Compound Statements, the Definition of Syllogism, and the Kinds of Argument: Syllogism, Induction, Enthymeme, and Example

Orientation #

He opens with “a little review” of statements “so we can do these things,” and refers back to the if-then syllogism “we looked at the form of” and “the ones we were talking about last time.” Near the end he mentions Thomas arguing that the Father is not before the Son, as something the class has met. The neighbouring classes work through the figures of the categorical syllogism and, next time, two senses of induction applied to divine simplicity.

The class, in order #

1. Review: what a statement is (“speech signifying the true or false”) #

Point: rebuild the definition of statement by its genus and its first division.

• Speech and name are both sounds that signify, by custom rather than by nature. Speech has at least two parts that signify by themselves; the name is “the ultimate thing that’s signifying,” no part of which signifies by itself.
• Statement = speech signifying the true or false; definition is also a speech, but “speech signifying what something is.” So you can define statement.
• First distinction of statements: simple vs. compound. Simple: affirming or denying “something one of something one.” Compound: combining two, sometimes more, simple statements.
• “True or false” has one meaning in the simple statement and a different one in the compound. His standing example: a true compound made of two false simples: “If I am the number seven, then I am an odd number”; “If I am a mother, then I am a woman.”

2. The three kinds of compound statement and what “true” means in each (“nothing hypothetical about that”) #

Point: at least three main kinds, each with its own meaning of truth.

• Either-or (they call it disjunctive); the conjunction (“has and in it”); the if-then, which they call hypothetical, but he avoids the word: “if I am the number seven, then I am an odd number” is “real strong thinking,” not a hypothesis.
• If-then: truth does not mean the if-part is true, nor the then-part, but that “if the first one is, then the second one will be so.” It can be true while the thing is false.
• Either-or: “A human being is either a man or a woman or a boy”: not true, because incomplete; truth depends on having exhausted the possibilities. Hence when Thomas argues that the Father is not before the Son, he has to take Aristotle’s senses of “before” in the post-predicaments as exhaustive: “the chief senses,” with any other sense attached to one of these.
• Conjunction: “I am a philosopher and I am a grandfather,” shortened to “I am a grandfather and a philosopher”; still two things said of one thing, two simple statements combined. Truth: both must be true; “I am a philosopher and a great-grandfather” is false, “so far as I know.” You don’t tend to argue from this kind, or if you do, you go back to the simple statements.

3. The if-then syllogism: form and matter (“If A is so, then B is so”) #

Point: of the four ways of arguing from an if-then, two hold by form, two only by matter.

1. Lay down: if A is so, then B is so (A, B standing for the simple statements). Then look at A or at B.
2. A is so → B is so: “the obvious form.”
3. A is not so → B is not so? Only when the matter is convertible: “If this number is two, it is half of four; it is not two, so not half of four” works because of the matter. “If this number is two, it is less than ten; it is not two, so not less than ten”: no, could be three, four, five… So by form it does not follow, though “some people will think it’s going to follow.”
4. B is so → A is so? No: the tryst example (they went to the motel, “it doesn’t follow”); “If I am a man, I am an animal; I am an animal, therefore a man”; same with dog.
5. B is not so → A is not so: yes, shown by the first form: if A were so, B would have been; B is not; so A cannot be. He stresses this “because it’s very important for reasoning.”

4. Arguing from the either-or (“eliminate all possibilities”) #

Point: affirmative vs. negative use. Affirmatively: you know it is one of the possibilities, so eliminate all but one. Negatively, as Thomas wants to show the Father is not before the Son: you must eliminate all the possibilities.

5. His “confession” about the conjunction: I am the Alpha and the Omega (“God is the beginning and the end”) #

Point: the conjunction is not useful for syllogizing, but it is an important kind of statement; he retracts having “meanly put down” the conjunction.

• Apocalypse: first time only “I am the Alpha and Omega”; second time adds “the first and the last”; finally all three (the beginning and the end). Just one is a conjunction: put in the third person, “God is the beginning and God is the end,” shortened to “God is the beginning and the end.” (Alpha and Omega “fits on the tabernacle better.”)
• Why combine these two? A student: because of God as cause. Beginning is one kind of cause, end another; so it puts together every way God is a cause. Nothing is the beginning or end of itself, so he is beginning and end of creatures, “of all things other than himself,” and that by antonomasia. Contrast: “philosopher and grandfather” has a reason only from context (the hospital wanting to be sure he is the grandfather; teaching school).
• Summa Contra Gentiles, “my favorite book”: Book 1, God in himself or by himself; Book 2, God as beginning; Book 3, God as end, his providence directing things to the end. Aristotle’s third cause is sometimes called mover, sometimes maker; as beginning God is both maker and mover; in Book 3 he moves things toward himself. So the conjunction “explains the second and third book” against the first.
• Book 4 has the same three parts, crisscrossed with a second division: Books 1-3 what natural reason can know about God as well as faith; Book 4 what is known by faith alone. Reason for the division: asked by the head of the Dominicans to write for those talking to the Mohammedans in Spain; you can’t proceed the same way with both, so the Dominicans shouldn’t try to prove by reason that there are three persons. The Mohammedan charge is polytheism (Socrates, Plato, Aristotle are three men; Father, Son, Spirit would be three gods); Mohammed fought Arab polytheism and Christians seemed to have “relapsed.”
• Student question: if Allah is arbitrary and can contradict himself, could he make himself more than one? Answer: you could argue that, leaving him open to impossible things, but that belongs to the first book: omnipotence does not mean he can make a square circle; “that’s really nothing.”
• Aside: his old question to the kids, in how many of the four senses of cause (matter, form, mover, end) is God a cause? Beginning and end, and then the complication of exemplar: “two and a half causes.”

6. John’s prologue: standing for vs. meaning (“and the Word was God”) #

Point: the three-membered conjunction is needed because relatives are opposites.

• “In the beginning was the Word, and the Word was toward God, and the Word was God.” Having just read the post-predicament on opposites (one opposite is not the other; relatives are one kind), if the Word was toward God, “it can’t be God.” So it is important the compound have three members, not two.
• Reply: “God” there stands for God the Father. Non-controversial example: “I, Duane Berquist, am the son of Reno Victor Berquist from Parkers Prairie, Minnesota,” so I can’t be him; but “I am the son of a man” (true), so I can’t be a man? Everybody sees something wrong: “a man” there stands for your father, though that is not one of the meanings of “a man” (you won’t find Reno Victor Berquist in the unabridged dictionary). Hence the distinction between standing for and meaning. “Don’t be hasty.”

7. Augustine: a conjunction that becomes an if-then (“thou hast made us for thyself”) #

Point: Confessions, first book (perhaps first chapter): “thou hast made us for thyself, and our hearts are restless until they rest in thee” is a compound statement. The first member alone is simple but touches both maker (beginning) and “for himself” (end). And it can be turned into an if-then: if God made us for himself as end, then our hearts must be restless until they rest in him; “it’s not over until it’s over.” “A marvelous conjunction.”

8. The definition of syllogism, word by word (“speech in which some statements laid down”) #

Point: Aristotle’s definition, taken from the remote genus speech, is not too much and not too little.

• Genus: not argument (a student’s first answer) but speech, the more general genus. “Some statements”: not how many, usually two, as in the if-then of last time, but more in the either-or.
• “Laid down”: like laying down the law, you expect consequences.
• “Another statement follows necessarily”: another, other.
• “Because of those laid down”: why add it? Shakespeare: “to thine own self be true, and it must follow as the night the day, thou canst not then be false to any man” (married man true to his choice is true to his wife; using reason correctly is being true to yourself). But does night follow day necessarily because it was day? No: because the earth turns on its axis or the sun goes round the earth. So the addition specifies the cause (“cause in, cause out”); it was not superfluous. “Nothing too much, as the wise man said.” “He knew what he was doing, this Aristotle.”

9. Dividing argument: two or four (“syllogism and induction”) #

Point: Aristotle sometimes divides argument into two (syllogism, induction), sometimes four (adding enthymeme, example), as one divides human beings into man and woman, or into man, woman, boys and girls: the boy is an imperfect, undeveloped man, so in one way two, in another four; enthymeme is to syllogism, example to induction, as imperfect to perfect.

• Rhetoric (tradition: Plato assigned Aristotle to write on the art of persuasion, persuading crowd or jury). Three means of persuasion (“three is the first number about which we say all”): (1) the image you project of yourself (prudent, good-hearted): Aristotle calls it the strongest, which is why politicians worry about image; (2) moving the emotions of the audience (a whole treatise on how to arouse and calm anger); Aristotle says a well-regulated city would not allow emotional appeals in court, but since your opponent uses them you must; (3) the arguments or apparent arguments, “the least important,” seen in the Federalist Papers, published in newspapers to persuade approval of the Constitution.
• Digression on Nixon’s memoirs (1,100 pages, he is at 250): the false slush-fund story as vice-presidential candidate (money collected and accounted for; Stevenson’s fund was the crooked one; press wouldn’t go after him); his speech to the nation with the dog: emotional appeal “fully justified” since emotion was being used against him. Student: the televised Kennedy debate with the heat turned up so Nixon sweat; TV viewers thought Kennedy won, radio listeners Nixon: an example of the first means. Kennedy and Nixon friends from the House in 1947; Kennedy calling Nixon after the Bay of Pigs; the letters with Jackie.
• The two rhetorical arguments: enthymeme and example. Example is an equivocal word: here not a singular illustrating a universal, but an argument from one singular to another of the same kind: Federalist Papers arguing from the Greek city-states that failed to unite (Peloponnesian wars) to our states. He calls example “rhetorical induction.”
• Induction: from many singulars to the universal (this man has two ears, this one, this one…; aside on the War of Jenkins’ Ear). Example takes one singular as representative of the kind; its strength depends on how much alike the two singulars are.
• Etymology: induction and example are Latin words; syllogism and enthymeme Greek. The Latins had names only for the arguments from singulars and none for “the higher arguments,” which use something universal (syllogism rests on the dici de omni, dici de nullo [ed.: dictum de omni et nullo], “the said of all and the said of none”). Boethius: the thing singular in one sense, universal as understood. The linguist’s remark: the Greeks figured out their own grammar, the Latins imitated Greek grammar, the English imitated Latin; same with logic (Latin just made a word out of syllogism); Vatican statues Greek or copies; the Iliad superior to Virgil; Cicero calling Aristotle a golden river.
• Enthymeme: an argument from likelihood or from signs. Likelihood = what is true for the most part in human affairs: “boys will be boys,” though a boy sometimes acts manly; so it lacks necessity (“he’s a boy, he must have acted like a boy” won’t quite do). His Jewish examples: his father letting the business friend pay for dinner because he’d be insulted otherwise; Warren Murray given the discount because the storekeeper took him for Jewish. Signs: a sign strikes the senses and brings to mind something other than itself; most signs are less than universal: a man coming out of a bar stumbling seems drunk, but brain-injured men (his wife’s work) walk like drunks, and old men stumble. So enthymeme is like syllogism but from verisimilitude, lacking complete universality; example may rest on one singular: his brother Richard’s Notre Dame landlady afraid of all blacks because some beat her husband, “a very weak argument,” much weaker than induction.

10. Is fiction a fifth means? (“They need something universal”) #

Point: sometimes they add fiction, poetry, to the four kinds of argument as a way to persuade: the novel that turned Americans against slavery (Uncle Tom’s Cabin). A weak argument: “I’ve read Romeo and Juliet, I know what young lovers are like”: should you rather say that from my knowledge of young lovers I judge Shakespeare represented them well? The critic following Shakespeare round the world, audiences saying “that’s us.” Verdict: they need something universal. The class ends here.

His words #

• statement; speech signifying the true or false.
• definition; speech signifying what something is.
• simple vs. compound statement; one of one, vs. combining simple statements.
• either-or statement; his name for the disjunctive.
• if-then statement; his name for the hypothetical, which “can be misleading.”
• conjunction, “and statement”; both parts must be true.
• convertible; matter that lets “A not so, B not so” follow.
• antonomasia; God the beginning and end of all other things by antonomasia.
• standing for vs. meaning; “a man” standing for my father without meaning him.
• laid down; the premises, like laying down the law.
• enthymeme; argument from likelihood or signs, imperfect syllogism.
• example; argument from one singular to another of the same kind, “rhetorical induction” (equivocal with example as illustration).
• likelihood, verisimilitude; what is true for the most part in human affairs.
• sign; what strikes the senses and brings to mind something other than itself.
• dici de omni, dici de nullo; “the said of all and the said of none” [ed.: dictum de omni et nullo].

Texts #

Read in class

• Aristotle, definition of syllogism, read phrase by phrase (Prior Analytics, inferred).
• Apocalypse, “I am the Alpha and the Omega, the first and the last, the beginning and the end.”
• John, prologue: “In the beginning was the Word…”.
• Augustine, Confessions, book 1 (first chapter, he thinks): “thou hast made us for thyself…”.
• Shakespeare, “to thine own self be true…” (Hamlet, inferred).

Mentioned

• Aristotle, Categories, post-predicaments: senses of “before”; opposites, relatives.
• Aristotle, Rhetoric: three means of persuasion; enthymeme and example; treatise on the emotions.
• Thomas Aquinas, Summa Contra Gentiles, division of the four books.
• Federalist Papers (Hamilton, Jay); Shakespeare, “a long farewell to all my greatness.”
• Boethius on singular and universal; Cicero on Aristotle as a golden river.
• Richard Nixon’s memoirs; Uncle Tom’s Cabin; Romeo and Juliet; Iliad and Virgil.

His questions #

• What is the genus of statement? Speech (sound signifying by custom, with parts signifying by themselves).
• What does truth mean in the if-then, the either-or, the conjunction? Consequence of the then upon the if; that the possibilities are exhausted; that both parts are true.
• If A is not so, does B not follow? If B is so, does A follow? Neither, by form; the first only when the matter is convertible.
• Is there a reason to put “beginning” and “end” together in one statement? Yes: they name every way God is a cause, of all things other than himself.
• If the Word was toward God, can it be God? Yes, once you see “God” there stands for the Father; standing for is not meaning.
• Why does Aristotle add “because of those laid down”? To specify the cause; night follows day necessarily but not because of what day is.
• Are there two or three means of persuasion? Three: image, emotions, arguments.
• Is “I’ve read Romeo and Juliet, so I know young lovers” a good argument? No; you judge Shakespeare by knowing lovers; they need something universal.