Logic as Tool and Liberal Art: Ordering Thoughts Through Words

Orientation #

He opens by turning to “page five of your book” and later says “let’s go back to the starting point”: logic is about three acts of reason (prev. lecture), and “as we said before” art is right reason about making. He refers forward: “we’ll be distinguishing the syllogism and induction.” The previous class treated Thomas’s proemia to the Peri Hermeneias and Posterior Analytics on the three acts of reason and the division of logic; the next takes up the definitions of name and speech and the opening of the Posterior Analytics.

The class, in order #

1. Logic is not a “looking” science but a tool of science (“not so much a science as a tool of science”) #

Point: Thomas (commenting on the work on the Trinity, handout p. 5) places logic under speculative philosophy not as a principal part but as “reduced to it.”

• “Looking” [ed.: speculative] sciences—mathematics, natural philosophy, first philosophy or wisdom—are about things known for their own sake (as the beginning of the Metaphysics makes clear). The things logic is about are not sought for themselves but as a help to the other sciences.
• Logic supplies speculative philosophy with its tools—syllogisms, definitions “and others of this kind”—whence, “according to Boethius in his commentary on Porphyry,” logic is not so much a science as a tool of science.
• What is “a little more new to us”: logic is not only the tool of philosophy but is in a way about tools. Aside: Porphyry’s Isagoge, the introduction to the Categories, was a standard text through the Middle Ages; Albert the Great, Cajetan, and Boethius all commented on it.

2. Definition, the tool of the first act (“a number equal to the sum”) #

Point: the tools Thomas names are matched to the three acts already on the board (understanding what a thing is; understanding the true or false; reasoning); definition is the tool that makes the first act possible.

• Perfect number: “a number equal to the sum of everything that measures it.” Six (measured by 1, 2, 3; 1+2+3 = 6) is the first; four is not (1+2 ≠ 4). The examples only illustrate; it is through the definition that one understands.
• Composite number: measured not only by the one but by some other number (four, not three or five); prime: measured only by the one.
• Blank verse: unrhymed iambic pentameter; iamb: two syllables with the accent on the second.
• Square: equilateral, right-angled quadrilateral—one cannot “even understand clearly what a square is” without it. Conclusion: definition is a tool “necessary often” for the first act.

3. Statement, the tool of the second act (“never found any piece of truth in the ground”) #

Point: to understand the true or false one must first make a statement, because truth and falsity are found only in statements.

• Argument: there is no truth or falsity in the room, the ground (digging Mike’s holes and hitting rocks and roots), the ocean, the air. Nor in the first act: “man,” “animal,” “stone” on a true-or-false exam—you wouldn’t know what to do. But “man is an animal / man is not an animal,” “man is a stone / is not a stone” are each true or false.
• Hence statement is to the second act what definition is to the first. His stock answer to “where is truth?”: “in the same place that falsity is, in statements.”

4. Argument, the tool of the third act; tools vs. acts (“tools that enable us to see some things”) #

Point: the tool of reasoning is argument—syllogism the most perfect, but generally argument.

• He previews the kinds: syllogism and induction, the two main kinds; enthymeme and example, weaker (“but I like those two”).
• Student question: isn’t the tool of the second act “composition and division”? Reply: Thomas uses that more properly for the act—putting together in an affirmative statement what is otherwise separated—so act and tool are not the same thing.
• Glasses, microscope, telescope: none is an act of the eye, none is “a see,” yet they let us see things we could not otherwise, or see them better. So definition, statement, argument are tools “necessary to complete or perfect these three acts.”
• Distinction: logic is about the three acts as its end or purpose (to perfect, direct, order them) vs. about the three tools as its subject—just as glasses are for the sake of seeing. “You got to see them as related to the end or purpose.”

5. Making a statement does not tell you whether it is true (“Berquist is standing now”) #

Point: three ways we know a statement true or false.

1. By sense: “Berquist is standing now / is not standing now”—one is true, and you know which by looking.
2. By understanding the parts (first act): define triangle and square and you see no triangle is a square; define square and quadrilateral and you see a square is a quadrilateral.
3. If neither, by reasoning: Euclid’s three angles of a triangle equal two right angles—knowing what a triangle and right angles are, you still don’t see it; you must use a number of arguments.

• He adds: some statements must be known without reasoning, by sense or by understanding their parts, “otherwise you’d have no statements to reason from.” Closing observation: logic is called the organon of philosophy, yet as Thomas shows it is also about the tools.

6. Art carried over to the liberal arts (“right reason about making”) #

Point: art originally is right reason about making in some matter; the word is carried over to the liberal arts, where the making is mental.

• Seven liberal arts, going back to Pythagoras and Plato; divided in the Middle Ages into the trivium (grammar, rhetoric, logic) and the quadrivium (arithmetic, geometry, music, astronomy, from Pythagoras). Plato in the Charmides talks about the liberal arts; at that time logic was only being anticipated, rhetoric a little earlier developed, grammar just being understood. “Trivial” comes from the trivium—what everybody would know—but not trivial in our sense.
• Thomas’s text read: the liberal arts are called arts as well as sciences because they have not only knowledge but “some work that is immediately of reason itself”—to construct syllogisms (make a syllogism, definition, statement: logic), to form speech (grammar; he says take it of rhetoric too), to number and measure (arithmetic, geometry), to form melodies (music), to compute the course of the stars (astronomy). Other sciences either have no work but knowledge only (divine and natural science) or a bodily work (medicine, chemistry), and so cannot be liberal arts, since bodily acts belong to man by the part that is not free. Aside: a learned grammarian told him the Greeks figured out their own grammar; the Romans, “too stupid” to work out Latin, imitated Greek grammar and got their cases screwed up; we imitated the Latin grammarians and fouled up our understanding of English. The Greeks are “fathers of everything”—grammar, rhetoric (Cicero called Aristotle’s Rhetoric a golden river), logic; the harder logical terms (syllogism, enthymeme) the Romans had no name for, while induction is Latin.

7. Working and the work, in reason as in exterior acts (“the making of a chair and the chair”) #

Point: Thomas’s next passage distinguishes act from product in the works of reason.

• Exterior acts: the making of a chair vs. the chair; the building of a house vs. the house. Works of reason: the act (understanding what a thing is, understanding the true or false, reasoning) vs. what is constituted by the act—in “looking reason,” definition, statement (composition or division), syllogism or argument in general.
• Restatement: logic is about the three acts as its end, to perfect, direct and order them; its subject is more the three tools which make those acts possible or more perfect.

8. How do we order our thinking? (“How do we order our thinking”) #

Point: from the proemium to the Nicomachean Ethics (“an order which reason, by considering, makes in its own act, as when it orders its thoughts to each other, and the signs of thoughts which are signifying vocal sounds”) he draws out what he calls “very subtle” and “a kind of key.”

1. We order our thinking about things by ordering our thoughts about things. Thinking and a thought differ as imagining and an image, but are closely tied: to imagine is to form an image, to think is to form a thought; each is a likeness. Order the images and the imagining is ordered—as in memorizing, where if you get lost mid-passage you go back to the beginning and follow the order.
2. But thinking and thoughts cannot be sensed or even imagined. An animal with reason, whose natural road is from the senses into reason, needs something sensible to get at them.
3. So we order our thoughts about things by ordering the words that signify things through thoughts; and the original words are the vocal sounds, not the written ones. Conclusion: logic is about using words, insofar as they signify things through thoughts, to order our thoughts and consequently our thinking. He notes he is “splitting up” the second part of Thomas’s sentence to get this.

9. Words and the inward act: prayer (“Words without thoughts”) #

Point: three illustrations that the sensible words are not the inward act yet are the way to order it.

• The apostles asked “Teach us how to pray” and Christ gave them words; the words are not the inward prayer, but to teach he must use outward sensible sounds. A child learning the Our Father and Hail Mary says words not fully comprehended, gradually ordering desires and requests to God as understanding grows.
• Psalm 18: “the words of my mouth and the thought of my heart find favor before you”—the words come first, the thoughts must go along.
• The king in Hamlet, after the reenacted murder, kneels saying words to God but cannot repent; rising, he sees his inward state is not conformed to the words: “Words without thoughts never to heaven go.” (Hamlet, passing by, will not kill him at prayer—“too nice a way to go”; he wants him drunk or in some activity.) Likewise words as mere physical sounds do nothing; only as signifying things through thoughts can they order thought.

10. Logos and the shock that logic is about vocal sounds (“logic is about vocal sounds”) #

Point: the genus in the definitions of definition, statement and syllogism is logos, and Aristotle means vocal sound.

• Logos can mean word (spoken, later written), speech, and later thought. Student suggests Aristotle uses it in the definitions in the sense of thought or words; he answers: words, and in the Peri Hermeneias Aristotle “makes it crystal clear” he means vocal sound, as Thomas, “very concrete,” says.
• The shock: it seems to lower logic; people want logic to be about thoughts. His reply: in a sense it is—about thinking—but you cannot order thinking without ordering thoughts, and the sensible tool for that is words signifying things through thoughts. What is “up front” is the sensible tool, a logical name or a speech.
• Comparison: the genus of the seven sacraments is sign—for Thomas always Augustine’s definition, that which strikes the senses and brings to mind something else. Saying “seven sensible signs” rather than “seven graces” seems to lower them, yet it is their genus: God condescends to an animal with reason, leading it from the sensible to what is above it. Contemporary catechisms call the sacrament “an encounter with Christ”; that is what happens through the sacrament, not its genus—the sacrament is a sensible sign through which one encounters Christ or his power. The recording breaks off mid-sentence: “Aristotle makes it crystal clear that logos is—” [unclear in recording].

His words #

• looking sciences / looking philosophy / looking reason: sciences pursued to see or understand for their own sake [ed.: speculative]
• reduced to looking philosophy: contained under it not as a principal part but as its tool
• the three acts: understanding what a thing is; understanding the true or the false; reasoning [ed.: simple apprehension, judgment, reasoning]
• tools: definition, statement, argument (syllogism chiefly), each perfecting one act
• composition or division: Thomas’s name for the second act, not its tool
• end/purpose of logic vs. subject of logic: the three acts vs. the three tools
• organon: tool, the name for logic in relation to philosophy
• art: originally right reason about making in matter; carried over to mental making in the liberal arts
• trivium / quadrivium: grammar, rhetoric, logic / arithmetic, geometry, music, astronomy; “trivial” from the trivium
• thinking vs. thought: as imagining vs. image; the thought is a likeness formed in thinking
• words that signify things through thoughts: the sensible tool by which thoughts, and so thinking, are ordered
• logos: word (spoken, then written), speech, later thought; as genus of definition, statement, syllogism it means vocal sound
• sign (Augustine): that which strikes the senses and brings to mind something else

Texts #

Read in class

• Thomas Aquinas, commentary on the work on the Trinity (he says “Augustine’s”; later “the Boethius” [ed.: Boethius’ De Trinitate]), on logic as tool of science and on the liberal arts — handout p. 5
• Thomas Aquinas, passage on working and the work in exterior acts and works of reason (locus not stated) — handout
• Thomas Aquinas, proemium to the commentary on the Nicomachean Ethics, on the order reason makes in its own act — handout “The Proemia to Logic”, pp. 19–21
• Psalm 18 (verse on words of the mouth and thought of the heart)
• Shakespeare, Hamlet, the king at prayer (“Words without thoughts…”)

Mentioned

• Aristotle, Metaphysics, beginning (sciences sought for their own sake)
• Boethius, commentary on Porphyry; Porphyry, Isagoge; commentaries by Albert the Great and Cajetan
• Aristotle / Thomas, Peri Hermeneias (logos as vocal sound)
• Euclid (angles of a triangle equal two right angles)
• Plato, Charmides (on the liberal arts)
• Cicero on Aristotle’s Rhetoric (“a golden river”)
• The Gospel: “Teach us how to pray”; the Our Father and Hail Mary
• Augustine’s definition of sign

His questions #

• How would I help a student understand what a perfect number is? Define it: a number equal to the sum of everything that measures it.
• Where do you find truth or falsity? Not in things or in the first act, but in statements—the same place as falsity.
• What tool corresponds to the third act? Syllogism, or in general argument.
• Isn’t the tool of the second act composition and division? (student) No; Thomas uses that for the act itself, not the tool.
• How do you know which of “Berquist is standing / not standing” is true? By looking—by sense.
• What do you do if you can’t see a statement’s truth by sense or by understanding its parts? Reason to it, as with Euclid’s two right angles.
• How do we order our thinking about things? By ordering our thoughts about things; and those by ordering words that signify things through thoughts.
• Can you see, hear, smell, taste, touch, or even imagine a thought? No—so reason needs something sensible, the vocal sound.
• When the apostles asked to be taught to pray, what did Christ give them? Words to use—not the inward prayer, but the sensible means to it.
• What is the genus of the seven sacraments? Sign, something sensible; not “encounter with Christ.”