The Beauty of Order: Numbers in the Treatise on the Trinity, Limit in Art, and Why the Genera of Being Are Not the First Distinction

Orientation #

He says nothing about last time; today “we’re going to look at quantity,” and he defers the question of the first distinction “until I study the first philosophy.” Verified sources: about 19 minutes are read from his handout “Quantity – Chapter Six” (Categories ch. 6); the first 44 minutes fall between chs. 5 and 6 (inferred). The previous class finished the properties of substance and announced quantity; the next takes up Metaphysics V on quantity.

The class, in order #

1. Numbers in the treatise on the Trinity (“the square of three is what”) #

Thomas’s remark that the square and cube of a number carry the meaning of the number is tested on the Trinity: 3, 9, 27.

• The Trinity begins at q. 27 of the prima pars; it is divided into three parts, following “the order of teaching”: processions, the relations arising from them, the persons.
• Two processions (generation; the “want of name” procession of the Holy Spirit, “breather and breathed”) give four relations (father/son, son/father, and the common spirating/spirated); but only three persons, because relations distinguish only when opposed (Father and Son by paternity/filiation; both against the Holy Spirit by the common proceeding). 2 + 4 + 3 = 9. “Was that intentional?” — Thomas discovered it.
• Names: the Son has three (Son, Word, Image); the Holy Spirit three (Holy Spirit, Love, Gift). No separate question on the Son being son, since it is seen from the Father being father. Image is taken last because it presupposes both Son (like the one from whom he proceeds, same in nature) and Word (a thought is a likeness of what it is of). Gift is taken last because Love is “the first gift”: whatever else I give someone I give because I love them.

2. Secondary causes, the beauty of order, and knowing when to stop (“the beauty of the order of causes”) #

Why God does not make everything immediately, as he made Adam: two reasons from Thomas, tied to Aristotle on beauty.

1. God wants to share the nobility of being a cause (a cause is better than its effect); so I thank God for my soul, and God-through-my-parents for my body.
2. So there can be “the beauty of the order of causes.”

• Aristotle, Metaphysics XIII: good in its primary sense is the end, and geometry does not demonstrate through the end (the triangle is not pointed to defend itself, like a porcupine or thorny plant); but there is beauty in geometry. Beautiful = “what pleases when seen,” more generally “when known” (Mozart pleases the ear). Three kinds, in his order: order, symmetry, limit — “striking” that order comes first.
• Order: Homer’s plot has beginning, middle and end (plot is the soul of tragedy); the best thing after God is the order of the universe, its “form,” seen most in the angels (Msgr Dionne compared the order of teachers to the angels: Aristotle, then Thomas, then “I explain Thomas for you”; some teachers are fallen). Thomas also gives the beauty of the Church as a reason for its distinctions of orders and states — a hierarchy imitating the angels.
• Limit: Sherlock Holmes on the villain of “the Norwood Builder” (he thinks): “he lacked the supreme gift of the artist, knowing when to stop”; the critic on Titian’s Assumption, “he always knew where to stop”; critics on Mozart, who “arrives at his goal but never goes beyond” (ending of Don Giovanni, “the opera of operas”; Kierkegaard: Don Giovanni is the opera as the Iliad is the epic; Beethoven would go on bar after bar); cosmos, a beautiful ordered whole, and cosmetics — which help until “slathered on” (Fr Hardon called cosmetics role-playing).
• Student: are there levels of sharing in God’s causality — procreation, higher angels teaching lower? Yes, ordered all the way down; an angel illumines the one just below, being more proportioned to him; “brevity is the soul of wit”: the wiser angel knows more in fewer thoughts and must divide them “for the dummies below.”
• Tying it up: Shakespeare’s definition of reason culminates in “looks before and after”; looking before and after is looking for order (cause and effect); finding it pleases the mind. Thomas is “looking before and after” in ordering Love before Gift.
• Asides: Mozart’s 18th and 24th piano concertos (“how can I have been so deaf”); Boswell would skip Johnson for a Handel concert; Montaigne’s habit of carrying one sentence for a week and his own undergraduate problem solved “BAM” while writing on Dionne; Corelli’s concertos better than Vivaldi’s, “in a qualified sense”; calling Shakespeare greater than Homer “presumptuous” (Warren Murray).

3. Defining an accident, and what the Categories distinguishes (“substance is one genus of being”) #

Quantity is “size”; an accident is defined by what it is of, and the Categories distinguishes the genera of being.

• De Anima II opens “substance is one genus of being”; Thomas compares the definition of the soul to that of an accident: an accident is “something of another” — quantity the size or measure of substance, quality its disposition, health a good condition of the body (not itself a body). The soul is likewise defined by what it is the form of, though it is in the genus of substance: material substance is divided into matter, form, and the composite.
• What is distinguished in the Categories? Not the “highest genera” (his usual phrase) but, following Thomas, the genera of being: being is not a genus, since a genus is said with one meaning of things differing in kind, and being is not said with one meaning.
• Where the species under the genera are studied: discrete quantity (number, speech) in arithmetic; continuous (line, surface, solid, angle; place and time) in geometry and Physics IV (De Koninck gave a whole semester on place, another on time, ending with the definition of eternity); meter in the Poetics; material substance in natural philosophy, substance in general in first philosophy; under quality, habit in ethics, powers of the soul in the De Anima, shape in geometry. “So you see how this is higher.”
• Aside: “Natural Hearing” is the actual title of what we call the Physics; his mnemonic for the ten (not repeated).

4. Is this the first distinction? Confused before distinct (“What kind of knowledge do I have”) #

Being is most universal, yet other distinctions seem to come before the genera of being.

• Physics proem: the mind starts with confused knowledge. Examples: his Canaletto looked “straight down the canal” from both sides of the room — what knowledge had he before noticing? the Jupiter Symphony before Warren Murray told him five melodies combine in the finale; “what do you use in your salad dressing?”; his brother Mark naming the wines in a California “Burgundy” blend, which he himself could not do; Chianti with 10% Cabernet (“I’m confused still — buy another bottle”); Aristotle’s child calling all men father, his own children’s “look at that mother,” a child calling a cat a dog.
• Student: everything can be actual or potential. He develops it: Aristotle in Wisdom first divides being per se from per accidens (a “Christian geometer,” a “philosophical grandfather”: there is a way to become a geometer, a Christian, a grandfather, but no way to become the combination); then being per se in two ways: by the figures of predication (= the genera of being) and into ability and act.
• Ability/act is not a distinction of the genera but of “senses” or “ways” (Latin: modes) of being, and seems more universal, since in any genus there is ability and act, and even God, in no genus, comes under act: from the one middle term “pure act” follow infinity, perfection, simplicity (“bang, bang, bang”); ability too, as the power God is said to have (“almighty”).
• Yet in the fourteen books of Wisdom Aristotle takes up being by the figures of predication (substance, VII–VIII, led in from logic, then from natural philosophy) before ability and act (IX). Why here first? Perhaps because ability/act is reached by dividing substance into matter and form — “puzzling.” He leaves the question “until I study the first philosophy.”
• Asides: De Koninck never lectured on the Physics without seeing something new; Dionne showed him something in Rome at the Council; his own rereading of the prima pars; his teacher Kasurik [ed.: name uncertain in recording]: compared to Aristotle we have “the brain of an angleworm.”

5. Being and non-being: the prior distinction by opposites (“the same knowledge of what”) #

Plato and Aristotle hold there is the same knowledge of opposites, and being’s opposite is non-being.

• Distinguishing by opposites is a chief way; Aristotle will divide quantity by contradiction: parts have a common boundary (line at a point, semicircles at a line, body at a surface, past and future at the now) vs. parts do not (in seven, the two and five do not meet). Compare “set up or not set up” at the beginning of the Categories.
• Being/non-being: “to be or not to be”; the first statement, nothing can both be and not be at the same time in the same way, is in these terms. So the distinction being/non-being (something/nothing) seems before the distinction of the genera of being.
• Aside on omnipotence: “a stone so big he couldn’t lift it,” a square circle — not things at all; “nothing is impossible for God.” The ten genera are the most general kinds of things that can be — no wonder Boethius was impressed.

6. The structure of chapter six (handout) (“This chapter is divided into two parts”) #

Read from his handout: first part, the species of quantity, separating quantities per accidens from quantities per se (the species); second part, three properties of quantity. The species are distinguished in two ways, both by looking at parts: whether parts have a common boundary or not; whether parts have position with respect to each other or not; each way then unfolded.

7. Why quantity is divided by its parts, and “how much” (“every quantity consists in some multiplication of parts”) #

His question: why is quantity understood in its species by its parts?

1. Thomas (Summa Contra Gentiles, “my favorite book”): every quantity consists in some multiplication of parts; hence number is the first of quantities. Class agrees: every quantity is made up of parts.
2. Aristotle’s word is not the abstract “quantity” but poson, “how much / how many” — more concrete, proportioned to us — which ties to parts but also to measure: “how many chairs?” is not answered by “a plurality”; you count by one, or measure the table with a ruler.
3. Aristotle’s terms are concrete throughout: pros ti, “towards something” (Albert: ad aliquid; Gospel: pros ton theon), not “relation”; “how much / how it is” for quantity and quality (beaten into him by his first-grade teacher, so to say, Roman Kasurik [ed.: uncertain]).
4. The first sense of whole and part (composed whole) is in quantity, so it is natural to divide quantity by parts. Metaphysics V: quantity is divided into parts that are in it “somewhat in act” (not fully, being undivided), each apt to be one and a this-something — unlike the universal whole: dog, cat, horse are not actually in animal, nor red, blue, green in color, but only in ability; whereas the pieces are already somehow in the pie, and seven ones actually in seven.

• Senses of “in” recalled: in place; part in whole; genus in species (all actual); species in genus (ability); form in matter — genus is like matter, so in natural philosophy things not sharing matter (heavenly bodies vs. bodies here) are not in the same genus; “species” is named from form in Greek.
• Asides: the West Point plebe made to cut a pie into five even pieces; his son’s haircut (“what are you, a hippie?”); his own shoes at the military academy (“try a dozen”).

His words #

• “the order of teaching” — Thomas’s reason for treating processions, then relations, then persons.
• “beautiful” — what pleases when seen, more generally when known.
• “order, symmetry, limit” — Aristotle’s three kinds of beauty, in that order.
• “looks before and after” — Shakespeare’s definition of reason; looking for order.
• “Wisdom” [ed.: Metaphysics]; “Natural Hearing” [ed.: Physics].
• “the genera of being” — what the Categories distinguishes (not “highest genera”); being is not a genus.
• “confused” vs “distinct” knowledge — the mind’s starting point (Physics proem).
• “being per se” / “being per accidens” — Christian geometer.
• “figures of predication” — the division of being per se that yields the genera.
• “ability” [ed.: potency] and “act” — two “ways” (Latin: modes) of being; God is “pure act.”
• “common boundary” — the mark of continuous vs discrete quantity, an opposition of contradiction.
• poson — “how much / how many,” Aristotle’s concrete word for quantity.
• pros ti / ad aliquid — “towards something,” for relation.
• “multiplication of parts” — Thomas’s account of every quantity.
• “somewhat in act” — how parts are in a quantitative whole, against the universal whole.

Texts #

Read in class

• Aristotle, Categories, ch. 6, via the handout “Quantity – Chapter Six” (division of the chapter; the two ways of distinguishing species).
• Thomas Aquinas, Summa Contra Gentiles (sentence on quantity and multiplication of parts; locus not stated).
• Aristotle, Metaphysics V (quantity divided into parts somewhat in act), as quoted in the handout.

Mentioned

• Thomas Aquinas, Summa Theologiae, prima pars, q. 27 ff. (Trinity; names of Son and Holy Spirit); prima pars on secondary causes; on the states and duties of the Church.
• Aristotle, Metaphysics XIII (beauty in geometry); VII–IX (substance, then ability and act); the division of being per se / per accidens.
• Aristotle, De Anima II, beginning; Physics, proem and book IV; Poetics (plot; meter).
• Albert the Great’s paraphrase of the Categories; Boethius; Euclid’s Elements; Shakespeare (Hamlet, inferred); Conan Doyle, “The Norwood Builder” (as he recalls it); Kierkegaard on Don Giovanni.

His questions #

• Where do 3, 9 and 27 come into the treatise on the Trinity? q. 27 begins it; three parts; 2 processions + 4 relations + 3 persons = 9.
• Why does Thomas take up Gift last, and Image last? Love is the first gift; Image presupposes Son and Word.
• Why doesn’t God make everything immediately? To share the nobility of causing, and for the beauty of the order of causes.
• What are you distinguishing in the Categories? The genera of being — being not being a genus.
• Is the distinction of the genera of being the first distinction? Being per se / per accidens, ability / act, and being / non-being all seem prior; left open until first philosophy.
• Ability and act — a distinction of the genera of being, or of what? Of senses or ways (“modes”) of being, more universal, reaching even God.
• Do the two and the five meet in seven? No: discrete parts have no common boundary.
• Why is quantity understood in its species by its parts? Every quantity consists in a multiplication of parts, and quantity is the first sense of whole and part.
• What does “how much / how many” imply besides parts? A measure — you must count the chairs, measure the table.
• Are dog, cat, horse actually in animal? No, only in ability; parts of a quantity are in it somewhat in act.