The Art of Definition II: Substance and Accident, and How to Hunt Down a Definition

Orientation #

He is working through a handout on definition: “page five” gives a third distinction among definitions; “page six and seven” turn to how one arrives at a definition. He refers back to “the proemium to wisdom” and “the sixth attribute of the wise man” as already looked at, and to the earlier distinction “by cause or by effect, by difference or by property” (prev. lecture). A text-matching system found the handout “The Royal Fragment”, p. 15 (about 10 minutes read from it) and the printed volume DHB Vol I – The First Philosophers, p. 31, in this episode’s audio; the transcript itself does not name them. The previous class treated definition of a thing by genus and difference against looser definitions by property or effect, and the next takes up division of a whole into its parts.

The class, in order #

1. A third distinction: defined by itself vs. defined as something of another (“a third distinction, but quite different”) #

The point: the first two distinctions concerned how we define (cause/effect, difference/property); this one is based on the kind of thing being defined, so that the definitions cannot be of the same kind at all.

• Root case: substance vs. accident from Aristotle’s Categories. Man and dog: a thing that exists, not in another, a subject. The health of the man: exists only in the man. Example: leave the man in this room and put the dog in the next, fine; but you cannot put the man in one room and his health in the next.
• Etymologies: substance, “to stand under” (the accident); accident, “to happen to” something else.
• So health must be defined as something of another: roughly “the good condition or good disposition of the body”; sickness a bad disposition. Substance is complete in itself; accident is incomplete, something of another.
• Tension with the word “definition” (from limit): within the limits of Worcester or my field there should be nothing but Worcester or my land; yet defining an accident brings in something other (the body, in the genus of substance). Hence in the “seventh book of wisdom” [ed.: Metaphysics VII] Aristotle says either there is no definition of accident or there is definition in a secondary sense.

2. Wisdom, love, and the soul as “something of another” (“the highest or the greatest perfection of reason”) #

The point: the distinction is broader than substance/accident — it is between what can be defined by itself and what must be defined as something of another.

• Wisdom: Thomas calls human wisdom “the highest or greatest perfection of reason.” All reasoned knowledge (geometry too) is a perfection of reason; wisdom is the highest. Not yet complete, but already wisdom is being defined of reason.
• The sixth attribute of the wise man (proemium to wisdom; Thomas quotes it in the proemium to the Nicomachean Ethics and gives the reason): he orders and directs others — because wisdom is the highest perfection of reason and it is proper to reason to order. Shakespeare’s definition of reason, “the ability for a large discourse, looking before and after,” where before and after define order. So one cannot understand human wisdom without understanding reason.
• Love is something of the heart, as desire is. Love or liking: the conformity or agreement of the heart with its object; desire or wanting: the heart seeking the object not yet had; joy, delight, pleasure: the heart resting in the object once possessed. You cannot know love without saying what it is of the heart.
• The human soul is not an accident but a substantial form, yet it too must be defined as something of another. Aristotle, after the dialectic of Book One of On the Soul, gives six divisions in Book Two: as Thomas explains, three on the side of the soul and three on the side of that of which the soul is something — just as defining wisdom means first saying something about reason.
• He stresses: “this is an extremely important distinction”, and note it is “much different” from the first two, which concerned how perfectly one defines.

3. Logic cannot be wholly separated from things (“you can’t separate logic entirely from things”) #

The point: since substance and accident require different kinds of definition, logic must take account of things, against the modern symbolic or mathematical logicians who want a purely formal logic and forget that logic exists to help us know things (man and health, soul, wisdom and reason).

• Aristotle in the Topics calls the first category “what it is” instead of substance; but health too is in some way “what it is” — more fundamentally “how you are” (how are you today? sick, healthy). Aristotle: “healthy seems more real than health,” because “healthy” brings out that it is something of another; likewise “wise” than “wisdom”.
• Student: is wisdom then an accident of an accident? He answers only in general: it is something of another; you cannot understand wisdom without reason, health without the body.
• Analogy (there is a gap in the recording here): the wine glass, the mug, the water glass are tools for drinking, and some differences among liquids matter for the tool (wine wants a stemmed glass to swirl and sniff; hot chocolate and coffee can share a mug; he likes a clear mug to see the colour of tea, irrelevant for coffee), while others do not. Definition is a tool for understanding what a thing is: the difference between defining square and defining circle is irrelevant to the logician (geometry’s business, not a different kind of definition), but defining health against defining man needs a different kind of definition, as coffee and water need different receptacles.
• Likewise definition by cause vs. by effect concerns things (cause and effect are in things); the whole of ethics depends on what kind of definition you have of good and bad.
• Aside: a symbolic logician at the University of Minnesota told a friend that symbolic logic is useless for knowing things — “a moment of honesty”; he will not go quite that far.

4. Finding a definition is not automatic (“logic is not a substitute for thinking”) #

The point (pages six and seven): the logician must also know how to arrive at a definition, and these ways must be followed but still require thinking — unlike adding, subtracting, multiplying, dividing, which become automatic.

• Example from his own work: judging whether a student has said something takes thought; averaging the marks is mechanical.
• The definitions of motion, soul, eternity, time are “a major work of reason.”

5. The castle: three places to begin (“three ways of attacking that castle”) #

The point: Plato and Aristotle compare defining to hunting (the Posterior Analytics uses a word from thērion, a beast that tries to escape); he prefers a military metaphor, the enemy castle guarding “what it is.”

• Three attacks: from the side (battering ram, knock down walls); from below (undermine by tunnels — the North Koreans’ tunnels; defenders dig counter-tunnels); from above (catapult, airplane, flaming missiles).
• Dropped into logical terms: above = the more universal, below = the less universal or singular, side = the equally universal. Why the more universal is “above”: we place animal above man, dog, cat, horse, quadrilateral above square and oblong; species is “a particular kind of thing placed under a genus”; we say “man is an animal” rather than “animal is a man”; the subject (sub, under) is that of which something is said; hence Porphyry’s tree, which spreads out downward like a Christmas tree (aside: at a Christmas party they once gave the logician a Porphyry’s tree as a joke).
• A division into three: more, less, equal — “what else is there?”; a distinction fitted to reason, since the universal exists only in the mind.
• More precisely: from above you start from a genus; from below, from examples (species of a genus, or individuals); from the side, from a property or proper effect, or even an encircling definition.
• Where people spontaneously begin: a child asked what a circle is points to the clock; Socrates’ interlocutors answer with examples (virtue; Euthyphro on piety; “episteme” or science, likely the Theaetetus (inferred)); students say “a dog is an animal,” “love is an emotion” (at most one kind of love is an emotion, and emotion is a genus), “a sonnet is a poem,” “a chair is something to sit on” (benches and sofas too — like a genus); “a comedy is a play that makes you laugh” starts from the equally universal.

6. The road from examples: compare and separate out what is common (“Compare them to find what is common”) #

The point: from many examples you compare, separate out what they have in common, and leave aside their differences — simple to state, long in practice.

• Shakespeare’s 154 sonnets: at first the same length; more carefully, all 14 lines; then a meter; then the rhymes — lines 1 and 3, 2 and 4, 5 and 7, 6 and 8, 9 and 11, 10 and 12, then a final rhyming pair — three quatrains with alternate rhyme completed by a rhyming couplet; and what Shakespeare is doing, making a likeness of some thought or feeling. His definition: a likeness of thought and feeling in fourteen lines of iambic pentameter, divided into three quatrains with alternate rhyming and completed by a rhyming couplet. Not reached all at once; others may help.
• Definition itself: compare the definitions at the start of Euclid, see each has something like a genus and differences, and arrive at “speech composed of the genus and differences.”

7. The road from the genus: divide and test convertibility (“By dividing, right? You divide by differences”) #

The point: from the more universal you start with something one, divide the genus by differences, see under which difference the thing falls, add it to the genus, and check whether the resulting speech is convertible; if not, divide again.

• Square: quadrilateral → parallelogram or trapezium; opposite sides and angles equal, so parallelogram; right-angled or obtuse → right-angled; but “right-angled parallelogram” is not yet convertible with square, so another division is needed.
• Thinking is required at each step: which differences are appropriate to this genus, under which the thing comes, whether the result converts. No little machine can go from genus to difference.
• The two beginnings are contraries: above, something one; below, many. Aristotle treats both ways in Posterior Analytics II, because definition is the beginning of demonstration (why Euclid starts with definitions); one way is more proportioned to us, the other more rigorous. It is like his later distinction between syllogism and induction: induction goes from many particular statements to a general one, and comes first for us because it starts from the singular and sensible.

8. The road from the equally universal: reasoning inward (“What road did you take to get in there? Reasoning”) #

The point: from a property, proper effect or encircling statement, you reason from outward knowledge to inward.

• Wisdom (“two birds with one stone”): start from “wisdom is the best knowledge,” which converts. What does “best” mean? Better than all the rest (my best student, the salesman’s best model, the best cut of meat). Why is one knowledge better than another? At the start of On the Soul Aristotle says: if it is about a better thing or if it is more certain (smelling a rose vs. smelling [what he leaves unsaid], hearing Mozart vs. noise, seeing a beautiful painting vs. the ash can); in the Parts of Animals he adds that being about a better thing is the more important criterion — better to know a better thing imperfectly than a lesser thing perfectly. And before seeing before and after you must see a distinction; the fundamental distinction between knowledges is what they are of. Hence: knowledge of a better thing is better knowledge (seen inductively from the examples).
• Conditional syllogism: if knowledge of a better thing is better knowledge, then knowledge of the best thing is the best knowledge; but the antecedent holds; so the best knowledge is knowledge of the best thing. Then: wisdom is the best knowledge; the best knowledge is knowledge of the best thing; the best thing is God (known, or believed); therefore wisdom is the knowledge of God.
• Aside (garbled): Galileo, and more so Einstein, who wanted to know the universe as a whole.
• Moral virtue: start from “moral virtue is a praiseworthy quality.” At table, what is praised? Not eating too much or getting drunk; not eating too little, as with women suffering anorexia, who are killing themselves. What is praised is in the middle, not the extremes. So, syllogizing: moral virtue is in the middle — only the beginning of reasoning out what it is.

9. Using all three attacks together (“attacking in three different ways at the same time”) #

The point: in practice nobody uses only one way; as in the siege, one attacks from all sides until the thing “surrenders.”

• Investigating moral virtue one also looks at examples. Moderation in eating and drinking: Teresa of Avila, seen enjoying partridges brought to the convent — “Penance is penance, and partridge is partridge”; one can err by defect and waste good food. The woman who cooked a specialty for St Francis, a fastidious man who was always thankful: food a woman goes out of her way to make should be received with open arms, not refused because pleasurable. Still, most go to the other extreme.
• Liberality or generosity lies between the stingy man and the extravagant: a fifty-dollar bottle of wine with dinner would be extravagant for him; taking his wife to McDonald’s for their anniversary is fine if that is all he can afford; when his daughter marries he will spend far more than on a family dinner — the right amount is fixed by the event. A wealthy Maharaja who gave about twenty dollars to charity at a family wedding: stinginess, inappropriate for him.
• Aristotle in Nicomachean Ethics II does all three: reasons that what is praised hits the golden mean, looks at particular virtues to see what they have in common (each in the middle), and starts from quality or habit and divides it.
• Against Leibniz and the founders of mathematical logic (“when men disagree, we’ll sit down and calculate”): thinking is not that simple; logic never becomes automatic like counting; it is a help to thinking, not a substitute.

10. Student question: reasoning vs. calculating (“logike… and then you had logistike”) #

The point: the modern error rests on not distinguishing reasoning from calculating.

• Counting the people, books or chairs is immediate; defining takes thought. The Greeks had two arts: logikē (defining and reasoning) and logistikē (counting and calculating — the word “logistic” has a different meaning now). He learned to count and calculate in grade school, logic only as a high-school senior from a college friend.
• Likeness: both are discourse; counting precedes calculation as defining precedes rigorous reasoning. But counting men does not tell what a man is, and “animal with reason” does not tell how many men are here; each must help the other (one must recognize men to count them).
• Student: is that because one deals with substance and the other with the accident quantity? He: there is something accidental there, but the point is that they are different questions — what is water, and how much water is there in the world.

11. Student question: the senses of “reason” (“Is the word reason here univocal or equivocal”) #

The point: a student, reading Thomas on Providence and predestination (Providence defined through ratio ordinis), asks whether the senses of ratio need distinguishing; he answers by distinguishing reason as ability, act and object.

• “Reason is the ability to give a reason”: is that a bad definition, using the defined word in the definition? Not if the word shifts meaning — the first is the ability Shakespeare defined, the second its object. Parallel: “taste” as one of the five senses vs. the taste of the food; likewise “smell”. And “to reason” names the act. Three senses: ability, act, object.
• What is the best reason one can give for a statement? Two straight lines intersect: are the angles equal? Reasons: they look equal; measure them (even hundreds — induction — does not show they must always be); Euclid says so (authority); the best is the reason why it must be so. That is demonstration: Aristotle defines it as a syllogism making us know the cause, that of which it is the cause, and that it cannot be otherwise.
• The reason: because the lines are straight, A + X = two right angles and B + X = two right angles (an early theorem: a straight line meeting a straight line makes angles equal to two right angles); by the axioms (equals to the same are equal; equals from equals leave equals), A = B. Plato saw this before Aristotle in the Meno: right opinion is also true, but knowledge is tied down by the cause — here the straightness of the lines.
• So to define reason as “the ability to give the reason why it must be so” is to define it by the most perfect reason it can give — already contained in “looking before and after,” since the cause is before the effect.
• Parallel from Thomas on holy orders: defined in reference to the Eucharist, the greatest sacrament and end of the others (the others contain Christ’s power, this alone Christ himself); because the priest can consecrate and distribute the Eucharist he must be able to forgive sins, else one would be unfit to receive. One defines a thing by the greatest thing it can do; the ultimate thing for reason is to give the reason why it must be so — which is why he calls the fifth sense of “before” Aristotle gives after the four “the crowning sense.”
• The class ends mid-remark: “to reason” as the name of the act.

His words #

• substance: from Latin “to stand under”; a thing that exists not in another, a subject (man, dog).
• accident: from Latin “to happen to”; something of another, e.g. health, defined as “the good condition or disposition of the body”.
• definition: from the word for limit; nothing other should be contained within it — hence the difficulty with accidents.
• seventh book of wisdom [ed.: Metaphysics VII]: either no definition of accident or definition in a secondary sense.
• wisdom: “the highest or the greatest perfection of reason” (Thomas); “the best knowledge”; reasoned out as “the knowledge of God”.
• reason: Shakespeare’s “the ability for a large discourse, looking before and after”; later “the ability to give the reason why it must be so”.
• love / liking: conformity or agreement of the heart with its object; desire / wanting: the heart seeking its object; joy, delight, pleasure: the heart resting in the object possessed.
• substantial form: what the human soul is, not an accident, yet defined as something of another.
• what it is: Aristotle’s name in the Topics for the first category.
• thērion: beast; Aristotle’s hunting word in the Posterior Analytics for pursuing a definition.
• Porphyry’s tree: the more universal placed above and dividing downward.
• species: “the name of a particular kind of thing placed under a genus”.
• subject / predicate: that of which something is said (sub, under) / what is said of it.
• convertible: test for a definition reached by adding a difference to a genus.
• encircling [ed.: definition by property/effect]: a starting point equally universal with the thing.
• conditional / hypothetical syllogism: the “if… then” form used for the best knowledge.
• golden mean: what is praised in moral virtue, the middle between extremes.
• logikē vs. logistikē: the art of defining and reasoning vs. the art of counting and calculating.
• demonstration: “a syllogism making us know the cause, that of which it is a cause, and that it cannot be otherwise”.
• right opinion vs. knowledge (Plato, Meno): both true; knowledge is tied down by the cause.
• ratio ordinis: raised by a student from Thomas on Providence; he does not translate it.
• the crowning sense: his name for Aristotle’s fifth sense of “before” (cause before effect).

Texts #

Read in class

• Handout on definition, pages five, six and seven (his own text; the verified handout “The Royal Fragment”, p. 15, and DHB Vol I – The First Philosophers, p. 31, were matched to the audio).
• Euclid, Elements: the vertical-angles demonstration worked through on the board (no proposition number stated).

Mentioned

• Aristotle, Categories (substance and accident); Topics (“what it is”).
• Aristotle, Metaphysics (“wisdom”) Book VII; proemium, sixth attribute of the wise man.
• Thomas Aquinas, proemium to the Nicomachean Ethics commentary.
• Aristotle, On the Soul Book I (dialectic; how good the knowledge of the soul is) and Book II (six divisions, per Thomas).
• Aristotle, Parts of Animals (better thing outweighs more certain).
• Aristotle, Posterior Analytics Book II (two ways to the definition); syllogism vs. induction.
• Aristotle, Nicomachean Ethics Book II (what moral virtue is).
• Plato: dialogues generally (hunting), Euthyphro, the dialogue on episteme (Theaetetus, inferred), Meno.
• Euclid, definitions at the beginning of the Elements.
• Shakespeare, the sonnets (154); the “large discourse” line.
• Thomas Aquinas on Providence and predestination (ratio ordinis) — student’s reference; Thomas on holy orders and the Eucharist.
• Leibniz on calculating disagreements; Galileo and Einstein (aside).

His questions #

• Why can you define man or dog by itself but not health? Because health is not something by itself but something of another; it exists only in the man.
• What do the three attacks on the castle correspond to? Beginning from the more universal (genus), the less universal or singular (examples), and the equally universal (property or proper effect).
• If you begin with examples, what road do you take to the definition? Compare them, separate out what they have in common, leave aside their differences.
• How do you go from the more universal down to the species? Divide by differences, see under which the thing comes, add it to the genus, and check whether the result is convertible.
• Is “right-angled parallelogram” convertible with square yet? No; another division and difference are needed.
• What does “best” mean, and why is one knowledge better than another? Better than all the rest; because it is about a better thing or is more certain, the former chiefly.
• What is praised at table — eating to excess or too little? Neither; what is praised is in the middle.
• Is “reason is the ability to give a reason” a bad definition? Not if “reason” means the ability in one place and its object in the other.
• What is the best reason you can give for a statement? The reason why it must be so — a demonstration; for the angles, the straightness of the lines.