True and False in the Simple Statement: Saying More or Less Than the Truth, and Contradictories

Orientation #

He says the composing parts of the statement had to be understood first, and now come the properties of the simple statement and then truth and falsity in it; truth and falsity in the compound statements comes “later on”, and at the close he turns to the compound statements and their composing parts. Verified source: he reads from his handout “The Art About Statement”, pp. 3–4 (about 19 minutes; also printed in DHB Vol. III, p. 635). The previous class defined statement and divided it into simple/compound and affirmation/negation; the next treats if-then and either-or statements and the square of opposition.

The class, in order #

1. A property of the simple statement (“has an opposite statement with the same subject and predicate”) #

The point: every simple statement has an opposite statement with the same subject and predicate; you replace “is” by “is not” or vice versa.

• Examples: “man is a stone” / “man is not a stone”; “man is not an animal” / “man is an animal”.
• It is a property, “something that follows upon every statement”. Truth and falsity of these opposites, and what the opposition can be, come later.
• Aside (opening, partly garbled): the composing parts have to be understood first, then the subject parts.

2. What true and false mean in the simple statement (“saying of what is that it is”) #

The point: since a simple statement says something is or is not (was or was not), truth and falsity are defined by whether what it says matches things.

• Truth: saying of what is that it is, or of what is not that it is not. Example: “Berquist is standing now” (he is) says what is, is; “Berquist is not sitting now” says what is not, is not — both true.
• What is common to the two: the mind is in conformity, in agreement, with things.
• Falsity: saying what is, is not; or saying what is not, is. Example: “Berquist is not standing” (while standing) says what is, is not; “Berquist is sitting” says what is not, is. “So there’s two ways of being false.”

3. The courtroom oath (“the whole truth, and nothing but the truth”) #

The point: the second and third phrases of the oath are not mere emphasis; each excludes one of the two kinds of falsehood.

• “The whole truth” is opposed to saying what is, is not — subtracting from the truth.
• “Nothing but the truth” is opposed to saying what is not, is — adding to the truth.
• Aside: he suspects that if he spelled this out during jury selection he would not be seated; people do not stop and think what the phrase means, yet it is “very active”.

4. Shakespeare and the bartender (“nor more, nor clipped, but so”) #

The point: Shakespeare has the same triple structure, more clearly: truth as “modest”, between “more” and “clipped”.

• King Lear: Kent, the faithful old servant — “All my reports go with the modest truth, nor more, nor clipped, but so.” Saying more than the truth = saying what is not, is; saying less (clipped) = saying what is, is not.
• Falstaff, “a great liar”: those who say more or less than the truth are villains and sons of darkness. Shakespeare often puts a saying in the mouth of someone who exemplifies its opposite; so Polonius says “brevity is the soul of wit” and Hamlet calls him a tedious old fool — “you’re either wise or brief”.
• The same triple phrase in Othello, about a soldier.
• Bartender example: John and Thomas alone were at the bar between nine and ten on Friday. Testifying “John, Thomas and Paul were there” says what (who) was not, was — adding, more than the truth. Testifying “John was there” leaves off Thomas, says what was, was not — subtracting, less than the truth. Mapped back on the oath: “the truth” (John and Thomas), “the whole truth” (against just John), “nothing but the truth” (against adding Paul).
• Aside: Shakespeare says “nor … nor” where we would say “neither … nor”; you also see “or … or” in Shakespeare — just a change of language.

5. Truth as equality and as a mean; the two mysteries (“the equality of the mind with things”) #

The point: “more or less” fits calling truth the equality of the mind with things — not in a “democratic sense” that the mind is equal to everything (it speaks of things greater than itself, God, and less, a tree), but that it says neither more nor less than what is out there. “Equality” and “more/less” are more concrete than “agreement” or “conformity”. Adding to the truth is as bad as subtracting from it.

• These four places (three from Shakespeare, one the courtroom) are “signs” that this is what truth and falsity are: why two ways of being false, why two phrases excluding them.
• Like the moral virtues (generosity between stinginess and extravagance, courage between foolhardiness and cowardice), truth is a mean between two extremes, more than truth and less than truth.
• The Trinity and Incarnation are “just the reverse” of one another: one nature, three persons vs. one person, two natures. Both errors occur historically:
  • Trinity, more than the truth: three natures because three persons (Arius) — saying what is not (second and third nature), is. Less than the truth: one person because one nature (the Patripassians, who say the Father suffered) — saying what is (three persons), is not.
  • Incarnation (student supplies “two persons”): two persons because two natures (Nestorius [ASR "the story says"]) — what is not (a second person in Christ), is. One nature because one person (the monophysites) — what is (two natures), is not.
• Sign that the middle is the truth: each extreme has a part of the truth (one nature; three persons; one person; two natures) and infers the rest; if one extreme were true the other would have no part of truth at all, “not very plausible”. Empedocles: men are creatures of the day who see a part and boast of having seen the whole.
• Student: theology and philosophy speak of erring by excess and erring by defect. He agrees: it is the custom of those making mistakes to go to extremes (“everything’s necessary” / “everything is contingent”).
• Later, comparing with the other kinds of truth and falsity, we will see why this is the basic sense: the agreement of the mind with things, since the mind wants to know the way things are.

6. The last paragraph: what follows from the definitions (“both cannot be true, both cannot be false”) #

The point: from induction and the definitions, if an affirmative is true its opposite negative is false and vice versa; and the same statement cannot be both true and false.

1. A true affirmative says what is, is; the opposed negative then says what is, is not — the definition of false.
2. A true negative says what is not, is not; the opposed affirmative says what is not, is — false.
3. Saying what is, is cannot be saying what is, is not; so no statement is true and false at once.

• Contradictory statements, spelled out: (i) simple statements; (ii) same subject and same predicate; (iii) one affirmative, one negative. Their opposition: both cannot be true, both cannot be false, one must be true and the other false — whether or not you know which.
• Example: “President Bush is sitting now” / “is not sitting now”: same subject, same predicate, one affirmative, one negative; both cannot be true, both cannot be false; which is which “we don’t know”.
• The logic of the second act sees that they are contradictories but does not tell you which is true.

7. Three ways of knowing which contradictory is true (“don’t let the logic of the second act do more than it can”) #

The point: knowing which of a pair is true comes from something other than the logic of the second act.

1. By the senses: “Berquist is sitting / is not sitting” — you judge by looking; no logic needed. Senses are other than the mind.
2. By understanding the parts, which may require a definition (logic of the first act): “no odd number is even / some odd number is even” — not by senses, you cannot see all odd numbers, but by knowing one is divisible into two equal parts and the other not; “no circle is a square” — you may start from drawings, but you know it by understanding what circle and square are.
3. By reasoning: “the interior angles of a triangle equal two right angles” — you know what a triangle and two right angles are but do not see they go together; you must reason it out.

• Repeated in terms of the definition: if the affirmative says what is, is, the negative is false; if it says what is not, is, the negative is true — but whether the affirmative says what is or what is not, logic does not tell (for Bush, you would have to phone and believe someone). “Man is an animal”, “square is a quadrilateral”: known by understanding the parts.
• “Don’t let the logic of the second act do more than it can, but don’t give it less credit than it has.”

8. Half true, half false (“half are true and half are false”) #

The point: since every statement has exactly one contradictory and one of the pair must be true, of all possible statements half are true and half false.

• But of statements actually made, “probably more than half are false”, because people do not make both of a pair: 2+2 is four, five, six, seven, eight — many false, one true; Thales (water), Anaximenes (air), Heraclitus (fire), the poets (Mother Earth) as the beginning of all things — if one is right, three are false. Only if each is paired with its negation do you get exactly half and half.
• Aside: on a true/false exam students guess at 50/50; once he set one with a point off for blank and two off for wrong, “on purely Socratic grounds” — one for not knowing, one more for thinking you know when you don’t.

9. Strict contradiction vs. loose contradiction (“three is an odd number, three is an even number”) #

The point: people get confused because words are used loosely; strictly, contradictories need the same subject and predicate and opposite quality.

• “Three is an odd number” / “three is an even number”: both affirmative and different predicates, so not contradictories strictly; loosely a contradiction, because “three is not an odd number” follows from the second, and that is the strict contradictory of the first. The contradiction is a consequence, an inference.
• “Some women are beautiful”: have I said some are not? No — someone may infer I think so, but I have not said it. “Some twos are half a four” does not say some are not, even though every two is. “Some of you have passed” (he may have corrected only half the papers) says nothing about the rest, though students run off and tell the others. So “some women are beautiful” does not contradict “every woman is beautiful”, nor “some have passed” “every student has passed”.
• “You want to learn to speak very precisely.” (The word “some” is to be treated later.)

10. Turn to the compound statements (“first again, their composing parts”) #

He closes: next the compound statements, first their composing parts, then truth and falsity in them, since the parts must be understood first.

His words #

• property (of the statement): something that follows upon every statement — that it has an opposite statement.
• opposite statement: same subject and predicate, “is” replaced by “is not” or vice versa.
• truth (in the simple statement): saying of what is that it is, and of what is not that it is not; conformity / agreement / equality of the mind with things.
• falsity: saying what is, is not; or what is not, is — two ways.
• adding to / subtracting from the truth; more than / less than the truth; “modest truth”, “clipped” (Shakespeare’s word for less).
• erring by excess / by defect (student’s phrase, accepted).
• contradictory statements: simple, same subject and predicate, one affirmative and one negative; both cannot be true, both cannot be false, one must be true and the other false.
• logic of the second act: analysis of the statement; logic of the first act: definition.
• Patripassians: those who say the Father suffered, became man, died.
• monophysite: one nature in Christ.

Texts #

Read in class

• Berquist, handout “The Art About Statement”, pp. 3–4 (property of the simple statement; definitions of true and false; last paragraph on opposite statements) — also DHB Vol. III, p. 635.
• Shakespeare, King Lear: Kent, “All my reports go with the modest truth, nor more, nor clipped, but so.”
• Shakespeare, Falstaff: those who say more or less than the truth are villains and sons of darkness (Henry IV, inferred).

Mentioned

• Shakespeare, Othello: “more or less than the truth”, of a soldier.
• Shakespeare, Hamlet: Polonius, “brevity is the soul of wit”; Hamlet on the tedious old fool.
• Empedocles: men are creatures of the day, see a part and boast of the whole.
• Thales, Anaximenes, Heraclitus, the poets on the beginning of all things.
• Arius, the Patripassians, Nestorius (inferred from “the story says”), the monophysites.

His questions #

• What is the property of the simple statement? Every simple statement has an opposite statement with the same subject and predicate.
• When I add “the whole truth and nothing but the truth”, am I just reiterating that I will tell the truth? No: the two phrases exclude the two kinds of falsehood — subtracting from and adding to the truth.
• To say the whole truth is opposed to which kind of falsity? Saying what is, is not; “nothing but the truth” is opposed to saying what is not, is.
• In the Incarnation, what error corresponds to Arius’s three natures? Two persons because two natures (Nestorius); the reverse, one nature because one person, is the monophysite.
• Can “President Bush is sitting now” and “is not sitting now” both be true, both be false? Which is true? Neither both true nor both false; one must be true, the other false; which one, we don’t know.
• Do you know “no odd number is even” by the senses? No, by understanding what odd and even are; three ways: senses, understanding the parts (definition), reasoning.
• Are half of the statements people actually make true? No; of all possible statements half are true, but people make more false statements than true.
• Are “three is an odd number” and “three is an even number” contradictories strictly speaking? No: both affirmative and different predicates; the contradiction is a consequence (“three is not odd” follows).
• When I say “some women are beautiful”, have I said some are not? No; someone may infer it, but it is not said; “some” does not contradict “every”.