The Syllogism, Its Likeness to Calculation, and Dividing the Four Arguments

Orientation #

He opens by saying the syllogism is “the last kind of argument” and “the chief subject of the logical third act”; “next time, we’ll be starting to study the syllogism.” He refers back to the restaurant, students-in-black and Caesar examples used for example, induction and enthymeme (prev. lecture). The verified handout “Reasoning and the Four Kinds of Argument”, p. 6, is the text he is working from. The previous class treated example, induction and enthymeme; the next begins the syllogism proper with its three kinds.

The class, in order #

1. The definition: “a speech in which some statements laid down” (“another follows necessarily because of those laid down”) #

Point: the syllogism is defined as a speech (or argument) in which, some statements being laid down — “just two, really, in every syllogism” — another follows necessarily because of those laid down.

• He recalls what speech is: vocal sound signifying by custom or human agreement, having parts that signify by themselves.
• “Laid down”: Aristotle’s word; Latin positis. Thomas, commenting on St. Paul’s being “laid down” (as an apostle), draws out three elements: (1) you do not lay yourself down, something else does — here reason lays down the statements, God laid down Paul; (2) firmness — the statements are at rest in the mind; (3) order towards something — a task for Paul, a conclusion for the premises.
• English parallel: “I’m going to lay down the law” — someone lays it down, there is a new firmness (“you’re not going to be fooling anymore”), and a behaviour is expected to follow.
• The conclusion “is not really part of the syllogism, but a conclusion of it, an effect of it.”
• Aside: Washington D.C. speed cameras that photograph you and mail the notice — the law “laid down” with firmness; his joke about a machine that throws a canopy over speeding cars.

2. “Follows necessarily” separates the syllogism (“really separates the syllogism from the other three”) #

Point: necessity of following is what the other three arguments lack.

• Restaurant good last week: does not follow necessarily it is good this week (example). This student, this student, this student in black, therefore every student: does not follow necessarily (induction). Caesar refused the crown three times, therefore not ambitious: does not follow necessarily (enthymeme).
• Distinction: the conclusion follows necessarily vs. the conclusion is necessarily true. If even one premise laid down is not necessarily true, the conclusion, though it follows necessarily, is not necessarily true. Calculating parallel: multiply correctly, but if one of the numbers was only probable, the result is not necessarily the correct number.

3. “Because of those laid down” (“does night follow day necessarily”) #

Point: Aristotle adds the last clause because “follows necessarily” does not by itself mean “because of”.

• Shakespeare: “to thine own self be true, and it must follow as the night the day.” Night follows day necessarily, but not because of day — a third thing (the earth turning on its axis) causes both and their succession. Likewise learning necessarily follows ignorance (he corrects: ignorance necessarily precedes learning), but ignorance is not the cause of learning.
• Student: if statements follow necessarily, would it always be because of those laid down? He: “I don’t know,” his point is only that the phrase “follows necessarily” doesn’t mean “because of that.”
• The clause brings out that the premises are in some sense the cause, the maker, of the conclusion. Against those who call syllogism a “reverse induction” (whole to parts): it is more like reproduction — two dogs producing a third dog, two numbers producing a third number. Hence the great importance of this argument: all Euclid’s arguments are syllogisms.

4. Syllogism and calculating: likeness but not one art (“the Greek word for reckoning or calculating”) #

Point: the name “syllogism” is borrowed from reckoning, and there are real likenesses, but Aristotle and the Greeks never made one art of logike and logistike.

• Likenesses: you need at least two numbers to get a third, at least two statements to get a third; both have rigor. English keeps the borrowing: “I reckon”, “I figure”, “what does that add up to”. Children learn arithmetic before the syllogism.
• Argument that they are not one art:
  1. What is fundamental in calculating is counting (you must count before you have numbers to operate on).
  2. What is fundamental in Aristotle’s logic is understanding what something is.
  3. Neither reduces to the other: knowing what water is doesn’t tell how much is in the glass; knowing man is an animal with reason doesn’t tell how many men are in the room; counting the men (you need only recognise them) doesn’t help define man. The physicist counts things he doesn’t know what they are. To see that no odd number is even you must understand odd and even, and you must understand the statements you reason from.
  4. Therefore the mathematical logicians (back to Leibniz) who lump both under “deduction” are “deceived by the likeness.”
• Corollary he draws for demonstration: a demonstration is a syllogism whose conclusion is necessarily true, requiring both that the conclusion follow necessarily and that the premises be necessarily true. The Prior Analytics takes the argument apart to see if the conclusion follows; the Posterior asks how you know the premises are necessarily true. Checkbook: you get the wrong number either by subtracting incorrectly or by subtracting the wrong (misread) numbers — he has found both.
• Calculating is easier and yields less disagreement (check it over and you’ll agree); logic is much more difficult. Logic “is not a substitute for thinking; it’s a help to thinking” — students who think the computer will write the paper want something mechanical to replace thinking.
• Richard II’s “dull, barren, unfeeling ignorance”: ignorance is barren because it has no offspring, whereas knowledge of two numbers or two statements can give rise to another.

5. The four arguments divided by likeness (“enthymeme is like the syllogism”) #

Point: put in boxes — syllogism upper left, enthymeme lower left, induction upper right, example lower right — the arguments pair by likeness across the horizontal line: enthymeme with syllogism, example with induction.

• Syllogism has true universality: no odd number is even; every three is odd; therefore no three is even. Enthymeme proceeds from a very universal statement that is not truly universal: “boys will be boys” — but boys sometimes do the deeds of men, as the newspapers praise. So enthymeme is an imperfect syllogism, a syllogism secundum quid; Aristotle sometimes calls it a (rhetorical) syllogism, sometimes divides it against syllogism — as the boy is a man or divided against the man, kitten/cat, puppy/dog. Boundary case: if every man who staggers out of a bar is drunk, you have a syllogism; if a man may stagger from an ailment in his leg, the “in itself” required for necessity is lacking. The name enthymeme, “in the mind”, marks that the mind sees something, not a simple singular.
• Example is like induction: from your good meal at restaurant A last week you send me to A, implying the meal is symptomatic of the meals there — an extremely imperfect induction. You don’t say “therefore all meals are good” because the weakness is obvious, yet you must imply something about the meals in general. Aristotle sometimes calls example a rhetorical induction.
• Naming principle: a name common to two things is kept by the one that has its meaning fully; the imperfect one gets a new name. Parallel: definition vs. encircling — “wisdom is the best knowledge” draws a line around wisdom but does not tell what it is a knowledge of.
• Aristotle in the Rhetoric says every argument is either syllogism or induction, so enthymeme must be a syllogism and example an induction — as every human is male or female, so boy is male and girl female.

6. Divided by usefulness; rhetoric and Othello (“not in terms of likeness, but in terms of their usefulness”) #

Point: the more practical division — since logic is for use, not for knowing these things — pairs vertically: syllogism and induction for the universal, enthymeme and example for the singular.

• Induction goes from many singulars to the universal; syllogism concludes about the universal; both serve dialectic, and Socrates in Plato’s dialogues uses now one, now the other.
• Enthymeme and example conclude about the singular, especially in human affairs, so the Rhetoric treats them. Aristotle: political rhetoric uses example more (deliberating the future, you reason from the past — legislation citing another state or country, the Federalist Papers); courtroom rhetoric uses enthymeme more (who is likely to have done the murder). Both usable in both.
• Othello: Iago, with no basis, persuades Othello of Desdemona’s infidelity using example — she deceived her father by eloping (the father’s parting “she deceived me, she may deceive you”), so she does the same to you — and enthymeme from likelihood/opinion — Venetian women are known for deceiving husbands, she is Venetian. He uses no syllogism and no induction. The handkerchief planted on Cassio [ed.: he says “a man”] is a sign — weak, like a wife’s ring found on another man: it could be an exception (he found it), but to a man already suspicious it seems final confirmation.
• Rhetoric is an offshoot not only of logic (these arguments) but of ethical and political studies, since it persuades even more by moving emotions and by projecting an image of a believable person — Iago does both: a man who has your good in mind, who sees into people, slow to voice suspicions. Iago himself says that to the jealous “even the weakest proofs will seem like holy scripture.”
• Knives and forks: on the table they are grouped by likeness (dinner fork with salad fork, dinner knife with butter knife); when the steak comes you grab a fork and a knife — usefulness, though knife and fork are less alike than two forks. Likewise man/boy and woman/girl by likeness, man and woman together to reproduce — usefulness. “We imitate nature.”
• His judgment: the likeness division is useful for understanding; usefulness is finally what you’re interested in — how Iago or the Federalists are going to reason.
• Student asks whether there is another kind of argument; the answer is largely [unclear in recording].

7. Aristotle’s kinds of example (“he distinguishes three kinds of examples”) #

Point: he announces “three kinds” but names four: historical example, invented example, proportional example (“proportion is the likeness of ratios”), and fable. [ed.: count mismatch left as he gives it; he may treat proportional as a form of invented.]

• Aesop’s fable in defence of an office-holder grown rich by graft: a hedgehog (he thinks) wedged between rocks, bleeding, refuses to have the sated bugs chased off, since new hungry ones would come — so keep my client, who is satisfied; a replacement will take the rest.
• His standing classroom case, persuading a college student not to marry: historical example — so-and-so married as a sophomore, kids came, took a job, never finished. Invented/proportional — nations never appreciate freedom until they lose it (electing Hitler), so a bachelor doesn’t appreciate his freedom until married; weaker because the likeness is only parallel. Fable/parable — the goose that laid the golden egg killed for all the gold at once; each date is golden, so you want her all the time, and “[unclear in recording] spoils romance” — “much weaker,” “feeble.”
• The poetic argument is like an example, an invented one, placeable under it, “though in another sense maybe not strictly speaking an argument.”

8. Persuasion by representation (“it belongs to the poet to lead us”) #

Point: representations persuade, but whether they are arguments at all is doubtful; they work primarily through the emotions and imagination.

• WWII Hollywood films representing Soviet society falsely (religious freedom) so we would think well of the Russians; inauthentic historical films. Student: “inducement.” He: yes, because it is represented thus.
• Childhood: he and his brothers planned to protect neighbour Kenneth from his coming stepmother, cruel “like stepmothers are” — from fairy tales (Snow White); their mother corrected them. Uncle Tom’s Cabin represents slavery’s splitting of families — persuasive, but “is it really an argument at all?” More like custom, through emotions primarily.
• Thomas: Poetae est inducere ad aliquid virtuosum per convenientem repraesentationem — it belongs to the poet to lead us to something virtuous through a suitable representation. Thomas’s example: a food becomes abominable if represented under the likeness of something disagreeable. His own case: hating milk as a boy (mother bribing him, milkshakes from the drugstore), speculating it came from being given milk of magnesia and thereafter thinking of milk under that likeness; many irrational food dislikes come from how you picture the food.
• The poet moves emotions as rhetoric’s second means of persuasion does; Hollywood represents bad things as acceptable. Student: “judging by your imagination”; he: emotions primarily, but working through imagination too — false imagination. It is like rhetoric in its power to move emotions rather than in its argumentative aspect.

9. False imagination is not argument (“things are not the way you imagine them to be”) #

Point: we constantly imagine places, people and stages of life otherwise than they are, without any statements from which we reason.

• C. S. Lewis (quoted in a popular logic book) driven from the station through a part of England unlike what he imagined; the uncle: “what right did you have to think it was this other way?”
• His wife surprised by his hometown friends (Jim the former boxer, hard-drinking Jim); his own imaginings of college (a big athlete), graduate school, faculty life (constant intellectual conversation — in fact abstruse mathematicians and economists make small talk at lunch, “everybody doing their own thing”); the Arabian student who “never saw a camel”; historical novels; married life, better or worse but not as imagined; the Sahara not simply rolling sand.
• “Is that an argument? … It’s not from statements.” Student: by imagining you form opinions, and how far off you are shows how far off your imaginative reasoning is, “if you had such an animal.” He concedes there is something like putting things together in imagination, but “it keeps departing away from the strict example.”

His words #

• speech: vocal sound signifying by custom or human agreement, having parts that signify by themselves
• laid down (positis): placed by another (reason), with firmness, in order to something (the conclusion)
• follows necessarily: distinguished from “is necessarily true”
• because of those laid down: the premises as cause, maker, of the conclusion
• reckoning/calculating: origin of the word syllogism; “I reckon”, “I figure”
• logike / logistike: the art of reasoning vs. the art of calculating
• demonstration: a syllogism whose conclusion is necessarily true
• syllogism secundum quid: the enthymeme as imperfect syllogism
• rhetorical syllogism / rhetorical induction: Aristotle’s names for enthymeme and example
• encircling: an answer to “what is it?” that only marks a thing off from others (wisdom is the best knowledge) [ed.: description]
• dialectic: reasoning to conclusions about the universal
• likeness vs. usefulness: the two bases for dividing the four arguments
• proportional example: proportion is “the likeness of ratios”
• inducement: student’s word for persuasion by representation, accepted by him
• Poetae est inducere ad aliquid virtuosum per convenientem repraesentationem: it belongs to the poet to lead us to something virtuous through a suitable representation
• false imagination: imagining things otherwise than they are, without statements

Texts #

Read in class

• Handout, “Reasoning and the Four Kinds of Argument”, p. 6 (verified): definition of syllogism
• Shakespeare, “to thine own self be true, and it must follow as the night the day” (Hamlet, inferred)
• Shakespeare, Richard II: “dull, barren, unfeeling ignorance” (as he quotes it)
• Thomas Aquinas: Poetae est inducere ad aliquid virtuosum per convenientem repraesentationem (locus not given)

Mentioned

• Thomas Aquinas, commentary on St. Paul on being “laid down” (locus not given)
• Aristotle, Prior Analytics and Posterior Analytics (their respective tasks)
• Aristotle, Rhetoric (enthymeme/example; political vs. courtroom rhetoric; kinds of example)
• Euclid (all arguments are syllogisms)
• Plato’s dialogues (Socrates uses induction and syllogism)
• The Federalist Papers (example in political rhetoric)
• Shakespeare, Othello (Iago’s enthymemes, examples, the handkerchief)
• Aesop’s fables (the wedged animal and the bugs)
• Uncle Tom’s Cabin
• C. S. Lewis passage quoted in a logic book
• Leibniz (uniting calculation and logic)

His questions #

• Does night follow day necessarily? And is it because of day that night follows? Yes; no — a third thing causes both, so “follows necessarily” doesn’t mean “because of.”
• If the conclusion follows necessarily, is it necessarily true? No, not if even one premise is not necessarily true.
• Can you make one art out of calculating and reasoning? No: one rests on counting, the other on understanding what something is; there is only a likeness.
• Would you put syllogism with induction, or with enthymeme? By likeness, with enthymeme; by usefulness, with induction.
• Is example in some way like induction? Yes, an extremely imperfect induction implying something about meals in general.
• When the steak comes, do you grab the two forks or the two knives? Neither — a fork and a knife: usefulness, not likeness.
• Is a false Hollywood representation an argument, or what would you call it? Inducement — persuasion through emotions and imagination, not from statements.
• Is false imagination an argument? No, “it’s not from statements”; left partly open when a student proposes “imaginative reasoning.”