Deriving the Ten Categories: Substance, Inherent Accidents, and Extrinsic Denomination by Cause and Measure

Orientation #

He opens mid-course, “expanding the words of Thomas”: the threefold division of predication under the ten categories, continuing the previous class’s turn to Thomas’s parallel treatments (prev. lecture). He closes by announcing that “maybe next time we’ll look at the one from metaphysics,” the fifth book, to see if it differs from the one in the Physics. The neighbouring classes treat the end of the antepredicaments and Thomas’s Metaphysics V exposition of being’s division into the categories.

The class, in order #

1. First way of predication: of the essence (“in three ways all predication comes about”) #

Point: all predication is of something said of an individual substance; the first way is when what pertains to its essence or nature is said of it, and this is the predicament of substance.

• Examples: “Socrates is a man”, “man is an animal”, “Champion is a horse”, “Tabitha is a cat” — all say what the subject is.
• Aside: a National Review book review claims a hundred million domestic cats in the country; the cat is now “more prominent than the horse that Aristotle uses as example”. His wife wept as a little girl when Tabitha gave birth.

2. Second way: belongs to the subject but not of its essence (“either is on the side of the matter”) #

Point: what is said of a thing not as its essence but as inhering in it subdivides by its root.

• Root in the matter of the subject → quantity (“quantity properly follows upon matter”; Thomas notes Plato put the magnum, the great, on the side of matter).
• Root in form → quality. Some qualities are founded on quantity: colour is in the surface of a body; figures in lines and surfaces.
• Relation to another → relation: “man is a father” says nothing absolute of man but a respect towards another.
• He remarks Thomas’s abstract words (quantity, quality) against Aristotle’s concreteness, and that Thomas’s exposition of St John shows he should have learned more Greek.
• Student objection: if quantity were taken away, would something essential be lost? His answer: quantity follows upon your nature but is not your nature — as half of four follows upon two: “half of four is not really two; it’s something that follows upon two”, always and in every two. So quantity is a property, and a property is “essential in a certain sense”, against a mere accident.
  • Property vs. accident (Isagoge): both are outside the nature, added to it; a property follows upon the nature, an accident (green, triangle) does not. So an “accident” in the sense of the Categories can be a property in the Isagoge’s sense.
  • Porphyry’s strict property: belongs to one species only, to every member, and always (half of four to two). Looser: “logician” belongs only to man but not to every man; “less than ten” to every two but not only to two. Dropping part of the strict meaning yields a name equivocal by reason — not purely equivocal, since a connection to the nature remains.
• Aside: Father Dulac (his college logic teacher, Laval-trained) despaired of students ever seeing accident-as-predicable from accident-as-opposed-to-substance — “how much trouble a word that’s equivocal, even equivocal by reason, gives people”; Samuel Johnson’s remark on a second marriage, “a triumph of hope over experience”.
• He notes Thomas will state this a bit differently in the Metaphysics; here the second, third and fourth highest genera all sit in the second member of the threefold division, though one sometimes divides absolute (quantity, quality) from relative.

3. Relative is not absolute (“how much really is double”) #

Point: a relative says nothing absolute about how much or what.

• “I’ll give you half my money” — could be two pennies; half is only half towards something.
• Three is half (of six) and a third (of nine): impossible if absolute, possible towards different things.
• “Am I a father or a son? Yes” — both, but not towards the same man; taller and shorter, towards different men.

4. Third way: denomination from something extrinsic (“that man is whiteness”) #

Point: the third way is when something outside the subject is said of it by denomination (the way of naming from Categories ch. 1).

• Even for things existing in a man we speak denominatively: not “man is whiteness” but “man is white”. “Euclid is geometry”, “Mozart is music” are figures; strictly Euclid is a geometer, Mozart a musician.
• Extrinsic denomination is found in one way commonly in all (material) things, and in one way in what pertains to man alone: the category to have, habitus, “man’s category” (his teacher once gave a public lecture on it).
• Illustration: we change clothing for a wedding, a game, swimming, serious and merry occasions, soldiering. Aside: his ten-year-old son, asked to speak at the Trivium banquet, arrived so dressed that another guest gave up the title of best-dressed man.

5. Cause and measure; forcing the four causes (“What does that depend upon for being”) #

Point: the common extrinsic denomination is by the ratio of a cause or of a measure; Thomas recalls Aristotle’s four causes, which he says only Aristotle and his followers distinguished.

• Cause in general (student’s answer accepted): the source of the being or becoming of something; “that which something depends upon for being or for coming to be”.
• His method: force the admission by necessity.
  1. The word “cat” on the board depends on the letters C, A, T — remove them and it is gone. This dependence is called matter: that from which something comes to be, and which is in it. Table from wood; the carpenter is not in the table, so if he is a cause it is another way.
  2. The same three letters spell “act”: “cat” depends also on the order of letters — form, which completes the nature of what it is.
  3. Letters do not arrange themselves; someone writes them — the mover or maker, first beginning of motion.
  4. Why did Berquist write this order? To talk about his favourite animal; or “act” because he wants to teach act and ability, the ninth book of wisdom — the end or purpose.
• Not every subject calls for all four: in mathematics one does not talk of mover or end, nor of matter in the ordinary sense (a Minnesota professor claiming “four causes everywhere”, reported by his friend Warren Murray, got it wrong).
• Matter and form are interior causes; mover and end exterior, and denomination is from the exterior ones.
• Asides: materia from mother; Mother Earth as source of all things for the poets, who come first (infima doctrina), before the philosophers’ water, air, fire — showing matter is the most known cause. The lieutenant colonel’s small son who asked whether each family member “came from mama” and, told Berquist did not, said “well, then you don’t belong, but you can stay”.

6. From cause: action and passion (“the act from the agent to another”) #

Point: only the agent cause grounds a predicament of extrinsic denomination.

1. Matter and form are on the side of the essence; predication from them belongs to substance (“man is bodily” — genus from what is like matter; “man is rational” — difference from form).
2. The end causes nothing apart from the agent; it is a cause only as it moves the agent.
3. So only the agent remains. Denominated from an agent cause → passion/undergoing, “nothing other than to receive something from the agent”; the agent denominated conversely from its effect → action/acting upon, “the act from the agent to another”.

• Kicking: I must have something outside me to kick; you are kicked by something outside you. Kicking oneself is one part on another.
• Relation to motion (student’s question): motion is from the mover into the moved; pushing the glass — the glass is moved by something outside it (my hand is not part of the glass), I am moving something outside me.
• Student: could actio be in quantity or quality? Answer: Aristotle will later put motion itself in the categories — growth in quantity, alteration in quality, locomotion in where — as something imperfect reduced to the genus; but action and passion are said by reason of something outside you. Distinction:
  • becoming hot (water for tea): imperfect acquisition of a quality, in quality, considering only what goes on in the water;
  • being heated by the stove: undergoing, bringing in something outside; “the stove is hot” is a quality, “the stove is heating the water” is action.
  • Learning logic: acquiring a habit or disposition, first species of quality.
  • Student: isn’t any passio a passio in quantity or quality? “That’s a distinction he makes” — the same as above.
• Student: “It’s kind of a subtle distinction.” He: “it’s a real distinction” — the mind going from confusion to distinction.
• Asides: “you can’t understand making a cup of tea without logic”; Dr Douglas makes very good tea; the despairing logician seen burning exams “with joy”; his father never hit him; he himself whacked the table with a belt — “had to act upon the poor table”.

7. From measure: when, where, position (“the extrinsic measure is one thing”) #

Point: the other common extrinsic denomination is measure, which Physics IV ties to place and time.

• Examples of measuring by something outside: a cup of rice to two of water; children’s height against the wall; the doctor’s height machine (he has shrunk); estimating the March for Life crowd by area covered; Robinson Crusoe marking sunrises.
• Wine bottle: the inner surface containing the wine is a quantity; the wine’s being contained by a surface outside it is a measure of how much wine (the big bottle for Thanksgiving).
• Thomas: intrinsic measure (a thing’s own length, width, depth) denominates from something inhering — “a large mountain”, quantity. Exterior measures are time and place: from time, when (quando); from place, where (ubi); and position (situs) adds to ubi the order of one’s parts in place — in this room, but sitting, standing or lying.
• Position vs. intrinsic shape: falling from an airplane his parts keep the same order but he is not standing — standing needs something outside to stand on; knocked over he is not lying down without a bed or floor; the guest told “sit down” who squats is crouching, not sitting, lacking a chair. Even standing depends on the floor holding him up.
• Why no counterpart of situs for quando: “where” does not include order of parts, but time’s very definition does — “the number of motion according to the before and after”; the first sense of before and after is in time (post-predicaments). He flags this “very subtle”.
• Aside: Richard II, “time made me his numbering clock”.

8. Man’s category, and the order of the list (“Thomas is goofing it up here”) #

Point: what is special to man is denomination from something extrinsic that is neither cause nor measure — habitus.

• Order: Aristotle lists where, when, position, having, then acting upon and undergoing last; Thomas treats having last, and old logic books (the one used in his college) followed him. Reason for Aristotle’s order: where and when are tied to quantity, action and passion to quality, and quantity is before quality. Thomas’s motive: the common ones before “man’s oddball thing” — so Thomas “goofing it up a little bit”.
• Other animals are armed, clothed, shod by their own parts (fur thickening in winter), like a man said to have a hand or a leg; man is so denominated from something extrinsic (overcoat, knife and fork, hammer and saw). Latin habitus; the English “habit” has another sense, so beware. It is attributed to animals only when used by man — a parade horse, girls dressing a cat, Bob’s dog in a little jacket.
• Asides: cats outwit dogs in the leaf pile; Washington Irving on Sir Walter Scott’s cat pawing each dog; Christ the lion of Judah, Richard the Lionhearted, “the dogs are outside the city”, Thompson’s “Hound of Heaven”; an EWTN convert whom the Summa brought back to the faith wrote a book on the Dominican saints (name not recalled); Dominic’s mother’s dream of a dog.

His words #

• predicament — his term for category throughout
• “essence” — he calls it a “terrible word” (French essence = gasoline); prefers “nature, what it is”
• property vs. accident — Isagoge senses; property follows upon the nature
• equivocal by reason — a name equivocal by dropping part of its meaning while keeping a connection
• denomination / denominatively — being named from something (Categories ch. 1)
• habitus, “to have” — man’s category; not “habit” in the other sense
• ratio of a cause, of a measure — “notion”
• matter — that from which something comes to be and which is in it
• form — what completes the nature of what it is
• mover or maker — first beginning of motion [ed.: efficient cause]
• end or purpose — final cause, causes only by moving the agent
• “the Philosopher” — Aristotle, by antonomasia
• “undergoing” [ed.: passion]; “acting upon” [ed.: action]
• “Natural Hearing” [ed.: Physics]
• “act and ability” [ed.: act and potency]; “ninth book of wisdom” [ed.: Metaphysics IX]
• quando (when), ubi (where), situs (position: order of parts in place)
• time — “the number of motion according to the before and after”
• infima doctrina — said of the poets coming first
• magnum — Plato’s “great”, on the side of matter

Texts #

Read in class

• Thomas Aquinas, Commentary on the Physics, the passage on the threefold division of predication into the ten predicaments (locus not stated; handout pp. 12–13 on Categories ch. 4)
• Aristotle, Categories, ch. 4, the enumeration of the ten (handout)

Mentioned

• Aristotle, Categories, ch. 1 (denominative naming)
• Porphyry, Isagoge (property, accident)
• Aristotle, Physics IV (place and time)
• Aristotle, Metaphysics V (next time) and IX (act and ability)
• Post-predicaments (first sense of before and after in time)
• Thomas, exposition of St John (aside)
• Shakespeare, Richard II; Francis Thompson, “The Hound of Heaven”; Washington Irving on Scott

His questions #

• If I took away quantity, would I be taking away something essential from you? Not the nature itself, but a property that follows on the nature — like half of four on two.
• Can you have two without half of four? No; it follows upon two always, but towards another.
• How can three be half and a third? Towards different things — as one is father and son towards different men.
• What do you mean by a cause? That which something depends upon for being or coming to be.
• What does the word “cat” on the board depend upon? The letters (matter), their order (form), the writer (mover), and his purpose (end).
• Could actio belong to quantity or quality? Motion does, as imperfect; action and passion are said by reason of something outside.
• In what category would you put becoming hot? Quality, as something imperfect; “being heated” is undergoing.
• Would I be standing as I came down the sky? No; standing needs something outside to stand on — hence position, not shape.
• Why is there no category standing to quando as situs to ubi? Order of parts is already in the definition of time.
• Why does Aristotle put where, when, position before acting upon and undergoing? They are tied to quantity, the others to quality, and quantity is before quality.