Truth and Falsity in Statements: Either/Or and If-Then Statements and Syllogisms

Orientation #

He does not say what came last time or what comes next; he only signals that the if-then syllogism will be met “later on… in the logic of the third act”. The verified sources place the Shakespeare argument at the handout Shakespeare’s Exhortation to Use Reason, p. 5 (about ten minutes read from it), and the class in DHB Vol III, The School of Aristotle, p. 682. The previous class traced the second act of reason through definition and statement; the next continues into the if-then syllogism, the dictum de omni et nullo, and the figures.

The class, in order #

1. Truth and falsity are in the statement, not the name (“Aristotle himself points out where do you find truth”) #

The point: truth and falsity are found in things and in the mind, but in the mind only in the second act.

• “dog” alone: true or false? You must say something other than dog to make a statement. “A dog is a cat” (false), “a dog is an animal” (true), “dogs are ferocious”—Thomas says there are exceptions.
• He distinguishes the simple statement from the compound statement; simple first.

2. What true and false mean in a simple statement (“a square is a quadrilateral”) #

Four statements: a square is a quadrilateral (true); a square is not a circle (true); a square is not a quadrilateral (false); a square is a circle (false).

• Definition drawn from them: you are true when you say what is, is, or what is not, is not; false when you say what is, is not, or what is not, is. “Fairly easy to see.”
• To understand better: think out the division of a statement.

3. Division into two: noun and verb (“mainly a noun and a verb”) #

The point: thinking out the composing parts of a statement as a composed whole.

• Statement is a speech, composed at least of a noun and a verb: Socrates sits, eats, thinks, walks.
• Both noun and verb are names; the difference (student): the verb signifies with time.
• Greek and Latin use one word (onoma, nomen) for name and noun; so the noun keeps the common name as its own and the verb gets a new name, because it adds something noteworthy—signifying with time. “Very striking.”
• Consequence: you cannot make a statement grammatically without a verb, and a verb signifies time; so it is very hard to talk about God, who is not in time.
• The Greeks: whatever is must be somewhere; we likewise think whatever is must be in time. Our knowledge starts from the continuous, and place and time are species of the continuous (Categories).
• The first meaning of “before” is the temporal one; we cannot get beyond that use. Christ: “Before Abraham was, I am”—not before in time but in duration, eternity as an “eternal now”; “very strange”.
• The eight senses of “in”: Berquist once objected to Thomas, “you left out one—in time”; Thomas’s answer, that in-time stands alongside in-place (both an external measure). “You dummy!” That is where Thomas taught him that the senses of a name equivocal by reason are not all put in one line: the central senses go in a straight line, other senses are attached where there is an affinity—so in time is attached to in place.
• Where is God—up in the heavens with the astronauts? God is not in place. Where will my immortal soul be? Is heaven a place? No sense of “place” fits; “very hard for us” to see this.
• Aside: “Time is our master,” Shakespeare, Comedy of Errors.

4. Division into two, three, or both (“into both two and three”) #

The point: the rule “two or three” is more exactly “two or three or both”; a statement is a case of both.

• Family: parents and children (two) or father, mother, children (three)—both make sense.
• Name said of many: divided into two (one meaning, or more than one), then the “more” subdivided into equivocal by chance and equivocal by reason; or into three at once: entirely the same meaning, entirely different, partly the same and partly different. The last is equivocal by reason—there is a connection, an order among the meanings, and “reason looks before and after.”
• Caution about “analogy”: it seems to name one particular kind of equivocal-by-reason name, since analogy means proportional; Thomas sometimes uses “proportion” for ratio, as does Euclid. [ed.: the transcript’s “Townsley” and “length of a circle” are garbled; the point about proportion/ratio is what carries.]
• Statement into three: the square (subject), quadrilateral (predicate), “is”/“is not” joining them (copula). “Seems more natural” to divide it so; the copula fits the third part especially in the negative.
• Why the three-part division matters: it gets you to reasoning, the principles of the said of all and said of none: if A is said of all B, A is said of whatever B is said of; if of none, of none of what B is said of.
• Plot: two parts (tying knots, untying them) or three (beginning, middle, end). Aristotle: Homer taught the other poets to make a plot—not everything that happened to some man with no connection, but a course of action with beginning, middle, end. Philosophy too has a beginning, middle, end and ties and unties knots (“more untying”).
• A Summa article: objections, corpus, reply—“naturally divided into three” (a student offers “three and four”).

5. Compound statements: the either-or (“I call it the either or statement”) #

The point: three compound statements are common; the first is the either-or (he dislikes “disjunctive”).

• Full form, “either a number is odd, or a number is even”; contracted, “a number is either odd or even”—but it is really two statements put together. [ed.: he says “brevity of soul” here; left as spoken.]
• What’s important: you exhaust the possibilities—the either-or “depends upon sufficiency of your division.” Easy with odd/even; harder with Aristotle’s virtues of reason, natural understanding, episteme (reasoned-out knowledge), wisdom: “is that all?”
• Aside: he used to say a human being is either a man or a woman, but now nature and choice must be considered (“a woman by nature, by choice a man”); student: “by choice insane.” He objects to the distinction itself.
• An either-or may have two, three, or more members: in what sense of “before” does one sense come before another—“either this, this, this, or this.”
• Thomas on the Trinity: the Father is not before the Son—either in duration, or in nature, or in knowledge, or in dignity (“better than him”); he eliminates every sense. On how Father and Son are distinguished: either a material distinction or a formal one (student: does that exhaust it? yes); not material, since God is not a quantity of matter; formal distinction is either by contradiction, by lacking and having, by contraries, or by relations; three eliminated, the fourth concluded. So the either-or works even “in very proper, probable things” and in the highest matter. Euclid too sometimes argues from an either-or.
• Truth in the either-or: not what it means in a simple statement (which is it, odd or even?), yet connected: you are saying that one of the two simple statements is true and the other false—“either it’s true that this number is even, or it’s true that it’s odd.” You want to know which: this human being man or woman, this act good or bad.

6. The if-then statement (“I call it the if then statement”) #

The point: the second important compound statement; he avoids “hypothetical,” since in experimental science a hypothesis is something not stable, whereas an if-then is very stable.

• If this figure is a square, then it is a quadrilateral; if a number is perfect, then it is composite (not prime)—“very rigorous.”
• He likes the if-then because there is an order right in it.
• The odd thing: an if-then can be true though made of two false simple statements: “If I am a mother, then I am a woman”—both parts false of him, the if-then true. So truth here does not mean what it means in the simple statement: you say only that if the if-part is true, the then-part will be true; in fact both may be false.

7. The if-then syllogism, four cases (“if A is so, then B is so”) #

The point: given “if A is so, then B is so,” which additions yield a necessary conclusion?

1. A is so → B is so. Kind of obvious: the first statement did not assert A or B, only the connection; once A is admitted, B must be.
2. A is not so → nothing follows. A student says “B must not be so”—“you think it follows, but it doesn’t follow from the form.” Not a mother, still can be a woman. Two kinds of case: B more universal than A (“if I am a dog, then I am an animal; I’m not a dog, therefore not an animal”—no); or B an effect of many possible causes (“if Berquist dropped dead last night, he’ll be absent; he didn’t drop dead, therefore he won’t be absent”—could be an emergency, could be lazy; “if I drink this beer I’ll be drunk; I didn’t”—wine or whiskey). Also “three is half of four.”
3. B is so → nothing follows. Student: depends whether other causes of B than A. Berquist absent → dropped dead? No. Berquist is an animal → a dog? “If you are the man who robbed the bank, then you are a man; you are a man; therefore you robbed the bank—you’re all in prison.” “Wishful thinking, sir, not logical thinking.”
   • Weakness of experimental science: if my hypothesis is correct there will be an eclipse at 10:06; there is; “confirmation”—but it does not follow necessarily (student: the hypothesis is not the cause of the eclipse; he: at least the form itself does not give it). Yet a very precise prediction gives more probability—why it works better in physics than sociology; the more consequences that turn out so, the more probable. Like induction, where you never see all the singulars; Aristotle makes induction more a dialectical than a demonstrative argument. So cases 2 and 3 are not syllogisms (a syllogism being speech in which, some statements laid down, another follows necessarily).
4. B is not so → A is not so, necessarily. Not as obvious as case 1; the student who earlier thought something followed now thinks nothing does. Reason: if A were so, B would have been so; but B is not; so A is not. Hence the scientist’s hypothesis is rejected with more rigor than it is confirmed; “logic is not fair—it’s negative.”

• Convertible terms: “if this number is two, then it is half of four; it is half of four; therefore it is two”—this holds, but because the things are convertible, not from the form as stated.
• Shakespeare argues with necessity in this fourth form: if three is half of four, then three is no more than two; both false, but the if-then true; so, if man’s chief good were the chief good of the beast, man would be no more than the beast; but man is more than the beast; therefore his chief good is not the beast’s.

8. Counting the “befores and afters” (“reason looks before and after”) #

The point: in the if-then syllogism there are three befores; in the regular syllogism, two.

• His Monday-night example: “knowledge of the soul is better than knowledge of the body, because knowledge of a better thing is better”—you see two befores and afters: that it is better, and why.
• If-then syllogism: (1) premises before the conclusion (premise from praemittere, “sent before”; Thomas calls them principia, which come before); (2) the if-then statement before the simple statement in the discourse of reason—you look at antecedent or consequent and affirm or deny; (3) the if-then statement is itself a before-and-after: the if-part the antecedent, the then-part the consequent. “Very before-and-afterish.”
• Regular syllogism, simple statements only, B and A now terms: every B is A, every C is B, therefore every C is A—based on the said of all (if every B is an A, whatever is a B has to be an A). Major premise before minor: one before; the main before, premises before conclusion, marked by the line drawn. Two befores against the if-then’s three—“we people who love to look before and after really like that.”
• The recording ends mid-sentence.

His words #

• statement: speech signifying the true or the false; simple vs. compound
• true / false: saying what is, is / what is not, is not; the reverse is false
• noun / verb: both names; the verb signifies with time
• onoma / nomen: one Greek/Latin word for name and noun
• “eight senses of in”: in time attached to in place, both an external measure
• central senses in a straight line, others attached: his ordering of a name equivocal by reason
• equivocal by chance / equivocal by reason; “analogy” reserved for the proportional kind
• subject, predicate, copula
• said of all / said of none [ed.: dictum de omni et nullo]
• either-or statement [ed.: disjunctive]; requires sufficiency of division
• if-then statement [ed.: conditional/hypothetical]; antecedent, consequent
• if-then syllogism; four cases, two valid
• syllogism: speech in which, some statements laid down, another follows necessarily
• convertible: terms where the consequent case holds from the matter, not the form
• praemittere, principia: premises as “sent before”
• major premise / minor premise

Texts #

Read in class

• Shakespeare, “What is a man, if his chief good and market of his time be but to sleep and feed? a beast, no more” (handout p. 5; Hamlet, inferred) — worked as a deny-the-consequent argument
• “Before Abraham was, I am” (John 8:58, inferred)

Mentioned

• Aristotle, Categories (place and time species of the continuous)
• Aristotle on Homer and plot (Poetics, inferred)
• Aristotle on the virtues of reason: understanding, episteme, wisdom (locus not given)
• Thomas Aquinas on the eight senses of “in” (locus not given)
• Thomas Aquinas on the Father not before the Son; on the distinction of Father and Son (Summa, inferred, locus not given)
• Euclid (either-or arguments; proportion for ratio)
• Shakespeare, Comedy of Errors, “Time is our master”

His questions #

• “If I say dog—true or false?” You must say something other than dog; only a statement is true or false.
• “What’s the difference between a noun and a verb?” The verb signifies with time.
• “Does this true or false in the either-or mean what it means in the simple statement?” No, but it refers back: one of the two simple statements is true, the other false.
• “Could an if-then statement be true and yet be made out of two false simple statements?” Yes: “If I am a mother, then I am a woman.”
• “Suppose you find out that A is not so—does anything follow necessarily about B?” No; B may be more universal, or an effect of other causes.
• “Suppose B is so—can you say anything necessarily about A?” No; “wishful thinking, not logical thinking”; only probability, as with a confirmed hypothesis.
• “If B is not so, does anything follow about A necessarily?” Yes, A is not so—the less obvious of the two valid cases.
• “In each of these two syllogisms, how many befores do you see?” Three in the if-then syllogism, two in the regular one.