Logic's Three Acts of Reason, Univocal and Equivocal Names, and the Genus

Orientation #

He opens by recalling “last time”: the word logos (word, thought, reason), the naming of logic philosophia rationalis, and the definitions of name and speech “we defined last time” (prev. lecture). He announces “let me get a little bit into logic today” and “anticipates a bit” that after the five names come the categories. The text-matching system flagged a Physics I, lectio 13 handout (“The Before and After in the Acts of Reason”) for this episode; the transcript shows no reading of it, only a passing reference to the meanings of “before” and to first matter known by proportion in “the first book”. Follow the transcript.

The class, in order #

1. Two versions of the opening prayer (“God, who created you without you”) #

Aside on why the prayer says both “help us” and “move us”: Augustine, God who created you without you will not save you without you; “help us” implies we are trying and need help (our cooperation), “move us” makes God the principal agent.

2. Recap: logos and the order of its meanings (“the word is first in our knowledge”) #

Logos means first word, then the thought the word signifies, then reason which has thoughts: equivocal, but by reason. The order teaches something: the word is first in our knowledge because it is sensible, a sound. “That’ll be important when we get into logic.”

3. Thomas’s three acts vs. Albert’s two; Aristotle’s books (“Thomas divides logic into three parts”) #

Point: Thomas divides logic by the three acts of reason; Albert by the two kinds of unknown.

• Thomas (in the proemium, “major and minor”) recalls Aristotle, De Anima III: two kinds of understanding, (a) what something is, (b) the true or the false, called composition and division of the things understood in the first act; a third act is reasoning. So logic has three parts.
• Albert the Great divides into two: the art of coming to know the simple unknown (defining) and the art of coming to know the complex unknown (reasoning), placing statements under reasoning because statements are what you put together. His reason: logic is not for its own sake but for knowing what you don’t know, which is either simple or complex. “It makes a lot of sense.”
• Thomas divides Aristotle’s books by the three acts: Categories (first act); Peri Hermeneias, “On Interpretation” in Latin (second act, statements); all the rest for reasoning: the two Analytics (syllogism in general; demonstration, the syllogism “making you know the cause and that it cannot be otherwise”), then the dialectical syllogism, the sophistical, down to weak arguments and rhetoric, and the poetic art, “because that’s used to persuade”: Uncle Tom’s Cabin and the Civil War.

Student asks for the three divisions again. His answer with examples: first act, understanding what a square, a circle, an odd or even number is (“not so well what a dog is, but you know it’s a dog, not a cat”); second act, “a square is a quadrilateral”, “a square is not a circle” are true; “a square is not a quadrilateral”, “a square is a circle” false. Truth defined: a statement is true when it says what is is and what is not is not; false when it says what is is not or what is not is; tested with “you’re sitting now” / “you’re not standing” (true) vs. “you’re standing now” / “you’re not sitting” (false). Thomas calls it composition and division (affirmative composes, negative divides); he prefers “understanding the true or the false”. Third act: reasoning.

• Aside: brother Marcus’s “liberalism geometrically demonstrated”, mocking Spinoza; first theorem “to construct a pyramid of absolute power on a flattened federal republic”; liberal’s mind and reality like parallel lines.
• Aside: the Bible divided into two; the New Testament into three by Thomas; Matthew into three, John into two.

4. The three speeches: definition, statement, argument (“corresponding to each of these acts is a speech”) #

Point: to each act corresponds a speech often necessary to perfect it, and logic can be said to be about these three.

• Definition: “speech bringing out what something is” (he prefers “bringing out” to “signifying” because nature likes to hide, Heraclitus).
• Recap of name and speech (prev. lecture): each definition has about five parts, the first four the same: vocal sound, signifying, not by nature (a baby’s cry) but by human agreement or custom. The name has no parts that signify by themselves: “Duane”, the D-U means nothing. Etymology vs. meaning: “Johnson” does not mean son of John; “Bergquist” (mountain branch) does not mean we are a family of mountain branches.
• The definition is made of names, so you must distinguish the kinds of names in it from the name defined: square = equilateral, right-angled quadrilateral; what kind of name is each? “Go get Porphyry to find out.”
• Statement: speech signifying the true or the false. He prefers “statement” to “proposition”, since pro, placed before, better names the premise (Latin praemissa, sent before). Where do you find truth and falsity? Not in the ocean, air or ground: in statements. A contradiction: affirmative and negative statement, one true, the other false.
• Argument: speech putting statements together and drawing a conclusion. Syllogism: some statements laid down, another follows necessarily, the culmination of argument; other arguments where the conclusion does not follow necessarily but the mind is inclined.
• So logic is directing the three acts, or is about definition, statement, argument; each distinction helps understand the other.
• Aristotle vs. later writers: the only book of Aristotle for the first act is the Categories, which is not really about definition; Aristotle takes up definition as the beginning of demonstration. Two ways of defining: dividing the genus, or looking at many examples and separating out the common. Later writers add something on division and on definition after the categories, “but many take it from Aristotle”.
• Peri Hermeneias: hard Greek word; “simpler if it was called about statement”; transliterated as “hermeneutics”, “that’s terrible… some Germans”.
• No handout last week; printouts of “first distinctions and definitions of logic” to come.

5. What logic starts from: the universal, or the name said of many? (“the first thing to be considered in logic”) #

Point: all speeches are composed of names, so logic must start from names; he corrects Albert’s “universal” to “name said of many things”.

• Albert (who taught by the written word only) says the first thing considered in logic is the universal.
• Support from Shakespeare’s definition of reason: “large discourse, looking before and after”; of the six meanings of “large” found (prev. lecture), the first is a discourse about the large, i.e. covering a large area: the universal, said of endlessly many (man, number, people born every day). Contrast: the biographer of one man (Napoleon) is limited. Poetics: tragedy is more philosophical than history, being more about the universal: Hamlet, a type of man hesitant to act; “he’s a Romeo”; the poet presents the universal singularized. Othello a jealous man, “buttons getting pushed”; California story of a wife flirting to arouse a slack husband, ending horribly.
• But the natural road cannot be overlooked even in logic: the road from senses into reason. Reason: man is an animal that has reason; every animal has senses; the generic develops before the specific; so our knowledge begins in the senses. Followed most in natural philosophy: Aristotle and Einstein both say natural science begins and ends in the senses (universal ideas and equations tested by going back to the senses). Even logic, which like wisdom is about immaterial things, cannot avoid it.
• Conclusion: “I am more sensible when I say the first thing to be considered in logic is name said of many things.”

6. Categories and Isagoge: accusation and being-said-of (“The Ten Supreme Accusations”) #

Point: the first two logical books are titled from “being said of”, which is the way logic proceeds.

• The two first books from the Greek tradition: Aristotle’s Categories and Porphyry’s Isagoge, written as an introduction to the Categories for Chrysaorius, who could not understand genus, difference, species, property (eidos). Porphyry’s “magnificent proemium”: one must understand not only the categories but definition, division and demonstration.
• Albert’s paraphrase; in Latin Predicabilia and Predicamenta, both from “being said of”. Kategoria means accusation; Warren Murray’s proposed title “The Ten Supreme Accusations”: to accuse you I must accuse you of something (murderer, thief, embezzler); the Gospels use the word of those attacking Christ.
• Fits Thomas (a passage in the Metaphysics commentary): natural philosophy proceeds per modum motus, logic by way of predication. Even nature is defined by motion (beginning and cause of motion and rest in that in which it is as such, not by accident); you know natures by what they do. In logic everything goes back to how something is said of something, and “being sensible again”, to how a name is said of many things. Hence “book of the five names” and “book of the ten names”: following the natural road.

7. Univocal, equivocal by chance, equivocal by reason, “analogous” (“said equivocally can be divided into two”) #

Point: a name said of many is divided into two and one member subdivided, giving three; he warns against narrowing “equivocal by reason” to “analogous”.

• Univocal: said of many with one and the same meaning in mind: number of two, three, four (a multitude composed of ones, measured by one); animal of dog and cat (what they have in common, not the differences); quadrilateral of square, oblong, rhombus, rhomboid, trapezium (a figure contained by four straight lines). “Not very many words are univocal.”
• Equivocal: said with many meanings; “many” here opposed to one, not to few, so two meanings suffice.
• Distinction: equivocal word vs. said equivocally. A student: can an equivocal word be said univocally? Yes, under one of its meanings; it depends on what you have in mind. “People have a hard time seeing it.”
• Equivocal by chance: no connection; three Richards (brother, student, package-store manager); Judas “not the Iscariot”, now called Jude because the other is so famous.
• Equivocal by reason: some order, connection, “before and after” among the meanings: logos; “concept” (mind conceiving; the concept of God is his Son).
• Thomas’s threefold division: meaning entirely the same, entirely different, partly same and partly different; the last, equivocal by reason, “in between”. Thomas then uses univocal / equivocal / analogous. “You got to be careful with that”: analogous has the sense of proportion, which is only one way a word becomes equivocal by reason; people get too narrow an understanding.
• How “equivocal” itself became equivocal by reason: sometimes a name said univocally of two is kept by one as its own and a new name given to the other. Kitten is a cat, puppy is a dog, but “a puppy’s not a dog yet” (the grown one has the full nature); a boy is a man, yet man is distinguished against boy. Two causes: one has the common meaning perfectly, the other imperfectly; or the one that keeps the name has nothing noteworthy (wisdom is knowledge, but an excellence, knowledge of God, so it gets a new name; the rest keeps “knowledge”). So equivocal by chance, having nothing but many meanings, keeps the name “equivocal”; equivocal by reason, having the noteworthy order, gets “analogous”.
• Proportion as one such order: “before” carried from its second to its third meaning by a proportion: this can be without that but not vice versa; this can be known without that but not vice versa. Proportion is very important: most scientific theories result from seeing proportion; Aristotle, first book (of the Physics, inferred): first matter, being nothing actual, cannot be known by itself but by proportion, as clay is to sphere and cube, so first matter is to man and dog (“you and Habiba”). Hence his hesitation about “analogous” even though Thomas uses it.
• Runs through philosophy: the angel’s mind is called intellectus, understanding; ours could be, but we understand little, slowly, by discourse, so ours is called reason, “a darkened understanding”. Kasurik, wisest man at the College of St. Thomas: compared to Aristotle “I have the brain of an angleworm”; compared to an angel, so has Aristotle; hence praying to the guardian angel.
• Anticipation: the five names of the Isagoge are said univocally; each category is said univocally of what is below it, but what is above the categories is said equivocally by reason.
• Aside: pro-abortion people cannot be trusted not to abort the truth; the Planned Parenthood worker’s book, the woman who saw the remains.

8. The Isagoge: title and the five names (“It is by antonomasia the Isagoge”) #

Point: the title and list of Porphyry’s book.

• As Newton’s Principia Mathematica Naturalis Philosophiae is called “the Principia” (its first word; 20th-century physicists call earlier physics classical or Newtonian), so “Introduction to the Categories” is called simply Isagoge, leading-in, same etymology as “introduction”. By antonomasia: Thomas says logic must be learned before the other parts of philosophy because it shows the way of using reason in all of them, so the introduction to logic is the introduction to the beginning of science.
• Five names: genus (Greek genos), difference (diaphora), species (eidos; “idea” doesn’t keep its meaning), property, accident. “Accident” is also used in the Categories with a different, not purely equivocal, meaning; Father De Lacy despaired of getting students to see accident as a predicable vs. accident as opposed to substance.

9. Genus (“one man from whom many have descended”) #

Point: from the first meanings of genus to its logical definition, with examples from all the sciences.

• First meaning: one man from whom many descend (himself, then Paul and Maria and Marcus, then their children: the “Christmas tree”, the tree of Porphyry; genealogy, generation). Second meaning: the multitude descended, “my tribe”. Interesting: one and many both called genus; the second is something like the universal, one said of many, not one from whom many descend. Aside on Hegel: deducing the universe from the vaguest thought, being; it actually came from “I am who am”.
• Logical genus: a name said with one meaning of many things other in kind (Latin species, singular and plural spelled the same; Greek eidos), signifying what it is: not different individuals only, but other in kind.
• Quadrilateral, said of square, oblong, rhombus (“a jerked square”), rhomboid (“a jerked oblong”), trapezium (irregular): all other in kind; the first four are parallelograms (opposite sides and angles equal), so quadrilateral can also be divided into parallelogram and trapezium. Of each, “a plane figure contained by four straight lines” is said with exactly the same meaning; it answers “what is a square?” in general, not completely.
• “General” has the same two senses as genos: one from whom many descend, one who commands many. MacArthur is not said of his soldiers; “soldier” is more like the genus, said with one meaning of many men.
• Triangle of scalene, isosceles, equilateral: says what each is, not fully. Where a species has no name (equilateral triangle) a speech functions as the name, as “equilateral right-angled quadrilateral” for square.
• Number of odd and even: same meaning (multitude composed of units) said of kinds that differ.
• Why mathematical examples: mathematics is more proportionate to our mind; Marcus, told to teach geometry and logic, taught geometry first and used it to exemplify definition and syllogism.
• Ethics: habit (firm, stable disposition) is the genus of virtue and vice (“there are other kinds, you don’t know that yet”). Government: Aristotle, “rule of two or three”, three times two: rule by one, few, many, good and bad: monarchy/tyranny, aristocracy/oligarchy, republic/democracy. Logic itself: syllogism is the genus of demonstrative (known with certitude) and dialectical; statement of affirmation and negation. “It runs through all the sciences”, so logic is useful for all.
• Aside: a recently bought book with the Constitution, Franklin’s letter on what to expect in America, a Congress open letter to the people (1780s), Hamilton on the people as a beast; “democracy is a majority of the worst in some ways”.

His words #

• philosophia rationalis: logic named from reason.
• the three acts of reason: understanding what something is; understanding the true or the false (Thomas: composition and division); reasoning.
• simple unknown / complex unknown: Albert’s two objects, of defining and of reasoning.
• true / false: says what is is and what is not is not / says what is is not or what is not is.
• definition: speech bringing out what something is.
• statement: speech signifying the true or the false; preferred to “proposition”, which names the premise [ed.: proposition].
• argument: speech putting together statements and drawing a conclusion; syllogism: the one where the conclusion follows necessarily.
• name: vocal sound signifying by agreement, none of whose parts signify by themselves.
• large discourse, looking before and after: Shakespeare’s definition of reason (prev. lecture).
• the natural road: from the senses into reason.
• per modum motus: how natural philosophy proceeds; logic by predication.
• Predicabilia / Predicamenta: Latin titles for Isagoge and Categories, from “being said of”.
• kategoria: accusation; “The Ten Supreme Accusations” (Warren Murray).
• book of the five names / book of the ten names: Isagoge / Categories.
• said univocally / said equivocally: with one meaning in mind / with many meanings.
• equivocal by chance / equivocal by reason: no connection among meanings / an order among them.
• analogous: Thomas’s word for the partly-same case; he restricts it to connection by proportion.
• darkened understanding: reason, vs. the angel’s intellectus.
• antonomasia: the common name taken as proper, “the Isagoge”, “the Principia”.
• genus: name said with one meaning of many things other in kind, signifying what it is (in general).
• species: things other in kind; eidos.

Texts #

Read in class (recalled, paraphrased, or expounded; no passage is read verbatim)

• Thomas Aquinas, proemium (major and minor) to the logical commentaries: the three acts and the division of Aristotle’s books.
• Porphyry, Isagoge: proemium; the five names; genus. Mentioned
• Aristotle, De Anima III (two kinds of understanding).
• Albert the Great, twofold division of logic; paraphrase of the Isagoge.
• Aristotle, Categories, Peri Hermeneias, the two Analytics, Topics (dialectical syllogism), Sophistical Refutations, Rhetoric, Poetics (titles as he names them; the last for “tragedy more philosophical than history”).
• Thomas Aquinas, commentary on the Metaphysics (natural philosophy per modum motus; locus not stated).
• Aristotle, first book (Physics I, inferred): first matter known by proportion.
• Augustine: “God who created you without you will not save you without you.”
• Heraclitus: nature likes to hide.
• Shakespeare, “large discourse, looking before and after” (Hamlet, inferred).
• Newton, Principia Mathematica Naturalis Philosophiae.
• Gospel of John, the “Judas, not the Iscariot”.
• Hegel (deduction from being); Spinoza (philosophy geometrically demonstrated).

His questions #

• Could you tell me what the three divisions of St. Thomas are again? (student) Understanding what something is; understanding the true or the false; reasoning.
• Where do you find truth and falsity, in the ocean, in the air, in the ground? In statements.
• What kind of a name is quadrilateral, equilateral, right-angled, square? Deferred: “go get Porphyry to find out.”
• The natural road is the road from what? From the senses into reason.
• Can an equivocal word be said univocally? Yes, under one of its meanings; what matters is what you have in mind.
• Why did three men have the name Richard? By chance; no one saw something common and named them for it.
• What way of being equivocal does the word “equivocal” itself have? A univocal name kept by one (equivocal by chance) while the other, having something noteworthy, gets a new name (analogous).
• Is “General MacArthur” a genus of his soldiers? No; he commands many but is not said of them; “soldier” is more like the genus.
• Does “quadrilateral” answer completely what a square is? No; it answers in general, not in particular.
• Number is said of odd and even with one meaning? Yes: a multitude composed of units, true of both, though they differ in kind.