The Order of Thinking Out: Definition, Understanding What a Thing Is, Name and Speech

Orientation #

He picks up from “all of these” senses of thinking out drawn from the senses of “in” (prev. lecture) and from “thinking out the order better in knowledge” which “we were doing”; he looks ahead to “later on, when we study the third act” (reasoning and argument). The previous class worked through the eight senses of “in” and their corresponding senses of thinking out, and the next examines On Interpretation on truth and falsity in statements.

The class, in order #

1. Ordering the senses of thinking out: distinction, division, definition (“think out a distinction is more general”) #

The point: Aristotle’s eight senses of “in” and Thomas’s ordering of them were not a waste of time, because we may use all the senses of thinking out, and they themselves have an order.

• Start: knowledge is confused; the first step out is to think out a distinction; then a division.
• Distinction vs. division: division is a distinction of the parts of some whole; distinction is more general. Boundary cases: the meanings of “in” are not parts of the word “in” — a distinction that is not a division; likewise act vs. ability.
• Division subdivides by kind of whole: the composed whole and the universal whole (Aristotle distinguishes these two in “the fifth book of wisdom” [ed.: Metaphysics V]); Thomas points out a third, the potestative whole — Aristotle calls the powers of the soul its “parts”, a different kind of part from either, “in the same light as both”.
• Definition: thinking out the parts of a definition is thinking out a composed whole, yet defining is different from dividing a genus into species — “you’re not defining something, are you?”
• His summary: distinction, division, definition go from the more universal to the less universal; a definition has “the aspect of a division” but brings something out differently.

2. Thinking out order; why the first act comes before the second (“I see some reason there”) #

The point: from a distinction one may go on to order — its definition, its senses — and one order to think out is that of the acts of reason.

• Argument for the order of the acts: you must understand what a square is and what a quadrilateral is before you can understand that a square is a quadrilateral; you must understand square and circle before understanding “square circle”.
• Objection (raised in his phone joke, pressed by a student): isn’t the first act then better? You cannot know whether “a square is a quadrilateral” is true, or “a square is a circle” false, except by going back to understanding what each is; the axiom “the whole is more than a part” likewise requires understanding whole and part. The second act “can’t even accomplish some task there” without the first.
• His reply: nobody said the first act was not necessary. But understanding square and understanding circle are two different understandings, had one and then the other; in the second act, understanding that a square is not a circle, “I’m understanding square and circle at the same time, and I’m kind of angelic” — angels know many things distinctly at one thought. Aside: a little paper on the calculus where one figure becomes another, so you seem to know both together, “a simple way of being like an angel”.

3. Statement, conclusion, cause and effect (“ending up with the Pythagorean theorem”) #

The point: after distinction and definition come thinking out a statement (second act), a conclusion, and cause and effect.

• Euclid, Elements Book One as the order in which we think things out: first definitions; then statements thought out (the whole is more than a part; if equals are added to equals the results are equal; things equal to the same are equal); then about forty theorems, ending with the Pythagorean theorem.
• Cause and effect, illustrated by the “transgender stuff”: what is the cause of being man or woman? Everyone used to know: by nature. Now one is a man or woman by choice — “they don’t know what the cause is”; they “don’t look before and after”. By contrast, husband or wife is by choice (“do you take so and so”). Time magazine photo of a woman modified into a man, holding a baby the way a woman does: “taking the form of a man, but not really a man.” Student’s story: a woman suing a Catholic hospital for refusing a hysterectomy, reported as “he is suing them for refusing to do a hysterectomy on him” — the sentence makes no sense because they refuse to look at nature: men do not have uteruses. He notes this case uses almost all the senses, in a bit of an order.
• Student asks about the last sense (the end): he is not sure there is a sense of thinking out there, but if so it is thinking out the means to some end, the means being “part of the love ordered to that end”; entering the kingdom of heaven is “hard to enter”.

4. Thomas’s three acts; what the logic of each act is about (“understanding what a thing is”) #

The point: the first two acts are both a kind of understanding (intelligere), distinguished by their objects; the third is reasoning (Thomas, proemium to logic).

• Logic of the first act: a student says understanding names; “more basically” understanding what something is. Hence Aristotle, “father of logic”, gave the Categories: the ten highest genera, and a genus is a name said with one meaning of many things other in species, signifying what it is.
• The Categories is only the beginning; it is the task of the parts of philosophy to divide and subdivide: Aristotle does not divide number into odd/even or prime/composite (Euclid does), but in ethics he divides habits into virtues and vices and subdivides the virtues.
• Logic of the second act: Thomas, following De Anima III, calls it composing or dividing — putting together things understood in the first act; in the proemium to Peri Hermeneias, understanding the true or the false.

5. Even, odd, perfect numbers; definition as “that by which” (“the first perfect number is six”) #

The point: students understand what even and odd numbers are by definition, and come to know what a perfect number is the same way — so definition is connected with, but not the same as, understanding what a thing is.

• Even: a number divisible into two equal parts; odd: not so divisible; a “good discovery”, a second definition of odd: a number differing from an even by one.
• Perfect number: a number equal to the sum of everything that measures it evenly. Six: measured by one, two, three (not four or five); 1+2+3=6. Next is 28; further ones take higher math. Aside: “I don’t need examples” / “depends upon the senses” — the material distinction, discrete and continuous; the “dust of battle” (Fr. Hardon’s phrase for the occupational hazard of lecturing).
• Distinction: understanding what a thing is (distinctly) vs. having a definition. A student proposes confused/distinct; he answers that here one understands distinctly by the definition, yet they still differ: the definition is that by which you understand or can understand what a thing is — what enables you.
• Analogy from the eye: a telescope is not seeing at a distance but that by which one sees at a distance (his father’s friend’s son’s reflecting telescope; clouds hid the moon, but the rings of Saturn, never visible to the naked eye, were “really something”); a microscope is that by which one sees very small things (cells). “That’s an important distinction.”
• Extended to the third act: a syllogism is an argument in which some statements being laid down, another follows necessarily from them; an argument is not the act of reasoning but an ordering of statements enabling you to reason well. Proportion reached with the class: definition : understanding what a thing is :: statement : understanding true or false :: argument : reasoning. So definition and statement must be thought out.

6. Name and speech: what they share (“distinction of name and speech”) #

The point: name (nomen) and speech (oratio) share a genus before they differ.

• Both are sound; both vocal sound — his knuckle on the wood is a sound but neither name nor speech; the logician leaves how vocal cords produce sound to another science (he follows the logical, not the grammatical order; grammar and logic are two liberal arts).
• Both signify: Augustine’s definition of sign — something that strikes the senses and brings to mind something other than itself; he likes “strike” because it brings out that you are undergoing.
• Both signify by custom (or choice), not by nature: the baby’s cry is a vocal sound signifying a bodily need, but by nature, so the mother comes running (his own head-whack on the garage corner, his mother bathing it); “berkelium” named by choice at Berkeley; ordinary names are more by custom than choice.

7. Name vs. speech; etymology vs. meaning (“no parts signify by themselves”) #

• Difference: speech has parts (at least two) that signify by themselves; a name is the negation — no part signifies by itself.
• Objection: “Johnson” — John means something, son means something. Reply: as it functions as a family name, John and son do not signify separately (the daughter is not a son, her father not John). Hence Thomas’s distinction between the etymology of a name and its meaning, often confused.
• His own name: Berg (mountain) + quist (branch) in Swedish, but he is not a “mountain branch”; only the whole sound “Bergquist” signifies him. Asides: his father dropped the G; his mother’s maiden name Burke (she joked she slipped it in); his son’s West Point nickname “BQ”.

8. Definition and statement as two kinds of speech (“we name a thing before we can define it”) #

• The tradition called the first two books of logic the book of the five names (genus, difference, species, property, accident — Porphyry’s introduction) and the book of the ten names (substance, quantity, quality…). But a definition is not a name; it is speech.
• Aristotle: going from confused to distinct, we name a thing before we can define it; the definition gives more distinct knowledge. Experience: parents know what a word means but hesitate when asked to define it; try defining “love”.
• Definition vs. statement, both speech, distinguished (student: “by their end”) by what they signify: definition = speech signifying what a thing is; he sometimes says “making known” what a thing is (the definition, helped by an example, made known what a perfect number is) or “bringing out” what a thing is — “nature loves to hide” (Heraclitus). Statement = speech signifying the true or the false. How to think out the definition of truth and falsity is raised, not treated. Aside: “serious computer problems”.
• “Proposition”: from pro-pono, placed before; Euclid’s theorems are propositions because he states beforehand what he proposes to prove (“I propose to show the angles of a triangle are two right angles”), in Greek likely the word for proposal. Closer to “premise”; he prefers the word statement.

His words #

• thinking out — reasoning, as through the senses of “in” [ed.: ratiocinari]
• ability — as against act [ed.: potency]
• what division / what definition — his verbal habit; not a technical term
• potestative whole — whole whose parts are powers, e.g. the soul’s
• “the fifth book of wisdom” [ed.: Metaphysics V]
• intelligere — understanding; the first two acts of reason (Thomas)
• composing or dividing — the second act (Aristotle, De Anima III)
• genus — a name said with one meaning of many things other in species, signifying what it is
• perfect number — a number equal to the sum of everything that measures it evenly
• that by which — definition to understanding what a thing is; telescope to seeing at a distance
• syllogism — an argument in which some statements being laid down, another follows necessarily
• argument — an ordering of statements enabling you to reason well, not the act of reasoning
• nomen / oratio — name / speech; both vocal sound signifying by custom
• sign (Augustine) — something that strikes the senses and brings to mind something other than itself
• name — no part signifies by itself; speech — parts (at least two) signifying by themselves
• etymology vs. meaning of a name (Thomas)
• definition — speech signifying (making known, bringing out) what a thing is
• statement — speech signifying the true or the false; preferred to “proposition” (pro-pono, placed before)

Texts #

Read in class (recalled and commented on, no reading aloud):

• Euclid, Elements, Book One: definitions, common notions, ~40 theorems to the Pythagorean theorem
• Augustine’s definition of sign (locus not stated)

Mentioned:

• Aristotle, Physics IV, eight senses of “in” (prev. lecture)
• Aristotle, Metaphysics (“wisdom”) V, two kinds of whole
• Aristotle, Categories; Porphyry’s introduction (five names)
• Aristotle, De Anima III, composing and dividing
• Aristotle, Ethics, division of habits into virtues and vices
• Thomas Aquinas, proemium to logic (three acts of reason) [ed.: proemium to the Posterior Analytics commentary (inferred)]; proemium to Peri Hermeneias
• Heraclitus, “nature loves to hide”
• Time magazine piece on gender

His questions #

• Are the meanings of the word “in” parts of the word “in”? No — so that is a distinction that is not a division.
• Why does the first act of reason come before the second? You must understand what a square and a quadrilateral are before understanding that a square is a quadrilateral.
• Isn’t the first act then better than the second? He does not concede it; the second act understands two things at once, “kind of angelic”.
• What is the cause of being man or woman — nature or choice? And husband or wife? Nature; husband or wife is by choice.
• Why did Aristotle, father of logic, give us the Categories? Because the first act is understanding what a thing is, and the categories are the ten highest genera.
• What is a perfect number, and how do I make it known? A number equal to the sum of what measures it evenly (6, then 28) — by definition plus example.
• Is a definition the same as understanding what a thing is? No; it is that by which you understand, as a telescope is to seeing at a distance.
• Is an argument the same thing as reasoning? No; it is an ordering of statements enabling you to reason well.
• What do name and speech have in common, and how do they differ? Both vocal sound signifying by custom; speech has parts signifying by themselves, a name does not.
• How would you distinguish definition and statement, both being speech? By what they signify: what a thing is vs. the true or the false.