Richard Nixon's Memoirs; How We Know a Statement Is True; Dividing Logic in Two or Three

Orientation #

He opens by reading from Nixon’s memoirs, then asks “Do we need to review a little bit?” and returns to the definitions of speech, definition and statement, and to the division of statements “we divided last time.” He refers to something “I mentioned last week” about people building on one insight and setting up a straw man. The previous class treated induction, divine simplicity and syllogistic figures; the next treats conditional and disjunctive syllogisms and the three figures.

The class, in order #

1. Reading from Nixon’s memoirs (“the Nixon Market, huh?”) #

An extended pre-class reading, not on the logic: Nixon’s father moving to Whittier, opening a service station and the family store where Nixon rose at four to buy produce; his wife Pat nursing her father and working through college; his brother Arthur’s death and Nixon’s freshman English essay on childhood belief and the child’s prayer “If I should die before I awake”; his mother’s note at his 1953 vice-presidential inauguration about keeping his relationship with his Maker. Berquist’s comments: “that’s kind of a marvelous thing”; the Quakers may not have known much of Christ’s divinity, “but it can come a good way”; and the remark (he thinks quoting Johnson) that “politics is worse than war… in politics you die many times,” which struck him—“it’s war under a different name.”

2. Review: definition and statement as two speeches (“So, what is a statement?”) #

Point: definition and statement share the genus speech but are defined by their end.

• Speech vs. name: both vocal sounds signifying by custom; the name has no part signifying by itself, speech has at least two signifying parts. So “signifying by custom” is not what makes a statement a statement.
• Definition = speech making known (bringing out) what something is. Statement = speech signifying the true or the false.
• The difference he presses: would we say the statement is speech making known the true or the false? No. By contradiction you know “Father Michael is sitting / is not sitting” cannot both be true nor both false—but the statement itself does not tell you which is which. “Statement doesn’t make anything known, does it?”
• Example of a definition really making known: students knew odd and even but not perfect number; Euclid’s definition (a number equal to the sum of everything that measures it evenly) plus six (1+2+3, not 4 or 5) made it known.

3. Three ways to know which contradictory is true (“how do you know whether a statement is true”) #

Point: since the statement does not make its own truth known, there must be other ways; he collects three.

1. By the senses: “Patrick is sitting” is true right now because I see it (may not be true later today). Student proposes “you can see”—accepted. “Marin is sitting: I don’t believe that, I know it through my senses.”
2. By understanding the terms (the first act of reason): “a whole is more than one of its parts”; “a square is a quadrilateral”; “a square is not a circle”—seen by knowing what square and circle are. Such statements are called “known to itself” [ed.: per se nota]; caution: this cannot mean you prove the statement by itself, “that would be very bad logic”; it means known through its parts.
3. By reasoning: “a triangle’s angles are equal to two right angles”—I know what triangle and two right angles mean, but do not see it from those alone; it is reasoned from statements like “the whole is more than the part.”

• Student proposes testimony of others; he says that is getting into belief. “George Washington was the first president”—he holds it, “but this is kind of a belief,” not known the way Patrick’s sitting is known. If you believe he is 81, you don’t strictly know it; if God revealed it you would know it for sure; a trustworthy man may still be mistaken. Aside: at his father’s death there were two conflicting birth dates from the town of Parkers Prairie, Minnesota.

4. Thomas’s division of logic into three (“Thomas divides logic into three parts”) #

Point: logic divided according to the three acts of reason—understanding what something is, understanding the true or false, reasoning.

• In his proemium Thomas assigns Aristotle’s books: Categories to the first act (genera tell what something is); Peri Hermeneias to the second (the statement); Prior and Posterior Analytics, “the book on places” [ed.: Topics] and the Sophistical Refutations (garbled as “physical affections”), and to some extent the Rhetoric, to the third.
• Trivium/quadrivium and rhetoric-vs-logic mentioned; more precisely, Aristotle calls rhetoric a parergon (“offshoot”) of logic, since the rhetorician uses arguments, though weak, and also an offshoot of political studies—“a mixed science in a sense.” Its argument is the enthymeme, from one singular to another of the same kind (recalled from earlier).

5. Albert’s division into two; the rule “two or three, or both” (“So who’s right, Thomas or Albert?”) #

Point: Albert’s twofold division is also right; divisions by two and by three can both stand.

• Context: as a first-year student (transcript gives “Leval”/“Louvain” [ed.: likely Laval]) they read Porphyry’s Isagoge, the first book of logic; Thomas has no commentary, so they used Albert the Great.
• Albert’s argument: if you knew everything you wouldn’t need logic; logic is for coming to know the unknown; the unknown is twofold: simple unknown (what a perfect number is, what the soul is) vs. complex unknown (that the human soul is immortal). Hence two arts: the art of defining and the art of reasoning.
• Where the statement goes: Thomas’s logic of the second act is included by Albert under reasoning, since reasoning is from two or more statements to another.
• “Who’s right? Both.” His rule of two or three, or both, with examples:
  • Aristotle praises Homer for teaching the Greeks the plot—not everything that happened to somebody, but one course of action with beginning, middle, end (three); later in the same book he divides the plot into tying and untying the knots (two). “Was Aristotle right when he divided into three, and wrong when he divided into two, or vice versa?” Good to do it both ways.
  • Names said of many: univocal vs. equivocal (two), then equivocal subdivided into by chance vs. by reason (two). Equivocal by chance: his Wednesday student Richard and his brother Richard share a name for no reason (the brother is named after their grandfather). Thomas instead divides into three: same meaning, entirely different meanings, meanings partly same and partly different—the last called “analogous,” the middle name, which is the same as his “equivocal by reason.” “Anything wrong there? No.”
  • Playful exam question: “should you divide names said of many things into two or three?”

6. Is God a philosopher? (“Is God a philosopher?”) #

Point: the answer depends on what “philosopher” means; the word’s history teaches humility.

• Philosopher from philos (lover) and sophia (wisdom). If-then: if philosopher means lover of wisdom, then God is a philosopher, and there is reason for friendship with him, as Aristotle says. But we would confuse people saying so—it puts God among the modern philosophers, who “are not really lovers of wisdom.” Aside: the last President Bush named Jesus Christ his favourite philosopher; the media was not overjoyed; “Jesus Christ was a lover of wisdom.”
• Origin: Pythagoras, on discovering his theorems, was called wise and replied “Don’t call me wise, God alone is wise.” So, as Aristotle says, only God is wise in the full sense; man wise only in a diminished sense, and few men. A sign of humility: the philosopher needs love of wisdom and humility.
• Thomas: pride is a cause of error in two ways—(a) a man attempts to judge what he is not capable of judging; (b) he is not docile to those wiser than him. Thomas was docile to Augustine and Aristotle; great minds “pull us back from many errors.” Without humility “you’re going to be a bad philosopher.”
• Remark attributed to “Ketchum” [ed.: probably Cajetan, inferred] that Thomas so reverenced the Fathers he seemed to have inherited the mind of all of them; likewise Thomas inherited the mind of Aristotle. His rule of thumb: “Aristotle means what Thomas says he means”—Thomas on stupid interpretations: so great a philosopher on so great a matter could not be saying that.

7. Return: two-part logic in Oesterle, and the three ways again (“Logic, the art of defining and reasoning”) #

Point: the twofold division has a reason, but the statement needs its own treatment.

• Oesterle’s college logic book (his oldest grandchild studies it) is titled by Albert’s distinction. Reason: definition makes known a simple thing (square, virtue); reasoning makes known a statement not known before; but understanding a statement does not tell whether it is true or false—hence the three ways recapped: senses (you sitting / not standing), understanding the parts (square not a circle), reasoning.
• God as philosopher “a little more complicated”: if from Pythagoras, philosopher means one who is not wise but loves wisdom, so not God; if just love-of-wisdom, God could be called one—but be careful. The early Fathers call theology “Christian philosophy”; Thomas gives sapientia as the Latin synonym for philosophy, and theology is wisdom even more than first philosophy; still it confuses, since custom matters in how words are used and we are not accustomed to call God a philosopher.

8. Reading the modern philosophers (“three reasons for reading them”) #

Point: Pius XII’s three reasons for reading modern philosophers; how they differ from Aristotle’s way with predecessors.

• Pius XII: (1) the scraps of knowledge in them; (2) to know their errors so as to refute them and not be taken in; (3) to know your own position better by contrast. So there is an obligation.
• He teaches Kant, Hegel, Marx; doctoral thesis compared Descartes and Aristotle (“the three roads”). On retiring from Assumption College he left the modern philosophy books behind: “I was going to think about God in my retirement.” Reading Aristotle is for “the way things are,” not for what Aristotle thinks.
• Student: was Descartes intellectually honest or playing games? “A little bit of both.” Aristotle disagrees with predecessors but recalls what they said, why, and why it is wrong; the moderns say the opposite of Plato or Aristotle without recalling why they said it. They build on some insight nobody had, setting up a straw man to knock down (recalled from last week).
• Friend Rodney Nockin asked “Why don’t you do your own philosophy?"—“I don’t get very far.” Thomas: Plato and Aristotle are the chief philosophers; Plato thanked the gods for being born a man not a woman, a Greek not a barbarian, and for meeting Socrates; no Socrates, no Plato; no Plato, no Aristotle—“a magnificent buildup.”
• Mozart: no master whose works he has not gone over many times; dedicated six quartets to Haydn “because he taught me how to make a quartet”; Haydn told Mozart’s father he was the greatest composer he knew—humility again.

9. Division of statements: simple and compound (“Did you divide statements into two or three?”) #

Point: statements were divided last time into simple and compound; each is subdivided.

• Simple: affirmative vs. negative (two).
• Compound: three important ones—if-then (he dislikes the textbook term “hypothetical”), either-or (clearer than “disjunctive”), and conjunction (“and”).
• Test: Augustine’s “Thou hast made us for thyself, and our hearts are restless until they rest in thee”—compound, joined by “and.” Playfully it could be made an if-then: if God made us for himself, then our hearts are restless until they rest in him, because pursuing an end not yet possessed, the heart is in motion, not at rest “until she says yes.”

His words #

• speech: vocal sound signifying by custom, with at least two parts that signify; name: no part signifying by itself
• definition: speech making known / bringing out what something is
• statement: speech signifying the true or the false (not “making known”)
• perfect number: number equal to the sum of everything that measures it evenly (Euclid)
• known to itself: known through its parts, not proved by itself [ed.: per se nota]
• first act of reason: understanding what something is; second: true or false; third: reasoning
• parergon: “offshoot” (rhetoric as offshoot of logic and of politics)
• enthymeme: argument from one singular to another of the same kind
• simple unknown vs. complex unknown (Albert)
• art of defining / art of reasoning (Albert’s two parts of logic)
• rule of two or three, or both
• equivocal by chance vs. equivocal by reason; Thomas’s middle name “analogous”
• tying the knots / untying the knots (Aristotle’s twofold plot)
• philosopher: philos + sophia, lover of wisdom
• sapientia: Thomas’s Latin synonym for philosophy
• if-then statement (not “hypothetical”); either-or (not “disjunctive”); conjunction

Texts #

Read in class

• Richard Nixon, Memoirs: early life, Pat, brother Arthur’s death, freshman essay, mother’s note (1953)
• Euclid, definition of perfect number
• Augustine, “Thou hast made us for thyself…” (Confessions, inferred)

Mentioned

• Thomas Aquinas, proemium on the division of logic and of Aristotle’s logical works
• Aristotle, Categories; Peri Hermeneias; Prior and Posterior Analytics; Topics (“book on places”); Rhetoric
• Aristotle on Homer and plot (Poetics, inferred)
• Porphyry, Isagoge; Albert the Great’s exposition
• Thomas on pride as cause of error (no locus given)
• Oesterle, Logic: The Art of Defining and Reasoning
• Pius XII, text on reading modern philosophers (no locus given)
• Aristotle on God alone being wise; on friendship with God (no loci)

His questions #

• Would I define the statement also as speech making us know the true or the false? No: it signifies true or false, but does not make known which of the two is true.
• How do I know which one is true, which one is false? By the senses, by understanding the terms, or by reasoning; testimony is belief, not strict knowing.
• If you believe me that I’m 81, do you really know that I’m 81? Not strictly; a trustworthy person may still be mistaken.
• So who’s right, Thomas or Albert? Both.
• Was Aristotle right when he divided the plot into three and wrong into two, or vice versa? Good to do it both ways.
• Should you divide names said of many things into two or three? Playful exam question; both divisions stand (equivocal by reason = analogous).
• Is God a philosopher? If philosopher means lover of wisdom, yes; but it confuses, and on Pythagoras’ sense (not wise, loving wisdom) no—“be careful.”
• Was Descartes honest or playing games? “A little bit of both.”
• Did you divide statements into two or three? Simple/compound; simple into affirmative/negative; compound into if-then, either-or, conjunction.
• Is Augustine’s “Thou hast made us for thyself, and our hearts are restless” simple or compound? Compound, joined by “and”; could be recast as an if-then.