by a two-step or a one-step division.
• Goods of man: the Greeks (Socrates in the Apology; Aristotle, Politics VII) divide into goods of soul, body and outside goods, an exhaustive three; “early to bed, early to rise makes a man healthy, wealthy and wise” touches all three. But he sometimes divides into two: goods inside man (soul or body) vs. outside him (car, house, clothes). Also exhaustive.
• Plot in the Poetics: beginning, middle and end (Homer praised for seeing that a plot’s unity is a course of action, not one man); later in the Poetics, two parts, tying the knot and untying it. A case where the two divisions differ more.
• Family: parents and children, or father, mother and children. “We need that division nowadays.”

2. Why start from the contraries and not from the subject? (“kind of stand out in the idea of change”) #

Student: could Aristotle have started from the underlying thing that all posit, and then added that change needs the contraries? His answer:

1. Change is “becoming different than you were,” so the opposition between the way it was and the way it has become stands out first.
2. The third thing, the subject, is obscure because it is an ability, and ability is less known than act.

• Butter: is it hard or soft? It is able to be both, in a way one ability for both, though it cannot be actualized in both. “An obscure thing when you come down to it.” Student: is it rather so obvious we do not think of it? He: in some ways it was more obscure; the difficulty people have understanding ability will come up as the course goes on. In the ninth book of wisdom [ed.: Metaphysics IX] Aristotle mentions the Megarians, who deny there is any such thing as ability. Heisenberg (Gifford lectures) says people wrongly transfer the actuality of things around us down to the fundamental particles, which “exist only in potency”; and “we know matter only through the forms of matter,” which Aristotle said long before.

3. Three is enough, and often three is all (“Three is enough, and sometimes three is all”) #

Point: Aristotle’s “two is not enough, but three is all you need” is so common in the arts, sciences and life that “one should stop and think about that.”

• Book on the universe [ed.: De Caelo]: only three dimensions. Geometry proves it: draw two lines at right angles, a third perpendicular to the page at right angles to both; no fourth line can be at right angles to all three. Aristotle assumes the geometrical reason and gives only a sign, from language: of two we say “both,” and three is the first number of which we say “all.” “We’re both going” vs. “we’re all going.”
• Not always the case, and Aristotle himself does not think so; but “common enough that it’s worth stopping and noting.”

4. Daily life (“Three is enough, huh? Interesting”) #

• Three meals a day; skipping lunch leads to stuffing yourself at night.
• A main course needs three things: meat or fish, potato or rice, a vegetable. Brother Mark as a bachelor cooked two and felt something missing, and filled in with San Francisco sourdough.
• Quebec restaurant sign “repas complet”: appetizer, main course, dessert; “not complete without those three things.” Not philosophers, just how we speak.
• Aside: student trick in Quebec, eat the fries, send the undercooked meat back, get the whole plate back.

5. The trivium: logic, rhetoric, grammar (“three means of persuasion”) #

Logic:

• Three acts of the mind: understanding what a thing is, the true or false, reasoning. “That’s all there is.”
• Syllogism: two premises, three terms, “three and two.”
• A definition has at least three parts, because (Porphyry) even a difference is said of more than one species, so you need at least two differences: square = equilateral, right-angled quadrilateral. Rhetoric, the art of persuasion:
• Aristotle discovered there are three means of persuasion: the image the speaker projects of himself, moving the emotions and prejudices of the audience, the arguments or apparent arguments. Rhetoric began in the Greek cities of Sicily after the tyrants were cast out; at first emotions were emphasised, some reason had to be given, and Aristotle saw the neglected importance of image (why politicians worry about their image).
• Othello as the example of the three in order: Iago first makes himself credible (friend of Othello, perceptive observer, reluctant to voice suspicions: “I like not that… nothing, my lord”); then arouses jealousy, since, as Iago says, a flimsy proof seems like holy writ to a jealous man; then gives the weak argument of the handkerchief. To possess the art fully you need all three, and that is all.
• Three species of rhetoric: political (persuading about the future), courtroom, ceremonial (Memorial Day praise). Three kinds of signs in the enthymeme, compared to the three figures of syllogism. Three kinds of example: historical, proportional (invented), fable.
• His own classroom examples for one conclusion (don’t marry in college): historical (the man who never finished his degree); proportional (nations don’t appreciate liberty until they lose it); fable, the weakest (the goose that laid the golden egg; “climax spoils romance”). Grammar (from a learned grammarian):
• The noun is the fundamental part of speech, standing under everything else like a substance. Add a word presupposing a word: adjective (“wise man”) or verb (“the man walks”). Then a word presupposing a word that presupposes a word: the adverb (“very wise,” “runs fast”). No fourth is needed: “three is enough” to express your thoughts (articles aside).

6. Poetry and fiction (“You don’t want any more than what three”) #

• Plot’s beginning, middle and end (“later on we’ll talk about it a bit with the Trinity”). Aristotle in the Poetics: drama reached perfection when Sophocles introduced the third actor. Sartre’s No Exit: three people in hell who cannot get along; the “love triangle” makes things interesting.
• Trilogies (C. S. Lewis); Divine Comedy’s three parts; Paradise Lost’s twelve books fall into three: action forward (four books), the angel’s account of creation and the fall of the angels (four), the temptation and fall (four). Tom Jones’s eighteen books: countryside, inns on the way to London, London, six each.
• Shakespeare’s sonnet on old age: three quatrains, three images, late autumn, twilight after sunset, the dying fire on the ashes of youth, “properly arranged” since each period is shorter than the last, then the couplet sums up.
• A speech professor’s rule: never give more than three examples, the audience can’t take in more. Even Aristotle in the first reading gave three kinds of example that the confused is before the distinct. Macbeth’s “Out, out, brief candle”: walking shadow, poor player, tale told by an idiot, three images, and he stops.

7. Music (“three is what enough”) #

• Trio sonata (Tang’s notes on Handel Op. 5): two treble instruments and continuo, the simplest ensemble able to display most aspects of musical craft; established by Corelli (four sets of twelve, 1683-94). Lang: Handel’s Op. 5 trios stand with Bach’s at the head of Baroque chamber music.
• Girdlestone: before Mozart the three-movement concerto plan was not yet predominant; all Mozart’s piano concertos have three movements (orchestral prelude, andante, rondo). Vienna made four movements traditional for quartets and symphonies, but Mozart’s Milan quartets and the 34th and 38th symphonies have three and are complete works; the only great two-movement symphony is known as Schubert’s “unfinished.”
• Concerto vs. symphony: the concerto is closer to a drama, with a plot (beginning, middle, end); the symphony more an imitation of a virtue: Jupiter and Linz symphonies, both in C major, represent magnanimity (De Koninck: “you’re probably right”).
• Plot of the 23rd concerto in A major: joyful first movement with underlying sadness; second in F sharp minor where the sadness comes out and is purged; third’s bright melodies “like sunlight into a dark room,” with the sadness brought back and overcome, not escaped.
• Girdlestone on the first movement: textbooks divide it into four (double exposition, development, recapitulation), but for the listener the real development begins with the solo entry, so a threefold division is more sensible, as for sonata and symphony. Mozart’s Italian operas likewise go tonic, dominant, tonic: a beginning, middle and end as a whole, and each part again.
• Asides: first hearing the Linz Symphony at the Saint Paul Public Library; meeting De Koninck at Kasurik’s house, who answered his questions and offered to publish his Mozart ideas, never written up; the 23rd as favourite of Brother Mark, Jay Hubbard, his wife.

8. Natural science (“There must exist a third universal constant”) #

• Aristotle distinguishes three kinds of motion, giving the three parts of natural science: change of place, change of quality, growth; our physics, chemistry, biology.
• Heisenberg (Physics and Philosophy; “Planck’s Discovery” in Across the Frontiers): relativity is connected with one universal constant (velocity of light), quantum theory with another (Planck’s quantum of action); “there must exist a third,” for dimensional reasons: a complete set of units needs at least three (CGS: centimetre, gram, second; or length, velocity, mass), and the third natural unit would be a length of about 10^-13 cm, the order of small atomic nuclei; only such a theory could determine the masses of elementary particles. He asks “how many?” like the question at the head of this reading. Berquist: “I don’t think it’s established now.”

9. Theology: beginning, middle and end as vestige of the Trinity (“perfection in three, as in a beginning, middle, and end”) #

• Theology’s threes: the Trinity; the Incarnation’s three offices of Christ as man, king, priest, prophet or teacher, which Vatican II uses for bishop, priest and laity, each sharing the three in a different way; faith, hope and charity, by which Augustine and Thomas divide catechetical instruction.
• Thomas (Sentences), on the Trinity known only by faith: objection from the book on the universe (De Caelo et Mundo), where Aristotle says by the number three we praise God. Reply, following the commentator: Aristotle did not intend a Trinity of persons, but since in all creatures perfection appears in three, beginning, middle and end, the ancients honoured God with threefold sacrifices and prayers.
• Sentences article “whether the parts of the vestige [footprint] of the Trinity are three only or two”: the creature’s perfection is not in its beginnings, matter and form, neither of which has perfect being by itself, but in its joining to its end; nature does not join distant things without a middle; so beginning, middle and end (Pythagoras’s perfection of each creature) represent the distinction of persons, the Son the middle, the Holy Spirit the term of the procession. Objection: creatures represent many divine attributes (Dionysius, Divine Names ch. 9), so more than three parts. Reply: however many, they have the order of beginning, middle and end. Elsewhere: because the perfection of every quantity is comprehended by three, a threefold difference is laid down.
• Three stages of charity (beginners, middle, perfect) match Augustine’s and Thomas’s division of the Psalms into three fifties, ending in a psalm of asking forgiveness, of good action, of praise: fighting vices, advancing in virtue, resting in God. Some see three so prevalent in preachers because of the Trinity.
• Lighter close: fairy tales always have three people; Shelley on London tavern signs (Three Cups, Three Tuns, Three Nuns…), explained by heaven, earth, water; Pythagoras’s perfect number; Jove, Neptune, Pluto; fates, furies, graces, muses. He adds the angels: three hierarchies, each of three orders (seraphim, cherubim, thrones; dominations, virtues, powers; princes, archangels, angels), and Dionysius says each order has a beginning, middle and end.
• “This is not complete,” and wisdom, when we get there, “is about three things.”

His words #

• rule of two or three: the same thing can sensibly be divided into two or into three, sometimes both.
• equivocal by reason / equivocal by chance: same name with many meanings, connected or not [ed.: a consilio / a casu].
• ability: what the subject is, less known than act; “an obscure thing” [ed.: potency].
• ninth book of wisdom [ed.: Metaphysics IX].
• book on the universe [ed.: De Caelo]; Latin title De Caelo et Mundo.
• “three is enough,” “three is all”: Aristotle’s “two is not enough, but three is all you need.”
• both / all: the sign from language that three is the first “all.”
• repas complet: the three-part Quebec meal.
• means of persuasion: image, emotions, arguments.
• vestigium: “footprint,” the vestige of the Trinity as against its image.

Texts #

Read in class

• Aristotle, Physics I via Aquinas, lectio 11 (verified handout); closing line “the beginnings are neither one nor more than two or three.”
• Handouts: “Whether the beginnings are two, three or more,” p. 2; “Foreword to Logic,” p. 8 (verified; the division of equivocal names).
• Shakespeare, sonnet on old age (inferred: Sonnet 73); Macbeth, “Out, out, brief candle.”
• Tang, notes on Handel’s trio sonatas Op. 5; Lang, Handel biography; Girdlestone, Mozart’s Piano Concertos.
• Heisenberg, Physics and Philosophy (Gifford Lectures); Across the Frontiers, “Planck’s Discovery.”
• Thomas, Sentences: reply on De Caelo praising God by three; article on the parts of the vestige of the Trinity, with the Dionysius objection; a passage on threefold difference.
• Shelley, The Inns and Taverns of Old London. Mentioned
• Plato, Apology; Aristotle, Politics VII, Poetics, Rhetoric (means, species, signs, examples), Metaphysics IX (Megarians), De Caelo (three dimensions).
• Porphyry on the difference; Shakespeare, Othello; Sartre, No Exit; Dante, Divine Comedy; Milton, Paradise Lost; Fielding, Tom Jones; C. S. Lewis trilogy.
• Dionysius, Divine Names ch. 9 and the angelic hierarchies; Vatican II documents on bishop, priest, laity; Augustine and Thomas on the Psalms and catechesis.

His questions #

• Could Aristotle have started from the underlying thing all posit, and then added the contraries? No: the opposition of contraries stands out in “becoming different,” while the subject, an ability, is obscure.
• Is the subject obscure because it is too obvious? In some ways it was more obscure; the difficulty of understanding ability comes later in the course.
• Can you draw a fourth line at right angles to three mutually perpendicular lines? No; hence three dimensions, and the sign from “both” vs. “all.”
• How many meals do you need? What does “repas complet” mean? Three; appetizer, main course, dessert.
• Did three have anything to do with logic? Three acts of the mind; three terms in the syllogism; at least three parts in a definition.
• How many means of persuasion, and how many species of rhetoric? Three and three: image, emotions, arguments; political, courtroom, ceremonial.
• What is the third word, presupposing a word that presupposes a word? The adverb; no fourth is needed.
• Did Heisenberg’s third universal constant happen? “I don’t think it’s established now”; left open.
• Are the parts of the vestige of the Trinity three only or two? Three: beginning, middle and end, since perfection is in the joining to the end through a middle.